ABSTRACT 
 
Title of Dissertation: THE EFFECT OF PHASE CONSTITUTION AND 
MORPHOLOGY ON ROOM TEMPERATURE 
DEFORMATION BEHAVIOR OF BINARY 
TITANIUM ALLOYS 
 
 Zane William Wyatt, Doctor of Philosophy, 2011 
 
 
Dissertation Directed By: Professor Sreeramamurthy Ankem 
 Department of Materials Science and Engineering 
 
 
 
 Currently, titanium alloys are used in a variety of applications, including defense, 
aerospace, biomedicine, and even common consumer products such as bicycles and golf 
clubs.  In many applications such as the landing gear of aircraft and geothermal energy 
production, titanium components may be subjected to stresses for extended periods of 
time.  It has long been known that single-phase ? (HCP), single-phase ? (BCC), and two-
 phase ? + ? Ti alloys can creep at low temperatures (<0.25Tm).   For this reason, creep is 
an important factor to consider when designing titanium alloys for various applications. 
 The first part of this investigation is concerned with single-phase ?-Ti alloys.  It 
was found that the twin size (lamellar thickness) decreases with an increase in strain rate.  
This behavior is unexpected based on the classical understanding of instantaneous 
twinning.  This investigation was able to for the first time demonstrate a time-dependent 
twinning phenomenon during high strain rate tensile deformation. 
 The second part of this investigation is concerned with experimentally and 
theoretically studying low-temperature creep deformation behavior of two-phase ? + ? Ti 
alloys.  Deformation mechanisms were seen in two-phase ? + ? Ti alloys that are not 
 
 
present during creep of the respective single-phase alloys with compositions equivalent to 
the individual phases. 
To investigate the possible interphase interaction stresses, 3D anisotropic Finite 
element modeling (FEM) was used.  These simulations revealed that due to the Burgers 
orientation relationship between the two phases, deformation such as slip or twinning in 
the ? phase can create very high additional shear stresses on different slip systems in the 
? phase.  This work also revealed that the interfacial stresses that develop between the 
two phases during elastic deformation will often be much greater than the applied stress.  
These results were used to help explain the addition deformation mechanisms seen in 
two-phase alloys that are not seen in the respective single-phase alloys during creep. 
This work was supported by the National Science Foundation under Grant 
Number DMR-0906994. 
  
 
 
 
 
 
 
 
 
 
 
THE EFFECT OF PHASE CONSTITUTION AND MORPHOLOGY ON 
ROOM TEMPERATURE DEFORMATION BEHAVIOR OF BINARY 
TITANIUM ALLOYS 
 
 
By 
 
Zane William Wyatt 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the 
University of Maryland, College Park, in partial fulfillment  
of the requirements for the degree of  
Doctor of Philosophy 
2011 
 
 
 
 
 
 
 
Advisory Committee: 
 Professor Sreeramamurthy Ankem, Chair 
 Professor Abhijit Dasgupta, Dean?s Representative 
 Professor Lourdes Salamanca-Riba 
 Professor Mohammad Al-Sheikhly 
 Professor Aris Christou 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
?Copyright by 
 
Zane William Wyatt 
 
2011 
ii 
 
Acknowledgements  
 
 
 
 I first want to thank my wife, Renika, for your love, support, encouragement, and 
above all, patience.  ??m fairly certain ? would have lost my mind without your doses of 
reality.  I would also like to thank my family?the people in my life who never once 
doubted my abilities and pushed me to always be better and continue to grow.  A very 
special thank-you goes to Mom and Dad; two people who taught me that science is cool 
and hard work is rewarding. 
 I would like to thank my advisor, Dr. Ankem, for guiding my research and 
challenging my conclusions.  I will remember the last minute deadlines just as fondly as 
the celebratory lunches afterword.  I would like to thank the entire faculty and staff of the 
Materials Science and Engineering Department, the staff of the FabLab, and of the NISP 
lab at the University of Maryland; this place has been my home for over four years and 
all your efforts make it much more enjoyable.  I also sincerely appreciate the time and 
effort of my Dissertation Committee for reviewing this work.  One last shout-out goes to 
a very deserving Dr. Phil Piccoli for his help with the numerous microprobe sessions. 
 Big thanks go to my co-workers, particularly Will Joost, Paul Lambert, Alex Kao, 
and Ryan Mulholland, for their friendship, conversations, and laughs. 
 Finally, I am extremely grateful for the financial support of this Department and 
the NispLab which is supported in part by the National Science Foundation as a Materials 
Research Science and Engineering Center (MRSEC) Shared Experimental Facility.  My 
ultimate financial acknowledgements go to the National Science Foundation who funded 
this work under Grant Number DMR-0906994. 
iii 
 
Table of Contents  
 
List of Tables  v  
 
List of Figures  v i 
 
Chapter 1:  Introduction and Project Aims  1  
 
Chapter 2:   Technical Background  5  
?.? The ? and ? phases 
2.2 Low temperature deformation mechanisms of Ti alloys 
2.3 Plastic deformation of two phase alloys 
2.4 Elements of twinning 
?.? Recent developments in ?-Ti alloys 
?.? Recent developments in ?-Ti alloys 
2.7 Recent developments in two-phase Ti alloys 
2.8 What is not known, but should be  
 
Chapter 3:  Experimental Procedures  17  
3.1 Heat treatment 
3.2 Tensile and creep specimen preparation 
3.3 Attachment of fiducial grids 
3.4 Tensile testing 
3.5 Creep testing 
3.6 SEM and optical microscopy 
3.7 TEM sample preparation  
3.8 TEM procedures  
3.9 Manual calculation of resolved shear stress 
 
Chapter 4:  Deformation Mechanisms and Kinetics of Time -  28  
 Dependent Twinning in an ? - Ti- 1.6wt% V alloy  
4.1 Crystallography of time-dependent twinning 
?.? Time dependent twinning during creep of ?-Ti-1.6V 
4.3 Model for diffusion of oxygen at twin front 
4.4 Model for stress-assisted interstitial diffusion in ?-Ti 
4.5 Tensile testing results 
4.6 Optical and SEM microscopy 
4.7 TEM mi croscopy 
?.? ?ffect of strain rate on twinning in ?-Ti-1.6V 
4.9 Concluding remarks 
 
Chapter 5:  The Effect of ? - p hase Metastability on Low  52  
 Temperature Deformation Behavior of ? and ? + ? Ti alloys 
?.? ?-phase metastability 
5.2 Deformation mechanisms in metastable Ti alloys 
iv 
 
?.? The role of ?-phase stability on tensile deformation mechanisms 
?.? The role of ?-phase stability on creep deformation mechanisms 
5.5 Concluding remarks 
 
Chapter 6:  Influence of Microstructure and the  73  
 Second Phase on the R oom Temperature Creep  
 Deformation Mechanisms of ? + ? Ti - V Alloys 
6.1 Experimental procedures 
6.2 Results 
6.3 Discussion 
6.4 Summary of creep deformation process 
6.5 Conclusions 
 
Chapter 7:  Finite Element Studies of the Interaction Between  104  
 ? and ? Phases in Two - Phase Ti Alloys  
7.1 Input properties and model development  
7.2 Coordinate system development  
7.3 Geometry of the two -phase system 
7.4 Mesh generation  
?.? ?esh generation incorporating slip or twinning in ? 
7.6  Results 
7.7  Discussion 
7. 8  Conclusions 
 
Chapter 8:  Conclusions  128  
 
Chapter 9:  Suggestions for Future Work  131  
 
Appendices  132  
 
References 1 63  
 
Curriculum Vitae  1 76  
  
v 
 
List of Tables  
 
Table 4.1.   ?echanical testing results of ?-Ti-1.6V tested at different strain rates at 
298K.  
 
Table 4.2 .   ?uantitative analysis of deformation twinning in selected area in ?-Ti-1.6V 
tensile tested to 3% strain at 298K.  The values for twin volum e fraction are accurate to 
+/ - 3%.  
Table 4. 3 .   Results of the experimental calculations and results of the constitutive 
relations for twinning observed during the tensile investigations.   The modified 
constitutive relation incorporated a stress factor into the predictive equation described by 
Eq. (4.2). 
Table 7.1 .   ?a?imum resolved shear stresses in ? Ti, normali?ed to applied stress in ?, 
on twinning and hexagonal martensite shear systems. 
 
 
 
  
vi 
 
List of Figures  
Figure 2.1.   Titanium rich end of the Ti-V phase diagram and respective alloy 
compositions used in this investigation [2, 3] . 
Figure 2.2.   Schematic illustration of planes and directions associated with twinning. 
 
Figure 2.3.   Schematic illustration of {10 1? ?? twinning in the HC? lattice of ?-titanium.  
Projection of the lattice is onto the {11 2? 0} plane.  (a) Shear of  the lattice in the <1? 101? > 
direction moves only atoms in A-type sites (blue) directly to twinned position.  (b) 
Arrows give the shuffles required to move the atoms in B-type sites (red) to either the B 
(red) or C-type sites (green) in the twinned lattice.  Reorientation of the lattice will 
eliminate the octahedral sites (marked with an ???) where an o?ygen atom could reside.  
These models are an extension of earlier twinning models by Song and Gray [43, 44], but 
now include the corresponding movements of octahedral sites [45].  
 
Figure 2.4.   Projection of bcc substitutional and octahedral interstitial atoms onto (  ? ) 
plane. (a) Untwinned structure showing direction of [113] twinning shear, and (b) Final 
twinned structure showing mirror symmetry across twin-matrix interface [23 ].  
 
Figure 2.5.  (a) TEM micrograph and (b) SEM image showing connection between 
twinning in ?-phase and stress induced martensite in ?-phase [21, 22].  
 
Figure 2.6.  High resolution TEM (HREM) micrograph of the slightly rough, semi-
 coherent ??? interface of Ti-8.1V, viewed from the [1 2? 10] ? // [1 1? 1] ? direction [21, 22].  
 
Figure 2.7.  High resolution TEM micrograph showing the interface of stress induced 
martensite (??) and the ? phase.  ?otice the ???1? 1} twin relationship between the phases.  
Selected area diffraction patterns from each phase and the interface taken parallel to the 
(12? 10) zone axis are inset. [21, 22]  
 
Figure 4.1.   Schematic illustration of {10 1? ?? twinning in the HC? lattice of ?-titanium.  
Projection of the lattice is onto the {11 2? 0} plane.  (a) Shear of the lattice in the < 1? 101? > 
direction moves only A-type Ti atoms (large, dark circles) directly to twinned positions.  
(b) Arrows give the shuffles required to move the Ti atoms in B-type sites (large, lighter 
circles) to their twinned B-type or C-type positions.  Reorientation of the lattice 
eliminates the octahedral sites (small circles with ??? mark) where o?ygen could reside.  
(c) Schematic illustration of a completed {10 1? 2} twinning event.  The completed 
positions for B-type Ti atoms and the corresponding possible octahedral sites and the 
completed positions for C-type Ti atoms and the corresponding possible octahedral sites 
are indicated by the arrows.  These models are an extension of earlier twinning models by 
Song and Gray (Song and Gray, 1995b,c), but now include the corresponding movements 
of octahedral sites where oxygen may reside [45] . 
 
vii 
 
Figure 4. 2.   ?echanical testing results of ?-Ti-1.6V tested at different strain rates.  (a) 
True stress ? true strain curves of alloy tested at different strain rates.  (b) Strain 
hardening rate of the plastic region of each of the curves.  The alloy exhibits a low strain 
hardening rate for all tested strain rates. 
 
Figure 4. 3.   Before and after optical micrographs of deformation twinning in ?-Ti-1.6V 
at (a) 10-1 /s, (b) 10 -2 /s, (c) 10 -4 /s, and (d) 10 -6 /s.  All samples were tested to 3% strain.  
All micrographs were taken at ???? magnification.  The fiducial grids are ?? ?m s?uare.  
Note the gradual increase in twin thickness as the strain rate decreases, as indicated by 
the arrows. 
 
Figure  4.4.   Optical micrograph taken under different polarizing light conditions of ?-Ti-
 ?.??, showing multiple twins.  T ? ????, ? ? ?.??, strain rate ? ??-6 /s.  The fiducial 
grids are ?? ?m s?uare.  ?ote twins at the arrows which disappear under non-polarized 
light.  This method of twin identification was used for the other strain rates as well but is 
not shown here. 
 
Figure 4. 5.   Bright field T?? micrograph from tensile deformed ?-Ti-1.6V, of {1 1? 02} 
twin and SADPs of the {2 1? 1? 0} foil plane from: (a) the untwinned matrix, (b) inside the 
twin, and (c) across the twin-matri? interface.  T ? ????, ? ? ?.??, strain rate ? ??-1 /s.  
 
Fig ure  4. 6.   Bright field T?? micrograph from tensile deformed ?-Ti-1.6V, of {1 1? 02} 
twin with [2 1? 1? ?? ?one a?is.  T ? ????, ? ? ?.??, strain rate = 10 -1 /s.  Note the twin 
indicated by the arrow. 
 
Figure  4. 7.   ?ptical micrograph from tensile deformed ?-Ti-?.??.  T ? ????, ? ? ?.??, 
strain rate = 10 -1 /s.  Note the very fine twins indicated by arrows.  
 
Figure 5.1.   A schematic of a pseudo-binary equilibrium diagram showing the ranges of 
? and ? stability as a function of added ? stabili?er ????].  
Figure 5.2.  Selected area diffraction pattern comparing the degree of formation of 
omega phase in the ? phase of the ? + ? (a) Ti-?.? wt pct ?n (?-phase MoE=19.9) and 
(b) Ti-?.? wt pct ? (?-phase MoE=9.9) alloys.  Note pre -omega-phase streaking of ? 
spots of the ? phase of ? +  ? Ti-6.0 wt pct Mn SADP, which are consistent with 
incommensurate ? formation, compared with the sharply defined spots of the ?-phase ? +  
? Ti-8.1 wt pct V SADP.  The ? phase indices and orientation are provided.  The extra 
spots in the Ti-8.1V pattern ar e due to double diffraction [21, 22, 156 ].  
Figure 5.3.   Illustration of the [1 2? 10](0001)//[1 1? 1](110) Bur gers orientation relationship 
between the ? and ? phases in an ? + ? titanium alloy with ?idmanstatten 
microstructure. Diagram shows the (0001)? and (110)? planes. The interface plane is (5?
 140)//( 3? ??)? which is normal to the (????)? and (???)? planes and is indicated as a trace 
in each phase [21, 22 ].  
viii 
 
Figure 5.4 .  ?lastic interaction stress on ? and ? phases of a titanium alloy. The 
interaction of the stronger but lower modulus ? phase with the ? phase initially increases 
the stress in ?. ?nce significant plastic deformation occurs in ?, elasto-plastic interaction 
stresses act on the ? phase ???, ??].  
Figure 6.1.  ??? micrograph of ? + ? Ti-8.1V with Widmanst?tten microstructure before 
testing; showin g fiducial grid used in these investigations. 
 
Figure 6.2.  Tensile curves of Ti-4.3wt% V, tested at a strain rate of 3.28 x 10 -5 /s to a 3% 
total strain. 
 
Figure 6.3.  Creep curves of Ti-4.3V alloys, creep tested at ambient temperature at 95% 
of their respective YS. 
 
Figure 6.4. ??? micrographs of ? + ? Ti-4.3V (a) before and (b) after creep deformation 
at 95% YS for 200 hours to 0.86% total plastic strain.  There are n o coarse deformation 
features visible on the polished and etched surface, although fine slip in the ? phase 
(light) was noted due to an increase of the fiducial line spacing during testing. 
 
Figure 6.5. Bright field TEM micrograph of fine slip lines in the ?-phase of Ti-4.3V.  
Slip is <a> type dislocations on prism planes.  The dislocations are of the type b = 
1/3<11 2? 0>.  
 
Figure 6.6. ??? micrographs of ? + ? Ti-4.3V with Widmanst?tten microstructure (a) 
before and (b) after creep testing at 95% YS for 200 hours to 0.90% total plastic strain.  
?ote the coarse deformation features spanning multiple ? (light) and ? (dark) grains.  
These were identified during this study as stress induced martensite in the ? phase and 
coarse slip or twinning in the ? phase. 
 
Figure 6.7. ??? micrograph of ? + ? Ti-4.3V with Widmanst?tten microstructure creep 
tested to ?.??? total plastic strain.  ?ote the coarse deformation features spanning the ? 
(light) and ? (dark) phases.  These features were identified as coarse slip and twinning in 
the ? phase and stress induced martensite (??) in the ? phase. 
 
Figure 6.8. T?? bright field micrograph of slip bands in the ? phase of ? + ? Ti-8.1V 
with Widmanst?tten microstructure.  
 
Figure 6.9. TEM bright field micrograph showing a he?agonal martensite plate (??) in the 
? phase connected to a ???1? ?? type twin in the ? phase.  The twin was classified 
specifically as (1? 012)[10 1? ??.  ?ccompanying diffraction patterns are from the (a) ??twin 
interface and (b) the ???? interface.  ?one a?is is ??2? 10] ? // [1 1? 1] ?.  
 
Figure 6.10. Bright field TEM micrograph showing thee stress induced hexagonal 
martensite plates (??) within the ? phase of Ti-8.1 V creep tested at 95% YS for 200 hours.   
ix 
 
Accompanying diffraction patterns show that both planes have a near{10 1? 1} twin 
relationship to the ? phase.  The ?one a?is is ??1? 1] ? // [1 2? 10] ??. 
 
Figure 6.11. Tensile curves of Ti-8.1wt% V, tested at a strain rate of 3.28 x 10 -5 /s to a 
3% total strain.  
 
Figure 6.12. Creep curves of Ti-8.1V alloys, creep tested at ambient temperature at 95% 
of their respective YS. 
 
Figure 6.13. ??? micrographs of ? + ? Ti-8.1V (a) before and (b) after creep 
deformation at 95% YS for 20 0 hours to 0.41% total plastic strain.  Note the coarse 
deformation features in the ? phase (dark).  These features were identified to be coarse 
slip and stress induced martensite.  ?ine slip has been noted in the ? phase (light) due to 
an increase in the fiducial line spacing during testing.  Note that deformation features do 
not cross phase boundaries. 
 
Figure 6.14. ??? micrographs of ? + ? Ti-8.1V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.41% total plastic strain.  Note the coarse 
deformation features in the ? phase (dark).  These features were identified to be coarse 
slip and stress induced martensite.  ?ine slip has been noted in the ? phase (light) due to 
an increase in the fiducial line spacing during testing.  Twinning in the ? phase was also 
noted, but was rare. 
 
Figure 6.15. Bright field T?? micrograph of stress induced he?agonal martensite (??) 
plate in the ? phase of Ti-4.3V.  To the right are selected area diffraction patterns taken 
from the (a) ? phase and (b) ?? plate.  The zone axis is [1 1? 1] ? //  [1 2? 10] ?. 
 
Figure 6.16. ??? micrographs of ? + ? Ti-8.1V with Widmanst?tten microstructure (a) 
before and (b) after creep testing at 95% YS for 200 hours to 0.52% total plastic strain.  
Note the coarse deformation features spanning many grains.  These features were 
identified to be twinning or coarse slip in the ? phase (light) and stress induced martensite 
in the ? phase (dark). 
 
Figure 6.17.  Bright field TEM micrograph showing stress induced martensite plates in 
the ? phase and twins in the ? phase of Ti-8.1V with Widmanst?tten microstructutre.  The 
martensite plates and twins alternate across the width of the ? and ? grains ????. 
 
Figure 6.18.  Tensile curves of Ti-12.6wt% V, tested at a strain rate of 3.28 x10 -5 /s to a 
3% total strain.  
 
Figure 6.19.  Creep curves of Ti-12.6V alloys, creep tested at ambient temperature at 
95% of their respective YS.  
 
x 
 
Figure 6.20.  ??? micrographs of ? + ? Ti-12.6V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.11% total plastic strain.  Note the stress 
induced plates (SIP) in the ? phase (dark) and lack of coarse deformation features in the ? 
phase (light). 
 
Figure 6.21. T?? micrograph of ? + ? Ti-12.6V showing diffraction of stress induced 
plate which is { 3? 2? 3}[ 1? 31] twin.  The additional spots are from the ? phase and double 
diffraction. 
 
Figure 6.22.  ??? micrograph of ? + ? Ti-12.6V after creep deformation at 95% YS for 
200 hours to 0.11% total plastic strain.  Note the stress induced plates (SIP) and coarse 
slip in the ? phase (dark) and lack of coarse deformation features in the ? phase (light).  
The SIP are {332}<113> twins.  
 
Figure 6.23.  ??? micrographs of ? + ? Ti-12.6V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.12% total plastic strain.  Note the stress 
induced plates (???) in the ? phase (dark) connected to deformation twinning in the ? 
phase (light). 
 
Figure 6.24.  T?? micrograph of ? + ? Ti-12.6V alloy with Widmanst?tten 
microstructure with {332}<113> twinning.  Alloy was creep tested at 95% YS for 200 
hours.   Diffraction pattern was taken from inside the twin.  Zone axis is <110>.  
 
Figure 6.25.  ??? micrographs of ? + ? Ti-12.6V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.12% total plastic strain.  Note the stress 
induced plates (???) in the ? phase (dark) connected to deformation twinning in the ? 
phase (light) and no visible deformation in the ? phase. 
 
Figure 6.26.   Composite graph of the creep curves of the two different microstructures 
for the three different alloys.  As shown, the effect of microstructure decreases with 
increasing volume fraction of ? phase. 
 
Figure 6.27 .  Graph showing the relationship between creep strain of the alloys compared 
with what the law of mi?tures would predict.  ?s shown, the ? phase e?erts a much 
stronger influence on alloy behavior than predicted. 
 
Figure 6.28 .  ? graph of the creep constants from the e?uation ? ? ?? + B ln(t) for each of 
the tests during this investigation.  As shown, the constants do follow general self-
 consistent trends. 
 
Figure 7.1.  A stereographic projection showing the interface plane (5? 140)//( 3? 34), 
Burgers orientation relationships <12? 10>(0001)//<1 1? 1>(110), the standard 
crystallographic orientations and the prime coordinates (Widmanst?tten orientation) for 
the FEM models in this investigation. 
 
xi 
 
Figure 7.2.  Test scenario schematic showing coordinate system orientation and reference 
points A-N for the bicrystal model base used in this investigation. 
 
Figure 7.3.  ????? bicrystal meshed for the study of elastic interactions between ? 
(blue) and ? (red) phases of titanium alloys. 
 
Figure 7.4.  A stereographic projection showing the relationship between the orientation 
of the ? phase in the ????? coordinate system, and the orientation of the twinned region 
in the ANSYS coordinate system. 
 
Figure 7.5.  A schematic diagram showing the relationship between the twinning and 
basal slip systems to the oriented model in the ANSYS simulation. 
 
Figure 7.6.  ????? bicrystal meshed for the study of elastic interactions between ? 
(blue), ? twin (purple), and ? (red) phases of titanium alloys. 
 
Figure 7.7.  Displacements of the nodes in the ?? direction.  ?ote that the displacement of 
the top nodes is appropriate for the elastic compliance values in the [0001] direction for 
an applied stress of 359 MPa. 
 
Figure 7.8.  Normal stresses in the ?? direction.  ?ote the higher stresses in the ? phase as 
opposed to the ? phase. 
Figure 7.9.  Resolved YZ shear stress for elements in the two-phase titanium bicrystal 
shown in Figure 7.6.  Note the interaction stresses at the interface.  
 
Figure 7.1 0.  The resolved shear stress distribution for a horizontal row of elements in the 
mesh shown in ?igure ?.?.  ? phase is on the left and ? phase is on the right.  ?otice the 
very high interaction stresses at the interface. 
 
Figure 7.11.  The resolved shear stress distribution for a horizontal row of elements in the 
mesh shown in ?igure ?.?.  ?ote that for this orientation of ? phase, the resolved shear 
stress on the martensite system is higher than on the twinning system. 
 
Figure 7.12.  The ANSYS simulation results of stresses in the ?? direction.  ?ote that the 
stresses have been relieved in the twin (as appropriate) and the ? phase e?periences 
higher stresses than the ? phase. 
 
Figure 7.13.  The resolved YZ shear stress nodal results as produced by the ANSYS 
simulation.  Note increase in interfacial shear stresses as well as the stresses on the 
twinning planes. 
 
Figure 7.14.  The resolved shear stress distribution for a horizontal row of elements 
between points ??? in the schematic shown in ?igure ?.?.  ?ote that for this orientation 
of ? phase, the resolved shear stress on the martensite system is higher than on the 
twinning system and the presence of a twin magnifies that effect. 
 
xii 
 
Figure 7.15.  The resolved shear stress distribution for a horizontal row of elements along 
line ??? in the schematic shown in ?igure ?.?. 
 
 
 
 
1 
Chapter 1  
Introduction and Project Aims  
 
Titanium (Ti) and its alloys are technologically important.  With applications in 
various areas such as aerospace, naval, industrial, and biomedical, the superior specific 
strength, excellent corrosion resistance and biocompatibility of these materials is making 
them more and more popular.  Its higher cost compared to aluminum or steel is justified 
by its performance.  Products using titanium alloys can now be found in sports 
equipment, architecture, fashion, and electronics, and the applications for titanium alloys 
are certain to grow in the 21st century, making it critical to understand the microstructure 
and mechanical behavior of these alloys.   
Over the years, considerable research has been performed examining and seeking 
to improve the mechanical properties of titanium.  For the purpose of this investigation, 
low temperature will be defined as less than 0.25*T m, where Tm is the melting 
temperature of the material in question (1941 K for Ti).  Many previous studies have 
been performed to examine the low-temperature tensile deformation mechanisms of 
single-phase ? and ?, as well as two-phase ? +  ? titanium alloys. These ? +  ? and ? 
titanium alloys are specifically important because they have excellent mechanical 
properties including a high strength to weight ratio.  However, in many of these 
applications, low temperature creep resistance is an important factor.  It has long been 
known that titanium alloys may plastically deform over time under constant load, or 
creep, at low temperatures, which could compromise the mechanical reliability of 
titanium components.  Creep is an important consideration in high-pressure vessels, 
2 
aircraft components, structural components and artificial joints such as hips or knees.  
Given the importance of reliability in these cases, it is vital to understand the deformation 
mechanisms of Ti alloys under these conditions.  In this sense, the tensile strength and 
creep resistance of the two-phase ? + ? Ti alloys are dependent upon a number of 
parameters such as microstructure, the properties of the component phases, interactions 
between phases, and ?-phase stability. 
There is currently a lack of understanding regarding some of the fundamental 
aspects of low temperature deformation of Ti alloys, which will be addressed in this 
investigation.  Of particular interest in this investigation is deformation twinning.  Slow 
twin growth (hereafter known as time-dependent twinning) has been identified as a low 
temperature creep deformation mechanism in coarse grained (???? ?m) single-phase ? 
and single-phase ? titanium alloys.  ?urthermore, time-dependent twinning itself is 
unusual because twinning is classically understood as a deformation mechanism which 
occurs at speeds close to the speed of sound in the material (5,090 m/s in Ti) and only at 
high strain rates or very low (cryogenic) temperatures.  It has been suggested in previous 
investigations that interstitial impurities, particularly oxygen, may be responsible for slow 
twin growth and some crystallographic models were developed to explain this. 
In regard to two-phase titanium alloys, it was found that the deformation 
mechanisms in these alloys could be quite different from those of the single-phase alloys.  
The reasons for this unexpected behavior are not known.  A clear understanding of this 
behavior will lead to the development of new titanium alloys for improved low 
temperature creep resistance and specific strength.  To address some of these issues, a 
systematic investigation has been undertaken.  The unique aspect to this investigation is 
3 
the combination of both experimental and theoretical studies to build a model of 
twinning-based deformation in titanium alloys.  The specific aims and components of this 
investigation are as follows: 
1. Carry out tensile studies with varying strain rates (10-6 - 10-1 ?s) on an ?-Ti-
 1.6wt% V alloy to determine what effect if any strain rate has on deformation 
twinning.  If there is an effect, determine how this effect be related to the 
time-dependent twinning phenomena observed during creep deformation of 
this alloy.  
2. Determine the tensile and creep properties at 298 K of ? + ? Ti-8.1 wt% V 
(???? ?, ??? ?) with a fine-grained equiaxed type microstructure.  Compare 
these properties with those of the same alloy with a Widmanst?tten 
microstructure.  Determine how the results would best help us optimize the 
microstructure for improved low temperature creep resistance. 
3. Carry out tensile and creep studies at 298 ? of the ? + ? Ti alloys Ti-4.3wt% 
? (? ??? ?, ??? ?) and Ti-12.6wt% V (~ 17 % ?, ??? ?) for both 
Widmanst?tten and equiaxed microstructures.  This information will help in 
optimizing the volume fraction of phases and morphology for improved low 
temperature creep resistance. 
4. Systematically identify and characterize the deformation products by optical, 
scanning electron microscopy (SEM), and transmission electron microscopy 
(TEM), with a particular focus on the interactions between deformation 
mechanisms and how the microstructure (i.e. grain size or orientation) or 
volume fraction of phases may affect creep behavior. 
4 
5. Determine the effect of interphase interactions for both Widmanst?tten and 
equiaxed microstructures with three-dimensional anisotropic finite element 
(FEM) modeling of the elastic interaction stresses between the inter-phase 
interfaces of ???, twin in ??martensite in ?, and twin in ??twin in ?. 
 
A thorough literature review and technical background is provided in Chapter 2.  
Chapter 3 gives an outline of the experimental procedures.  The results and discussion of 
the strain rate effect of twinning in ?-Ti alloys is provided in Chapter 4.  Chapter 5 is a 
comprehensive review of the effect of the second phase on low temperature deformation 
mechanisms.  The results and discussion of the experimental work with regard to creep 
and tensile testing of two-phase Ti alloys are contained in Chapter 6.  Chapter 7  provides 
the FEM analysis of the experimental work seen in the earlier chapters.  Lastly, Chapter 8  
gives the main conclusions and Chapter 9 provides some potential avenues for future 
work. 
  
5 
Chapter 2  
Technical Background  
 
 This chapter consists of a brief review of titanium, titanium alloys, titanium 
phases, creep deformation behavior, and the previous studies which are most relevant to 
the present investigation. 
 
2.1 The ? and ? p hases  
The titanium ?-phase is a hexagonally close packed (HCP) crystal structure.  The 
titanium ?-phase is a body centered cubic (BCC) structure.  Pure titanium will undergo 
an allotropic phase transformation from ??? as the temperature is increased above 1156 
K (883 ?C).  Alloying elements are most often added to pure titanium to enhance its 
material properties.  Elements that have little effect or increase the transformation 
temperature are called ?-stabilizers, where elements that decrease this transformation 
temperature are called ?-stabilizers.  Elements that have been shown to stabilize the ?-
 phase include Al, Ga, Sn, and O [ 1] .  Elements that have been shown to stabilize the ?-
 phase are generally transition metals and noble metals, including, V, Nb, Ta, Mo, and Mn 
[ 1] . 
As mentioned before, titanium alloys can be commercially available as either a 
single phase ? or ? microstructure, or present as a two-phase ? +  ? microstructure of 
several different morphologies.  Single-phase titanium alloys have very good mechanical 
properties; however, they are often characterized by a lower strength to weight ratio th an 
other alloys available.  The ? alloys, like other BCC metals have a ductile to brittle 
6 
transformation temperature, and have some processing difficulties including the inherent 
instability of the ?-phase.  Two-phase alloys have the advantage of desirable mechanical 
properties as well as stabilized phases.  The two-phase alloys used in this study are ?-
 stabilized binary alloys that have a sufficient amount of ?-stabilizing element to retain the 
?-phase upon quenching; the ?-phase is then nucleated and grown by heat-treatment in 
the ? +  ? field of the phase diagram, as shown in Figure 2.1 [ 2, 3] . 
 
 
 
  
ALLOY 
ALLOYING 
ELEMENT 
PHASES 
 V (wt%)   
1*  1.6 ~ 100% ? 
2 4.3 ~80% ?, 20% ? 
3 8.1  ~50% ?, 50% ? 
4 12.6 ~17% ?, 83% ? 
5*  14.8  ~100% ? 
 
Figur e 2.1.   Titanium rich end of the Ti-V phase diagram and respective alloy 
compositions used in this investigation [2, 3] . 
7  
2.2 Low temperature deformation mechanisms of titanium alloys  
Various mechanical properties of two-phase alloys, including low temperature 
creep, have been recently reviewed by Ankem et al [ 4] .  Among these two-phase alloys, 
titanium alloys are of particular interest.  The attractive properties of titanium and its 
alloys include: high strength to weight ratio, excellent corrosion resistance, and 
biocompatibility. For these reasons, they are used in a number of high technology areas.  
In many of these applications, components are subjected to constant loads over extended 
periods of time at low temperatures (<0.25Tm).  For example, titanium alloys were being 
considered as candidate materials for use in the nuclear waste storage system at the 
Yucca Mountain Nuclear Waste Repository [ 5] , titanium alloys make up a large fraction 
by weight of the F-35 Joint Strike Fighter (JSF) [ 6] , the largest fraction by weight of any 
material in the F-22 series of military fighter jets [ 7 ] , and titanium alloys are used 
extensively in the biomedical field [ 8 -13] .  Additionally, there are many other 
applications where low temperature creep is important, including pressurized fuel tanks 
found in satellites [ 14] . 
In addition to creep deformation leading to creep failure, creep deformation can 
also affect other failure modes such as fatigue failure and stress corrosion cracking.  This 
is due to the fact that low temperature creep deformation can result in such features as 
twins and martensite [ 15-25]  that can act as fatigue crack initiation sites.  There are many 
deformation mechanisms which play a role during creep of titanium.  ?n regards to ? 
titanium alloys, it was found that slip and time-dependent twinning play a significant role 
[ 15, 24] .  Further, it was shown that a decrease in grain size results in a decrease in time-
 dependent twinning and hence lower creep strain [ 15, 24] .  Similarly, in the case of ? 
8  
titanium alloys, both slip and time-dependent twinning were found to be important 
mechanisms [ 17 , 23, 25] .  ? decrease in grain si?e in ? alloys was also found to decrease 
creep strain as in ? alloys [ 17 , 23, 25] .  Further, it has been shown that for a given grain 
si?e, an increase in stability of the metastable ? alloy will result in a decrease in creep 
strain [ 17 , 23, 25] . 
In regard to ? +  ? titanium alloys, the deformation mechanisms found include? 
slip, interface sliding, twinning, and stress-induced martensite formation [ 21, 22] .  
?dditional deformation mechanisms were found in ? and ? phases of ? +  ? alloys when 
compared to deformation mechanisms in the single-phase ? and ? alloys [ 21, 22] .  The 
reasons for this are not known.  ?n addition, the creep strain of the ? +  ? alloy with low 
stability of the ? phase was found to be high.  It is important to know how the 
morphology and volume fraction of the phases affects the creep mechanisms and hence 
creep strains in the ? + ? alloys with low stability of the ? phase.  This is the focus of the 
present investigation.  The outcomes of the investigation will be of great help in 
designing new titanium alloys and optimizing the processing parameters of the existing 
alloys for improved low temperature creep resistance. 
 
2.3  Plastic deformation of two phase  titanium alloys  
The deformation behavior of two-phase alloys depends upon the properties of the 
component phases, the morphology and volume fraction of the component phases and the 
orientation of the interface between the phases.  When two-phase alloys are subjected to a 
stress, the individual phases deform differently, resulting in elastic, elasto-plastic, and 
9 
plastic deformation [ 26] .  Therefore, deformation in these two-phase alloys is a process 
that cannot be modeled just on individual phase deformation and the rules of mixing. 
One characteristic of titanium alloys is that they are prone to creep at low 
temperatures (<0.25Tm) and at low stresses [ 27 -29] .  Creep can cause failure in 
components by a change in dimensional tolerances [ 29-36] ; oftentimes, components that 
depend heavily on titanium, such as aircraft landing gear, require precise part tolerances 
so predicting low temperature creep becomes very important.  Creep in ?-titanium alloys 
has been primarily explained by slip [ 33] .  However, in comparison with ?-titanium, 
studies of low temperature creep in ? and near-? alloys have been very limited with a few 
exceptions [ 17 , 18 , 25, 37 -40] .  Creep studies of two-phase titanium alloys have primarily 
concerned commercial alloys [ 29, 30, 32-36, 41] , and have been attributed to slip in the 
individual phases as well as across the interphase boundaries. 
 
2.4. Elements of Twinning  
As twinning will be the focus of the majority of this investigation, the elements of 
twinning will be reviewed here.  According to the classical theory of deformation, the 
original untwinned (matrix) lattice is transformed by displacements which are equivalent 
to, or an integral fraction of, a simple shear of the lattice points [ 42] .  There are two 
planes which are not distorted by the shear of the lattice.  One of these, denoted K 1 , is 
referred to as the twinning plane and the shear direction is given by ??.  The second 
undistorted, or conjugate plane is denoted K 2 .  The plane of shear, P, contains ???and the 
normals to K 1  and K 2 .  The intersection of K 2  and P gives the conjugate or reciprocal 
shear direction, ??.  When describing a twin, it is typical to identify the twin by the shear 
10 
plane, K 1  and the shear direction, ?1 , i.e. 
? ?uvwhkl
 .  Twins are typically classified as 
Type I or Type II depending on the nature of the twinning elements [ 42] .  The planes and 
directions associated with twinning are schematically illustrated in Figure 2.2. 
 
 
2.5. Recent developme nts in ? - Ti alloys 
?hen an ?-Ti-?.?? alloy with a coarse grain si?e (????m) was creep deformed in 
tension at a stress level of 95%YS and 298  K, time -dependent twinning was observed 
[ 15, 24] .  Similar phenomena were also observed earlier in a coarse-grained ?-Ti-0.4wt%  
Mn alloy [ 16, 20] .  To prove that the features observed were indeed twins, TEM 
investigations were carried out [ 24] . 
The next question is why the twins grow so slowly.  It has been traditionally 
believed that twins grow at speeds approaching the speed of sound.  To understand this 
phenomenon, a crystallographic model was developed.  The model in Figure 2.3 is an 
extension of the model proposed by Song and Gray [ 43-45] , where the movement of  
Figure 2.2.   Schematic illustration of planes and directions associated with twinning. 
11 
 
interstitial sites in addition to the movement of the parent atoms are shown.  This figure 
shows that none of the octahedral sites are conserved, i.e. they are all displaced.  What 
this means is that if oxygen is present at these interstitial sites, the oxygen atoms will 
interfere with the twin propagation, and the oxygen must diffuse away from the 
twin/matrix interface before the twin can grow.  Therefore, originally a shear and shuffle 
process for the formation of the twin, is now controlled by the diffusion process of 
oxygen atoms.  If indeed the oxygen diffusion controls the twin growth, then the 
activation energy for the twin growth would correspond to the activation energy of 
o?ygen diffusion in ?-Ti.  The activation energy of twin growth in ?-Ti was calculated by 
measuring individual twin growth rates.  This activation energy was found to be 66 
kJ/mol [ 24] .  This activation energy was compared to the activation energy of diffusion 
Figure 2.3.   Schematic illustration of {10 1? ?? twinning in the HC? lattice of ?-
 titanium.  Projection of the lattice is onto the {11 2? 0} plane.  (a) Shear of the lattice 
in the <1? 101? > direction moves only atoms in A-type sites (blue) directly to twinned 
position.  (b) Arrows give the shuffles required to move the atoms in B-type sites 
(red) to either the B (red) or C-type sites (green) in the twinned lattice.  
Reorientation of the lattice will eliminate the octahedral sites (marked with an ???) 
where an oxygen atom could reside.  These models are an extension of earlier 
twinning models by Song and Gray [43, 44], but now include the corresponding 
movements of octahedral sites [45].  
  
12 
of oxygen in ?-Ti.  At 298K, the experimentally measured activation energy for oxygen 
in ? titanium ranges from about ?? - 200 kJ/mol [ 46] .  The low end of this range is close 
to the value of the model, suggesting that the growth of twins is controlled by the 
diffusion of oxygen.  Details are reported by Oberson and Ankem [ 24] .   
 
2.6. Recent developments in ? - Ti alloys 
?imilar to ?-titanium alloys, it was found that twinning also plays a significant 
role in the low temperature creep behavior of some coarse-grained ?-titanium alloys, 
depending on the stability of the ? phase [ 17 , 23] .  In these investigations [ 17 , 23] , the 
creep behavior of a coarse-grained ?-Ti-??.?? with a grain si?e of ??? ?m was studied 
which was deformed at 95% yield stress and at 298  K.  It was found that slip as well as 
{332}<113> twinning are the major deformation mechanisms [ 17 , 23, 25] .  ?imilar to ? 
titanium alloys, a detailed crystallographic mechanism was proposed for the growth of 
twins, the results of which are shown in Figure 2.4.  These results show that oxygen can 
play a significant role in controlling the growth of twins; thereby controlling the extent of 
creep strain.  A comparison for the activation energy of diffusion of o?ygen in ?-titanium 
and a calculated activation energy based on the twin growth rates suggests that the 
growth of twins is controlled by the diffusion of oxygen in BCC titanium as well.  As in 
the case of ?-titanium, the predominant deformation mechanism at the beginning of the 
creep deformation process was found to be slip, followed by slip and twinning at later 
stages of deformation [ 23] . 
13 
 
 
2.7 . Recent developments in two - phase  Ti alloys 
?n regard to ? +  ? titanium alloys, it was found that the deformation mechanisms 
could be quite different from those observed in single-phase ? and ? alloys.  ?or e?ample, 
in the case of 51%  ? - 49%  ? Ti-?.??, with ?idmanst?tten ? +  ? microstructures, creep 
deformation mechanisms were found to be twinning in ? and stress-induced martensite in 
? [ 21, 22] .  The creep tests were conducted at 95%YS at room temperature (298  K).  
There were at least two surprising results here.  First, twinning along with slip 
was found to be the major deformation mechanisms in single phase ?-Ti-1.6V where the 
grain size was >60  ?m [ 15] .  However, in the case of this two-phase alloy, twinning was 
observed in ? even though the ? plate thickness is about ?.? ?m (twinning was not 
previously seen in small grain si?e ?-Ti alloys).  Second, in the case of the single-phase ? 
alloy discussed above, twinning, along with slip were found to be the major mechanisms.  
Figure 2.4.   Projection of bcc substitutional and octahedral interstitial atoms onto 
(  ? ) plane. (a) Untwinned structure showing direction of [113] twinning shear, and 
(b) Final twinned structure showing mirror symmetry across twin-matrix interface 
[23 ].  
14 
However, in this two-phase alloy, stress induced martensite was found to be a major 
mechanism in the ? phase, a phenomenon which had not previously been seen [21, 22] .  
  
2.8.  What is not known, but shoul d be  
The interesting results from Section 2.7  were explained on the basis of elastic 
interaction stresses [ 4, 21, 22] , but there are still many unknowns.  For example, as 
shown in Figures 2.5, 2.6, and 2.7 , the twins in ? are connected to the martensite in ? and 
it is not known which one started first or how these interfaces will change with a change 
in volume fraction of the phases.  Further, it is not known how these elastic interactions 
decay from the ??? interface.  ?n addition, it is not known if such combination of twinning 
in ? and stress-induced martensite (??) in ? will e?ist if the morphology of ? and ? phases 
are changed from the morphology shown in Figure 2.4, to equiaxed microstructure.  
?urthermore, it is not known which one is the slower process?  twinning in ? or stress 
induced martensite in ?.  The slower of the two processes will control the extent of creep 
deformation.  In the proposed investigation, all these issues will be addressed. 
 
a 
Figure 2.5.  (a) TEM micrograph and (b) SEM image showing connection between 
twinning in ?-phase and stress induced martensite in ?-phase [21, 22].  
15 
 
 
Figure 2.6 .  High resolution TEM (HREM) micrograph of the slightly rough, semi-
 coherent ??? interface of Ti-8.1V, viewed from the [1 2? 10] ? // [1 1? 1] ? direction [21, 
22].  
16 
 
 
  
Figure 2.7 .  High resolution TEM micrograph showing the interface of stress 
induced martensite (??) and the ? phase.  ?otice the ???1? 1} twin relationship 
between the phases.  Selected area diffraction patterns from each phase and the 
interface taken parallel to the (12? 10) zone axis are inset. [ 21, 22]  
17  
Chapter 3  
Experimental Procedures  
 
The following are general procedures used in the course of this investigation. 
They are referenced as required in Chapters 4 and 5 for individual investigations.  A 
selection of single and two-phase Ti-V alloys were selected such that the chemistry of the 
single-phase ? and ? alloys researched previously [ 17 , 47 ]  would match the component ? 
and ? phases of the two-phase alloys.  Two different microstructures were also used in 
this investigation to study the effects of phase morphology and grain size on the creep 
deformation mechanisms.  The extent of low temperature creep strain in titanium alloys 
has been shown by many researchers to be dependent on grain size [ 16, 17 , 19, 47 -52] .  
Additionally, it has been shown previously that certain microstructures can result in 
deformation mechanisms not present in the single-phase alloy versions of the respective 
phases [ 53] .  As such, both of those effects will be addressed here. 
 
3 .1. Heat treatment  
The Ti-1.6wt% V, Ti -4.3wt%  V, Ti-8.1wt%V , and Ti-12.6wt% V  alloys used in 
this investigation were melted as 13.6 kg ingots and processed to 1.74 cm diameter bars 
at RTI International Metals, Inc. in Niles, Ohio.  The final rolling step to a 60% reduction 
in area was carried out in the ? +  ? field at ??? ?.  To obtain the desired microstructure, 
the Ti-1.6V alloy was vacuum encapsulated in quartz tubes at 10-5 Pa, then annealed at 
1173 K for 2 hours, furnace cooled to 963 K and annealed for 200 hours, then water 
quenched to room temperature.  To obtain the fine equiaxed microstructure for the Ti-
18  
4.3V, Ti-8.1V, and Ti -12.6V alloys, the bars were vacuum encapsulated in quartz tubes at 
10-5 Pa, then heat treated for 200 hours at 963 K (just below the tie line), followed by a 
water quench.  To obtain the coarse equiaxed microstructure for the three intermediate 
alloys, the bars were vacuum encapsulated and then heat treated for 168 hours just below 
the beta transus temperature and then furnace cooled 10 degrees every 48 hours to 963 K.  
The samples were then annealed for 200 hours at 963 K, followed by a water quench.  To 
obtain the Widmanst?tten microstructure, the alloys were vacuum encapsulated and then 
heat treated for 2 hours just above the beta transus temperature followed by a furnace 
cool to 963 K.  After annealing for 200 hours at 963 K, the bars were then water 
quenched.  The quartz tubes were broken right before quenching to ensure a fast quench.  
The chemical compositions are actual chemical compositions of the alloys after 
fabrication as determined by wet etch method and shown in Appendix A. 
 
3.2. Tensile and creep specimen  preparation  
 Tensile and creep specimens were then machined from the bars according to the 
specifications detailed in Appendix B, with flat surfaces cut onto the gage length sections 
by electric discharge machining (EDM).  The flat gage sections were then mechanically 
polished using progressively finer grit down to 1200 grit, followed by a final polishing 
step on a Chemomet? polishing cloth with a ?.? ?m Buehler Mastermet? silica solution.  
After polishing, the specimens were etched with a combination of A-etch (2.5 mL HF, 
2.5mL HNO3, 5.0 mL glycerin) and R-etch (16 mL glycerin, 14 mL ethanol, 7.5 g 
benzalkonium chloride, 10 mL HF) for a few seconds each.  The A-etch will reveal grain 
boundaries while the R-etch dyes the beta phase for imaging in SEM. 
19 
 
3 .3.  Attachment of fiducial grids  
Gold-palladium fiducial lines were deposited on the polished specimen surfaces. 
The fiducial grid serves several purposes: to allow easy identification of the same area for 
pre and post testing microscopy, to measure strain in local areas, and to aid in the 
identification of interphase interface sliding, indicated by displacement of lines across 
boundaries.  
Shipley Microposit 950 A10 PMMA positive electron resist was spun onto the 
specimen surface at 3300 RPM for 50 seconds on a Headway EC-101 spinner in a UV 
free clean room (FabLab) and pre-baked at 170?C for 30 minutes. The specimens were 
transported inside a film bag to guard the resist from light. A JEOL JXA 8900R  
microprobe was used to expose the resist.  The specimen is placed into the microprobe 
with the lights off to avoid prematurely exposing the resist.  The grid line spacing was set 
to ?? ?m.  Beam writing conditions were 30kV, 25x magnification, and an aperture size 
of 4.  Test lines were drawn with beam currents ranging from 1 ? 100 nA and exposure 
times ranging from 1 ? 10s.  This procedure should be performed for any new batch of 
photoresist.  The optimal settings for this investigation were 10 nA and 10s.  The resist 
was then developed for 90s with agitation and light swabbing in Shipley MIBK:IPA 1:3 
developer.  The specimen surface was etched lightly for 15 seconds by dilute titanium 
etch (2 mL HF, 4 mL HNO3, and 194 mL H2O) to facilitate removal of the resist after 
sputtering.  Gold-palladium was deposited to a thickness of 20 nm (120 seconds) by an 
Anatech LTD Hummer X sputtering system.  To remove the remaining photoresist, the 
specimen was sonicated in acetone for 10 ? 30 minutes. 
20 
 
3 .4. Tensile testing  
 Tensile testing was conducted at room temperature in an Instron 8502  floor model 
servo-hydraulic materials testing machine with a 500kN load cell. Testing was performed 
at a strain rate of 3.28x10 -5/sec to a total strain of 3% for all two-phase specimens and at 
1x10-6, 1x10-4, 1x10-2, and 1x10-1 /s to a total st rain of 3% for the single -phase ? 
specimens. An Instron clip on extensometer with a 12.7 mm gauge length and 5% 
maximum extension was used to measure strain. 
 
3 .5. Creep testing  
Specimens examined for this work were creep tested in an ATS lever arm creep 
test machine at 95% of the measured y ield stress.  Interrupt creep tests were performed 
and the samples were taken off for imaging after 60 s, 10 minutes, 1 hour, and 200 hours.  
A clip-on extensometer was used for recording the strain and data sampling rates ranged 
from 10 per second early in the testing to one per hour after 8 hours of testing.  SEM 
micrographs were taken of the same area on the samples before testing as well as at each 
of the interrupts and after 200 hours of total testing time. 
 
3 .6. SEM  and optical microscopy  
 SEM micrographs were taken of the polished specimen surfaces prior to and 
following tensile and creep deformation. This procedure is useful for separating 
deformation products that arise during tensile and creep testing from those that may be 
21 
present prior to testing. A  Hitachi S-3400N (FabLab) and Zeiss ICM 405 inverted 
metallographic light microscope were used to record images of the alloys. 
 
3 .7. TEM sample preparation  
The success of transmission electron microscopy (TEM) depends on the careful 
preparation of specimens, which must (1) remain unadulterated and (2) be sufficiently 
thin for electron transparency. There are many common preparation methods, some better 
suited to the two-phase metallic specimens than others for a variety of reasons. Several 
basic steps are involved for the preparation of specimens from titanium tensile and creep 
samples. These are outlined below.  
 
3 .7.1 Cutting TEM samples from creep or tensile specimens  
The first step is removal of a specimen from the bulk material. A Buehler Isomet 
Low Speed Saw with diamond wafering blade was used to slice sections of material from 
the bulk, from both the deformed material in the gage length and the undeformed material 
in the threaded ends of the tensile and creep specimens. Buehler Isocut ?  fluid was used to 
lubricate and cool the wafering blade while removing debris and a saw speed of 5 was 
selected. Cutting speeds were kept slow to prevent sample damage due to cutting forces. 
One slice was made initially to reveal the interior of the sample material of interest, and 
then subsequent slices were made by moving the sample holder a set distance in relation 
to the blade. This is accomplished by dialing in the attached micrometer the desired 
displacement. 18 divisions of t he micrometer yielded specimens of approximately 120 
?m thick.  A Gatan model 659 disc punch was then used to produce 3 mm discs from the 
22 
cut slices.  The Gatan punch is designed such that no additional deformation is introduced 
into the specimen. 
 
3 .7.2 Pre - thinning  
 Pre-thinning was performed with jet-polishing.  Jet polishing is a chemical 
process that uses a combination of an acid containing electrolyte and electric current to 
remove material from the sample.  A South Bay Technology Inc. Model 550 jet thinning 
electropolisher was used for this investigation.  An electrolyte solution of 94% methanol, 
3% sulfuric acid and 3% hydrochloric acid cooled to 210 K ( -60?C) in a dry-ice/ methanol 
bath was used.  The samples were polished using a pump speed of 4, sensor sensitivity of 
5, and a current of 25 mA.  It will be necessary to adjust the voltage between 75 ? 100 V 
to maintain a constant current.  The polishing should take about 2 minutes per side and 
leave a very shiny surface.  If the surface is not shiny, the voltage will need to be 
adjusted.  The Ti alloys used in this investigation will build up a surface oxide layer at the 
contact point with the polisher after an extended amount of time.  Therefore it is 
important to only flip the sample once during polishing to maintain a clean contact.  Jet -
 polishing is relatively rapid, but etches the ? phase of the two-phase titanium alloys more 
rapidly than the ? phase. The result is a thickness difference at the ??? interface that 
makes any study of the interface, difficult.  To solve for this, an additional ion-milling 
thinning step was performed. 
 
 
 
23 
3 .7.3 Final thinning  
Final thinning was performed with ion milling.  The ion milling machine used is a 
Fischione Instruments Model 1010 Ion Mill.  Milling was performed at a 10? incidence to 
the sample, with power settings of 5.0 V and 3.0 mA to perforation. The laser sensitivity 
was set to 2.  The specimen stage was cooled with liquid nitrogen and maintained at ? -30 
?C .  Depending on the thickness and unevenness of the sample, the initial milling step 
may take up to 1 hour.  Once a hole is formed in the sample, the power was reduced to 
3V and 3.0 mA for an additional milling time of 30 minutes and then to 1 V and 3.0 mA 
for 10 minutes in order to remove amorphous material from the sample edge and leave a 
very thin sample area.  The complete instructions for operating the ion mill are included 
in Appendix C. 
 
3 .8. Transmission electron microscopy ? TEM 
 TEM was used for the majority of characterization and analysis in this study. A 
JEOL 2100F field emission TEM (NispLab) as well as a JEOL 2100 LaB6 TEM 
(NispLab) both operating at 200 keV were used.  A combination of many techniques was 
required to understand the microstructure and deformation mechanisms, including 
selected area diffraction (SAD), bright field imaging, and dark field imaging.  A complete 
description of these techniques is beyond the scope of this chapter, but an excellent 
resource for various TEM techniques is ?Practical Electron Microscopy in Materials 
Science? by J.W. Edington [ 54] .  Several important points must be kept in mind for the 
safety and operation of the instruments which are outlined in Appendix D.  In order to 
determine some deformation mechanisms, the diffraction pattern must be oriented 
24 
correctly with respect to the image.  This rotation depends on the magnification of the 
image.  This calibration is provided in Appendix E. 
 The various deformation mechanisms were identified in several ways.  Slip was 
identified by dark field imaging using three different g vectors, and 
bg?
 analysis.  To 
determine if slip involving screw dislocations with a Burgers vector 
0211
 3
 1
 ?b
 ?  were 
gliding on basal or prism planes, bright and dark field images were taken along both 
0211
  and 
? ?0001
  zone axes and tilted slightly to determine if the dislocation lines 
visible were single dislocations or stacks of dislocations on single planes in projection.  
This was necessary because a-type screw dislocations in hexagonal crystals can glide on 
basal or prism slip planes. 
To identify twins in the ? phase, selected area diffraction patterns (SADPs) were 
taken from the matrix, the twin/matrix interface, and where possible the twin. In general 
to identify the type of twin the specimen must be tilted along a zone axis that contains the 
g vector for the twin plane common to both the twin and the matrix. For the 
? ? 01112110
  twins observed in this investigation it was required to tilt along a 
?
 0211
 zone axis. In the case of 
? ?2110
  twins there is a rotation of ~94? between the [0001] 
planes of the twin and matrix.  The e?act rotation depends of the c?a ratio of the ? phase. 
The spots in the interface diffraction pattern will be mirrored across the g vector of the 
twin plane.  Since there are three independent 
?
 0211
 directions, and the twin plane 
contains only one of these directions, for each twin there is only a 1/3 chance that the 
correct zone axis for identification will be attainable, as tilting 60? to the next 
?
 0211
  
25 
axis is impossible due to limits of the TEM specimen holder.  In even more cases the 
alignment of the ? grain where the twin is visible is oriented close to the 
? ??0001
  zone 
axis, where a tilt of ~90? would be required.  Therefore identification of any given twin is 
extremely difficult, and some twins could not be identified due to the tilt limits of the 
specimen holder.  Persistence and patience must be used during this process. 
 As discussed briefly in the introduction, there have been several type of stress 
induced martensite reported in titanium alloys.  To identify which type of martensite was 
present, the martensite selected area diffraction patterns were indexed and measured. The 
crystal structure was identified as hexagonal, and the Burgers orientation relationship 
? ? ? ??? 110//0001 ?
 , which exists between the martensite and the  ? phase, was obeyed. This 
was evidence for stress induced hexagonal martensite as opposed to the orthorhombic 
martensite.  The stress induced hexagonal martensite can form in six orientations in any 
given ? grain with the 
? ? ? ??? 110//0001 ?
 relationship, so the martensite may not be oriented 
along an e?uivalent ? ?one a?is to the one aligned with the beam, so identification of an 
individual martensite plate is difficult. 
 It should be noted at this time that undeformed material was examined to insure 
that the deformation mechanisms in the deformed material were the result of testing and 
not TEM specimen preparation. Also, the frequency of twins and martensite is quite low, 
therefore slow and careful surveying of each TEM specimen was necessary to find areas 
with twins and martensite for analysis. The objective lens aperture must be used in order 
to distinguish these plates from the matrix, and even then the contrast can be faint. 
 
 
26 
3.9. Manual calculation of resolved shea r stresses  
 ?n order to understand the effect of interactions between ? and ? phase 
deformation mechanisms, the magnitude of resolved shear stress that the observed ? 
phase deformation mechanisms place on the shear systems for twinning and the ???? 
(hexagonal martensite) transformations were calculated for all possible combinations of 
observed deformation mechanisms.  Due to the Burgers orientation relationship between 
the ? and ? phases and the ?? and ? phases, the orientation of the various directions and 
planes are fixed in relation to one another within the alloy system.  
The 4-index 120? coordinate systems for the he?agonal ? and ?? phases were first 
transformed to a 90? 3 -coordiante Cartesian system. Transformation matrices were 
calculated  to transform directions and planes in the ? phase into parallel directions in the 
? phase, as shown in Appendix F.  Directions and planes important for calculating 
resolved shear stresses, such as slip planes, Burgers vectors, twinning planes and 
directions, and planes and directions important for the ???? transformation were then 
converted to equivalent directions in the ? phase. The result is a common Cartesian 
coordinate system to perform calculations of resolved shear stresses between the ?, ?, and 
?? phases.  
Within this coordinate system the magnitude of resolved shear stress from 
deformation products in the ? phase were calculated. The ma?imum shear stresses for the 
basal slip systems, prism slip systems, and twinning shear systems were resolved onto the 
maximum possible shear systems for twinning and ???? stress induced transformation.  
The magnitude of these resolved shear stresses was calculated for every combination of 
27  
the above deformation products in a Microsoft Excel spreadsheet using the equations for 
vector transformation given below [ 55] : 
xzyz
 xyzzyyxxyx
 ??????????
 ???????????
 )()(
 )(
 12211221
 1221212121 ???????
   (3.1) 
where:     
kj
 jj
 ij
 ki
 ji
 ii
 ???
 ???
 ???
 ???
 ???
 ???
 2
 2
 2
 1
 1
 1
 ?
 ?
 ?
 ?
 ?
 ?
  
and 
? ?ijk
  is the original vector and 
? ?kji ??
  is the vector on which the stress is resolved. 
The complete results of these calculations are presented in Appendix G. 
    
28  
Chapter 4  
Deformation Mechanis ms and Kinetics of Time - Dependent Twinning in 
an ?- Ti- 1.6V alloy  
 
With some exceptions [ 50, 56-60] , few researchers have studied the strain-rate 
sensitivity of ?-titanium alloys at ambient temperatures.  In the present study, the strain-
 rate response of polycrystalline ?-titanium is examined, with particular focus on the 
deformation mechanisms which control that response. 
 The unique challenge associated with studying deformation mechanisms in HCP 
metals, such as ?-titanium, stems from the occurrence of both slip and twinning during 
plastic deformation.  The three most common slip modes are the {10 1? 0} , {10 1? 1}, and 
{0001} planes, with <11 2? 0> as the slip direction.  These three glide planes with the slip 
direction in the basal plane make up four independent slip systems [ 61] .  However, five 
independent slip systems are necessary for the polycrystalline material to be able to 
homogeneously plastically deform.  ?t?s also the case that none of the slip systems 
identified can support deformation in the c-direction.  Therefore, twin systems or <c+a> 
pyramidal slip are necessary to maintain deformation compatibility and the two 
deformation mechanisms will occur together [ 56, 62, 63] . 
 Commonly occurring in:  metals [ 42, 50, 64-68 ] , ceramics [ 69] , intermetallics [ 70 , 
71 ] , nanocrystalline materials [ 72 ] , superconductors [ 73 , 74 ] , and geological systems 
[ 75 ] , twinning is an important deformation mechanism.  The rate of twin growth has 
traditionally been observed to be approaching the speed of sound in the material (i.e. 
?,??? m?s in ?-titanium) [ 42, 76 ] .  Recent observations have shown however that twin 
29 
growth rates can be many orders of magnitude smaller than the speed of sound, on the 
order of 1 nm/s,  in single -phase ? (he?agonal close-packed) and ? (body centered cubic) 
titanium alloys [ 16, 23-25] .  A crystallographic model was recently developed which 
attributes the slow twin growth rates to the diffusion of oxygen from interstitial sites near 
the twin boundary [ 23, 24, 45] .  When twinning occurs, these interstitial sites are not 
always conserved and the oxygen atoms must diffuse away from those sites before 
twinning can take place.  According to previous twinning models, there should be no time 
dependence in twin growth rates; hence strain rate should not affect twin growth rate, for 
a constant applied stress.  However; recent work  showing a significant effect of strain 
rate on twinning, supports the theory that twinning in these materials can be controlled by 
a process which is much slower than the speed of sound, such as the diffusion of oxygen. 
This study presents a comprehensive look at the deformation mechanisms, 
twinning behavior, and resultant mechanical properties of these alloys and uses these 
results to explain how traditional views on deformation twinning do not explain the slow 
twin growth observed in single-phase ?-titanium alloys.  The broader purpose of this 
investigation is to develop a constitutive equation which describes the strain rate 
sensitivity of twinning as a function of oxygen diffusion.  Further, both optical and 
electron microscopy are used to identify and characterize the deformation products 
present at the differing strain-rates. 
 Under the conditions of a tensile loading test, the applied stress is continually 
increased such that the strain rate remains constant.  However, creep occurs at a constant 
stress that is oftentimes below the yield stress of the material.  Since a finite amount of 
stress is available to supply the activation energy required for creep deformation 
30 
mechanisms, additional stresses that can contribute to creep deformation are only 
available from internal sources.  These internal stresses (most often caused by interphase 
interactions) are the focus of this work.  To design alloys and processes for improved 
creep resistance, these interactions must be understood.  It should be noted that the results 
of this investigation can also be applicable to any other hexagonal-close-packed (HCP) 
system, including Zirconium alloys. 
Mechanical twinning was best incorporated into the experimental studies and 
constitutive models of Zerilli and Armstrong [ 77 ]  and Kalidindi [ 78 ] .  Tom? et al. [ 79 ]  
developed a constitutive equation for the combined slip/twinning deformation in HCP 
metals.  Meyers et al. [ 50]  were then able to introduce a constitutive description which 
could describe the onset of twinning as a function of a critical twinning stress.  This 
critical twinning stress can be described in terms of strain-rate, grain-size, texture, and 
stacking-fault energy [ 50] .  It should be noted however, that all of these studies assume 
unstable twin growth after twin nucleation.  The objective of this research effort is to use 
these constitutive descriptions [ 50, 77 , 79 ]  as a basis to obtain a linkage between the 
twinning nucleation/growth patterns and the strain rate.   
 
4 .1. Crystallography of time - dependent t winning  
Fortunately, the crystallography and quantitative analysis of deformation twinning 
in HCP metals has been extensively studied [ 80 -85 ]  and the lattice relationships between 
the matrix and the twin on the most common twin planes are known [ 43, 44] .  The 
twinning crystallography in HCP metals is complex because atomic shuffles as well as 
twinning shear are an important factor in producing a twinned structure.  With regard to 
31 
?-titanium, there are four predominant twinning modes, of which the {10 1? 2} and {11 2? 1} 
twin planes involve the smallest shear and simplest shuffles respectively.  Of these two, 
the {10 1? 2} sys tem is the most common because the Burgers vector for <a> type slip 
along the <112? ?? direction doesn?t have a c-axis component and twinning is necessary to 
accommodate strain along [0001].  The conventional twinning models in HCP materials 
presented by Song and Gray [ 43, 44]  demonstrate atoms moving to a twinned position by 
a simple shear process without shuffles of the interstitial sites.  Other models by Crocker 
[ 86 , 87 ]  demonstrate atoms moving by both shear and shuffle mechanisms in {1 1? 02} 
twinning; however, neither of these models co nsider the conservation of the octahedral 
interstitial sites if atoms such as oxygen reside there.  Oberson & Ankem [ 45, 88 ]  were 
the first to develop a {1 1? 02} crystallographic twinning model based on the models of 
Song and Gray [ 43, 44]  showing the octahedral interstitial sites which are not conserved 
and must be reformed for the twin front to advance.  These theories are supported by 
studies done by Cerreta et al. who have shown interstitial oxygen to have a significant 
effect on deformation mechanisms of ?-titanium and zirconium [ 89 , 90] .  In particular, it 
was shown that interstitial oxygen can inhibit twinning and form a resistance to lattice 
shear [ 89 , 90] .  In addition, Khan et al. also demonstrated interstitial oxygen inhibiting 
direct shear deformation mechanisms [ 91]  which can be attributed to the elimination of 
octahedral interstitial sites.  Figure 4.1 is an extension of Figure 2.3 and shows the 
crystallographic model of the untwinned and twinned HCP lattice which accounts for 
these sites and explains the observed behavior. 
According to the model developed by Oberson et al. [ 45] , the growth rate of twins 
in ?-titanium at room temperature should be controlled by diffusion of oxygen away from  
32 
 
Figure 4.1.   Schematic illustration of {10 1? ?? twinning in the HC? lattice of ?-
 titanium.  Projection of the lattice is onto the {11 2? 0} plane.  (a) Shear of the lattice 
in the <1? 101? > direction moves only A-type Ti atoms (large, dark circles) directly 
to twinned positions.  (b) Arrows give the shuffles required to move the Ti atoms 
in B-type sites (large, lighter circles) to their twinned B-type or C-type positions.  
Reorientation of the lattice eliminates the octahedral sites (small circles with ??? 
mark) where oxygen could reside.  (c) Schematic illustration of a completed {10 1?
 2} twinning event.  The completed positions f or B-type Ti atoms and the 
corresponding possible octahedral sites and the completed positions for C-type Ti 
atoms and the corresponding possible octahedral sites are indicated by the arrows.  
These models are an extension of earlier twinning models by Song and Gray (Song 
and Gray, 1995b,c), but now include the corresponding movements of octahedral 
sites where oxygen may reside [45] . 
(c) 
33 
eliminated octahedral interstitial sites.  Classical observations of twinning suggest that the 
growth of twins is controlled by a shear process which would mean that for a given 
amount of strain, twin thickness at various strain-rates should be approximately equal. 
 
4 .2. Time dependent twinning during c reep of ? - Ti- 1.6V  
 Time dependent twin growth has been previously observed during creep of single-
 phase ?-titanium alloys [ 24, 92] .  A model was presented to explain the slow twin growth 
as a function of the diffusion of oxygen atoms away from octahedral interstitial sites in 
the matrix.  Two important features were identified: (1) the activation energy for creep 
was very close to the activation energy for oxygen diffusion in this alloy, and (2) 
twinning is the primary plastic deformation mode as opposed to slip in creep deformation 
of ?-Ti-1.6V [ 24] . 
The activation energy for tensile deformation of ?-titanium at temperatures less 
than 0.4*T m was first measured by Conrad [ 93] .  It was suggested at the time that the 
rate-controlling process is the thermally activated overcoming of interstitial solute atoms 
by dislocations gliding on first order prism planes.  There have been a number of 
subsequent studies considering factors such as microstructure and strain rate [ 57 , 94-97 ] , 
but all have assumed unstable twin growth after nucleation. 
 
4.3 . Model for diffusion of oxygen at t win  front 
 According to the crystallographic model for ?-titanium developed by Oberson et 
al. [ 45] , the growth rate of twins is limited by the diffusion of oxygen away from 
eliminated octahedral interstitial sites.  The advancing twin front accompanied by 
34 
diffusion of oxygen atoms can be related to the diffusion of an interstitial species into the 
bulk of a sample, such as carbon into a bulk sample of iron.  In such a case, the effective 
penetration distance is the point at which the concentration of the diffusion species has a 
value equal to the average of the initial concentration in the bulk and the surface 
concentration [ 98 ] .  For the twin growth model, growth is assumed to be one-
 dimensional, in a direction normal to the center plane of the twin.  The center plane of the 
twin corresponds to the surface of the material and the thickness of the twin (from the 
center plane to the widest point) corresponds to xeff.  This effective penetration distance, 
xeff is defined as Eq. (4.1) [ 23, 98 ] : 
 ???? ???  (4.1) 
where D is the diffusivity and t is time.  Further, interstitial diffusion in alloys is 
governed by Eq. (4.2): 
 ?????????
 ??
 ??
 ?  (4.2) 
where D is the diffusivity of a species, D0 is the pre-exponential diffusion constant, Q is 
the activation energy for diffusion, T is the temperature, and R is the ideal gas constant in 
units of J mol K -1.  As modeled by Oberson et al., oxygen can either diffuse deeper into 
the parent grain or it can diffuse into the twin side of the interface; therefore it is not 
believed that there will be a significant pile-up of interstitial oxygen atoms at the 
interface so the values for D0 and Q should not change during the duration of the test 
[ 45] . 
 
 
 
35 
4.4 . Model for stress - assisted interstitial diffusion in ? - Ti 
 Elastic fields, which can be generated by defects such as twins, influence the 
diffusion process.  The study of stress effects on diffusion have been characterized 
experimentally for decades [ 99-102] ; however, understanding the effects of stress and 
strain on diffusion in alloys is fairly limited.  Eq. (4.2) has been modified to describe 
various field influences on diffusion; however, this express ion does not take into account 
the difference between the effect of electric fields or thermal energy which affect an 
individual atom and an elastic field which influences the neighbors of an atom.  It is clear 
that any modification to Eq. (4.2) to account for a stress must consider the position of 
neighboring atoms and crystallographic structure [ 103-105] .  The clearest theoretical 
derivation for tracking the effects of stress or strain states on diffusion has been done by 
M.J. Aziz et al. [ 106-109] .  Aziz theorized that the effect of stress could be characterized 
by a migration strain modification factor which describes the dimension changes of the 
crystal parallel and perpendicular to the direction of net transport [ 109] .  As such, the 
stress-induced change in the diffusivity could be described by Eq. (4.3).  
 
??
 ??
 ?????
 ???
 ???
 ?  (4.3) 
In Eq. (4.3), D? is the diffusivity under stress, D0 is the diffusivity under zero stress, ? is 
the applied stress, kB is the Boltzmann Constant, T is the temperature in degree Kelvin, 
and V? is a material specific atomic migration volume which we can assume to be a 
constant factor for o?ygen diffusion in ?-titanium [ 109] . This factor, V?, contains the 
information about the dimension changes for the crystal both parallel and perpendicular 
to the direction of net transport when the point defect reaches its saddle point.  As the 
diffusivity of an interstitial atom is proportional to the product of the concentration and 
36 
the mobility of the defect, the effect of stress on diffusivity in a specific direction can be 
described using this factor [ 109] . 
 
4.4.1. Effect of stress on activation energy of interstitial diffusion  
 When studying the effect of stress on interstitial diffusion, a component besides 
the change in volume of the crystal must also be considered.  An atom?s ability to diffuse 
is not only controlled by the activation energy required to move from one saddle point to 
another (a function of volume of the unit cell) but also the energy that the atom possesses 
to begin with.  This energy can be increased (making the jump to the required activation 
energy easier) through electrical and thermal means.  With an increase in strain rate, there 
is also an increase in work done to the sample.  This increase in work is converted within 
the sample to heat and this increase in heat can change the activation energy required for 
diffusion.  Since both Equations 4.2 and 4.3 have a Temperature term, this increase in 
sample temperature could have a significant impact on values obtained.  The increase in 
sample temperature is found according to the equation ???
 ?
 ??
 ???? [ 95] , in which ? ? 
0.9 (assuming 90% of work of deformation was converted to heat), ? is the density of the 
sample (~  4.506 g cm-3) and C is the heat capacity of the sample (~  25.060 J mol -1 K -1).  
It was found during the course of this investigation however, that even the highest strain 
rate experiment only gave rise to a 5?  increase in the sample temperature which would 
make this change in activation energy for diffusion insignificant and can thus be 
neglected. 
 
  
37  
4.5 . Tensile t esting  results  
The true stress versus true strain curves are shown in Figure 4.2.  The small slope 
of the curves in the plastic range indicates a low strain-hardening rate which is common 
for most titanium alloys [ 110-112] .  The strain-rate sensitivity of titanium alloys 
decreases with increasing strain.  A summary of the tensile properties obtained at 
different strain rates is given in Table 4.1.  Three tensile tests were performed for each 
experiment but only one was polished and etched for microscopy.  The results of the 
tensile test were within +/ - 2% (< 7 MPa).  It can be seen that the flow stress of the 
titanium alloy increases with increasing strain rate.  The increase in flow stress will have 
an effect on the twinning behavior of this alloy as discussed in Section 4.8.2.   
 
 
Figure 4. 2.   ?echanical testing results of ?-Ti-1.6V tested at different strain rates.  
(a) True stress ? true strain curves of alloy tested at different strain rates.  (b) Strain 
hardening rate of the plastic region of each of the curves.  The alloy exhibits a low 
strain hardening rate for all tested strain rates. 
38  
 
4.6. Optical and SEM m icroscopy  
Tensile specimens were examined before and after testing by optical and SEM 
microscopy to look for evidence of deformation mechanisms such as slip and twinning.  
The fiducial grid serves as a reference to identify the same area of the specimen before 
and after testing.  The micrographs shown in Figure 4.3 are of the ?-Ti-1.6V before and 
after tensile testing at (a) 10-1 /s, (b) 10 -2 /s, (c) 10 -4 /s, and (d) 10 -6 /s respectively, 
showing deformation mechanisms, specifically deformation twinning as the dominant 
deformation mechanism across all strain rates.  To ensure that the deformation features 
seen under optical microscopy were twins and not another type of deformation feature or 
sub-divided grain, polarized light was used and the polarization was changed to see if the 
features changed.  The results for the sample tested at 10-6 /s are shown in Figure 4.4 , but 
this technique was performed with the other strain rates as well.  As is evident, the 
deformation features will disappear under certain polarization and are indeed twins.  
Twinning behavior was characterized using optical microscopy.  An area of ~ 10 mm 2 on 
each sample was mapped and microstructural features were recorded manually.  The 
results of the deformation maps are organized into Table 4.2.  
 
 
Strain Rate 10-1 /s  10-2 /s  10-4 /s  10-6 /s  
0.2% Yield S tress (MPa) 420 399 357  305 
Flow Stress @ 3% Strain (MPa)  460 437  399 346 
Elongation (%)  3 3 3 3 
 
Table 4.1.   ?echanical testing results of ?-Ti-1.6V tested at different strain rates at 
298K.  
39 
 
Figure 4. 3.   Before and after optical micrographs of deformation twinning in ?-Ti-
 1.6V at (a) 10-1 /s, (b) 10 -2 /s, (c) 10 -4 /s, and (d) 10 -6 /s.  All samples were tested to 
3% strain.  All micrographs were taken at 100x magnification.  The fiducial grids are 
?? ?m s?uare.  ?ote the gradual increase in twin thickness as the strain rate decreases, 
as indicated by the arrows. 
40 
 
4.7 . TEM m icroscopy  
 TEM foils were prepared from specimens tested at each of the strain rates to 
identify and characterize the deformation products present.  There are four main twinning 
modes which have been identified in HCP materials.  In the case of tensile deformed 
titanium, the {1 1? 02}<10 1? 1? > twin; hereafter called the {1 1? 02} twin, is the most common.  
Figure 4.5 shows a {1 1? 02} deformation twin and the associated selected area diffraction 
patterns (SADPs) occurring in the 10-1 /s sample.  The SADPs were taken from the 
untwinned matrix (a), inside the {1 1? 02} twin (b), and across the twin -matrix interface (c). 
 In addition to identifying the type of twins present during tensile deformation of 
this alloy, the aim of the TEM investigation was to determine if the twins seen during the 
optical investigations were single twins or close-knit groups of very fine (??.? ?m) twins.  
As can be seen from the TEM micrographs in Figures 4.5 and 4.6, as well as the high-res 
optical micrograph in Figure 4.7 , the twins present in this investigation are of an 
appreciably higher thickness than ?.? ?m and therefore the calculated twinning thickness 
averages should not be distorted by an excessive number of unresolvable fine twins.  
Strain Rate 10-1 /s  10-2 /s  10-4 /s  10-6 /s  
Number of grains in selected area, Ng 125 115 121 123 
Number of twinned grains in selected area, Ntg 51 41 44 44 
Percent of grains twinned,  Gt 41%  36%  36%  36%  
Number of twins in selected area, Ntw ~625  ~210  ~150  ~135  
Volume fraction of twins in twinned grains, Vtg 7%  7%  9%  22%  
Total twin volume fraction, Vt 2.9%  2.5%  3.2%  8%  
Approximate average twin thickness, W ?.??m ?.? ?m 12.5 
?m 
20.0 
?m 
 
Table 4.2 .   ?uantitative analysis of deformation twinning in selected area in ?-Ti-
 1.6V tensile tested to 3% strain at 298K.  The values for twin volum e fraction are 
accurate to +/ - 3%.  
41 
 
 
Figure  4.4.   Optical micrograph taken under different polarizing light conditions of 
?-Ti-?.??, showing multiple twins.  T ? ????, ? ? ?.??, strain rate ? ??-6 /s.  The 
fiducial grids are ?? ?m s?uare.  ?ote twins at the arrows which disappear under 
non-polarized light.  This method of twin identification was used for the other 
strain rates as well but is not shown here. 
Figure 4. 5.   Bright field T?? micrograph from tensile deformed ?-Ti-1.6V, of {1 1?
 02} twin and SADPs of the {2 1? 1? 0} foil plane from: (a) the untwinned matrix, (b) 
inside the twin, and (c) across the twin-matri? interface.  T ? ????, ? ? ?.??, strain 
rate = 10 -1 /s.  
42 
 
 
Fig ure  4. 6.   Bright field T?? micrograph from tensile deformed ?-Ti-1.6V, of {1 1?
 02} twin with [2 1? 1? ?? ?one a?is.  T ? ????, ? ? 3.0%, strain rate = 10 -1 /s.  Note the 
twin indicated by the arrow. 
Figure  4. 7.   ?ptical micrograph from tensile deformed ?-Ti-?.??.  T ? ????, ? ? 
3.0%, strain rate = 10 -1 /s.  Note the very fine twins indicated by arrows.  
43 
4.8.  Effect of strain- rate on twinning in ? - Ti- 1.6V  
 The critical event in twinning has traditionally been viewed as nucleation.  Based 
on previous research, there seems to be a critical stress for twin nucleation which is 
temperature insensitive.  This issue has been debated in the literature [ 113, 114] , but for 
the purpose of the subsequent calculations, it will be assumed that the twinning stress has 
no temperature dependence.  Because growth can occur at stresses that are a fraction of 
the nucleating stress, it has often been assumed that twins can grow at speeds 
approaching the speed of sound in the material (~5,090 m/s  in ?-Ti).  Given that the flow 
stress in ?-titanium is higher at a given strain at higher strain rates, if at all, the thickness 
of twins at higher strain rates should be larger than at low strain rates.  However, twin 
thickness was found to be much higher at lower strain rates, contrary to twin growth 
based on the classical understanding of twinning.  This suggests that there may be 
another controlling mechanism which is a much slower process, such as the diffusion of 
solute atoms, for the growth of twins as proposed earlier by the authors and their 
coworkers [ 15, 16, 23, 45] . 
 
4.8 . 1.  Twin thickness predictions and o bservations   
During a previous investigation, it was found that during creep, the activation 
energy for twinning is ~66 kJ mol -1, which is in agreement with experimentally 
calculated activation energies for the diffusion of o?ygen in ?-titanium (65 ? 200 kJ/mol) 
[ 46] .  For this creep test, the activation energy for creep (47 kJ/mol) was lower th an for 
the activation energy for twinning [ 24] .  This was attributed to twinning not being the 
sole rate-limiting mechanism as slip was still an active deformation mechanism and 
44 
twinning can reorient a lattice such that new slip systems can become active.  For the 
experiments conducted during this investigation however, it has been shown that 
twinning will be the rate-controlling mechanism [ 15, 50] .  This is important because 
assumptions are made regarding the activation energy for deformation being equal to the 
activation energy for twinning.  To determine the effect of stress on diffusivity, some 
postulations were made to determine the parameters of Eq. (4.3) using information 
obtained by Oberson and Ankem [ 24]  .   
 The ?-Ti-1.6V alloy used in this investigation has an oxygen concentration of 
about 0.07 wt.% (0.21 at.%).  At such a concentration value, the experimentally measured 
activation energy for the diffusion of o?ygen in ?-titanium ranges from about 65-200 
kJ/mol [ 46] .  Oberson and Ankem determined that the activation energy for diffusion-
 controlled time dependent twinning was close to the low end of that range.  Assuming an 
activation energy of 65 kJ/mol, and a diffusion coefficient of 1.0 x 10 -4 m2/s [ 46] , the 
diffusivity of o?ygen in ?-titanium under zero stress and at room temperature (D0) can be 
calculated using Eq. (4.2) and is approximately 4.04 x 10-16 m2/s.  As introduced in 
Section 4.3, the ability of a twin to propagate is directly related to the diffusivity of 
o?ygen in ?-titanium.  If the assumption is made that an advancing twin boundary is 
related to the diffusion of a species from the surface into the bulk of a specimen, the 
center plane of a twin would correspond to the surface of the specimen and the distance 
from the center plane of the twin to the twin boundary at the farthest point corresponds to 
the effective diffusion distance [ 98 ] .  If the average twin thickness is represented by W, 
then xeff = 1/2 W.  Using this relationship and the test duration of the four experiments, the 
45 
average predicted twin thicknesses were calculated using Eq. (4.?) as? ?.?? ?m (??-1 /s), 
?.?? ?m (??-2 ?s), ?.?? ?m (??-4 ?s), and ?.?? ?m (??-6 /s).  
The predicted twin thicknesses as calculated all under-estimate the true lamellar 
thickness of the observed twins.  The average twin thickness for the 10-1 /s strain rat e was 
??.? ?m.  Therefore xeff is e?ual to ?.?? ?m.  Here is it assumed that during the ??
 -1 /s 
strain rate experiment, twin nucleation occurred at the start of the test.  With such a short 
test duration (0.3 s) and very high ramp rate, the specimen very quickly reaches plastic 
flow and the authors feel this is a valid assumption.  Instantaneous twinning has also been 
seen in an ?-Ti-0.4wt.%Mn alloy [ 16] .  Inserting the values for xeff and t into Eq. (4.1) 
gives a diffusivity of oxygen under stress (D?) of 2.08 x 10
 -13 m2/s.  The peak flow stress 
(?app) observed during this test was ~460 MPa.  Using these values in Eq. ( 4.3), the value 
of the activation volume constant for this alloy (V?) can be solved for and is ~5.59 x 10 -29 
m3.  This value for V? can now be used to calculate what the diffusivity of oxygen should 
be at different stress levels.  The calculated values for oxygen diffusivity under stress are: 
2.09 x 10-13 m2/s (10 -1 /s), 1.52 x 10 -13 m2 /s (10 -2 /s), 9.09 x 10 -14 m2 /s (10 -4 /s), and 4.43 x 
10-14 m2/s (10 -6 /s).  U sing Eq. (4.1), the corresponding twin thicknesses should be 
appro?imately? ?.? ?m (??-1 ?s), ?.? ?m (??-2 ?s), ??.? ?m (??-4 ?s), and ?? ?m (??-6 /s).  
These results are in much closer agreement with the observed results as obtained by SEM 
and optical microscopy.  The complete results, including the corresponding activation 
energies for each of the testing situations are shown in Table 4.3.   
46 
 
The predicted effective penetration distance was at first found to be well off from 
the experimental results; however, it is known that higher reso lved shear stresses can 
yield thicker twins [ 94] , and after applying the strain modification factor caused by an 
applied stress with Eq. (4.3), the predicted measurements were much closer.  The lowest 
strain rate experiment was overestimated by a significant margin, but this is not 
concerning because many factors come into play which could limit a twins final 
thickness, including the grain size of the material, the orientation of the grain with respect 
to the stress axis, and the presence of other twins and their stress fields in a particular 
grain.  These factors are discussed in the following sections (Sections 4.8.2 and 4.8.3) 
and the results are consistent with the measurements obtained by this study. 
The activation energies calculated from the experimental twin thicknesses are all 
very close for the three larger strain rates (10-1, 10-2, and 10-4 /s).  This suggests that the 
 Strain 
Rate 
Experimental Predicted Modified 
?verage Twin Thickness (?), ?m 10-1 /s  0.5 0.02 0.50 
 10-2 /s  3.5 0.07  1.35 
 10-4 /s  12.5 0.70  10.44 
 10-6 /s  20 6.96 72.91  
Diffusivity (D), m2 /s  10-1 /s  2.08E -13 4.04E-16 2.08E -13 
 10-2 /s  1.02E-12 4.04E-16 1.52E-13 
 10-4 /s  1.30E-13 4.04E-16 9.09E-14 
 10-6 /s  3.33E-15 4.04E-16 4.43E-14 
Activation Energy for 
Deformation Twinning (Q), 
kJ/mol  
10-1 /s  50 65 50 
10-2 /s  46 65 50 
10-4 /s  51 65 52 
10-6 /s  60 65 53 
 
Table 4. 3 .   Results of the experimental calculations and results of the constitutive 
relations for twinning observed during the tensile investigations.   The modified 
constitutive relation incorporated a stress factor into the predictive equation described 
by Eq. (4.2). 
47  
same general mechanism is operating across the very different testing conditions.  The 
calculated activation energies are also much higher than the activation energy for slip in 
?-titanium which verifies that twinning is the rate-controlling mechanism for 
deformation.  The theory of oxygen diffusion dependent twinning also holds because the 
activation energy for stress assisted diffusion (50 - 53 kJ/mol) is very close to the 
activation energy for twinning (46 ? 60 kJ/mol).  It is suggested that the lowest strain rate 
experiment deviates from the trend because other restrictions to twin growth discussed in 
Sections 4.8.3 and 4.8.4 prevent the twin from growing for the duration of the test which 
would affect the final thickness (W).  It has been seen before [ 16]  in an ?-titanium alloy 
that twinning can initiate instantaneously, but after a period of time the stress field 
surrounding the twin becomes high enough that the twin will stop growing even as the 
material continues to strain. 
 
4.8.2 . Effect of flow s tress and internal stresses on diffusion  
When a stress is applied, randomly distributed interstitial solute atoms will tend to 
move to a position of minimum local strain energy (position of maximum strain), where 
there is the most room for the interstitial.  With an advancing twin front, that position of 
minimum local strain energy is away from the twin boundary and away from soon-to-be 
annihilated sites.  It has been shown that the rise in critical twinning stress with interstitial 
content is much more significant than the rise in critical slip stress [ 61] .  This agrees with 
the postulation that for twins to grow in ?-titanium, oxygen atoms must first diffuse away 
from the twin front.  The diffusivity of a species is directly related to its concentration.  
The more interstitial sites that are occupied, the more difficult it will be for these atoms to 
48  
diffuse into neighboring lower energy sites.  Additionally, as strain rate increases, the 
stress level in deformed samples increases, which also increases the driving stress for 
twin nucleation.  Therefore more twin embryos will be nucleated per unit area, 
effectively reducing the twin boundary spacing and resulting in thinner twins. 
 The authors speculate that the twin thickness observed at the lowest strain rate test 
does not correlate well with the predictions because of a backstress acting on the twin 
domain due to the resistance in accommodating the large twin shear by the surrounding 
grains.  Twin growth is a competition between this backstress and the local applied stress.  
As has been researched before [ 15, 50, 91, 94] , twinning in HCP materials is strongly 
dependent upon grain size.  When a twin is formed, it essentially sub-divides the grain 
further reducing the effective grain size and reducing the ability of the twin to propagate.  
More importantly, at high strain rates the diffusion of oxygen away from annihilated 
octahedral interstitial sites limits twin growth so more twin nucleation is required to 
accommodate more strain. 
 
4.8.3 . Volume fraction of t wins  
A key point to note about the experiments conducted in this study is that all 
samples were tested to only 3% strain.  At higher strains, twinning begins to saturate and 
the ability to detect an effect on twinning by strain rate disappears [ 50, 56] .  This study, 
as well as previous research [ 56, 94, 115] , shows no statistically significant difference in 
the volume fraction or area fraction occupied by twins at different strain rates when the 
volume fraction of twinning is determined using the ASTM E562 method.  Based on the 
ASTM method and the size of the grid that was used to determine the volume fraction, 
49 
the volume fraction values are accurate to +/ - 3%.  Although the error in the volume 
fraction determination is larger than the volume fraction occupied by twins that was 
measured for a few of the tests, the authors do not feel this is a problem.  The values 
calculated support the theory that the volume fraction occupied by twins does not change 
with strain rate rather than refuting it.  If there was a change in the volume fraction of 
twins with strain rate, then a statistically significant margin would have been seen.  
Although the average twin thickness significantly decreases, the number density of 
twinning increases with an increase in stress and strain rate, verifying that strain is the 
dominant parameter controlling the extent of deformation twinning [ 50] . 
 
4.8.4 . Effect of grain s ize on volume fraction of t wins  
 The proposed model begins to deviate greatly from the observed experimental 
results at the very lowest strain rate.  This model does not account for the ultimate grain 
size of the grain containing a specific twin; therefore, given the right conditions it may be 
possible for a predicted twin thickness to be larger than the grain containing it.  As such, 
at the faster strain rates the predicted twin thickness is much smaller than the grain size of 
the material so grain size effects would be very small; however, the twin thickness 
predicted for the slowest strain rate approaches almost ? the diameter of the gra in.  At 
this size it is obvious that grain size constraining effects would be in effect.  The effect of 
grain si?e on twinning has been e?tensively studied in ?-titanium and other HCP 
materials [ 15, 17 , 25, 42, 50, 66, 71 , 84 , 116] .  While the propensity for twinning 
increases with an increase in grain size, a twinning event essentially sub-divides a grain 
and the effective grain size decreases with increasing strain.  Since the model presented 
50 
here does not address the influence of grain boundaries, other twin boundaries, 
dislocations, and other features which inhibit deformation twinning, the size limited twins 
at lowest strain rate could easily be accounted for by these mechanisms.  It should be 
noted that the alloys used in this investigation had sufficiently large grain sizes to best 
reduce the effect of these mechanisms which could inhibit twinning. 
 
4.9. Concluding r emarks  
 A systematic investigation of the low temperature (<0.25Tm) twinning behavior of 
a large grain si?ed (??? ?m) ?-Ti-1.6V alloy at four distinct strain rates was performed.  
Specimens were tested at strain rates of 10-1 /s (a), 10 -2 /s (b), 10 -4 /s (c), and 10 -6 /s (d).  
It was found that deformation twinning was the primary deformation mechanism during 
these tests and that the number of twins increased with increasing strain rate as expected.  
It was also found that twin thickness decreases with increasing strain rate which is 
contrary to previous thought about the growth behavior of twins.  In addition, it was 
found that for a given strain, the total volume fraction of twins did not vary with a change 
in strain rate. 
 It has been previously postulated that the unexpected twinning behavior is the 
result of twin growth being dependent upon oxygen diffusion away from annihilated 
interstitial sites.  Based on this assumption and the knowledge of the activation energy for 
oxygen diffusion at room temperatures, predicted twin thicknesses were calculated for the 
four different strain rates (a-d) used in this investigation.  Every one of these predictions 
under-estimated the average thickness of twins actually characterized. 
51 
 To address the discrepancy between the predicted values and the actual 
measurements, a stress modification factor was added to the constitutive relation, which 
predicted twin thickness as a function of the relative flow stress for a given strain rate.  
After this modification factor was used, the predicted values for average twin thickness, 
as well as activation energy for twinning/oxygen diffusion, were much close r to the 
measured values and only the slowest strain rate experiment (10-6 /s) deviated from the 
predictions, where twin thickness was predicted to be much larger than experimentally 
measured. 
 The reason for this final discrepancy was attributed to many factors which were 
not accounted for by the constitutive model but discussed in relation to diffusion-based 
twinning mechanisms.  These include:  grain size constraints, number of twins nucleated 
per unit area as a function of flow stress, backstresses acting on the twin fronts which 
would be in competition with the applied stress, and test duration.  However, the authors 
feel that the results of these experiments verify the theory that twinning in HCP titanium 
is highly dependent upon interstitial solute atoms in the alloy and twin growth in ?-
 titanium relies on oxygen diffusion away from the twin front.   The results of this 
investigation demonstrate a way to control deformation twinning and in turn the 
mechanical properties of these alloys, helping to develop advanced materials with much 
improved properties.  
52 
Chapter 5  
The Effect of ?- phase Metastability on Low Temperature Deformation 
Behavior of ? and ? + ? Ti ?lloys 
 
In the last two decades, there have been many papers demonstrating the effect of 
?-phase stability on the mechanical properties of the metastable titanium alloys, but no 
effort has been made yet to present a comprehensive look at the deformation mechanisms 
influenced by ?-phase stability and grain size in these single phase ? and two phase ?+ ? 
alloys.  The aim of this paper is to take a comprehensive look at the previous research and 
put together a methodology for what factors will control ? phase stability, what 
deformation mechanisms ?-phase stability influences, and how these deformation 
mechanisms affect the mechanical properties of these alloys. 
 
5?? ? - p hase metastability  
Previous research has well established that the stability of the BCC structure in 
single and two-phase titanium alloys [ 3, 17 , 117 -134]  depends on the extent of alloying 
elements and heat treatments as shown in Figure 5.1 [ 119] .  The amount of ? stabili?er 
re?uired to retain ???? of the ? phase at room temperature is defined by the 
Molybdenum Equivalency (MoE) [ 117 ] .  ?o? is used as a measure for the amount of ? 
stabilizer required to prevent a martensitic transformation when quenching to ambient 
temperature.  The MoE for a given stabilizing element is defined as the ratio of the 
amount of ? stabili?ing element to the amount of ?olybdenum (?o) re?uired for the  
 
53 
 
same degree of ?-phase stability.  A simple formula for Molybdenum equivalency of 
some of the more common alloying elements of titanium may be derived as: 
 
 MoE = 1.0  (wt.%Mo) + 0.67 (wt.%V) + 1.53 (wt.%Mn)  Eq. 1 
         + 0.44 (wt.%W) + 1.6 (wt.%Cr) + 0.28 (wt.%Nb)  
         + ? 
(5.1) 
 
? 
? 
??+? 
?+? 
?+? 
MS 
Stable 
?-Ti 
Alloys 
Metastable ?-Ti Alloys 
? ?tabili?er (?), ? 
Figure 5.1.   A schematic of a pseudo-binary equilibrium diagram showing the ranges 
of ? and ? stability as a function of added ? stabili?er ????].  
54 
During a ?uench from the ?-phase, there are other non-equilibrium phases that can form 
including martensites (including ??), ?-phase and ??-phase.  Jepson et al. [ 135]  showed 
that the local effect of alloying inhibits martensitic transformation and the speed of 
transformation.  ?ll ? alloys have been found to deform at ambient temperature by coarse 
and fine slip only [ 126] , by slip and formation of stress induced plates (SIP) such as twins 
or martensite [ 126] , or by the formation of new stress-induced metastable phases like the 
?-phase [ 118 , 131, 136-140] .  It has also been observed that as the alloying element is 
increased, i.e. the stability of the ?-phase is increased; the deformation mode changes 
from twinning/martensite formation to slip [ 120, 124, 125, 128 ] .  This review will also 
address the effect of the ?-phase on the deformation mechanisms of the ?-phase, and 
vice-versa, in ? +  ? titanium alloys and their relationship to the behavior of single-phase 
? alloys. 
 
5.1.1 The r ole of the ?- p hase  
 As can be seen in the previous phase diagram (Figure 5.?), the ?-phase would be 
present for most alloys of titanium using transition metals and tested at room temperature, 
depending on the stability of the ?-phase.  The ? phase is present in the lower stability 
metastable alloys.  For e?ample, when the ? stability ?o? is ??.? for a Ti-Mn alloy , only 
diffuse streaking is observed, indicating that the ? phase is about to form.  However, 
when the ? stability ?o? is ?.? for a Ti-? alloy, the ? phase has not completely formed, 
as shown in Figure 5.?.  The ?-phase is metastable with respect to both the ? and ? 
phases, and is a nanostructured phase present within the ?-phase.  The ?-phase has been 
shown to have drastic effects on the mechanical behavior of metastable ? titanium alloys  
55 
 
[ 141-144] , and so therefore must be also considered here.  The ?-phase is formed when 
titanium is alloyed with ?-stabilizers and can form either upon quenching from the ?-
 phase field, or from ageing of such a ?uenched alloy.  The ?-phase has a hexagonal 
structure and forms a coherent interface with a (110)[111] ?||(11 ??0)[0001] ? relationship to 
the surrounding ?-phase. 
 
5.2.  Deformation m echanisms  in metastable Ti al loys 
 
5.2.1.  Single Phase ?- Ti Alloys 
The room temperature deformation of single-phase ? alloys, such as Ti-1.6V and 
Ti-0.4Mn, has been extensively covered in the works of Oberson, Greene, and Ankem 
[ 16, 24, 145]  as well as others [ 33, 146-150] .  It was shown first by Ankem et al. [ 16]  that 
extensive creep deformation can occur at room temperature in coarse grained alpha 
Figure 5.2.  Selected area diffraction pattern comparing the degree of formation of 
omega phase in the ? phase of the ? + ? (a) Ti-?.? wt pct ?n (?-phase MoE=19.9) 
and (b) Ti-?.? wt pct ? (?-phase MoE=9.9) alloys.  Note pre -omega-phase streaking 
of ? spots of the ? phase of ? +  ? Ti-6.0 wt pct Mn SADP, which are consistent with 
incommensurate ? formation, compared with the sharply defined spots of the ?-
 phase ? +  ? Ti-8.1 wt pct V SADP.  The ? phase indices and orientation are 
provided.  The extra spots in the Ti-8.1V pattern ar e due to double diffraction [21, 
22, 156].  
56 
titanium alloys, when tested at below the 0.2% yield stress.  The phen omena was 
attributed to slip as well as time dependent {1  ?02}<10  ? ? > or {1  ?01}<10  ???> twinning.  
Later, Neeraj et al. reported that primary creep in single phase ? Ti-6Al alloys can also 
occur at low temperatures in coarse grained materials.  This phenomenon was attributed 
to planar slip.  These studies therefore show that the alloying elements can determine 
whether the primary creep at room temperature is due to time dependent twinning and 
slip or solely due to planar slip.  While these earlier studies show that the time dependent 
twinning is due to the coarse grain size, the later studies indicated that in the presence of 
the ?-phase, the twinning can also occur even if the ?-platelet size is thin in two phase ? 
+  ? titanium alloys, as described later. 
 
5.2 .2 Single p hase metastable ? - Ti Alloys 
Single-phase ? alloys have long been shown to have excellent mechanical 
properties including creep resistance.  Additionally, they show a good response to heat 
treatment and their microstructures can be easily modified.  While the deformation modes 
for ? titanium alloys can vary widely depending upon grain size and alloy composition 
[ 25, 117 , 119-122, 124, 126, 128 , 151] , one trend involving ? stability and resulting 
deformation mechanisms is apparent and discussed.   
While ? titanium alloys show good creep resistance in general, it is evidenced 
from previous research [ 17 , 25] , that the net creep strain increases as the grain size 
increases.  There also exists a greater amount of deformation with coarser slip lines in 
larger grain sized specimens of Ti-13.0Mn, Ti-9.4Mn, and Ti-14.8V [ 17 ] .  The 
deformation features observed before and after creep deformation match those observed 
57  
during tensile deformation and are detailed in the next section.  It should be noted that the 
creep strain for these specimens increases significantly with increasing grain size.  This 
observation at room temperature is opposite of what is observed at high temperature.  
This difference in the effect of grain sizes between high temperature and room 
temperature has been attributed to the difference in operational deformation mechanisms 
[ 17 ] .  Specifically, at high temperatures, the predominant deformation mechanism is 
grain boundary sliding; where an increase in grain size would result in decreased creep 
strain. 
To demonstrate the effect of ?-phase stability on the deformation mechanisms of 
? titanium alloys, two model systems will be reviewed.  ?ingle-phase Ti-V and Ti-?n ? 
alloys have been selected for review due to the extensive amount of research performed 
on these alloys by Ankem et al. [ 17 , 25, 119, 126, 152] .  In addition, the deformation 
mechanisms discovered for the single phase ? alloy, Ti-9.4Mn [ 17 ]  will also be discussed 
to help illustrate the effect of ? stability in one alloy system.  Tensile testing, optical 
microscopy, scanning electron microscopy (SEM), and transmission electron microscopy 
(TEM) studies have all been performed during the course of the investigations reviewed.  
The deformation of single-phase ? alloys such as Ti-13.0Mn and Ti-14.8V are dependent 
upon ?-phase stability as well as grain size.  The MoE has been calculated as 19.9 for Ti-
 13.0Mn and 9.9 for Ti-14.8V [ 17 ] ; therefore the stability of Ti -13.0Mn is much higher 
than that of Ti-14.8V.  During tensile tests conducted at a strain rate of 3.128 x 10 -5 s-1, 
Ti-13.0Mn generated a YS of 940 MPa and deformed solely by coarse and wavy slip [ 21, 
22, 146] .  Alternatively, Ti-14.8V exhibited a YS of 774 MPa and deformed by slip and 
the formation of stress-induced {332}[113] twins [ 25, 152] .  These twins contained two 
58  
orientations of the ?-phase.  Additionally, it was found that the Ti-9.4Mn alloy (MoE = 
14.3) [ 17 ]  had a YS of 1030 MPa with negligible work hardening and deformed by 
extensive slip [ 17 ] .  It should be noted now that in the Ti-14.8V alloy (less stable MoE), 
the modes of deformation were stress-induced plates (SIP) and slip; whereas in the Ti-
 13.0Mn alloy (more stable MoE), the predominant deformation mechanism was slip [ 17 , 
146] .   
The assumption would be that in an alloy with intermediate stability, there should 
be slip accompanied by some SIP formation.  In the Ti-9.4Mn alloy, there was no SIP 
observed which suggests that there is some critical ?-phase stability above which slip is 
the only operating mode of deformation [ 17 ] .  The TEM analysis of the undeformed and 
deformed Ti-?.??n specimen revealed the presence of ?-phase as discrete spots in the 
BCC ?-matrix.  These investigations showed no evidence or indication of SIP formation 
and twinning. The matrix appeared to be unchanged after tensile deformation evidently 
showing that there is no SIP formation or twining. One should note that in a Ti?14.8V 
alloy [ 25] , the ?-phase is present before deformation, and in a higher stability Ti?13.0Mn 
alloy, there is no ?-phase except for a pre-?-phase streaking.  This implies that in a more 
stable ?-alloy, the ?-phase is absent and the deformation is due to slip [ 17 ] . These results 
lead to the important conclusion that the formation or presence of ?-phase in the three ?-
 alloys considered here is associated with the stability of ?-phase and not a result of 
deformation [ 17 ] ;  additionally, the presence of the ?-phase may also be contributing to 
the formation of twins. 
During creep tests, the single-phase alloy, ?-Ti-??.??n (?-phase of Ti-6.0Mn), 
with a grain size of 200 ?m, showed negligible creep strain of only 0.03% strain over a 
59 
test period of 400 hours and deformed only by rare coarse slip, with no observed 
twinning [ 16, 119] .  Conversely, the single-phase alloy ?-Ti-??.?? (?-phase of Ti-8.1V) 
crept to a strain 0.101% and deformed by slip, instantaneous twinning, and time -
 dependent twinning [ 15] .  For comparison, the Ti-9.4Mn alloy crept to a strain of ~0. 07% 
and deformed by slip.  The deformation features for the creep tested Ti-9.4Mn alloy were 
very similar to those observed during tensile deformation.  Only slip was observed in the 
Ti-9.4Mn alloy, and from micrographs taken during the test, it was determined that most 
of the slip lines were generated in the first few minutes of the test [ 17 ] . 
?ther ? alloys have been shown to behave similarly.  ?pecifically, research 
performed by Xu et al. [ 128 ] , Grosdidier et al. [ 120, 153] , Zhao et al. [ 129] , and Kim et 
al. [ 122]  have presented similar results.  Explicitly, the work of Grosdidier et al. showed 
that microstructure as well as ? stability plays an important role in controlling the 
formation of martensite in a Ti ?-Ce? alloy.  ?or e?ample, large ? grains favor the 
formation of stress induced martensite, but a decrease in the martensitic temperature as 
controlled by a higher ? stabili?ed alloy inhibits the formation of ??? [ 120, 153] .  In 
regards to the newly developed Ti-Nb-Ta-?n?Cr ? alloys, ?u et al. showed that the lower 
? stability ?n based alloy deformed by martensite formation, twinning, and slip? whereas, 
the higher ? stability Cr based alloy only deformed by slip [ 128 ] . 
 
5.2.3 Two - p hase ? + metastable ? Ti Alloys 
Many investigations have studied the tensile and creep deformation mechanisms 
of various two-phase Ti alloys.  For reference, a few of these alloys will be discussed 
here.  To demonstrate the effect of ?-phase stability on the deformation mechanisms of ? 
60 
+  ? titanium alloys, two-phase Ti-V and Ti-Mn alloys have been selected for review such 
that the chemistry of the single phase ? alloy reviewed earlier would match the 
component ?-phase in the two-phase alloy.  Ti-6.0Mn and Ti-8.1V are two titanium 
alloys whose component ? phases have the same chemistry and therefore same MoE as 
the single phase Ti-13.0Mn and Ti-14.8V alloys.  This is due to the fact that all of the 
single and two phase alloys were heat treated or annealed at the same temperature where 
the phase composition is determined by the tie lines.  Tensile testing, creep testing, 
optical microscopy, SEM, and TEM have all been performed during the course of the 
investigations reviewed. 
It should be noted that all of the two-phase titanium alloys reviewed exhibited 
similar behavior in regards to grain size and ? stability effects on the resulting 
deformation products.  To illustrate this, the research of Ankem et al. [ 24, 131-134, 145] , 
Balcerza et al. [ 136] , and Gerland et al. [ 146] , who investigated the interactions between 
the two phases, is reviewed.  During tensile tests conducted by Jaworski & Ankem [ 21, 
22] , a two-phase alloy Ti-6.0Mn (higher MoE of metastable ? phase) demonstrated a YS 
of 623 MPa and showed some amount of strain hardening.  The ? +  ? Ti-6.0Mn alloy 
demonstrated fine slip in the ?-phase and some limited ?-phase {10 1? 2} type twin 
formation and interphase interface sliding [ 21, 22] .  In contrast, a ? +  ? Ti-8.1V alloy 
(lower MoE of metastable ? phase) yielded at approximately 597 MPa, showe d no 
significant strain hardening, and showed many coarse deformation products [ 21, 22] .  
After SEM and TEM analysis of the ? +  ? Ti-8.1V alloy, these products were shown to 
be twins in the ?-phase and stress-induced martensite (???) in the ?-phase, which 
spanned many grains of the specimen, not shown here [ 21, 22] .  Additionally, it should 
61 
be noted that T?? analysis also revealed the presence of the ?-phase in the lower 
stability alloy, as shown in Figure 5.2. 
Creep tests performed by Jaworski & Ankem [ 22]  resulted in similar deformation 
features to the tensile tests.  The ? +  ? Ti-?.?? alloy (total creep strain ? ? ?.???) 
exhibited 16% greater creep strain compared to the ? +  ? Ti-?.??n alloy (? ? ?.???) 
[ 22] .  Creep deformation in the ? +  ? Ti-6.0Mn alloy has been primarily attributed to fine 
slip in the ?-phase and some infrequent interphase interface sliding in SEM micrographs.  
In stark contrast, the deformation products in ? +  ? Ti-8.1V are highly visible and travel 
over the distance of many grains.  Using TEM analysis, these deformation features have 
been identified as slip bands or twins in the ?-phase and stress-induced hexagonal 
martensite in the ?-phase [ 22] .   
 The additional creep strain experienced by the ? +  ? Ti-8.1V over alloys such as 
? Ti-13.0Mn or even ? +  ? Ti-6.0Mn over the same test period can be explained by the 
difference in deformation mechanisms, specifically the formation of stress-induced 
martensite in the ?-phase and a greater number of twins in the ?-phase of ? +  ? Ti-8.1V 
[ 22] .  In both the ? +  ? Ti-8.1V and ? +  ? Ti-?.??n alloys, the ?-phase deformed by 
extensive fine slip with some coarse slip also observed in the ? +  ? Ti-8.1V alloy [ 22] . 
 The TEM analysis of the ? +  ? Ti-8.1V specimens as conducted by Jaworski & 
Ankem [ 21, 22]  revealed that the coarse lines visible in SEM micrographs were actually a 
combination of stress-induced hexagonal martensitic plates (??) in the ?-phase and either 
twins or coarse slip in the ?-phase [ 21] .  However, the single-phase ?-Ti-14.8V, which 
has the same chemical composition as the ?-phase of the ? +  ? Ti-8.1V, only showed 
time dependent {332} twinning and no martensite was observed [ 154] .  In metastable ? 
62 
alloys, two types of ??? are common?  he?agonal martensite (??) and orthorhombic 
martensite (???).  The plates in this alloy were confirmed to be he?agonal with selected 
area diffraction patters, not shown here.  Additionally, the Burgers orientation 
relationship was obeyed between the martensite and the ?-phase, and the martensite was 
not internally twinned with a straight ???? interface which suggests a habit plane.  These 
results clearly showed that the deformation mechanisms in the two-phase alloy could 
differ from those of the single-phase alloy even when the component phase chemical 
composition is equivalent to the single-phase alloy.  The phenomenon of interest is the 
formation of ??? in the ?-phase of ? +  ? Ti-8.1V as opposed to twins in th e single-phase 
alloy, as well as the formation of twins in the single phase ?-alloy even though the 
platelet size was small (<5 ?m).  Twinning and martensite formation become the 
dominant mechanisms at low ? stability even though there are many slip systems to 
accommodate deformation.  In order for SIM to occur in the place of twinning, the 
relative activation energy must be lowered relative to twinning or additional stresses must 
be applied. 
 
5.3.  Th e role of ? - p hase stability on t ensile deformation m echan isms  
5.3.1. Single - phase ? - Ti alloys 
In single-phase ? titanium alloys, the role of ?-phase stability and the role of the 
?-phase on the stability of the ?-phase are not very clear.  It is known that as the stability 
of the ?-phase is lowered through the lowering of the amount of a stabilizing element, or 
the use of a less-effective ?-stabilizer, the deformation products change from slip to 
twinning.  There are at least three reasons why the mechanisms of single-phase 
63 
metastable ? alloys can be different.  The first reason is related to the fact that in the 
higher stability alloys, the weight percent of alloying elements is higher.  It is possible 
that the addition of alloying elements can hinder the formation of twins more effectively 
than opposing slip; th erefore, it is possible to have only slip as you increase ?-phase 
stability.   
The second factor is related to the presence of the ?-phase.  As mentioned before, 
in the lower stability alloys, the ?-phase is present.  ?t is possible that this ?-phase is 
responsible for twinning in lower stability alloys.  It should be noted that coinciding with 
this transformation from slip deformation to twinning and martensite deformation is the 
appearance of the ?-phase in the ? microstructure.  This suggests that the ?-phase is 
playing a critical role to the deformation of the phase.  However, after twinning, the ?-
 phase is still present within the twinned region of the grain.  During a martensitic 
transformation, both the ?-phase and the ?-phase would be consumed.  The presence of 
the ?-phase within a twin suggests two possible scenarios.  ?ither the ?-phase sheared 
along with the ?-phase, or it dissolved during twinning and recrystallized along its 
preferred directions within the twin after twinning was complete.  It may be impossible to 
determine which of these mechanisms is operating.  Alternatively, it may be possible that 
the ?-phase is acting as a nucleation site for the twinning process.  Being that the ?-
 phase is an intermediate phase between the stable ?-phase and the metastable ?-phase, it 
may be possible that twinning is occurring in the low stabili?ed alloys because the ?-
 phase is lowering the ?crss for twinning close to or lower than slip.  The mechanisms for 
this however are not known and further investigations are needed. 
64 
The third reason for the change in deformation mechanisms may be related to the 
chemical free energy difference between the metastable ?-phase and the martensite (??) 
phase.  As the stability decreases, the chemical free energy difference between these two 
phases increases.  Therefore, any minor stresses developed because of various reasons, 
including cooling from high temperatures or applied stresses, can promote the formation 
of martensite.  
 
5.3.2 Two - phase ? + ? Ti alloys 
In addition to the factors mentioned above for single-phase metastable ? alloys, 
additional factors come into play in regard to the two-phase ? +  metastable-? alloys.  
These include elastic and elasto-plastic interaction stresses between ? and ? phases, 
crystallographic relations between phases, and residual stresses due to cooling from high 
temperatures.  It is quite possible to have residual stresses in the microstructure because 
the coefficient of thermal e?pansion is different between ? and ? phases? however, 
observations of the microstructures of the as-quenched alloys reviewed showed no twins 
and no martensite, indicating that these residual stresses may not be significant enough to 
produce these transformations.   
Initially, interaction stresses develop at the ?/ ? interfaces due to different 
amounts of strains for the same applied stress.  At lower stresses, for a given amount of 
applied stress, the ? phase deforms more than the ? phase because the ? phase is 
elastically softer than the ? phase, as shown in Figure 5.4.  Therefore, at the ?/ ? 
interface, the stress on ? has to come down and the stress on the ? phase has to go up so 
that the interfacial strain will be the same, to maintain compatibility.  This means that the 
65 
?-phase can apply a stress, in addition to the applied stress, on ?-phase causing slip or 
twinning in the ?-phase.  This can explain why twinning can be seen in the ?-phase even 
though the ? platelet size is very small.  Consequently, once slip or twinning initiates in 
the ?-phase, it can apply very strong interaction stresses on the ?-phase in addition to the 
applied stress, see Figure 5.4.  Such interaction stresses are found to be significantly 
higher in the martensitic system in the ?-phase as opposed to twinning in the ? phase [ 21, 
22] .  This is one of the reasons why martensite forms in ? instead of twinning in the 
presence of ?-phase. 
 
 
Figure 5.3.   Illustration of the [1 2? 10](0001)//[1 1? 1](110) Burgers orientation 
relationship between the ? and ? phases in an ? + ? titanium alloy with 
Widmanstatten microstructure. Diagram shows the (0001)? and (110)? planes. The 
interface plane is (5? 140)//( 3? 34); which is normal to the (0001) ? and (110)? planes and 
is indicated as a trace in each phase [21, 22 ].  
66 
 
The third reason that martensite (??) may form in the ?-phase, is related to the 
templating effect.  ?t was found that the martensite in the ?-phase and the ?-phase have a 
twin relationship.  This interface between ? and ?? has a lower misfit orientation than the 
?-? interface and so a martensitic formation is favored.  The additional stresses from slip 
and twinning in the ?-phase that act on the ? ? ?? transformation, as noted before, are 
only present in the two-phase alloys.  This is why twinning is the predominant 
mechanism in the single-phase alloy Ti-??.?? rather than ??? seen in the ? +  ? Ti-V 
alloys.  ?here ?-stability comes into play is when ??? is formed in the ? phase of Ti-
 Figure 5.4 .  ?lastic interaction stress on ? and ? phases of a titanium alloy. The 
interaction of the stronger but lower modulus ? phase with the ? phase initially 
increases the stress in ?. ?nce significant plastic deformation occurs in ?, elasto-
 plastic interaction stresses act on the ? phase ???, ??].  
67  
?.?? but not in the ? phase of Ti-6.0Mn or Ti-9.4Mn.  SIM occurs because the stress 
applied effectively raises the martensitic transformation temperature to ambient 
temperature.  The change in Gibbs Free Energy for a martensitic transformation is: 
???????????????????? (5.2) 
?n comparing ? titanium alloys with different stabilities, the less stable alloys will have a 
greater change in volume free energy upon transformation, resulting in a greater 
likelihood of martensitic transformation.   
? fourth reason for the differing mechanisms between single phase metastable ? 
alloys and two phase ? +  ? alloys may also be due to the presence of the ?-phase in the ?-
 phase of these alloys.  Kuan et al. [ 139]  suggest that the metastable ?-phase which is also 
present in Ti-?.??, is an intermediate phase between the ? and ? phases.  This 
intermediate phase would effectively lower the free energy change required to form 
martensite.  Because of the lack of ?-phase in the Ti-6.0Mn alloy, stresses required to 
form stress induced martensite (???) are higher.  The presence of the ?-phase is 
illustrated by Figure 5.2 [ 21] .  To properly address the relationship of ?-phase stability 
and deformation mechanisms, various other Ti-V alloys were reviewed.  Ramesh et al. 
[ 25]  found {332}[113] -type twins containing two variants of the ? phase in single-phase 
Ti-??.?? alloy, with the same chemistry as the ? component of the Ti-8.1 wt pct alloy. 
This result is consistent with the results of Oka and Teniguchi [ 151]  in a Ti-15.5V alloy. 
Kouland and Breedis [ 123]  found that the stress-induced plates in Ti-16.2V were 
he?agonal martensite (??).  Menon and Krishnan [ 155]  investigated Ti-V alloys with 5, 
10, and 20 wt. pct. V, and found SIM in the Ti-20V alloy.  Ling et al. [ 124]  investigated 
Ti-V alloys ranging from 20 to 40 wt pct V and found that, as the solute concentration 
68  
was increased, the deformation mechanisms changed from twinning in the 20 wt. pct. V 
alloy to fine slip and finally coarse slip in the Ti-40wt.%V alloy.  Additionally, Xu et al. 
[ 128 ]  found that in two ? alloys with differing ? phase stability, the stability of the 
second phase played a crucial role in whether or not a martensitic transformation would 
occur under room temperature stresses.   
Both o?ygen and hydrogen have marked effects on the ?-phase.  Oxygen 
depresses the temperature at which ? phase forms and hydrogen enhances thermal ?-
 phase formation.  These effects are important because the levels of these two elements 
can vary from alloy to alloy and would therefore affect the variation in the literature 
results mentioned above.  The interactions between the ?-phase and ?-phase become 
possible because of the high concentration of ?-phase within these lower stability ? 
alloys.  The observations suggest that the activation energy for twinning can decrease in 
the presence of ?-phase in the case of single-phase alloys.  In addition, the activation 
energy for the formation of martensite is also decreased in the presence of the 
intermediate ?-phase.  It is reasonable to believe that the activation energy for the 
formation of martensite is lower than that for the formation of twinning.  If the activation 
energy is met by the interaction stresses between ? and ? phases, which are much more 
prevalent on the martensite system as compared to twin system, then one can explain why 
martensite has formed in the presence of ?-phase even though only twins are found in the 
single-phase ? alloys. 
?dditionally, because the misfit strain between the ? and ? phases is high, at the 
places along the ??? phase interface where ? and ? phase interact the plastic deformation 
of the ?-phase places high stresses on the ?-phase planes and directions which facilitate a 
69 
???? transformation.  Because the resolved shear stresses from ?-phase slip or twinning 
act more strongly on the ?-phase shear systems than the ?-phase twinning systems, stress 
induced martensite becomes far more likely to occur.  It should also be considered that 
there are four main orientations of the ?-phase present in the ?-phase? of these, slip in ? 
affects two of them and twinning in ? affects the other two? so no matter the primary 
deformation mechanism in the adjacent ?-phase of a two-phase alloy, martensite will 
form in the ?-phase.  It has been shown here how the stress induced martensite may form, 
but the ?uestion as to how the martensite propagates through the ?-phase must also be 
considered.  If one looks at the orientation relationship between the ? and ? phases,  
{  ?010}<0001> ? / / {  ?12}<1  ?1> ?, it becomes apparent that each shear system for a ???? 
transformation is e?actly parallel to the ???? shear system.  ?hat this means is that once 
the transformation is started, it will propagate through the ?-phase along parallel systems. 
We can say conclusively that the deformation products for metastable ? titanium 
alloys are dependent upon the amount of stabilizing element, hence, as the stability is 
increased, the mechanisms change from SIM to twinning to slip. 
 
5??? The role of ? - p hase s tability on creep deformation mechanisms  
 Similarly to tensile tests which have been performed, deformation mechanisms 
during creep in the two-phase alloys differed from those observed in the single-phase 
alloys.  Creep test results mirrored the results of the tensile testing for Ti-8.1V and Ti -
 ??.?? (same composition ?-phase).  In the single-phase alloy, the stress-induced plates 
responsible for deformation were {332} typ e twins; whereas in the two -phase alloy, 
stress induced martensitic (??) plates were formed in the ?-phase.  As a single-phase 
70  
alloy, Ti-14.8V has a martensite start temperature low enough to prevent a martensitic 
transformation? however, the presence of ?-phase raises the temperature high enough that 
martensite can form during creep.  Specimens tested under creep conditions differ from 
tensile testing in that the load is constant and any additional stresses required to initiate 
creep must come from internal stresses.  Therefore, interaction stresses are even more 
important.  Schematics of the orientation relationship between the two phases and the 
interaction stresses experienced by the two phases are shown in Figures 5.3 and 5.4 [ 21, 
22] .  For twin nucleation and growth in the ?-phase (which is preferred), the ? phase must 
strain to accommodate the ?-phase strain.  ?f the ? phase is stable enough, it will retard 
the growth of twins as evidenced by the two-phase alloy Ti-6.0Mn.  The limited 
interphase interface sliding in Ti-6.0Mn is not enough to accommodate the growth in the 
?-phase, which limits the overall creep strain.  The creep results of the single phase ? 
alloys:  Ti-9.4Mn, Ti-14.8V, and Ti -13.0Mn were also compared.  It has been 
hypothesized [ 23, 24]  that interstitial oxygen atoms act as pinning sites at the twin/matrix 
interface to control time-dependent strain.  This diffusion of oxygen atoms away from the 
twin front would e?plain the increase in twin width with time for the ? alloys.  ? similar 
mechanism would also be possible for Ti-9.4Mn as well.  However, since slip was much 
more prevalent in Ti-9.4Mn than in Ti-13.0Mn, the pinning sites are not oxygen because 
the systems should respond in the same way [ 17 ] .  T?? diffraction patterns showed ?-
 phase spots before and after deformation in Ti-9.4Mn but were absent in the stable Ti-
 13.0Mn.  This means that the ?-phase could be responsible for pinning of slip lines and 
creep strain results from slip lines intersecting with the ?-phase and dissolution of the ?-
 phase [ 17 , 156] . 
71  
 
5.5. Concluding remarks  
This study was undertaken to gather together the information regarding the effect of 
the metastable ? phase on deformation in single phase and two phase titanium alloys.  As 
of yet, there had not been a comprehensive review of these relations, nor postulations as 
to how they affect the alloy?s final microstructure and mechanical properties.  The 
magnitude of metastability of the ?-phase plays a significant role on the deformation 
mechanisms and the deformation behavior during tensile and creep deformation.  The 
effect of metastability on single-phase ? alloys appears to be threefold.  The first reason is 
related to simply the amount of stabilizers added to the titanium.  Since the higher 
stability ?-alloys have more alloying elements, it is quite possible that the alloying 
elements can interfere more strongly with twinning as compared to slip.  Therefore, slip 
can be preferred in very highly stabilized alloys as compared to twinning.  As the stability 
decreases, it was found that ?-phase is present.  This ?-phase can also act as nucleation 
sites for twinning thereby promoting twinning in the lower stability ?-alloys.  It is to be 
noted however that slip is an operating mechanism even though twinning is present.  As 
the stability is decreased further, the chemical free energy difference between the 
metastable ? and martensite becomes so high, that any kind of disturbance can result in 
the initiation/formation of  martensite.   
In two-phase ? +  metastable-? alloys, additional factors come into play.  These 
include interaction stresses between the two phases and crystallographic relationships 
between the two phases.  Therefore, some of the deformation mechanisms which have 
been observed at much lower stability in single-phase ? alloys can also be seen in the 
72  
higher stability two-phase ? +  ? alloys.  ?or e?ample, the ?-phase can act as a template 
for the martensite in ?, promoting its formation? where in the absence of ?, this may not 
happen for the given stability of ?-phase. 
In regard to the creep deformation behavior, the deformation mechanisms are similar 
to tensile tests; however, the time -dependent effects are important to recognize.  Given 
that for example the twinning in ? can be a time-dependent phenomenon, it is quite 
possible that the growth of the martensite in ? in the lower-stability alloys is also time-
 dependent.  While these suggestions need to be confirmed experimentally, it is very 
important to recognize at this time how the two-phase alloys deform so that optimal 
chemistry and microstructure of the two-phase ? +  ? alloys can be selected for various 
structural applications. 
  
73  
Chapter 6  
Influence of Microstructure and the Second Phase on the Room 
Tempera ture Creep Deformation Mechanisms of ? + ? Ti - V Alloys 
 
 A detailed investigation of the ambient temperature creep deformation 
mechanisms of ? + ? Ti alloys was performed using Ti-4.3wt% V, Ti -8.1wt% V, and Ti -
 12.6wt% V with both Widmanst?tten and fine -grained equiaxed microstructures as the 
model two-phase systems.  The creep deformation mechanisms of the two-phase alloys 
differs from the mechanisms seen in the single-phase alloys with compositions matching 
those of the ? and ? component phases.  These deformation mechanisms in ? + ? alloys 
include twinning in fine-grained ? phase and stress-induced he?agonal martensite in the ? 
phase.  The effect of the ? phase on the deformation mechanisms of the ? phase and vice-
 versa has been investigated.  Several factors contribute to the creep deformation 
mechanism in the model two-phase alloys, including elastic interactions stresses and 
additional shear stresses due to deformation products in adjacent phases. 
  In contrast to the tensile plastic deformation of titanium alloys, creep deformation 
may take place at stresses much lower than the yields stress of the material.  Any stresses 
in excess of the applied stress which contribute to the activation of creep processes are 
only available from internal sources.  These internal interaction stresses are the focus of 
this investigation.  These interactions are what result in additional deformation 
mechanisms in both the ? and ? phases, and in turn result in increased creep strain.  ?n 
order to design alloys for improved creep resistance, these interactions must be fully 
understood. 
74  
6.1. Experimental procedure  
 The Ti alloys have been selected and prepared as discussed in Chapter 3.  Prior to 
creep testing, gold-palladium fiducial grid lines were sputtered onto the samples and grid 
line spacing was measured carefully.  This grid serves as a measurement to verify creep 
strain and also as a map to track areas of the sample both before and after testing.  
Ambient temperature (298 K) creep tests were performed on an ATS lever arm creep 
testing machine at a constant load equal to 95% o f the alloy?s respective ??, which was 
determined using ambient temperature tensile tests described in Chapter 3.  A Hitachi S-
 3400N SEM, JEOL 2100 LaB6 TEM, and JEOL 2100F TEM were used to obtain the 
images and diffraction patterns for this study. 
 
Figure 6.1.  ??? micrograph of ? + ? Ti-8.1V with Widmanst?tten microstructure 
before testing; showing fiducial grid used in these investigations.  
250 ?m 
75  
6.2. Results  
6.2.1 Single - phase ? and ? alloys 
 The single-phase ? and ? alloys have been creep tested at ??? of their respective 
yield stresses in several previous studies.  The creep strain of the single-phase ? alloys 
alloys depended on grain size of the material and the creep strain of the single-phase ? 
alloys depended on the stability of the ? phase.  ?ll of the single-phase alloys showed 
creep exhaustion behavior during the test periods. 
 The single-phase ? alloy Ti-1.6V with a grain size of 38  ?m crept to a strain 
(instantaneous plastic plus creep) of 1.92% and deformed by fine slip, instantaneous 
twinning and time-dependent twinning [ 15] .  The single-phase ? alloy Ti-14.8V with a 
large grain si?e (??? ?m) crept to a strain of ?.???? and deformed by slip, instantaneous 
twinning and time dependent twinning [ 152] .  The single-phase small grained Ti-14.8V 
alloys (18 ? ?? ?m) crept to ?.??1% strain and deformed primarily by slip, with no 
significant twinning [ 25] . 
 
6.2.2  Two - pha se ? + ? Ti - 4.3V alloy  
 The tensile true stress/true strain curves for the fine -grained equiaxed and 
Widmanst?tten microstructur e alloys are shown in Figure 6.2.  The fine-grained alloy 
exhibits a slightly higher ultimate tensile strength, while the elastic modulus and yield 
strength of each alloy is approximately equal.  The Widmanst?tten microstructure 
exhibits a 95% YS of approximately 380 MPa.  The fine -equiaxed microstructure 
exhibits a 95% YS of approximately 390 MPa.  Both alloys exhibit a slight amo unt of 
strain hardening. 
76  
 
The creep curves for the Ti-4.3V fine-grained equiaxed and Widmanst?tten 
microstructure alloys are shown in Figure 6.3.  The alloys were tested at 95% of their 
respective yield stress.  A clip on extensometer was used to record strain.  SEM 
micrographs were taken prior to and during testing in the same area of each specimen to 
record deformation mechanisms.  It has been shown that interrupt creep tests and 
continuous creep tests result in the same amount of creep strain for a given time [ 145] .  
The Ti-4.3V alloy with a Widmanst?tten microstructure exhibits a slightly greater creep 
strain (~0.8 %) than does the fine-equiaxed microstructure (~0.77 %) .  The creep strain for 
the Widmanst?tten mic rostructure is 4% greater than the equiaxed microstructure when 
the instantaneous plastic deformation of ~0. 10% is subtracted from the total strain of each  
Figure 6.2.  Tensile curves of Ti-4.3wt% V, tested at a strain rate of 3.28 x 10 -5 /s 
to a 3% total strain.  
77  
 
alloy.  Even though the lamellar thickness of the Widmanst?tten plates is approximately 
equal to the grain size of the equiaxed microstructure, there is a difference in the creep 
strain.  This difference is attributed to the difference in creep deformation mechanisms.  
The following analysis of creep deformation mechanisms was performed on the 
specimens. 
 
 
6.2.2 .1. Creep deformation mechanisms  
 Creep deformation in Ti-4.3V with a fine equiaxed microstructure is primarily 
due to fine slip in the ? phase, which is evidenced by a widening of the gold fiducial grid, 
as measured from before and after SEM micrographs, and TEM analysis.  No twinning or 
stress induced martensite was observed in either phase by TEM, although it is possible, 
but unlikely, that some very small twins may be present in the ? phase in a region of the 
specimen not investigated.  The lack of coarse deformation products can be attributed to 
Figure 6.3.  Creep curves of Ti-4.3V alloys, creep tested at ambient temperature at 
95% of their respective YS.  
78  
the ? phase grain si?e present in the two-phase alloy being much smaller than the grain 
size of the single-phase alloy with deformation twinning (??? ?m vs. ?? ?m) and the total 
strain of the creep tested specimen is also much less (6.67% vs. 0.9%).  However, the 
results are consistent with the fine grained Ti-1.6V.  Figure 6.4 shows SEM micrographs 
taken of the surface of Ti-4.3V prior to and following creep testing at 95% YS.  TEM 
investigations showed extensive <a> type slip on the prism plane  of the ? phase which is 
shown in Figure 6.5.  These dislocations are <a > type screw with b = 1/3<11 2? 0>.  No 
slip, twinning, or stress induced martensite (???) was observed in the ? phase of this 
alloy, which is not surprising considering the limited creep deformation of the single-
 phase ?-Ti-14.8V.  
 
  
Figure 6.4. ??? micrographs of ? + ? Ti-4.3V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.86% total plastic strain.  There are no 
coarse deformation features visible on the polished and etched surface, although 
fine slip in the ? phase (light) was noted due to an increase of the fiducial line 
spacing during testing. 
? 
? 
(a)  (b)  
 20 ?m   20 ?m 
79  
 
 In contrast to the creep deformation mechanisms of the fine equiaxed 
microstructure, coarse deformation features were present in creep tested samples of Ti-
 4.3V with Widmanst?tten microstructu re.  Figure 6.6 shows SEM micrographs taken 
prior to and following creep deformation of Ti-4.3V with a Widmanst?tten 
microstructure.  Notice the coarse deformation products that traverse over the phase 
boundaries of the ? and ? phases.  T?? analysis of these deformation products reveals 
them to be twins or coarse slip in the ? phase, and ??? (??) in the ? phase.  In addition, 
the linking of SIM and twins obviously is a result of the Burgers orientation relationship 
between the two phases of the Widmanst?tte n microstructure; as the platelet thickness is 
similar to the equiaxed microstructure tested.  This orientation relationship and additional 
deformation mechanism are responsible for the increased creep strain in the 
Widmanst?tten alloy.   
Figure 6.5. Bright field TEM micrograph of fine slip lines in the ?-phase of Ti-
 4.3V.  Slip is <a> type dislocations on prism planes.  The dislocations are of the 
type b = 1/3<11 2? 0>.  
 100 nm 
80  
  
Figure 6.7  is an SEM micrograph of coarse deformation products spanning many grains 
in the Ti-4.3V alloy.  Due to the Burgers orientation relationship between the ? and ? 
phases, the coarse slip planes of one phase are closely aligned with the coarse slip planes 
of the other phase.  This will be discussed later.  Figure 6.8 shows a TEM image of the 
coarse slip bands in ? which appeared to be twins in earlier ??? investigations.  These 
slip bands can also occur in tandem with stress induced martensite plates in the ? phase.  
Figure 6.9 shows a TEM image of an example of the stress induced martensite in ? linked 
with twinning in ? present in the creep tested Ti-4.3 V.  The common zone axis for the 
diffraction patterns was [1 2? 10] ? // [1 1? 1] ?.  The martensite plate was in a plane such that 
specific identification was not possible; however, it is known that there is a Burgers 
orientation relationship between the ? and ??, namely ?????(??2? )? // [2 1? 1? 3]( 2? 112)?? or 
[111]( 1? 01)? // [2 1? 1? 3]( 1? 011)?? and the specific orientation with respect to the grain will be 
dependent upon both the grain orientation as well as the loading axis.  The twin has been 
? 
? 
Figure 6.6. ??? micrographs of ? + ? Ti-4.3V with Widmanst?tten microstructure 
(a) before and (b) after creep testing at 95% YS for 200 hours to 0.90% total plastic 
strain.  ?ote the coarse deformation features spanning multiple ? (light) and ? 
(dark) grains.  These were identified during this study as stress induced martensite 
in the ? phase and coarse slip or twinning in the ? phase. 
  10 ?m   10 ?m 
(a)  (b)  
81  
 
 
 
Figure 6.7. ??? micrograph of ? + ? Ti-4.3V with Widmanst?tten microstructure 
creep tested to 0.90% total plastic strain.  Note the coarse deformation features 
spanning the ? (light) and ? (dark) phases.  These features were identified as coarse 
slip and twinning in the ? phase and stress induced martensite (??) in the ? phase. 
  ? 
  ? 
  5 ?m 
Figure 6.8. T?? bright field micrograph of slip bands in the ? phase of ? + ? Ti-
 4.3V with Widmanst?tten microstructure.  
  400 nm 
g = 112?0 
82  
 
characterized as a {10 1? 2}< 1? 011> type twin.  Figure 6.10 shows a TEM image of three 
martensite plates forming in two different orientations within a single ? grain.  ?ach 
martensite plate obeys the Burgers orientation relationship with the ? phase as 
demonstrated by the diffraction patterns.  ?ven though there wasn?t a twin present in the 
? phase to add additional stresses, the interphase interfacial stresses were enough to form 
?? in the ? phase.  This will be addressed later.  The interface of the ? phase and the stress 
induced hexagonal martensite plates should be coherent with a twin-like interface, 
specifically a {10 1? 1} near -twin relationship.  The coherency of this interface has been 
confirmed by Jaworski and Ankem  [ 22] . 
 
Figure 6.9. T?? bright field micrograph showing a he?agonal martensite plate (??) 
in the ? phase connected to a ???1? ?? type twin in the ? phase in creep tested Ti-
 4.3V with Widmanst?tten microstructure.  The twin was classified specifically as ( 1?
 012)[10 1? ??.  ?ccompanying diffraction patterns are from the (a) ??twin interface 
and (b) the ???? interface.  ?one a?is is ??2? 10] ? // [1 1? 1] ?.  
  ? 
  ? 
  ?twin  
  ?? 
  (a) 
  (b)   100 nm 
83  
  
Figure 6.10. Bright field TEM micrograph showing thee stress induced hexagonal 
martensite plates (??) within the ? phase of Ti-4.3V creep tested at 95% YS for 200 
hours.  Accompanying diffraction patterns show that both planes have a near{10 1? 1} 
twin relationship to the ? phase.  The ?one a?is is ??1? 1] ? // [1 2? 10] ??. 
  ? 
  ??2  
  ??1  
  ??1  
  ? 
  400 nm 
8 4 
6.2.3. Two - phase ? + ? Ti - 8.1V alloy  
 The tensile true stress/true strain curves for the fine -grained equiaxed and 
Widmanst?tten microstructure  alloys are shown in Figure 6.11.  The fine-grained alloy 
exhibits a slightly higher ultimate tensile strength, as well as a higher elastic modulus and 
yield strength.  The Widmanst?tten alloy exhibi ts a 95% YS of approxi mately 599 MPa.  
The fine-equiaxed alloy exhibits a 95% YS of approximately 684  MPa.  Both alloys 
e?hibit no strain hardening.  These characteristics are due to the added ? phase present in 
these alloys (50% vs. 20% in Ti -4.3V). 
 The creep curves for the Ti-8.1V fine grained and Widmanst?tten  alloys are 
shown in Figure 6.12.  The alloys were tested at 95% of their respective YS.  A clip on 
extensometer was used to record strain.  SEM micrographs were taken prior to and during 
 
Figure 6.11. Tensile curves of Ti-8.1wt% V,  tested at a strain rate of 3.28 x 10 -5 /s 
to a 3% total strain.  
85  
 
testing in the same area of each specimen to record deformation mechanism.  The Ti-
 8.1V alloy with a Widma nst?tten microstructure exhibits  a greater creep strain (~0.27 %) 
than does the fine equiaxed microstructure (~0 .22%).  The creep strain for the 
Widmanst?tten mi crostructure is approximately 13% greater than the equiaxed 
microstructure when the instantaneous plastic deformation of ~0.25 % (Widmanst?tten) 
and 0.18% (fine equiaxed) is subtracted from the total strain of each alloy.  Additionally, 
from the creep curves it is apparent that the fine equiaxed alloy experiences creep 
exhaustion where the Widmanst?tt en alloy continues to strain.  The lack of creep 
exhaustion suggests that the creep deformation mechanisms operating are increasing the 
internal stresses on other slip systems, resulting in further deformation.  This will be 
addressed in the next section.  The difference in creep deformation between the two 
microstructures is quite large and this difference is attributed to the difference in 
operating creep deformation mechanisms. 
Figure 6.12. Creep curves of Ti-8.1V alloys, creep tested at ambient temperature at 
95% of their respective YS.  
86  
6.2.3.1. Creep deformation mechanisms  
 There were many deformation mechanisms observed during creep deformation of 
Ti-8.1V with a fine equiaxed microstructure.  There was fine slip, coarse slip, and rare 
twinning in the ? phase, as well as coarse slip and stress induced martensite in the ? 
phase.  Figure 6.13 shows SEM micrographs taken before and after creep deformation of 
Ti-8.1V with a fine equiaxed microstructure.  Note the coarse deformation products in the 
? phase which were not present in the Ti-4.3V alloy.  Figure 6.14 shows SEM 
micrographs taken from a different area which show stress induced martensite as well as 
coarse slip in the ? phase.  Also note that unlike Widmanst?tten microstructures, the 
features do not cross phase boundaries.  TEM investigations were unable to locate coarse 
any coarse slip in the ? phase of this alloy; however, both twinning and stress induced 
martensite can be ruled out as possible features because of the wavy behavior of the 
features.  ?revious investigations determined that the ? phase slips by edge dislocations 
along b = 1/2 <111> .  TEM investigations also demonstrated that stress induced 
martensite could occur in a non-Widmanst?tten microstructured allo y, as shown in Figure 
6.15, suggesting that additional factors come into play other than the templating effect.  
Even though the Ti-8.1V alloy w ith equiaxed microstructure experienced less total creep 
strain than the Ti-4.3V alloy with equiaxed microstructure, there is still coarse 
deformation features in the ? phase suggesting that interaction stresses are responsible for 
the coarse features rather than the amount of strain, and partly due to the fact that the ? 
phase is now the primary phase in Ti-8.1V.  ?ven at very low strains, the single phase ? 
alloy exhibited coarse deformation features during creep; suggesting that the coarse 
deformation features seen here are not as surprising as one first thinks. 
87  
 
 
  
 
 
 
Figure 6.13. ??? micrographs of ? + ? Ti-8.1V (a) before and (b)  after creep 
deformation at 95% YS for 200 hours to 0.41% total plastic strain.  Note the coarse 
deformation features in the ? phase (dark).  These features were identified to be 
coarse slip and stress induced martensite.  ?ine slip has been noted in the ? phase 
(light) due to an increase in the fiducial line spacing during testing.  Note that 
deformation features do not cross phase boundaries. 
  10 ?m 
  ? 
  ? 
(a)  (b)  
Figure 6.14. ??? micrographs of ? + ? Ti-8.1V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.41% total plastic strain.  Note the coarse 
deformation features in the ? phase (dark).  These features were identified to be 
coarse slip and stress induced martensite.  ?ine slip has been noted in the ? phase 
(light) due to an increase in the fiducial line spacing during testing.  Twinning in the 
? phase was also noted, but was rare. 
  10 ?m   10 ?m 
  ? 
  ? 
(a)  (b)  
  10 ?m 
88  
 
 
  
In contrast to the creep deformation mechanisms of the fine equiaxed 
microstructure, the coarse deformation features in the Widmanst?tten microstructure were 
much more plentiful and crossed many grains as seen before in the Ti-4.3V alloy.  Figure 
6.16 shows the before and after SEM micrographs of a Ti-8.1V alloy with Widmanst?tten 
microstructure creep tested at 95% YS for 200 hours.  Note the coarse deformation 
features spanning many grains.  TEM analysis of these features reveals them to be twins 
or coarse slip in the ? phase and stress induced martensite (??) in the ? phase.  These 
results are consistent with previous research [ 21, 22] .  It should be noted that this linking 
of ?? and twins is due to the Burgers orientation relationship which exists in 
Widmanst?tten microstructured alloys.  This resulting additional deformation is 
responsible for the increase in creep strain experienced by this alloy. 
Figure 6.15. Bright field TEM micrograph of stress induced hexagonal martensite 
(??) plate in the ? phase of Ti-8.1V with equiaxed microstructure.  To the right are 
selected area diffraction patterns taken from the (a) ? phase and (b) ?? plate.  The 
zone axis is [1 1? 1] ? // [1 2? 10] ?. 
 ?? 
  ? 
  ? 
  400 nm 
89  
 
 
 
 Figure 6.17 is a TEM micrograph f rom Jaworski and Ankem showing the 
relationship between twinning and stress induced martensite over the span of many grains 
in a Widmanst?tten Ti8.1V alloy creep tested at 95% YS [ 22] .  The same alloy and 
microstructure was also tested during this investigation to verify previous results as well 
as verify the methodologies for testing, SEM characterization, and TEM characterization 
used here.  The results were perfectly replicated.   
Figure 6.16 . ??? micrographs of ? + ? Ti-8.1V with Widmanst?tten 
microstructure (a) before and (b) after creep testing at 95% YS for 200 hours to 
0.52% total plastic strain.  Note the coarse deformation features spanning many 
grains.  These features were identified to be twinning or coarse slip in the ? phase 
(light) and stress induced martensite in the ? phase (dark). 
  10 ?m 
  ? 
  ? 
  10 ?m 
(a)  (b)  
90 
 
6.2 .4. Two - phase ? + ? Ti - 12.6V alloy  
 The tensile true stress/true strain curves for the fine equiaxed grained and 
Widmanst?tten microstructure alloys are shown in Figure 6.18.  The two alloys exhibit 
almost exactly the same tensile behavior.  The 95% YS for  both alloys is approximately 
760 MPa.  The ultimate tensile strength at 3% elongation for the fine -equiaxed 
microstructure is only 5% greater than the Widmanst?tten alloy.  Neither alloy shows 
strain hardening behavior.  It should be noted that even though the UTS of the Ti-12.6V 
alloy is approximately equal to the Ti-?.?? alloy, the ??? ?? of the higher ? phase 
content alloys is significantly higher.  Conceptually, this makes sense because both of 
these alloys have the ? phase as the primary phase so the tensile behavior should be 
strongly dictated by that phase.   
Figure 6.17.  Bright field TEM micrograph showing stress induced martensite plates 
in the ? phase and twins in the ? phase of Ti-8.1V with Widmanst?tten 
microstructutre.  The martensite plates and twins alternate across the width of the ? 
and ? grains ????. 
91 
 
 The creep curves for the Ti-12.6V alloys are shown in Figure 6.19.  The alloys 
were tested for 200 hours at 95% of their respective YS.  A clip on extensometer was 
used to record strain.  SEM micrographs were used to record the same area of the 
specimen before, during, and after testing.  Both alloys demonstrate almost identical 
creep deformation behavior.  The alloys creep strain was about 0.10% 0.12% 
respectively, after 200 hours of testing.  For reference, the single-phase ?-Ti-14.8V alloy 
of a similar grain size crept to ~0.02% strain.  The difference in creep strain after 
~0.05 5% (instantaneous plastic strain) is subtracted from the total strain is about 16%.  
This demonstrates that even though both alloys appear to exhibit creep exhaustion and 
have very similar creep curves the difference between the two is still on par with the 
difference seen at the other compositions.    
Figure 6.18.  Tensile curves of Ti-12.6wt% V, tested at a strain rate of 3.28 x10 -5 /s 
to a 3% total st rain. 
92 
 
6.2.4.1. Creep deformation mechanisms  
 Creep deformation in Ti-12.6V with fine equiaxed microstructure is primarily due 
to fine slip in the ? phase and ?????????? twinning with b ? ???????? slip in the ? 
phase.  Figure 6.20 shows SEM micrographs taken before and after creep testing at 95% 
YS.  Note the stress induced plates similar to the previous investigations; however, TEM 
analysis revealed these plates to be {332}<113> twinning rather than stress induced 
martensite (SIM) as shown in Figure 6.21.  The zone axis is (110)?.  It should also be 
noted that with the fine equiaxed microstructure, coarse deformation features do not cross 
phase boundaries.  This is demonstrated quite drastically by Figure 6.22.  In Figure 6.22, 
there is a very large twin as well as e?tensive slip in the ? phase around an ? phase 
particle, yet the ? particle shows no signs of twinning or coarse slip, suggesting that the 
interaction stresses from ? on to ? act more strongly than those from ? onto ?.   
 
 
Figure 6.19.  Creep curves of Ti-12.6V alloys, creep tested at ambient temperature 
at 95% of their respective YS.  
93 
 
 
 
 
 
 
  10 ?m 
  ? 
  ? 
  10 ?m 
(a)  (b)  
Figure 6.20.  ??? micrographs of ? + ? Ti-12.6V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.11% total plastic strain.  Note the stress 
induced plates (???) in the ? phase (dark) and lack of coarse deformation features in 
the ? phase (light). 
Figure 6.21. T?? micrograph and diffraction pattern of ? + ? Ti-12.6V showing 
stress induced plate which is { 3? 2? 3}[ 1? ??? twin.  The additional spots are from the ? 
phase and double diffraction. 
  400 nm 
  ? 
  ?t 
  ? 
94 
 
 The creep deformation mechanisms of the Widmanst?tten microstructured Ti -
 12.6V alloy included fine slip and twinning in the ? phase as well as twinning in the ? 
phase.  Figure 6.23 shows SEM micrographs taken before and after creep deformation.  
With the presence of a Burgers relationship between the two phases, coarse deformation 
products can traverse phase boundaries.  It is expected that the Burgers orientation 
relationship will also act as a template for stress induced martensite in the ? phase? 
however, Figure 6.24 shows that the coarse features observed are twins just as with the 
equiaxed microstructure.  The slight difference in creep strain observed between these 
two alloys is attributed to the deformation twinning observed in the ? phase. 
  5 ?m 
  ? 
  ? 
Figure 6.22.  ??? micrograph of ? + ? Ti-12.6V after creep deformation at 95% 
YS for 200 hours to 0.11% total plastic strain.  Note the stress induced plates (SIP) 
and coarse slip in the ? phase (dark) and lack of coarse deformation features in the 
? phase (light).  The ??? are ?????????? twins. 
95 
 
 
 
 
 
 
 
 
Figure 6. 23.  ??? micrographs of ? + ? Ti-12.6V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.12% total plastic strain.  Note the stress 
induced plates (???) in the ? phase (dark) connected to deformation twinning in the 
? phase (light). 
  ? 
  ? 
  10 ?m 
(a)  (b)  
  10 ?m 
Figure 6.24.  T?? micrograph of ? + ? Ti-12.6V alloy with Widmanst?tten 
microstructure with {332}<113> twinning.  Alloy was creep tested at 95% YS for 
200 hours.   Diffraction pattern was taken from inside the twin.  Zone axis is <110>.  
  200 nm 
  ? 
  ?
 t
  
96 
 Figure 6.25 shows another area of the Ti-12.6V alloy with Widmanst?tten 
microstructure after creep testing.  In this case, even with the Burgers orientation 
relationship, only one of the two coarse deformation products were able to cross the 
phase boundary.  The reasons for this are discussed in the next section.  As mentioned 
before because twinning is the operating deformation mechanism in the ? phase, the 
aligned slip systems between ? and ? may not favor easy cross-slip as if the ? phase had 
transformed to martensite.   As such, the direction of a twin may be more important for it 
to resolve shear stresses onto the appropriate twinning planes in ?. 
 
 
 
 
 
 
Figure 6.25.  ??? micrographs of ? + ? Ti-12.6V (a) before and (b) after creep 
deformation at 95% YS for 200 hours to 0.12% total plastic strain.  Note the 
stress induced plates (???) in the ? phase (dark) connected to deformation 
twinning in the ? phase (light) and no visible deformation in the ? phase. 
  
(a)  (b)  
  10 ?m 10 ?m 
  ? 
  ? 
97  
6.3. Discussion  
6.3.1. Contribution of deformation mechanisms to creep strain  
For an equivalent lathe thickness the Widmanst?tten microstructure had a higher 
creep strain for all alloys tested over the same time period.  Figures 6.26, 6.27, and 6.28 
show the relationships between creep deformation behavior and microstructure.  As 
evidenced, these relationships follow general self-consistent trends.  This additional creep 
strain can be explained by a difference in deformation mechanisms, namely coarse 
deformation products in the ? phase such as stress induced martensite and twinning and 
the ability of these deformation products to trigger additional coarse deformation 
products in adjacent phases due to the Burgers orientation relationship that exists in a 
Widmanst?tten microstructured alloy.  An understanding of these creep deformation 
mechanisms is essential in order to design and process alloys for reduced creep strain. 
 
6.3.2.  The special importance of interaction stresses during creep deformation  
Interaction stresses between the ? and ? phases are responsible for the 
deformation mechanisms of the two-phase alloys, which differ from those of the single-
 phase alloys that constitute the individual phases.  Specimens examined in this study 
were creep tested at a constant 95% of their respective YS values. Any additional stresses 
required to initiate creep processes must be from internal sources. Therefore, internal 
stresses due to interactions between the ? and ? phases are even more important during 
creep deformation at low stresses compared to tensile deformation. There are several 
interaction stresses between the ? and ? phases that must be considered. These 
interactions are discussed, along with their consequences, below. 
98  
  
Figure 6.26.   Composite graph of the creep curves of the two different 
microstructures for the three different alloys.  As shown, the effect of 
microstructure decreases with increasing volume fraction of ? phase. 
Figure 6.2 7 .  Graph showing the relationship between creep strain of the alloys 
compared with what the law of mixtures would predict.  As shown, the ? phase 
exerts a much stronger influence on alloy behavior than predicted. 
99 
 
6.3.2 .1 .  Elastic interaction stresses 
 As the creep specimens are loaded to 95% of their respective yield stresses, there 
is an instantaneous elastic strain.  These stresses initially increase stress in the ? phase, 
contributing to the formation of twins and high dislocation densities in narrow grains, 
even at the relatively low applied creep stress. ?fter significant ? phase deformation, 
elasto-plastic interaction stresses can act on the ? phase, contributing to stress induced 
martensite nucleation or twinning.  Widmanst?tten platelets occur  in colonies of similarly 
oriented grains.  As soon as twin or SIM plate forms, the cascading effect can travel the 
entire width of the colony.  In the case of equiaxed microstructures, there can still exist a 
Burgers orientation relationship between the phases; however, it is very unlikely that the 
neighboring grain will be able to accommodate the deformation along the original plane.  
It is suggested that this is the primary reason behind the increased creep strain of the 
Widmanst?tten microstructure.  
Figure 6.2 8 .  A graph of the creep constants from the equation ? ? ?? + B  ln(t) for 
each of the tests during this investigation.  As shown, the constants do follow 
general self-consistent trends. 
100 
6.3 .2 .2 .  ? phase as a template for stress induced hexagonal martensite  
It is proposed that the presence of the ? phase is responsible for the formation of 
he?agonal ??? instead of twins in the ? phase of Ti-4.3V and Ti-8.1V. TEM analysis 
revealed a 
? ?1110
  twin relationship between martensite plates in the ? phase and the 
adjacent ? phase of creep deformed specimens. The identical crystal structure and the 
observed twin relationship between the ? and ?? makes the ? phase an e?ceptional 
template for the nucleation of stress induced he?agonal martensite in the ? phase in alloys 
with a Widmanst?tten microstructure. There is no such orientation relationship or 
crystallographic similarity between the ? phase and 
? ?332
 <113> twins in the ? phase. 
Therefore the interface created between the ? phase and the stress induced martensite 
plate is expected to be coherent, whereas the interface between 
? ?332
 <113> twins in ? 
and the ? phase would not be. ??? formation would be favored over twinning in ? due to 
a lower misfit strain and decreased surface free energy for martensite formation.  
 
6.3.2.3. {332}<113> twinning in Ti - 12.6V instead of SIM  
 ?n order for e?tensive twin nucleation and growth in the ? phase, the ? phase must 
strain to accommodate steadily increasing ? phase strain. ?f the ? phase constrains the ? 
phase sufficiently, the formation and growth of twins will be retarded. This is evidenced 
in the current study. Widespread twinning occurs in the ? phase of Ti-4.3V and Ti-8.1V, 
but rarely in Ti-??.??.  Because the volume fraction of the higher strength ? phase is 
significantly more in Ti-??.??, the ? phase will accommodate more strain than for the 
other two alloys.  ?f the ? phase twinning is retarded enough, the chances that a specific ? 
twin will be in the correct orientation to help nucleate SIM in an adjacent grain goes 
101 
down. ?n addition, the interfacial stresses decay ?uite rapidly away from the ??? interface.  
With less interfacial area, the probability for aligned shear systems goes down as well.  
Because formation of ??? becomes harder, the strain in the ? phase will be 
accommodated by twinning.  ?dditionally, the interaction stresses caused in the ? phase 
by the ? phase decay rapidly away from the phase interface.  With a higher volume 
fraction of ? phase present, the stresses e?erted on the ? phase would be less significant 
to overall resolved stresses. 
 
6.4 . Summary of creep deformation processes  
The following sequence of events results in the creep deformation of the alloys in 
this investigation.  When the specimens are first loaded to a stress equivalent to 95% of 
their yield stress, there is an instantaneous elastic deformation. Elastic interaction stresses 
are placed on the ? phase. The combination of the applied stress and the elastic 
interaction stress causes slip and?or twinning in the ? phase. Dislocations move slowly 
with time due to the relatively low applied stress, and begin to pile-up at the ??? interface. 
Time dependent twins can also form and grow, adding to the creep strain. ?s the ? phase 
deforms plastically, interaction stresses are reduced on the ? phase, and the ? phase must 
deform or there must be interphase interface sliding in order to accommodate further ? 
phase deformation.  
After sufficient time, the shear stress from the dislocation pileup or twinning is 
sufficient to nucleate stress-induced martensite in the ? phase of Ti-8.1V because of 
aligned shear systems in the ? and ? phases due to the Burgers orientation relationship.  If 
the ? phase was constrained enough that twinning could not occur, then time-dependent 
102 
twinning begins to occur in the ? phase.  When the martensite or twin spans the ? phase, 
twinning or coarse slip in the adjacent ? phase can be triggered. This is once again due to 
aligned shear systems in the ? and ? phases. This process can continue across many ? and 
? grains due to the Burgers orientation relationship of ? and ?. Twinning in the ? phase 
may be time dependent or instantaneous. The growth rate of martensite may also be may 
be instantaneous, controlled by the growth rate of twins or slip rate in the ? phase, or the 
martensite may have an inherent time-dependent mechanism. Further study is warranted 
to explore these possibilities.  
 
6.5 . Conclusions  
1. The creep strain of Ti-4.3wt% V, Ti-8.1wt%V , and Ti-12.6wt% V  decreases with 
increasing volume fraction of the ? phase when all alloys are tested at 95% of 
their respective yield stress. This is attributed to a difference in deformation 
mechanisms.  
2. The amount of creep strain exhibited by each alloy does not obey the Law of 
Mixtures.  The law of mixtures does not take into account interaction stresses.  In 
the case of the alloys studied during this investigation, interaction stresses are 
very significant to creep deformation and creep deformation mechanisms. 
3. The results seen during this investigation were contrary to the results seen during 
high temperature creep.  ?idmanst?tten structured ? + ? alloys demonstrate 
excellent high temperature creep resistance due to the colonies of Burgers 
oriented plates which resist interface sliding.  However, at low temperatures, these 
103 
same colonies transmit deformation mechanisms easily and contribute to 
increased creep strain. 
4. Deformation mechanisms in equiaxed microstructures very rarely cross phase 
boundaries.  This is attributed to the lack of a burgers orientation relationship 
which would otherwise align significant slip planes. 
5. ?ormation of he?agonal ??? plates during creep deformation in the ? phase of 
binary Ti-V alloys only occurs in the presence of ? platelets.  However, twinning 
occurs in the Ti-12.6V alloy, which has the same chemistry as the ? phase of Ti-
 4.3V and Ti-8.1V.  This is attributed to the greater constraints that the increase in 
volume fraction of ? phase e?erts on the ? phase. 
6. Twins in the ? phase occurred in response to stress induced martensite in the ? 
phase and vice versa. This is evidenced by TEM observations of twin-martensite 
pairings in Ti-4.3V and Ti-8.1V.   
7.  Interactions between phases are an extremely important consideration in creep 
deformation because they can be responsible for additional deformation 
mechanisms, resulting in increased creep strain. Understanding these interactions 
is important in the design and processing of two-phase alloys for improved creep 
resistance. 
 
 
  
104 
Ch apter 7  
Finite Element Studies  of the Interactions Between ? and ? Phases in 
Two - Phase Ti Alloys  
 
When materials consisting of two or more phases are deformed, where the phases 
have different elastic properties, elastic interaction stresses will develop to maintain 
compatibility at the interfaces [ 26, 157 , 158 ] .  These interaction stresses can occur during 
all types of deformation including tensile, creep, and fatigue.  These elastic interaction 
stresses are significant because, depending on the morphology of the multi-phase 
material, they can assist applied loads in initiating plastic deformation mechanisms even 
when the applied load resolved onto a slip system is below the critical value [ 26] .  In a 
similar sense, they can also hinder applied loads.  Ankem et al. [ 157 , 159]  have shown 
the role elastic interaction stresses play on the initiation of slip in two-phase materials.  It 
has not been shown however how these interactions decay away from the interfaces, as 
well as the effect of morphology of phases on these interaction stresses.   
Finite element modeling (FEM) can be a very powerful tool for analyzing 
material behavior and interaction stresses.  FEM provides the ability to directly control 
material characteristics and geometry as well as the ability to read out simulation results 
from nearly any point in the model.  In these investigations, 3D finite element modeling 
has been used to study the behavior of two-phase alloys.  It is the goal of this work to 
understand the interfacial stresses, in particular the resolved shear stress on a various slip 
planes, as a function of applied stress.  In particular, it will be the focus of this 
investigation to analy?e the relationships between twin systems in ?-Ti and 
105 
twin?martensite systems in ?-Ti.  A systematic study was undertaken to develop the 
methodology and process for using 3D finite element modeling to analyze elastic 
interaction stresses in two-phase materials.  This was accomplished with the sequential 
modeling of a two-phase bi-crystal of ? + ? Ti to simulate the possible interactions 
between the two phases of a ? + ? Ti-V alloy.  This simulation will incorporate the 
elements of 3D modeling, and material anisotropy; all important characteristics which 
will help to further the knowledge of this science.  To achieve this simulation, the FEM 
tool ANSYS [ 160]  will be used.  Two-phase titanium alloys will be used as the model 
system in this investigation due to their current technological relevance; however, the 
findings of this investigation can be extended to many other two-phase systems. 
 
7. 1. Inpu t p roperties  and model development  
The overall approach of this investigation will follow several sequential steps for 
various phase interaction scenarios and then compare those results to manually calculated 
techniques and also compare the results with the experimental results obtained in Chapter 
6.  The sequence for each model can be more simply broken down as: 1) determine 
geometry and orientation of the two-phase materials, 2) generate an FEM mesh, 3) 
perform the FEM calculations, and 4) graph and plot the results. 
While using isotropic values of material properties can yield satisfactory results 
for certain simulations, the desire to understand interaction stresses between two phases, 
while including the effects of orientation, demands that anisotropic material properties 
are used.  In particular, the stiffness or compliance matrix for each Ti phase must be used, 
rather than an aggregate ?oung?s ?odulus.  ?lpha titanium is a he?agonal close-packed 
106 
crystal structure with five independent elastic constants whereas ? titanium is a cubic 
crystal structure with three independent elastic constants.  The five elastic compliances 
for single crystals of pure ?-Ti are s11 = 0.9581 , s12 = -0.4623, s13 = -0.1893 , s33 = 0.69 8 0, 
and s44 = 2.14 10 in units of 10
 -11 Pa-1 [ 161-163] .  The three elastic compliances for single 
crystals of ?-Ti (Ti-10wt% Cr) are s11 = 1.857 0, s12 = -0.774 1, and s44 = 2.342 0 in units 
of 10-11 Pa-1 [ 157 , 163] .  These compliances refer to the principal crystallographic axes 
indicated by xo, yo, and zo in the stereographic projection in Figure 7.1.  Due to 
symmetry, the other components of the elastic constant tensor matrix may be found based 
on these values.  The complete standard compliance tensors may be found in Appendix J .  
The relative orientation between the ? and ? phases is not arbitrary.  ?n the case of a two-
 phase alloy with Widmanst?tten microstructure, the re is a Burgers orientation 
relationship between the two phases.  Figure 7. 1 also indicates this Burgers orientation 
relationship:  <12? 10>(0001) ?  // < 11? 1>(110) ?, as well as the interface plane { 5? 140} ? //  { 3?
 34} ? between ? and ? phases.  The elastic constants in the standard orientations for the 
two phases must be transformed to the new primed coordinate system corresponding to 
the desired morphology while maintaining the Burgers orientation relationship and 
interface plane. 
 
7.2. Coordinate system d evelopment  
 When considering an anisotropic material, the biggest deciding factor of material 
behavior is obviously orientation of that material.  The ??? interface of titanium alloys 
has a very specific relationship and it is important to accurately portray this relationship 
during model development and execution.  Hence, for the purpose of modeling, each 
107  
crystal structure or phase must be oriented such that the crystal directions and planes are 
aligned with not only each other (the relationship between phases) but also with the 
inherent Cartesian coordinate system used by ANSYS.  For the purpose of modeling, the 
crystal structure?s compliance tensor must be rotated such that it matches the chosen 
modeling coordinate system.  This involves some work because ?-titanium uses a 4 index 
he?agonal coordinate system and ?-titanium uses a standard Cartesian coordinate system. 
  
Figure 7.1.  A stereographic projection showing the interface plane (5? 140)//( 3? 34), 
Burgers orientation relationships <12? 10>(0001)//<1 1? 1>(110), the standard 
crystallographic orientations and the prime coordinates (Widmanst?tten 
orientation) for the FEM models in this investigation. 
108  
To rotate a tensor, one must first determine the direction cosines between the 
original coordinate system and the proposed coordinate system.  The first goal of this 
project was to convert ?-titanium?s tensor (which is based on a he?agonal coordinate 
system of axes a1, a2, a3, and c) to a 90? Cartesian coordinate  system with x, y, and z 
axes.  To transfer the {hkil} indices to a Cartesian coordinate system which is aligned 
with ?-titanium, the following equations are used: 
 ??????????? ?????????? ??   (7.1)  
 ????????  ?????????  ??   (7.2)  
??????????
 ?
 ?
 ??   (7.3)  
Other texts refer to the 90? hexagonal coordinate system as orthohexagonal with indices 
<U?V?W?>{H?K?L?}.  To convert from <uvtw>{hkil} to this system, the following 
relationships have been established: 
 ???
 ??
 ?
   ???
 ?
 ?
 ??  ???? 
 ????  ???????  ???? 
Both methods yields the same results for indexing directions; however, when a 4 index 
coordinate system is converted to only 3 index the direction [uvw] is no longer 
necessarily perpendicular to the plane (uvw).   For this reason if you are calculating the 
relationships between directions on a stereographic projection you must be sure to restrict 
yourself to Miller-Bravais indices. 
?rom here, the rotation of the ? or the ? phase to line up with the other phase is 
accomplished by using a stereographic projection of the individual crystals from the 
appropriate perspective.  A stereographic projection can be constructed which shows the 
relative positions of various planes.  In Figure 7. 1, the interface plane, original 
109 
coordinates, prime coordinates for the first FEM model, and Burgers orientation 
relationships are all shown.  Using a Wulff net and techniques described by Greene & 
Ankem and Edington [ 54, 159] , it is then possible to determine all of the direction 
cosines for the rotation of the two crystal structures to a common orientation.  In addition, 
the direction of the applied load must also be considered such that the orientation 
maximizes resolved shear stresses on certain slip systems.  The equations relating the 
original compliance tensors and the direction cosines are detailed in Appendix K  [ 164] .  
The result will be a 6x6 symmetrical compliance tensor which is used in the succeeding 
sections to uniquely specify the anisotropic nature and orientation of the material 
property for each element of interest.   
For the bi-crystal model, nodal solutions will be provided by ANSYS in terms of 
X, Y, and Z normal stresses as well as XY, YZ, and XZ shear stresses.  Unfortunately, 
the stresses of interest are the shear stresses on various slip systems.  To calculate these 
stresses, the resulting stress state of individual nodes will be rotated to other coordinates 
on the stereographic projection which correspond to a particular slip system.  For this 
study, two tensor operations are necessary: rotating the original compliance matrices to 
match the test scenario orientation, and rotating the resulting normal stress and shear 
stress tensors to evaluate resolved shear stress on a specific slip plane.  These tensor 
rotations can be accomplished using the relationship Tij? = aikajlTkl where T? is the 
component of the rotated tensor, a is the respective component of the direction cosine 
matrix, and T is the component of the original tensor.  This equation is written in the 
conventional dummy suffix notation and can be expanded accordingly [ 165] . 
 
110 
7.3. G eometry of the two - phase s ystem  
 To study the elastic interaction stresses between the ? and ? phases of a two-phase 
titanium alloy, the geometry of the systems to be investigated were carefully designed 
such that boundary conditions could be easily applied and the coordinate system would 
match the coordinates shown in the stereographic projection.  The ANSYS procedure for 
constructing the bi-crystal model is shown in Appendix L and the constraints refer to 
Figure 7.2.  The constraints used  for this model are as follows: 
 
Figure 7.2.  Test scenario schematic showing coordinate system orientation and 
reference points A-N for the bicrystal model base used in this investigation. 
 
111 
1) all nodes on plane ???H are constrained in the y? direction, ?) all nodes along lines ?? 
and ?? are constrained in the ?? direction, ?) the node at point ? is constrained in the ?? 
and ?? directions, ?) the node at point ? is constrained in all directions, and 5) the nodes 
on plane ?BCD are constrained to displace the same distance in the y? direction.  The 
model can simulate an actual test specimen; however, due to the nature of FEM the units 
could be any dimension from microns to miles, as long as applied stresses are consistent 
with the compliance matrices. 
 
7.4. Mesh generation  
 The elements chosen for this investigation were solid brick elements with 8 nodes 
per element.  The models used during this study were comprised of 20,000 ? 7 0,000 
individual elements.  The specific element name as designated by ANSYS is SOLID 185.  
?ach element is assigned a material property and then the elements are ?glued? together 
so that two adjacent elements would share nodes on their common face rather than each 
have their own set.  An applied displacement or load was then directed onto all of the 
nodes on plane ?BCD.  ?t was found that displacing plane ?BCD by an amount ??? was 
the stress e?uivalent of displacing planes ?BCD and ???H an amount ??????.  In this 
way, half of a specimen can be modeled where the non-modeled half would mirror the 
modeled half. 
 As mentioned before, the units of a FEM model do not necessarily mean 
anything, it is just the consistency among units and calculations that matters.  However, 
the mesh size for FEM models has a significant effect on model accuracy and 
computational time.  The model in this investigation has been chosen to be 70 units wide 
112 
(x direction), 10 units thick (z direction), and 100 units high (y direction).  Mesh sizes of 
1, 1.25, 2.5, and 5 units were all tested.  A mesh size of 1.25 units was decided upon as a 
good compromise between computational time and accuracy of results.  The simulation 
with a mesh si?e ? ?, took much longer but didn?t have any effect on model accuracy.  
Figure 7.3  is an image of the meshed model for a simple bicrystal as modeled in the 
ANSYS program.   
 
Figure 7.3.  ANSYS bicrystal meshed for the study of elastic interactions between 
? (blue) and ? (red) phases of titanium alloys. 
  
113 
??5? Mesh generation incorporating slip or twinning in ? 
 The ne?t model is also a bicrystal but also incorporates planes in the ? phase upon 
which shear stresses can be directly applied.  In this case, the crystallographic orientation 
of the phases is the same as for the bicrystal case? however, there is a new ?phase? 
present in the alpha phase.  The twinned structure of ? can be represented by a rotated 
version of the primed coordinates.  This relationship and necessary rotations are shown in 
the stereographic projection in Figure 7.4 .  The model can be represented by the test 
scenario shown in Figure 7.5.  The model is meshed as before  and the ANSYS simulation 
is shown in Figure 7.6.   
 
7.6 . Results  
 This investigation began with a check of the FEM calculation.  The two phases in 
the mesh shown in Figure 7.3  were given the same material property and a displacement 
was applied.  The results showed no interaction stresses at the interface and the stress 
divided by the strain exactly equaled the elastic modulus.  It is therefore assumed that 
these results confirm the validity of the FEM calculation and model constraints.  
Additionally, the bicrystal model results were then compared with earlier similar work 
[ 164] .  The results were also consistent in their behavior even if the actual calculated 
values were different.  The specific planes and directions of the plane/direction families 
that were used to resolve the shear stresses in the following analysis were the maximum 
resolved values as determined from Appendix G.  For example, to resolve YZ shear due 
to {10 1? 2}< 1? 011> twinning onto the {332}<113> twin plane, the (33 2? )[113] system was 
chosen because that system resolves the most stress. 
114 
 
Figure 7.4.  A stereographic projection showing the relationship between the 
orientation of the ? phase in the ????? coordinate system, and the orientation of 
the twinned region in the ANSYS coordinate system. 
115 
 
Figure 7.5.  A schematic diagram showing the relationship between the twinning 
and basal slip systems to the oriented model in the ANSYS simulation. 
116 
 
7.6 .1. Bic rystal model of ??? interaction stresses 
 The results from ANSYS are the displacements for all of the nodes and the 
stresses for all of the elements as mentioned above.  Figure 7.7  shows a color fringe plot 
of the displacements in the y? direction for all of the nodes in the ? + ? bicrystal.  ?ach 
color represents a range of values.  As expected, the nodes in the bottom plane of the 
model do not move in the y? direction.  The normal stresses in the y? direction and YZ 
shear stresses are shown in Figures 7.8  and 7.9 .  The units are Pascal since the elastic 
constants were entered in units of ?ascal.  ?ote that the normal y? stresses are higher in 
the ? phase than in the ? phase and are also not constant, varying at the interface. 
Figure 7.6.  ANSYS bicrystal meshed for the study of elastic interactions between 
? (blue), ? twin (purple), and ? (red) phases of titanium alloys. 
117  
 
F
 igur
 e
  7.7.
  Displ
 ac
 em
 en
 ts 
of
  the 
node
 s 
in
  the 
??
  dire
 cti
 on. 
 ?ote
  that 
the 
displ
 ac
 ement 
of
  the 
top 
node
 s 
is
  
appro
 p
 ri
 ate
  fo
 r the
  e
 lastic 
comp
 lian
 ce
  v
 alues in 
th
 e 
[0001
 ] dir
 ec
 ti
 on f
 o
 r 
an 
appl
 ie
 d s
 tr
 ess of 359 M
 P
 a.
  
118  
F
 igur
 e 
7.8.
  ?or
 mal 
stre
 sse
 s 
in 
the 
??
  dire
 cti
 on. 
 ?ote
  the 
hig
 h
 er 
stre
 ss
 es 
in 
the 
?
  
pha
 se
  a
 s opposed to the ?
  pha
 se
 . 
119 
F
 igur
 e 
7.9.
  R
 esolved
  Y
 Z
  sh
 ea
 r 
str
 ess
  fo
 r 
el
 ements
  in
  the
  tw
 o
 -ph
 as
 e 
ti
 taniu
 m
  
bic
 ry
 st
 al shown 
in 
F
 ig
 u
 re
  7.6.  Not
 e the inte
 ra
 ct
 ion s
 tr
 esses 
at 
th
 e in
 te
 rf
 ac
 e.
  
120 
  
The YZ interfacial stress distribution is shown in Figure 7.10.  As you can see, as 
the sample is elastically deformed the stress increases in ? and decreases in ?.  This 
increase in stress in the ? phase is responsible for the twinning that was not observed in 
the single phase alloy.  The stresses of interest are the shear stresses in the ? phase 
resolved onto the ? twinning system , and two possible martensite systems .  The result is 
plotted in Figure 7. 11 for the hori?ontal row of elements between points ??? in ?igure 
7.3.  
 
 
 
Figure 7.10.  The resolved shear stress distribution for a horizontal row of 
elements in the mesh shown in ?igure ?.?.  ? phase is on the left and ? phase is 
on the right.  Notice the very high interaction stresses at the interface. 
? 
? 
121 
 
 
7.6.2 ? Bicrystal model of ??? interaction stresses due to twinning in ? 
 Figure 7. 12 shows a color fringe plot of the normal streses in the y? direction for 
all of the nodes in the ? + ? bicrystal with a twin.  The YZ shear stresses are shown in 
Figure 7. 13.  The units are Pascal since the elastic constants were entered in units of 
?ascal.  ?ote that the normal y? stresses are higher in the ? phase than in the ? phase and 
are also not constant, varying at the interfaces.  Also note that stress has been relieved in 
the twin.  The stresses of interest are the shear stresses in the ? phase resolved onto the 
twinning system , and two possible martensite systems .  The result is plotted in Figure 
7. 15 for the hori?ontal row of elements between points ??? in ?igure 7.3.  
Figure 7.11.  The resolved shear stress distribution for a horizontal row of 
elements in the mesh shown in ?igure ?.?.  ?ote that for this orientation of ? 
phase, the resolved shear stress on the martensite system is higher than on the 
twinning system. 
122 
 
F
 igur
 e 
7.12.
  Th
 e 
A
 N
 S
 Y
 S
  si
 m
 ulatio
 n
  r
 esul
 ts
  o
 f 
str
 es
 se
 s 
in 
the 
??
  dire
 cti
 o
 n. 
 ?ote
  that 
the 
stre
 sses 
ha
 ve
  
be
 en re
 li
 ev
 ed in t
 he
  twin 
(a
 s app
 rop
 ria
 te)
  a
 nd the 
?
  pha
 se
  e
 ?
 pe
 rie
 n
 ce
 s hi
 g
 h
 er stre
 sses than th
 e ? pha
 se
 . 
123 
 
F
 igur
 e 
7.13.
  Th
 e 
re
 sol
 v
 ed
  Y
 Z
  sh
 ea
 r 
st
 re
 ss
  nod
 al
  r
 esul
 ts
  a
 s 
p
 rod
 u
 ce
 d
  b
 y
  t
 h
 e 
A
 N
 S
 YS
  si
 m
 ulation. 
 
N
 o
 te in
 cr
 ea
 se
  in 
inte
 rf
 ac
 ia
 l she
 ar st
 re
 sses 
as 
w
 el
 l 
as the str
 esses on th
 e twi
 n
 nin
 g
  plan
 es
 . 
124 
 
 
7.6.3 ? Bicrystal model of ??? interaction stresses due to slip in ? 
 To model slip in the ? phase, a feature of ????? called the ?working plane? 
must be used.  This is a coordinate system that is defined with respect to the global 
coordinate system.  Basal slip of the type (0001)<12? 10> will be used as the example for 
this investigation.  This slip system is indicated in green in Figure 7.5.  Using the 
relationships developed earlier, the angles between the global coordinate system (??, y?, 
and ??) and the working plane?s active coordinate system are found.  ?or this coordinate 
system, ??? is the slip direction, y?? is the normal to the slip plane, and ??? is the vector 
perpendicular to the other two as previously defined. 
Figure 7.14.  The resolved shear stress distribution for a horizontal row of 
elements between points ??? in the schematic shown in Figure 7.5 .  Note that for 
this orientation of ? phase, the resolved shear stress on the martensite system is 
higher than on the twinning system and the presence of a twin magnifies that 
effect. 
125 
 A load can then be applied on the slip plane and in the slip direction in the 
working plane.  This step is required because ANSYS can only apply normal stresses 
with respect to a defined coordinate system and the slip direction is not aligned with any 
of the global axis.  This normal stress is then resolved into normal and shear stresses in 
the global coordinate system.  The effect of the stresses due to basal slip in the ? phase on 
the ? phase are shown in ?igure ?.??.  Note, in this investigation the applied stress was 
directly applied to the slip plane.  In the previous sections, the stress was applied to the 
model as a whole.  Therefore, the stresses in Figure 7.15 are normalized with respect to 
the stress on the slip plane rather than normalized with respect to the stress applied to the 
model.   
 
Figure 7.15.  The resolved shear stress distribution for a horizontal row of 
elements along line ??? in the schematic shown in ?igure ?.?. 
126 
7.7. Discussion  
 The most important observed data is organized into Table 7.1.  In this table, you 
can see the relationship between the stresses observed by various systems during elastic 
deformation.  In this table, the following should be noted: 1) due to the Burgers 
orientation relationship, stresses in ? are always resolved higher in the martensite slip 
systems than in twin systems, 2) the FEM results are similar to direct manual 
calculations, and 3) the difference between the FEM results and the manual calculations 
can be attributed to interaction stresses.  The manual calculations only take into account 
the geometrical relationship between the individual slip planes and directions.  For this 
reason, these calculations can be a useful tool for predicting trends but as evidenced, 
FEM can be a very powerful tool to help show a more clear picture of the relationship 
between the two phases.  One of the most important observations is how an interaction 
stress may decay away from the ??? interface.  This information is crucial to the 
microstructure of the alloy.  ?or e?ample, the stresses in ? due to an ? twin can favor 
{332}<113> near the interface, but long -range stresses favor {011}<111> martensite.   
 
 ? Deformation Mechanism 
? ?hear ?ystem Sole Interaction Basal Slip {10 1? 2} Twin  
Manual Calculation {332}<113>  0.385  0.814  0.672  
Manual Calculation {112}<111>  0.472  0.866  0.793  
Manual Calculation { 011}<111>  0.408  1 0.849  
FEM Result {332}<113>  0.357  0.837  0.737  
FEM Result {112}<111>  0.409 0.874  0.849  
FEM Result {011}<111>  0.332 0.979  0.638  
 
Table 7.1 .   ?a?imum resolved shear stresses in ? Ti, normali?ed to applied stress 
in ?, on twinning and hexagonal martensite shear systems. 
127  
7.8. Conclusion s 
1. A three-dimensional anisotropic Finite Element Model (FEM) has been 
successfully employed to predict the elastic interaction stresses in ? + ? titanium 
alloys due to phase interactions, twinning in the ? phase, and basal slip in the ? 
phase.  This modeling can be applied to predict interaction stresses found in many 
types of deformation, i.e. creep, fatigue, or tensile deformation and to any 
multiphase material. 
2. For a two-phase bicrystal where the interface plane is parallel to the stress axis, 
the shear stresses in the ? martensite (??) system are higher than the ?????????? 
twinning system and the interaction stresses decayed away in about one-sixth of 
the plate thickness. 
3. These interaction stresses suggest that yielding in the ? phase near the ??? 
interface can occur even though the average applied shear stress is below the yield 
stress of the ? phase. 
4. These results agree with earlier studies of two phase ? + ? titanium alloys in 
which the ? phase deformed by stress induced martensite but the single-phase ? 
alloy of a similar composition deformed by twinning.  It is suggested that the 
interaction stresses from due to the ? phase so strongly affect the martensite slip 
systems that the ?crss for martensite is lower becomes lower than the ?crss for 
twinning. 
  
128  
Chapter 8  
Conclusions  
 
1. A crystallographic model was developed, including octahedral interstitial sites, to 
explain the time-dependent growth of twins in an ?-Ti-1.6V alloy.  This model for 
the movement of atoms in HCP titanium allowed for twinning to be a diffusion 
controlled deformation mechanism.  The model specifically addresses how 
octahedral interstitial sites (which can be occupied by o?ygen atoms in ?-Ti) are 
annihilated during the shear and shuffle of atoms required for a {10 1? 2} twin t o 
form. 
2. To test the theory of time-dependent twinning, ?-Ti-1.6V with a coarse equiaxed 
microstructure was tested at strain rates from 10-6 to 10-1 /s.  It was found that the 
twin size (lamellar thickness) decreases with an increase in strain rate.  Classical 
theories of twinning state that because the energy required for twin growth is so 
much less than the activation energy required for nucleation, twin growth rates 
can approach the speed of sound in the material.  Under the classical theory, twin 
sizes should either be independent of strain rate (as long as strain rate is less than 
speed of sound) or increase with strain rate due to the availability of higher 
nucleation stresses.  However, the opposite was seen to be true.  The behavior 
observed in this study has been attributed to a time-dependent growth process, 
namely the diffusion of oxygen.  It was shown that there exists a strong 
relationship between twin growth rates and stress assisted diffusion of oxygen to 
support this conclusion. 
129 
3. The creep deformation mechanisms of Ti-4.3V, Ti-8.1V and Ti -12.6V were 
studied for both Widmanst?tten and equiaxed microstructures.  The creep 
deformation mechanisms included slip and twinning in the alpha phase as well as 
slip, stress induced martensite, and twinning in the ? phase.  These deformation 
mechanisms were different from those seen during creep of the respective single-
 phase ? and ? alloys with the same compositions.  The difference in deformation 
mechanisms is attributed to interaction stresses between phases. 
4. The percentage difference in creep strain between the two microstructures was 
about equal for the three different alloys studied.  The Widmanst?tten 
microstructured alloys exhibited greater creep strain than the equiaxed 
microstructure for all compositions.  This was unexpected and the opposite of 
what occurs during high temperature creep.  This was explained as a result of the 
Burgers orientation relationship which e?ists between the ? and ? phases.  ?t high 
temperature creep this relationship prevents interface sliding and inhibits creep; 
however, at low temperatures this relationship provides a template for easy twin 
or martensite deformation transmission across phase boundaries. 
5.  Even though the equiaxed microstructure alloys can also have a Burgers 
orientation relationship between phases, they do not have colonies of aligned 
grains and so slip transmission is made more difficult, thus reducing creep strain. 
6. The law of mixtures was not applicable to determine the creep strain of an 
intermediate alloy.  This is attributed to the interaction stresses between phases 
which can initiate deformation mechanisms and increase internal stresses beyond 
what the individual phases would experience. 
130 
7.  To study the interaction stresses that occur between the ? and ? phases of 
titanium, a 3D anisotropic model was developed.  This model demonstrated that 
due to the Burgers orientation relationship between the ? and ? phases of 
titanium, the martensite slip systems are much more affected than the twinning 
systems by the interactions stresses due to phase interactions, slip in the ? phase, 
and twinning in the ? phase.  These results support the observations of stress 
induced martensite (SIM) formation in creep deformed two-phase ? + ? alloys 
with a ? ??? volume fraction of the ? phase. 
 
  
131 
Chapter 9  
Suggestions for Future Work  
 
1. Tensile and creep testing of equiaxed and Widmanst?tten microstructured Ti -
 4.3V, Ti-8.1V , and Ti-12.6V alloys at slightly elevated temperatures 358 -458 K. 
These studies will be useful for studying the tensile and creep deformation 
mechanisms over a larger temperature range, but may also give clues to the extent 
of the alteration of the ?s temperature of the ? phase due to interactions with the 
? phase. ?t is e?pected that as the testing temperature is raised that the ? phase 
deformation mechanism will change from stress induced martensite to twinning. 
The activation energy can also be calculated for the creep deformation processes, 
and correlated with published values of activation energy for stress induced 
martensite and TEM observations. 
2. Tensile tests should be conducted beyond 3% strain to fracture in order to study 
the effect of the newly discovered deformation mechanisms on fracture 
mechanics. In this regard, fatigue and creep-fatigue testing could also be 
performed. 
3. Three dimensional FEM studies that incorporate crystal plasticity and phase 
transformation to more accurately model the effect of twin formation and stress 
induced martensite formation on the interaction stresses between phases. 
  
132 
 
Appendix A  
 
Ti- V Phase Diagrams and Alloy Compositions  
 
 
 
 
Alloy #  Alloy Phase Vol. %  ? Phase Comp? ? Phase Comp? 
1 Ti-1.6wt% V  ???? ? ~Ti -1.6wt% V  N/A  
2 Ti-4.3wt% V  ~80 ? ?, ?20? ? ~Ti -1.6wt% V  ~Ti -14.8wt% V  
3 Ti-8.1wt% V  ???? ?, ???? ? ~Ti -1.6wt% V  ~Ti -14.8wt% V  
4 Ti-12.6wt% V  ???? ?, ?8 ?? ? ~Ti -1.6wt% V  ~Ti -14.8wt% V  
5 Ti-14.8wt% V  ???? ? N/A  ~Ti -14.8wt% V  
 
133 
 
Appendix B 
 
Tensile and Creep Specimen Specifications  
 
 
 
Specimen with flats for tensile and creep testing (to be cut by electric discharge 
machining) for pre and post testing optical and SEM microscopy. 
 
 
 
Method for calculating the cross sectional area of the gage length for specimens with the 
above geometry. 
 
 
 
134 
 
Appendix C  
 
Fischion e Model 1010 Ion Mill Operation Manual  
 
I.  Before Start 
1. Make sure the Gas (Argon) Flow is connected. 
2. The valve of gas tank is opened; the number of pressure is at two divisions.  
3. Power cord is connected. 
4. The cooling water flow is connected and valve is opened. 
5. The Dewar Conductor Rod is not engaged. 
 
II. Start Up  
1. Press the Main Power Switch on the lower rear instrument panel to on. 
2. Press the power button on the computer to on. The desktop screen will appear 
with icons for four Model 1010 programs: 
? Dewar Bakeout 
? ?og ?iewer 
? ?on ?ill 
? ?aser Calibration 
 
III. Dewar Bake out (Option: Perform this step before using cooling stage)  
1. Close all open programs. 
2. Remove all specimens from the stage if there is any specimen inside.  Heat 
from the bakeout could damage the specimen. 
135 
 
3. Double click the Dewar Bakeout icon on the desktop to initiate the Dewar 
flask heating program. 
4. Click Press to Enable Pumps to turn on the pumps. 
5. Engage the Dewar Conductor Rod until thermal contact is made with the 
specimen stage. 
a. Rotate the Dewar knob clockwise, as viewed facing the instrument?s 
rear panel. 
b. Rotate the Dewar knob until its pin contacts the pin stop, preventing 
further rotation.  When the specimen stage is heated to above setpoint 
(100 C) and the vacuum is less than 8 x 10 -4 torr, the Dewar valve 
opens. 
6. Click Press to Enable Bakeout to turn on the heater.  The high temperature 
setpoint is 100.0 C. 
7. Enter a time (hrs:min:sec ).  10 minutes is usually sufficient for daily, routine 
maintenance. 
8. Click Start.  When the time has expired, the heater and pumps will turn off, the 
Dewar valve will close, and a dialog box appears indicating the procedure is 
finished. 
9. Open the Ion Mill program 
10. Wait until the temperature drop back to 30~40  C. Temperature of the Dewar 
must be lower than 40 degree before filling with Liquid N.  Wait. Otherwise, 
it will damage the dewar. 
11. Click Vent to release the vacuum. 
136 
 
12. Disengage the Dewar conductor rod by rotating its knob counterclockwise, as 
viewed from the rear of the instrument. Rotate the Dewar knob until its pin 
contacts the pin stop, and no further rotation is possible. 
 
IV. Loading TEM Specimens  
1. Place the TEM specimen into the recessed bottom plate with manual or 
vacuum tweezers. 
2. For a cross-section specimen, align the epoxy joints of the specimen parallel to 
the supporter. 
3. Position the top plate and attached spring over the bottom plate. 
4. Compressing the spring with manual tweezers, insert the left, top, and finally 
right leg of the spring into the available groove. 
?. ?lign the double line on the gear so it points to the position ? (? o?clock 
direction) for using both ion sources, position ? (? o?clock direction) for using 
only top source, and position ? (? o?clock direction) for using only bottom 
source. 
 
V. Ion Milling  
1. Double click on the Ion Mill icon to start the Ion Milling Program . 
2. Wait until the initializing phase is completed. 
3. Click Vent to release the vacuum. 
4. Load TEM Specimen. (IV. Loading TEM Specimens) 
5. Click Pump to evacuate the specimen chamber. 
137  
 
6. Set the default parameters for the ion sources ( voltage and current ), stage  
rotation, and milling angle , duration time , ending point .  If the sample is 
thick (ex. > 10 ?m), start with high voltage (> 5 kev) and angle  (18 .0~23 .0).   If 
the sample is thin (< 5 ?m), start with low voltage (3~4 kev) and angle  (< 15.0) 
7. Wait until reach a vacuum of about 2 x 10 -5 torr. 
8. If the specimen needs to be cooled, engage the conductor rod by rotating the  
Dewar knob clockwise, as viewed from the rear of the instrument. Rotate until 
the pin on the knob contacts the pin stop. 
 
Skip steps 8~10 if the specimen is not to be cooled. Make sure perform step III  
before specimen cooling. 
 
9. Fill the Dewar with liquid nitrogen. 
10. Wait for the temperature to reach the minimum desired value, often -120.0 C. 
11. Make sure window shutter close and click Start to execute the process.  Stop 
ion milling once a small hole is found. Perform ion milling again at very low 
voltage (3 kev) and angle (5.0~10 .0) to remove all the defects caused by ion 
milling. 
12. When finished, if specimen cooling was used, disengage the conductor rod by 
rotating the Dewar knob counterclockwise until the knob?s pin contacts the 
pin stop. Vent chamber, stage temperature will heat up to > 20 .0 C and then 
vent automatically. 
13. Take out specimen. 
138  
 
VI. Shutdown Procedure  
1. If the instrument is vented, click Pump in the on Milling program. Verify that 
the vacuum level is 2 x 10-5 torr. 
2. Close the Ion Mill program. 
3. Shutdown the computer through Microsoft Windows. 
4. Press the main power switch to turn it off. 
5. Close the valves of gas and water supply to the instrument. 
6. Sign out the login-sheet. 
139 
 
Appendix D  
Operating Instructions for  
JEOL 2100F Field Emission TEM  
 
The following is a brief outline of the operating instructions for the JEOL 2100F 
Field Emission TEM.  This instrument should NOT be operated without proper training 
and certification by NISP Laboratory management.  This outline is not a substitute for the 
official TEM operating manual. 
 
PRELIMINARY STEPS 
1. Load specimen onto double tilt holder.  Specimen retainer is held down by a small 
screw.  Make sure specimen is secure and centered.  Check O-rings on the holder 
for lint which may compromise the vacuum. 
2. Fill cold-trap to the left of the column with liquid nitrogen. 
3. Raise High-Voltage Control window on the computer.  Under Auto HT & 
Emission, click on StartUp to begin accelerating voltage.  The status bar will 
show the time until the accelerating voltage of 200 kV is reached. 
 
INSERTING SPECIMEN HOLDER INTO COLUMN 
4. Open Specimen Property window on computer.  Select Double Tilt Holder from 
drop down menu.  Click Apply. 
5.  Align the specimen holder guide pin with the guide groove on the microscope 
column.  Push the holder into the goniometer until it stops and set the goniometer 
140 
 
PUMP/AIR switch to PUMP.  The yellow light will turn on and the evacuation 
will begin.  It will take about 10 minutes to pump down, until the green light on 
the goniometer goes on. 
6. When the green light is on, turn the specimen holder clockwise and push the 
holder into the goniometer as far as it will go. 
7.  Turn holder fully clockwise and push in into the yellow light on the goniometer 
goes off. 
8.  Connect the cable from the end of the double tilt holder into the port above the 
specimen holder. 
 
141 
 
Appendix E 
Rotation Calibration for JEOL 2100F Field Emission TEM  
The angle is rotation angle of bright field image from diffraction pattern. 
Magnification/ Camera length 60 cm 80 cm  100 cm 120 cm 150 cm 
50 71 o CW 71 o CW 71 o CW 71 o CW 71 o CW 
80  71  o CW 71  o CW 71  o CW 71  o CW 71  o CW 
100 71  o CW 71  o CW 71  o CW 71  o CW 71  o CW 
150 71  o CW 71  o CW 71  o CW 71  o CW 71  o CW 
200 71  o CW 71  o CW 71  o CW 71  o CW 71  o CW 
300 71  o CW 71  o CW 71  o CW 71  o CW 71  o CW 
400 64 o CW 64 o CW 64 o CW 64 o CW 64 o CW 
500 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
600 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
800  3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
1000 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
1200 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
1500 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
2500 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
3k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
4k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
5k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
6k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
8k  3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
10k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
12k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
15k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
20k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
30k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
40k 3 o CCW 3 o CCW 3 o CCW 3 o CCW 3 o CCW 
50k 0 o 0 o 0 o 0 o 0 o 
60k 3 o CW 3 o CW 3 o CW 3 o CW 3 o CW 
80k  2 o CCW 2 o CCW 2 o CCW 2 o CCW 2 o CCW 
100k 2 o CCW 2 o CCW 2 o CCW 2 o CCW 2 o CCW 
120k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
150k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
200k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
300k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
400k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
500k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
600k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
8 00k 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
1 M 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
1.2 M 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
1.5 M 28  o CW 28  o CW 28  o CW 28  o CW 28  o CW 
142 
 
Appendix F  
 
? Phase Coordinate Conversion to Parallel Directions in ? 
 
 
4 to 3 Coordinate Conversion Equations  
 
Conversion of ? coordinate directions ?hkl?? for the ? phase (hcp) or ? phase (???mmm) 
to directions in the 3 coordinate [xyz] Cartesian system. Consideration for the c/a ratio 
hexagonal crystal must be taken to calculate the correct z coordinate with respect to the x 
and y coordinates.  
 
 
 
x = h ? k sin30? - l sin30?  
 
y = k cos30? - l cos30?  
 
z = 
a
 cyx
 3
 22?  
  
 
 
??? Coordinate Conversion Matri? 
 
Conversion matri? for the calculation of parallel directions in the ? phase to a given 
direction in the ? phase of a two-phase titanium alloy with a Burgers orientation 
relationship 
? ? ? ??? 110111//00011021
 . If this conversion is used for planes, care must 
be taken to make sure that the plane normal is actually perpendicular to the plane. Planes 
and directions in the HCP system are not necessarily perpendicular as they are in a cubic 
system. 
 
?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ?
 ??
 ??
 072853.18392.1
 2
 2
 81902.2638797.
 2
 2
 81902.2638797.
  
 
 
x 
y 
z 
q 
h 
k l 
P
 rism 
S
 lip i
 n
  A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  Beta 
T
 w
 ins
  
A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
  
1
 1
 -2
 0
 1
 -2
 1
 0
 -2
 1
 1
 0
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 0
 .2
 6
 -0.
 2
 6
 -3.
 0
 7
 1
 .7
 3
 2
 -1.
 7
 3
 2
 1
 .7
 3
 2
 -1.
 9
 9
 2
 1
 .9
 9
 2
 1
 .3
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 1
 -1
 0
 0
 -1
 0
 1
 0
 0
 -1
 1
 0
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 1
 .2
 4
 1
 -1.
 2
 4
 1
 0
 .1
 3
 -0.
 7
 5
 0
 .7
 5
 1
 .4
 7
 2
 0
 .4
 9
 1
 -0.
 4
 9
 1
 .6
 V
 e
 c
 tor
 s
  o
 f t
 w
 in
 n
 in
 g
  s
 h
 e
 ar 
s
 ys
 te
 m
 s
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 3
 3
 -2
 1
 1
 3
 0
 .0
 5
 6
 -0.
 3
 6
 -0.
 3
 0
 5
 3
 -3
 2
 -1
 1
 3
 -0.
 7
 7
 2
 0
 .9
 3
 6
 0
 .1
 6
 3
 -3
 3
 2
 1
 -1
 3
 0
 .4
 7
 7
 0
 .5
 2
 3
 1
 3
 3
 2
 1
 1
 -3
 0
 .0
 5
 6
 -0.
 3
 6
 -0.
 3
 0
 5
 3
 -2
 3
 1
 3
 1
 -0.
 0
 6
 0
 .4
 7
 3
 0
 .4
 1
 3
 3
 2
 -3
 -1
 3
 1
 -0.
 5
 8
 2
 0
 .1
 3
 4
 -0.
 4
 4
 8
 3
 2
 3
 1
 -3
 1
 -0.
 5
 7
 8
 0
 .2
 5
 -0.
 3
 2
 8
 -3
 2
 3
 1
 3
 -1
 0
 .1
 4
 9
 -0.
 5
 -0.
 3
 5
 3
 -2
 3
 3
 3
 1
 1
 -0.
 1
 4
 9
 0
 .5
 0
 2
 0
 .3
 5
 3
 2
 3
 3
 -3
 1
 1
 0
 .5
 8
 2
 -0.
 1
 3
 0
 .4
 4
 8
 2
 3
 -3
 3
 -1
 1
 0
 .5
 7
 8
 -0.
 2
 5
 0
 .3
 2
 8
 2
 -3
 3
 3
 1
 -1
 0
 .0
 6
 -0.
 4
 7
 -0.
 4
 1
 3
 Appendix G
 143
P
 rism 
S
 lip i
 n
  A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 1
 1
 -2
 0
 1
 -2
 1
 0
 -2
 1
 1
 0
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 0
 .2
 6
 -0.
 2
 6
 -3.
 0
 7
 1
 .7
 3
 2
 -1.
 7
 3
 2
 1
 .7
 3
 2
 -1.
 9
 9
 2
 1
 .9
 9
 2
 1
 .3
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 1
 -1
 0
 0
 -1
 0
 1
 0
 0
 -1
 1
 0
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 1
 .2
 4
 1
 -1.
 2
 4
 1
 0
 .1
 3
 -0.
 7
 5
 0
 .7
 5
 1
 .4
 7
 2
 0
 .4
 9
 1
 -0.
 4
 9
 1
 .6
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 1
 2
 1
 1
 -1
 0
 .0
 6
 9
 -0.
 4
 4
 -0.
 3
 7
 2
 -1
 1
 2
 1
 -1
 1
 -0.
 5
 0
 8
 1
 0
 .4
 9
 2
 1
 -1
 2
 -1
 1
 1
 0
 .1
 4
 7
 0
 .7
 8
 3
 0
 .9
 3
 1
 1
 -2
 1
 1
 1
 0
 .0
 6
 9
 -0.
 4
 4
 -0.
 3
 7
 2
 1
 2
 1
 1
 -1
 1
 -0.
 2
 5
 4
 0
 .5
 0
 .2
 4
 6
 -1
 2
 1
 1
 1
 -1
 -0.
 4
 5
 6
 -0.
 0
 6
 -0.
 5
 1
 5
 1
 -2
 1
 1
 1
 1
 -0.
 5
 2
 5
 0
 .3
 8
 3
 -0.
 1
 4
 2
 1
 2
 -1
 -1
 1
 1
 -0.
 0
 7
 3
 -0.
 3
 9
 -0.
 4
 6
 5
 2
 1
 1
 -1
 1
 1
 0
 .0
 7
 3
 0
 .3
 9
 2
 0
 .4
 6
 5
 -2
 1
 1
 1
 1
 1
 0
 .4
 5
 6
 0
 .0
 5
 8
 0
 .5
 1
 5
 2
 -1
 1
 1
 1
 -1
 0
 .5
 2
 5
 -0.
 3
 8
 0
 .1
 4
 2
 2
 1
 -1
 1
 -1
 1
 0
 .2
 5
 4
 -0.
 5
 -0.
 2
 4
 6
 144
P
 rism 
S
 lip i
 n
  A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I
 I
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 1
 1
 -2
 0
 1
 -2
 1
 0
 -2
 1
 1
 0
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 0
 .2
 6
 -0.
 2
 6
 -3.
 0
 7
 1
 .7
 3
 2
 -1.
 7
 3
 2
 1
 .7
 3
 2
 -1.
 9
 9
 2
 1
 .9
 9
 2
 1
 .3
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 1
 -1
 0
 0
 -1
 0
 1
 0
 0
 -1
 1
 0
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 1
 .2
 4
 1
 -1.
 2
 4
 1
 0
 .1
 3
 -0.
 7
 5
 0
 .7
 5
 1
 .4
 7
 2
 0
 .4
 9
 1
 -0.
 4
 9
 1
 .6
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 0
 1
 1
 1
 -1
 0
 .3
 4
 3
 -0.
 4
 8
 -0.
 1
 3
 3
 1
 0
 1
 -1
 1
 1
 0
 .1
 2
 7
 0
 .6
 7
 8
 0
 .8
 0
 5
 -1
 0
 1
 1
 -1
 1
 -0.
 4
 4
 0
 .8
 6
 6
 0
 .4
 2
 6
 -1
 0
 1
 1
 1
 1
 0
 .2
 2
 4
 0
 .2
 8
 9
 0
 .5
 1
 2
 1
 1
 0
 1
 -1
 1
 0
 0
 0
 1
 1
 0
 -1
 1
 1
 0
 0
 0
 -1
 1
 0
 1
 1
 -1
 -0.
 5
 6
 7
 0
 .1
 8
 8
 -0.
 3
 7
 9
 -1
 1
 0
 1
 1
 1
 0
 .5
 6
 7
 -0.
 1
 9
 0
 .3
 7
 9
 0
 1
 1
 1
 1
 -1
 -0.
 2
 2
 4
 -0.
 2
 9
 -0.
 5
 1
 2
 0
 1
 1
 1
 -1
 1
 -0.
 4
 4
 0
 .8
 6
 6
 0
 .4
 2
 6
 0
 -1
 1
 -1
 1
 1
 0
 .1
 2
 7
 0
 .6
 7
 8
 0
 .8
 0
 5
 0
 -1
 1
 1
 1
 1
 -0.
 3
 4
 3
 0
 .4
 7
 6
 0
 .1
 3
 3
 145
Bas
 a
 l 
S
 lip i
 n
  A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  Beta 
T
 w
 ins
  
A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 1
 1
 -2
 0
 1
 -2
 1
 0
 -2
 1
 1
 0
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 0
 .2
 6
 -0.
 2
 6
 -3.
 0
 7
 1
 .7
 3
 2
 -1.
 7
 3
 2
 1
 .7
 3
 2
 -1.
 9
 9
 2
 1
 .9
 9
 2
 1
 .3
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 0
 0
 0
 1
 0
 0
 0
 1
 0
 0
 0
 1
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 1
 1
 0
 1
 1
 0
 1
 1
 0
 V
 e
 c
 tor
 s
  o
 f t
 w
 in
 n
 in
 g
  s
 h
 e
 ar 
s
 ys
 te
 m
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 3
 3
 -2
 1
 1
 3
 -0.
 6
 3
 2
 0
 .3
 6
 7
 0
 .2
 7
 4
 3
 -3
 2
 -1
 1
 3
 0
 0
 0
 -3
 3
 2
 1
 -1
 3
 0
 0
 0
 3
 3
 2
 1
 1
 -3
 0
 .6
 3
 2
 -0.
 3
 7
 -0.
 2
 7
 4
 3
 -2
 3
 1
 3
 1
 -0.
 5
 1
 8
 0
 .8
 1
 4
 -0.
 2
 6
 8
 3
 2
 -3
 -1
 3
 1
 -0.
 0
 2
 3
 -0.
 5
 0
 .5
 0
 3
 3
 2
 3
 1
 -3
 1
 0
 .1
 1
 4
 0
 .4
 4
 6
 -0.
 5
 4
 2
 -3
 2
 3
 1
 3
 -1
 -0.
 6
 5
 5
 -0.
 1
 3
 0
 .7
 7
 7
 -2
 3
 3
 3
 1
 1
 -0.
 6
 5
 5
 -0.
 1
 3
 0
 .7
 7
 7
 2
 3
 3
 -3
 1
 1
 -0.
 0
 2
 3
 -0.
 5
 0
 .5
 0
 3
 2
 3
 -3
 3
 -1
 1
 0
 .1
 1
 4
 0
 .4
 4
 6
 -0.
 5
 4
 2
 2
 -3
 3
 3
 1
 -1
 -0.
 5
 1
 8
 0
 .8
 1
 4
 -0.
 2
 6
 8
 146
Bas
 a
 l 
S
 lip i
 n
  A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 1
 1
 -2
 0
 1
 -2
 1
 0
 -2
 1
 1
 0
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
  
0
 .2
 6
 -0.
 2
 6
 -3.
 0
 7
 1
 .7
 3
 2
 -1.
 7
 3
 2
 1
 .7
 3
 2
 -1.
 9
 9
 2
 1
 .9
 9
 2
 1
 .3
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 0
 0
 0
 1
 0
 0
 0
 1
 0
 0
 0
 1
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 1
 1
 0
 1
 1
 0
 1
 1
 0
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 1
 2
 1
 1
 -1
 -0.
 3
 3
 1
 0
 .1
 9
 2
 0
 .1
 4
 3
 -1
 1
 2
 1
 -1
 1
 0
 0
 0
 1
 -1
 2
 -1
 1
 1
 0
 0
 0
 1
 1
 -2
 1
 1
 1
 0
 .3
 3
 1
 -0.
 1
 9
 -0.
 1
 4
 3
 1
 2
 1
 1
 -1
 1
 -0.
 4
 1
 3
 0
 .8
 6
 6
 -0.
 4
 2
 3
 -1
 2
 1
 1
 1
 -1
 -0.
 2
 4
 9
 -0.
 4
 8
 0
 .7
 1
 1
 -2
 1
 1
 1
 1
 -0.
 0
 8
 2
 0
 .6
 7
 4
 -0.
 5
 6
 7
 1
 2
 -1
 -1
 1
 1
 -0.
 5
 8
 -0.
 2
 9
 0
 .8
 5
 3
 2
 1
 1
 -1
 1
 1
 -0.
 5
 8
 -0.
 2
 9
 0
 .8
 5
 3
 -2
 1
 1
 1
 1
 1
 -0.
 2
 4
 9
 -0.
 4
 8
 0
 .7
 1
 2
 -1
 1
 1
 1
 -1
 -0.
 0
 8
 2
 0
 .6
 7
 4
 -0.
 5
 6
 7
 2
 1
 -1
 1
 -1
 1
 -0.
 4
 1
 3
 0
 .8
 6
 6
 -0.
 4
 2
 3
 147
Bas
 a
 l 
S
 lip i
 n
  A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I
 I
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
s
 lip 
d
 ir
 e
 c
 ti
 o
 n
 1
 1
 -2
 0
 1
 -2
 1
 0
 -2
 1
 1
 0
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
  
0
 .2
 6
 -0.
 2
 6
 -3.
 0
 7
 1
 .7
 3
 2
 -1.
 7
 3
 2
 1
 .7
 3
 2
 -1.
 9
 9
 2
 1
 .9
 9
 2
 1
 .3
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 lip 
p
 la
 n
 e 
in 
a
 lp
 h
 a
 0
 0
 0
 1
 0
 0
 0
 1
 0
 0
 0
 1
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 1
 1
 0
 1
 1
 0
 1
 1
 0
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 0
 1
 1
 1
 -1
 -0.
 2
 3
 8
 0
 .5
 -0.
 2
 4
 4
 1
 0
 1
 -1
 1
 1
 -0.
 3
 3
 5
 -0.
 1
 7
 0
 .4
 9
 3
 -1
 0
 1
 1
 -1
 1
 0
 .2
 3
 8
 -0.
 5
 0
 .2
 4
 4
 -1
 0
 1
 1
 1
 1
 -0.
 3
 3
 5
 -0.
 1
 7
 0
 .4
 9
 3
 1
 1
 0
 1
 -1
 1
 -0.
 4
 7
 6
 1
 -0.
 4
 8
 9
 1
 1
 0
 -1
 1
 1
 -0.
 6
 7
 -0.
 3
 3
 0
 .9
 8
 5
 -1
 1
 0
 1
 1
 -1
 -0.
 0
 9
 7
 -0.
 6
 7
 0
 .7
 3
 7
 -1
 1
 0
 1
 1
 1
 -0.
 0
 9
 7
 -0.
 6
 7
 0
 .7
 3
 7
 0
 1
 1
 1
 1
 -1
 -0.
 3
 3
 5
 -0.
 1
 7
 0
 .4
 9
 3
 0
 1
 1
 1
 -1
 1
 -0.
 2
 3
 8
 0
 .5
 -0.
 2
 4
 4
 0
 -1
 1
 -1
 1
 1
 0
 .3
 3
 5
 0
 .1
 6
 7
 -0.
 4
 9
 3
 0
 -1
 1
 1
 1
 1
 -0.
 2
 3
 8
 0
 .5
 -0.
 2
 4
 4
 148
1
 0
 1
 2
  T
 w
 in
 n
 in
 g
  in 
A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  Beta 
T
 w
 ins
  
A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 1
 0
 -1
 1
 -1
 0
 1
 1
 0
 1
 -1
 1
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 1
 .8
 8
 2
 0
 .3
 8
 1
 -1.
 4
 7
 0
 .3
 8
 1
 1
 .8
 8
 2
 1
 .4
 7
 2
 0
 .6
 4
 1
 1
 .6
 2
 2
 -1.
 6
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 -1
 0
 1
 2
 1
 0
 -1
 2
 0
 -1
 1
 2
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 0
 .5
 7
 5
 2
 .0
 7
 6
 2
 1
 .4
 7
 2
 2
 .0
 7
 6
 0
 .5
 7
 5
 -1.
 4
 7
 1
 .8
 1
 7
 0
 .8
 3
 5
 1
 .6
 V
 e
 c
 tor
 s
  o
 f t
 w
 in
 n
 in
 g
  s
 h
 e
 ar d
 ir
 e
 c
 ti
 o
 n
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 3
 3
 -2
 1
 1
 3
 0
 .5
 9
 1
 0
 .6
 7
 2
 0
 .6
 6
 2
 3
 -3
 2
 -1
 1
 3
 0
 .1
 8
 8
 0
 .1
 8
 8
 -0.
 4
 9
 8
 -3
 3
 2
 1
 -1
 3
 -0.
 4
 4
 2
 -0.
 4
 4
 -0.
 0
 3
 2
 3
 3
 2
 1
 1
 -3
 0
 .6
 7
 2
 0
 .5
 9
 1
 0
 .7
 5
 4
 3
 -2
 3
 1
 3
 1
 0
 .0
 7
 1
 0
 .0
 9
 3
 -0.
 0
 2
 9
 3
 2
 -3
 -1
 3
 1
 0
 .7
 5
 2
 0
 .8
 0
 .3
 0
 6
 3
 2
 3
 1
 -3
 1
 -0.
 1
 6
 2
 -0.
 2
 2
 -0.
 7
 3
 3
 -3
 2
 3
 1
 3
 -1
 -0.
 1
 9
 2
 -0.
 0
 6
 -0.
 0
 2
 3
 -2
 3
 3
 3
 1
 1
 0
 .0
 6
 2
 0
 .1
 9
 2
 -0.
 0
 2
 6
 2
 3
 3
 -3
 1
 1
 -0.
 8
 -0.
 7
 5
 -0.
 2
 6
 3
 2
 3
 -3
 3
 -1
 1
 0
 .2
 2
 1
 0
 .1
 6
 2
 0
 .7
 0
 3
 2
 -3
 3
 3
 1
 -1
 -0.
 0
 9
 3
 -0.
 0
 7
 -0.
 0
 9
 3
 149
1
 0
 1
 2
  T
 w
 in
 n
 in
 g
  in 
A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  Beta 
T
 w
 ins 
(co
 n
 tin
 u
 ed
 )
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 0
 -1
 1
 1
 1
 -1
 0
 1
 -1
 1
 0
 1
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 1
 .6
 2
 2
 0
 .6
 4
 0
 5
 1
 .6
 0
 2
 2
 .3
 7
 3
 -0.
 1
 1
 0
 .1
 3
 -0.
 1
 1
 2
 .3
 7
 3
 -0.
 1
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 0
 1
 -1
 2
 -1
 1
 0
 2
 1
 -1
 0
 2
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 0
 .8
 3
 5
 1
 .8
 1
 6
 7
 -1.
 6
 0
 .0
 8
 5
 2
 .5
 6
 7
 -0.
 1
 3
 2
 .5
 6
 7
 0
 .0
 8
 5
 0
 .1
 V
 e
 c
 tor
 s
  o
 f t
 w
 in
 n
 in
 g
  s
 h
 e
 ar d
 ir
 e
 c
 ti
 o
 n
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 3
 3
 -2
 1
 1
 3
 0
 .7
 5
 4
 0
 .3
 8
 4
 0
 .3
 7
 7
 3
 -3
 2
 -1
 1
 3
 -0.
 4
 9
 8
 0
 .3
 3
 9
 0
 .3
 3
 9
 -3
 3
 2
 1
 -1
 3
 -0.
 0
 3
 2
 0
 .4
 3
 4
 0
 .4
 3
 4
 3
 3
 2
 1
 1
 -3
 0
 .6
 6
 2
 0
 .3
 7
 7
 0
 .3
 8
 4
 3
 -2
 3
 1
 3
 1
 0
 .0
 9
 3
 0
 .5
 0
 1
 0
 .4
 0
 3
 3
 2
 -3
 -1
 3
 1
 0
 .2
 6
 3
 0
 .3
 5
 6
 0
 .4
 4
 8
 3
 2
 3
 1
 -3
 1
 -0.
 7
 0
 3
 -0.
 4
 4
 -0.
 5
 3
 5
 -3
 2
 3
 1
 3
 -1
 0
 .0
 2
 6
 -0.
 4
 9
 -0.
 4
 0
 3
 -2
 3
 3
 3
 1
 1
 0
 .0
 2
 3
 0
 .4
 0
 3
 0
 .4
 8
 8
 2
 3
 3
 -3
 1
 1
 -0.
 3
 0
 6
 -0.
 4
 5
 -0.
 3
 5
 6
 2
 3
 -3
 3
 -1
 1
 0
 .7
 3
 3
 0
 .5
 3
 5
 0
 .4
 4
 4
 2
 -3
 3
 3
 1
 -1
 0
 .0
 2
 9
 -0.
 4
 -0.
 5
 0
 1
 150
1
 0
 1
 2
  T
 w
 in
 n
 in
 g
  in 
A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 1
 0
 -1
 1
 -1
 0
 1
 1
 0
 1
 -1
 1
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 1
 .8
 8
 2
 0
 .3
 8
 1
 -1.
 4
 7
 0
 .3
 8
 1
 1
 .8
 8
 2
 1
 .4
 7
 2
 0
 .6
 4
 1
 1
 .6
 2
 2
 -1.
 6
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 -1
 0
 1
 2
 1
 0
 -1
 2
 0
 -1
 1
 2
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 0
 .5
 7
 5
 2
 .0
 7
 6
 2
 1
 .4
 7
 2
 2
 .0
 7
 6
 0
 .5
 7
 5
 -1.
 4
 7
 1
 .8
 1
 7
 0
 .8
 3
 5
 1
 .6
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 1
 2
 1
 1
 -1
 0
 .7
 5
 0
 .7
 9
 3
 0
 .8
 4
 1
 -1
 1
 2
 1
 -1
 1
 0
 .0
 0
 9
 0
 .0
 0
 9
 -0.
 4
 4
 6
 1
 -1
 2
 -1
 1
 1
 -0.
 3
 2
 1
 -0.
 3
 2
 -0.
 2
 0
 2
 1
 1
 -2
 1
 1
 1
 0
 .7
 9
 3
 0
 .7
 5
 0
 .8
 8
 9
 1
 2
 1
 1
 -1
 1
 0
 .0
 0
 5
 0
 .0
 0
 4
 -0.
 2
 8
 2
 -1
 2
 1
 1
 1
 -1
 0
 .5
 9
 0
 .6
 7
 7
 0
 .2
 5
 9
 1
 -2
 1
 1
 1
 1
 -0.
 1
 1
 6
 -0.
 1
 6
 -0.
 6
 5
 1
 2
 -1
 -1
 1
 1
 0
 .0
 9
 6
 0
 .2
 2
 5
 0
 .0
 8
 7
 2
 1
 1
 -1
 1
 1
 -0.
 2
 2
 5
 -0.
 1
 -0.
 1
 1
 5
 -2
 1
 1
 1
 1
 1
 -0.
 6
 7
 7
 -0.
 5
 9
 -0.
 2
 3
 9
 2
 -1
 1
 1
 1
 -1
 0
 .1
 6
 0
 .1
 1
 6
 0
 .5
 8
 1
 2
 1
 -1
 1
 -1
 1
 -0.
 0
 0
 4
 -0.
 0
 1
 0
 .1
 6
 5
 151
1
 0
 1
 2
  T
 w
 in
 n
 in
 g
  in 
A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I (c
 o
 n
 tin
 u
 ed
 )
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 0
 -1
 1
 1
 1
 -1
 0
 1
 -1
 1
 0
 1
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 1
 .6
 2
 2
 0
 .6
 4
 0
 5
 1
 .6
 0
 2
 2
 .3
 7
 3
 -0.
 1
 1
 0
 .1
 3
 -0.
 1
 1
 2
 .3
 7
 3
 -0.
 1
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 0
 1
 -1
 2
 -1
 1
 0
 2
 1
 -1
 0
 2
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 0
 .8
 3
 5
 1
 .8
 1
 6
 7
 -1.
 6
 0
 .0
 8
 5
 2
 .5
 6
 7
 -0.
 1
 3
 2
 .5
 6
 7
 0
 .0
 8
 5
 0
 .1
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 1
 2
 1
 1
 -1
 0
 .8
 8
 9
 0
 .4
 6
 7
 0
 .4
 6
 3
 -1
 1
 2
 1
 -1
 1
 -0.
 4
 4
 6
 0
 .4
 4
 7
 0
 .4
 4
 7
 1
 -1
 2
 -1
 1
 1
 -0.
 2
 0
 2
 0
 .4
 9
 7
 0
 .4
 9
 7
 1
 1
 -2
 1
 1
 1
 0
 .8
 4
 1
 0
 .4
 6
 3
 0
 .4
 6
 7
 1
 2
 1
 1
 -1
 1
 -0.
 1
 6
 5
 0
 .2
 8
 2
 0
 .1
 6
 5
 -1
 2
 1
 1
 1
 -1
 0
 .2
 3
 9
 0
 .1
 4
 0
 .2
 5
 1
 -2
 1
 1
 1
 1
 -0.
 5
 8
 1
 -0.
 2
 1
 -0.
 3
 2
 6
 1
 2
 -1
 -1
 1
 1
 0
 .1
 1
 5
 -0.
 3
 -0.
 1
 9
 6
 2
 1
 1
 -1
 1
 1
 -0.
 0
 8
 7
 0
 .1
 9
 6
 0
 .3
 0
 1
 -2
 1
 1
 1
 1
 1
 -0.
 2
 5
 9
 -0.
 2
 5
 -0.
 1
 4
 2
 -1
 1
 1
 1
 -1
 0
 .6
 5
 0
 .3
 2
 6
 0
 .2
 1
 3
 2
 1
 -1
 1
 -1
 1
 0
 .2
 8
 2
 -0.
 1
 7
 -0.
 2
 8
 2
 152
1
 0
 1
 2
  T
 w
 in
 n
 in
 g
  in 
A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  I
 I
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 1
 0
 -1
 1
 -1
 0
 1
 1
 0
 1
 -1
 1
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 1
 .8
 8
 2
 0
 .3
 8
 1
 -1.
 4
 7
 0
 .3
 8
 1
 1
 .8
 8
 2
 1
 .4
 7
 2
 0
 .6
 4
 1
 1
 .6
 2
 2
 -1.
 6
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 -1
 0
 1
 2
 1
 0
 -1
 2
 0
 -1
 1
 2
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 0
 .5
 7
 5
 2
 .0
 7
 6
 2
 1
 .4
 7
 2
 2
 .0
 7
 6
 0
 .5
 7
 5
 -1.
 4
 7
 1
 .8
 1
 7
 0
 .8
 3
 5
 1
 .6
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 0
 1
 1
 1
 -1
 0
 .5
 2
 6
 0
 .5
 2
 5
 0
 .8
 2
 1
 1
 0
 1
 -1
 1
 1
 -0.
 3
 1
 5
 -0.
 2
 4
 -0.
 1
 8
 3
 -1
 0
 1
 1
 -1
 1
 0
 .0
 0
 8
 0
 .0
 0
 8
 -0.
 3
 5
 3
 -1
 0
 1
 1
 1
 1
 -0.
 8
 4
 9
 -0.
 7
 7
 -0.
 6
 5
 1
 1
 1
 0
 1
 -1
 1
 7
 E
 -0
 4
 -0
 -0.
 0
 6
 8
 1
 1
 0
 -1
 1
 1
 -0.
 0
 7
 5
 0
 .0
 7
 5
 -0.
 0
 1
 6
 -1
 1
 0
 1
 1
 -1
 0
 .2
 4
 8
 0
 .3
 2
 4
 -0.
 1
 8
 6
 -1
 1
 0
 1
 1
 1
 -0.
 3
 2
 4
 -0.
 2
 5
 0
 .2
 3
 7
 0
 1
 1
 1
 1
 -1
 0
 .7
 7
 4
 0
 .8
 4
 9
 0
 .6
 3
 5
 0
 1
 1
 1
 -1
 1
 0
 .0
 0
 8
 0
 .0
 0
 8
 -0.
 4
 2
 0
 -1
 1
 -1
 1
 1
 -0.
 2
 4
 -0.
 3
 2
 -0.
 1
 6
 7
 0
 -1
 1
 1
 1
 1
 -0.
 5
 2
 5
 -0.
 5
 3
 -0.
 8
 8
 9
 153
1
 0
 1
 2
  T
 w
 in
 n
 in
 g
  in 
A
 lp
 h
 a - Resol
 v
 ed 
S
 h
 e
 a
 r 
S
 tr
 e
 s
 s o
 n
  M
 a
 rt
 ensi
 te 
S
 h
 e
 a
 r 
S
 y
 ste
 m
  II
  (
 co
 n
 tin
 u
 ed
 )
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 A
 lp
 h
 a 
tw
 in
 n
 in
 g
  d
 ir
 e
 c
 ti
 o
 n
 0
 -1
 1
 1
 1
 -1
 0
 1
 -1
 1
 0
 1
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 P
 ara
 lle
 l d
 ir
 e
 c
 ti
 o
 n
  i
 n 
b
 et
 a
 1
 .6
 2
 2
 0
 .6
 4
 0
 5
 1
 .6
 0
 2
 2
 .3
 7
 3
 -0.
 1
 1
 0
 .1
 3
 -0.
 1
 1
 2
 .3
 7
 3
 -0.
 1
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 S
 h
 e
 ar p
 la
 n
 e 
in 
a
 lp
 h
 a
 0
 1
 -1
 2
 -1
 1
 0
 2
 1
 -1
 0
 2
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 P
 ara
 lle
 l p
 la
 n
 e 
in 
b
 et
 a
 0
 .8
 3
 5
 1
 .8
 1
 6
 7
 -1.
 6
 0
 .0
 8
 5
 2
 .5
 6
 7
 -0.
 1
 3
 2
 .5
 6
 7
 0
 .0
 8
 5
 0
 .1
 V
 e
 c
 tor
 s
  o
 f 
m
 arten
 s
 ite
  s
 h
 e
 ar 
s
 ys
 te
 m
  I
 I
 P
 la
 n
 e
 D
 ir
 e
 c
 ti
 o
 n
 1
 0
 1
 1
 1
 -1
 0
 .8
 8
 9
 0
 .4
 5
 8
 0
 .3
 9
 1
 0
 1
 -1
 1
 1
 -0.
 1
 6
 7
 0
 .4
 0
 .4
 6
 1
 -1
 0
 1
 1
 -1
 1
 -0.
 4
 2
 0
 .3
 5
 4
 0
 .4
 2
 1
 -1
 0
 1
 1
 1
 1
 -0.
 6
 3
 5
 -0.
 4
 1
 -0.
 3
 5
 1
 1
 1
 0
 1
 -1
 1
 0
 .0
 6
 8
 0
 .0
 6
 8
 -0.
 0
 6
 8
 1
 1
 0
 -1
 1
 1
 0
 .0
 1
 6
 -0.
 0
 6
 0
 .0
 6
 1
 -1
 1
 0
 1
 1
 -1
 -0.
 2
 3
 7
 -0.
 1
 1
 0
 .0
 2
 1
 -1
 1
 0
 1
 1
 1
 0
 .1
 8
 6
 -0.
 0
 2
 0
 .1
 0
 7
 0
 1
 1
 1
 1
 -1
 0
 .6
 5
 1
 0
 .3
 5
 1
 0
 .4
 1
 2
 0
 1
 1
 1
 -1
 1
 -0.
 3
 5
 3
 0
 .4
 2
 1
 0
 .3
 5
 4
 0
 -1
 1
 -1
 1
 1
 -0.
 1
 8
 3
 0
 .4
 6
 1
 0
 .4
 0
 -1
 1
 1
 1
 1
 -0.
 8
 2
 1
 -0.
 3
 9
 -0.
 4
 5
 8
 154
155 
 
Appendix H 
Compliance Tensors of ? and ? Titanium 
 
The original compliance tensor for ?-Ti in units of 10-11 Pa-1 is: 
 
0.9581  -0.4623 -0.1893  0 0 0 
 0.9581  -0.1893  0 0 0 
  0.6980  2.141 0 0 
   2.141 0 0 
    2.141 0 
     2.938  
 
The original compliance tensor for ?-Ti in units of 10-11 Pa-1 is: 
 
1.857  -0.774  -0.774  0 0 0 
 1.857  -0.774  0 0 0 
  1.857  0 0 0 
   2.342 0 0 
    2.342 0 
     2.342 
 
 
156 
 
The transformed compliance tensor for ?-Ti in units of 10-11 Pa-1 for the bi-crystal model 
is: 
 
0.9581  -0.1893  -0.4623 0 0 0 
 0.6980  -0.1893  0 0 0 
  0.9581  0 0 0 
   2.141 0 0 
    2.8408  0 
     2.1410 
 
The transformed compliance tensor for the twinned ?-Ti in units of 10-11 Pa-1 for the bi-
 crystal model is: 
 
0.9581  -0.4623 -0.1893  0 0 0 
 0.9581  -0.4623 0 0 0 
  0.9581  0 0 0 
   2.1410 0 0 
    2.2948  0 
     2.1410 
 
 
 
157  
 
The transformed compliance tensor for ?-Ti in units of 10-11 Pa-1 for the bi-crystal model 
is: 
 
0.9445 -0.4090 -0.2265 0 -0.3650 0 
 1.1270  -0.4090 0 0.7300  0 
  0.9445 0 -0.3650 0 
   3.8020  0 1.460 
    4.532 0 
     2.342 
 
158  
 
Appendix I  
Transformation Equations for Cubic Crystals  
Direction Cosines: 
 
   x y z 
  ?? l1 m1 n1 
  y? l2 m2 n2 
  ?? l3 m3 n3 
 
 
Transformation Equations: 
???????????
 ???
 ?
  
???
 ? ???????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ??????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ??????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ???????????
 ????????
 ????????
 ?? 
???
 ? ???????
 ??????
 ??????
 ???? 
???
 ? ???????
 ??????
 ??????
 ???? 
???
 ? ???????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ??????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ???????
 ??????
 ??????
 ???? 
???
 ? ?????????
 ????????
 ????????
 ???? 
???
 ? ???????
 ??????
 ??????
 ???? 
159 
 
???
 ? ???????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ???????
 ??????
 ??????
 ???? 
???
 ? ???????
 ??????
 ??????
 ???? 
???
 ? ?????????
 ????????
 ????????
 ???? 
???
 ? ???????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ???????????
 ????????
 ????????
 ?? 
???
 ? ???????????
 ????????
 ????????
 ?? 
???
 ? ???????????
 ???
 ????
 ???
 ????
 ???
 ?? 
???
 ? ???????????
 ????????
 ????????
 ?? 
???
 ? ???????????
 ????????
 ????????
 ?????? 
  
160 
 
Transformation Equations for Hexagonal Crystals  
 
Direction Cosines: 
 
   x y z 
  ?? l1 m1 n1 
  y? l2 m2 n2 
  ?? l3 m3 n3 
 
 
Transformation Equations: 
???????????????????? 
????????????
 ???
 ?
 ? 
???
 ? ?????????
 ???????
 ? 
???
 ? ?????????
 ???
 ???????????????
 ??????
 ? 
???
 ? ?????????
 ???
 ???????????????
 ??????
 ? 
???
 ? ???????
 ?????????????????????????????????????? 
???
 ? ???????
 ??????????? 
???
 ? ???????
 ??????????? 
???
 ? ?????????
 ???????
 ? 
???
 ? ?????????
 ???
 ???????????????
 ??????
 ? 
???
 ? ???????
 ??????????? 
???
 ? ???????
 ?????????????????????????????????????? 
161 
 
???
 ? ???????
 ??????????? 
???
 ? ?????????
 ???????
 ? 
???
 ? ???????
 ??????????? 
???
 ? ???????
 ??????????? 
???
 ? ???????
 ?????????????????????????????????????? 
???
 ? ??????????
 ???
 ??????????????????????
 ??????
 ? 
???
 ? ??????????
 ????????????????????????????????? 
  ?????????????? 
???
 ? ??????????
 ????????????????????????????????? 
  ?????????????? 
 ???
 ? ??????????
 ???
 ??????????????????????
 ??????
 ? 
???
 ? ??????????
 ????????????????????????????????? 
  ?????????????? 
???
 ? ??????????
 ???
 ??????????????????????
 ??????
 ? 
 
162 
 
Appendix J  
 
ANSYS Operating Instructions for Simple Model Development  
 
 
The following steps were used to build this model and run the simulation 
 
1) Define Element Type 
Preprocessor > Element Type > Add/Edit/Delete  
The element type SOLID185  was selected. 
 
2) Set Material Properties 
Preprocessor > Material Props > Material Model  
The elastic, linear, anisotropic model was selected. ??aterial ?? was set to the 
properties of the ? phase. ??aterial ?? was set to the properties of the ? phase.  
??aterial ?? was set to the properties of the ? twin. 
 
3) Create Volumes 
Preprocessor>Modeling>Create>Volumes > By Keypoints  
 
4) Glue Areas 
Preprocessor>Modeling>Operate>Booleans>Glue>Areas  
The two areas created in step 3 were glued together to avoid issues with Node 
overlap. 
 
5) Set Material Properties 
Preprocessor>Meshing>Mesh Attributes>Picked Areas  
Each area was picked separately and set to the material properties as listed above. 
 
6) Create Mesh 
Preprocessor > Meshing > Mesh Tool  
The mesh tool was used to auto-generate the mesh for the piece. 
 
7)  Set Constrains 
Preprocessor > Coupling/Ceqn > Couple DOFs  
 
8)  Define Loads and Displacements 
Solution > Define Loads > Apply > On Nodes  
 
9) Solve 
Solution>Solve  
 
163 
 
References 
 
1. Collings, E.W., The Physical Metallurgy of Titanium Alloys. 1984, Metals Park, 
OH: American Society for Metals. 
2. Elliot, P., Constitution of Binary Alloys, First Supplement. 1965, New York: 
McGraw-Hill Inc. 617.  
3. Grewal, G. and S. Ankem, Solubility of Vanadium in Alpha-Titanium and Beta-
 Titanium. Metallurgical Transactions a-Physical Metallurgy and Materials 
Science, 1989. 20 (2): p. 334-337.  
4. Ankem, S., et al., Mechanical properties of alloys consisting of two ductile 
phases. Progress in Materials Science, 2006. 51 (5): p. 632-709.  
5. Neuberger, B.W., Greene, C., Gute, G., Creep Analyses of Titanium Drip Shield 
Subjected to Rockfall Static Loads in the Proposed Geologic Repository at Yucca 
Mountain. Mat. Res. Soc. Symp. Proc., 2002. 716 : p. JJ11.7.1 -JJ11.7.8.  
6. Air Force Technology F-35 Lightning II. ? Lockheed Martin Aeronautics 
Company  2011; Available from: http://www.airforce -
 technology.com/projec ts/jsf/ . 
7.  F-22 Raptor Team Website. ? Lockheed Martin Aeronautics Company  2009; 
Available from: http://www.f22 -raptor.com/ . 
8.  Akahori, T., et al., Improvement in fatigue characteristics of newly developed beta 
type titanium alloy for biomedical applications by thermo-mechanical treatments. 
Materials Science & Engineering C -Biomimetic and Supramolecular Systems, 
2005. 25 (3): p. 248 -254. 
9. Ankem, S., Unpublished Research. University of Maryland, College Park, 2008. 
Patent Pending . 
10. Cachinho, S.C.P. and R.N. Correia, Titanium scaffolds for osteointegration: 
mechanical, in vitro and corrosion behaviour. Journal of Materials Science -
 Materials in Medicine, 2008. 19 (1): p. 451-457.  
11. Geetha, M., et al., Ti based biomaterials, the ultimate choice for orthopaedic 
implants - A review. Progress in Materials Science, 2009. 54 (3): p. 397 -425. 
12. Rack, H.J. and J.I. Qazi, Titanium alloys for biomedical applications. Materials 
Science & Engineering C -Biomimetic and Supramolecular Systems, 2006. 26 (8): 
p. 1269-1277.  
164 
 
13. Yamamoto, O., Alvarez, K., Kikuchi, T., Fukuda, M., Fabrication and 
characterization of oxygen-diffused titanium for biomedical applications. Acta 
Biomaterialia, 2009. 5 : p. 3605-3615. 
14. Yamada, T., Kawab ata, K., Sato, E., Kuribayashi, K., Jimbo, I., Presences of 
primary creep in various phase metals and alloys at ambient temperature. 
Materials Science and Engineering A, 2004. 387 - 3 89 : p. 719 -722.  
15. Aiyangar, A.K., et al., The effects of stress level and grain size on the ambient 
temperature creep deformation behavior of an alpha Ti-1.6 wt pct V alloy. 
Metallurgical and Materials Transactions a-Physical Metallurgy and Materials 
Science, 2005. 36A (3): p. 637 -644. 
16. Ankem, S., C.A. Greene, and S. Singh, Time-Dependent Twinning during 
Ambient-Temperature Creep of Alpha-Ti-Mn Alloy. Scripta Metallurgica Et 
Materialia, 1994. 30 (6): p. 803 -808.  
17.  Doraiswamy, D. and S. Ankem, The effect of grain size and stability on ambient 
temperature tensile and creep deformation in metastable beta titanium alloys. 
Acta Materialia, 2003. 5 1 (6): p. 1607 -1619. 
18.  Greene, C.A., Ankem, S., Ambient Temperature Tensile and Creep Deformation 
Behavior of Alpha and Beta Titanium Alloys. Beta Titanium Alloys in the 1990's, 
ed. D. Eylon, Boyer, R.R., and Koss, D.A. 1993: TMS.  
19. Greene, C.A., Ankem, S., Singh, S., The Effect of Morphology and Alloying 
Elements on the Ambient Temperature Creep of Alpha and Alpha-Beta Titanium 
Alloys. Proceedings of the Eighth World Conference on Titanium, 1995. 
II(Birmingham, U.K., Eds. P.A. Blenkinshop, W.J. Evans, and H.M. Flower): p. 
1315-1322. 
20. Hultgren, C.A., C.A. Greene, and S. Ankem, Time-dependent twinning during 
ambient temperature compression creep of alpha Ti-0.4Mn alloy. Metallurgical 
and Materials Transactions a-Physical Metallurgy and Materials Science, 1999. 
30 (6): p. 1675 -1679.  
21. Jaworski, A. and S. Ankem, Influence of the second phase on the room-
 temperature tensile and creep deformation mechanisms of alpha-beta titanium 
alloys: Part I. Tensile deformation. Metallurgical and Materials Transactions a-
 Physical Metallurgy and Materials Science, 2006. 37A (9): p. 2739 -2754.  
22. Jaworski, A. and S. Ankem, Influence of the second phase on the room-
 temperature tensile and creep deformation mechanisms of alpha-beta titanium 
alloys, Part II: Creep deformation. Metallurgical and Materials Transactions a-
 Physical Metallurgy and Materials Science, 2006. 37A (9): p. 2755 -2765.  
23. Oberson, P.G. and S. Ankem, Why twins do not grow at the speed of sound all the 
time. Physical Review Letters, 2005. 95 (16): p. -. 
165 
 
24. Oberson, P.G. and S. Ankem, The effect of time-dependent twinning on low 
temperature (< 0.25*T-m) creep of an alpha-titanium alloy. International Journal 
of Plasticity, 2009. 25 (5): p. 881 -900. 
25. Ramesh, A. and S. Ankem, The effect of grain size on the ambient temperature 
creep deformation behavior of a beta Ti-14.8 V alloy. Metallurgical and Materials 
Transactions a-Physical Metallurgy and Materials Science, 2002. 33 (4): p. 1137 -
 1144. 
26. Ankem, S. and H. Margolin, A Rationalization of Stress-Strain Behavior of 2-
 Ductile Phase Alloys. Metallurgical Transactions a-Physical Metallurgy and 
Materials Science, 1986. 17 (12): p. 2209-2226. 
27.  Andenstedt, H., Creep of Titanium at Room Temperature. Metal Progress, 1949. 
56 : p. 658.  
28.  Luster, D.R., Wentz, W.W., Kaufman, D.W., Creep Properties of Titanium. 
Materials and Methods, 1953. 37 : p. 100. 
29. Thompson, A.W. and B.C. Odegard, Influence of Microstructure on Low-
 Temperature Creep of Ti-5 Al-2.5 Sn. Metallurgical Transactions, 1973. 4 (4): p. 
899 -908.  
30. Chu, H.P., Room Temperature Creep and Stress Relaxation of a Titanium Alloy. 
Journal of Materials, 1970. 5 : p. 633. 
31. Imam, M.A. and C.M. Gilmore, Room-Temperature Creep of Ti-6al-4v. 
Metallurgical Transactions a-Physical Metallurgy and Materials Science, 1979. 
10 (4): p. 419-425. 
32. Miller, W.H., R.T. Chen, and E.A. Starke, Microstructure, Creep, and Tensile 
Deformation in Ti-6al-2nb-1ta-0.8mo. Metallurgical Transactions a-Physical 
Metallurgy and Materials Science, 1987. 18 (8): p. 1451 -1468.  
33. Neeraj, T., et al., Phenonomenological and microstructural analysis of room 
temperature creep in titanium alloys. Acta Materialia, 2000. 48 (6): p. 1225-1238.  
34. Odegard, B.C. and A.W. Thompson, Low-Temperature Creep of Ti-6 Al-4 V. 
Metallurgical Transactions, 1974. 5 (5): p. 1207 -1213. 
35. Suri, S., et al., Mechanisms of primary creep in alpha/beta titanium alloys at 
lower temperatures. Materials Science and Engineering a-Structural Materials 
Properties Microstructure and Processing, 1997. 2 34 : p. 996-999. 
36. Suri, S., et al., Room temperature deformation and mechanisms of slip 
transmission in oriented single-colony crystals of an alpha/beta titanium alloy. 
Acta Materialia, 1999. 4 7 (3): p. 1019-1034. 
166 
 
37.  Greene, C.A., Fundamental Studies on the Ambient Temperature Creep 
Deformation Behavior of Alpha, Beta, and Alpha-Beta Titanium Alloys, in 
Department of Materials Science and Engineering. 1994, University of Maryland, 
College Park: College Park, MD. p. 92. 
38.  Huang, C. and M.H. Loretto, The Microstructure and Creep-Behavior of Ti-25al-
 10nb-3v-1mo (Super a(2)). Materials Science and Engineering a-Structural 
Materials Properties Microstructure and Processing, 1995. 193 : p. 722 -728.  
39. Ponsonnet, L., C. Quesne, and R. Penelle, Microstructure and creep deformation 
of a near beta titanium alloy 'beta-CEZ'. Materials Science and Engineering a-
 Structural Materials Properties Microstructure and Processing, 1999. 262 (1-2): p. 
50-63. 
40. Viswanathan, G.B., et al., Creep behaviour of Ti-6Al-2Sn-4Zr-2Mo: II. 
Mechanisms of deformation. Acta Materialia, 2002. 50 (20): p. 4965-4980.  
41. Ankem, S. and H. Margolin, Alpha-Beta Interface Sliding in Ti-Mn Alloys. 
Journal of Metals, 1980. 32 (12): p. 38 -38.  
42. Christian, J.W. and S. Mahajan, Deformation Twinning. Progress in Materials 
Science, 1995. 39 (1-2): p. 1-157.  
43. Song, S.G. and G.T. Gray, Structural Interpretation of the Nucleation and Growth 
of Deformation Twins in Zr and Ti .1. Application of the Coincidence Site Lattice 
(Csl) Theory to Twinning Problems in Hcp Structures. Acta Metallurgica Et 
Materialia, 1995. 43 (6): p. 2325-2337.  
44. Song, S.G. and G.T. Gray, Structural Interpretation of the Nucleation and Growth 
of Deformation Twins in Zr and Ti .2. Tem Study of Twin Morphology and Defect 
Reactions during Twinning. Acta Metallurgica Et Materialia, 1995. 43 (6): p. 
2339-2350. 
45. Oberson, P.G., Z.W. Wyatt, and S. Ankem, Modeling interstitial diffusion 
controlled twinning in alpha titanium during low-temperature creep. Scripta 
Materialia, 2011. 65 : p. 638 -641. 
46. Liu, Z. and G. Welsch, Literature Survey on Diffusivities of Oxygen, Aluminum, 
and Vanadium in Alpha-Titanium, Beta-Titanium, and in Rutile. Metallurgical 
Transactions a-Physical Metallurgy and Materials Science, 1988. 19 (4): p. 1121-
 1124. 
47.  Aiyangar, A.K., et al., The effects of stress level and grain size on the ambient 
temperature creep deformation behavior of an alpha Ti-1.6 wt pct V alloy. 
Metallurgical and Materials Transactions A, 2005. 36A (3): p. 637 -644. 
167  
 
48.  Gray, G.T., et al., Influence of strain rate & temperature on the mechanical 
response of ultrafine-grained Cu, Ni, AND Al-4Cu-0.5Zr. Nanostructured 
Materials, 1997. 9 (1-8): p. 477 -480.  
49. Grosdidier, T., et al., Effect of microstructure variations on the formation of 
deformation-induced martensite and associated tensile properties in a beta 
metastable Ti alloy. Metallurgical and Materials Transactions A, 2000. 31 (4): p. 
1095-1106. 
50. Meyers, M.A., O. Vohringer, and V.A. Lubarda, The onset of twinning in metals: 
A constitutive description. Acta Materialia, 2001. 49 (19): p. 4025-4039. 
51. Ramesh, A. and S. Ankem, The effect of grain size on the ambient temperature 
creep deformation behavior of a beta Ti-14.8 V alloy. Metallurgical and Materials 
Transactions A, 2002. 33 (4): p. 1137 -1144. 
52. Thompson, A.W. and B.C. Odegard, Influence of Microstructure on Low-
 Temperature Creep of Ti-5 Al-2.5 Sn. Metallurgical Transactions A, 1973. 4 (4): p. 
899 -908.  
53. Wyatt, Z.W. and S. Ankem, Advances in Low Temperature (<0.25Tm) Creep 
Deformation Mechanisms of alpha, alpha + beta, and beta Titanium Alloys. The 
Proceedings of the 12th World Conference on Titanium, 2011. 
54. Edington, J.W., Practical Electron Microscopy in Materials Science. Out of Print 
ed. 1976, Marietta, OH: CBLS Publisher & Book Distributor. 344.  
55. Dieter, E., Mechanical Metallurgy. Third Edition. 1986, New York: McGraw -Hill 
Book Company. 439. 
56. Chichili, D.R., K.T. Ramesh, and K.J. Hemker, The high-strain-rate response of 
alpha-titanium: Experiments, deformation mechanisms and modeling. Acta 
Materialia, 1998. 46 (3): p. 1025-1043. 
57.  Nemat-Nasser, S., W.G. Guo, and J.Y. Cheng, Mechanical properties and 
deformation mechanisms of a commercially pure titanium. Acta Materialia, 1999. 
47 (13): p. 3705 -3720.  
58.  Ramesh, K.T., Effects of high rates of loading on the deformation behavior and 
failure mechanisms of hexagonal close-packed metals and alloys. Metallurgical 
and Materials Transactions a-Physical Metallurgy and Materials Science, 2002. 
33 (3): p. 927 -935. 
59. Zhou, W. and K.G. Chew, The rate dependent response of a titanium alloy 
subjected to quasi-static loading in ambient environment. Journal of Materials 
Science, 2002. 37 (23): p. 5159-5165. 
168  
 
60. Zeng, Z.P., S. Jonsson, and  H.J. Roven, The effects of deformation conditions on 
microstructure and texture of commercially pure Ti. Acta Materialia, 2009. 
57 (19): p. 5822 -5833.  
61. Conrad, H., Effect of Interstitial Solutes on the Strength and Ductility of Titanium. 
Progress in Materials Science, 1981. 26 (2-4): p. 123-404. 
62. Williams, J.C., R.G. Baggerly, and N.E. Paton, Deformation behavior of HCPTi-
 Al alloy single crystals. Metallurgical and Materials Transactions a-Physical 
Metallurgy and Materials Science, 2002. 33 (3): p. 837 -850.  
63. Zaefferer, S., A study of active deformation systems in titanium alloys: 
dependence on alloy composition and correlation with deformation texture. 
Materials Science and Engineering a-Structural Materials Properties 
Microstructure and Processing, 2003. 344 (1-2): p. 20-30. 
64. Dieter, G.E., Mechanical Metallurgy. 1988, London: McGraw -Hill Book Co. 708.  
65. Reed-Hill, R., Abbaschian, R., Physical Metallurgy Principles. 1992, Boston: 
PWS-Kent.  
66. Song, S.G. and G.T. Gray, Influence of Temperature and Strain-Rate on Slip and 
Twinning Behavior of Zr. Metallurgical and Materials Transactions a-Physical 
Metallurgy and Materials Science, 1995. 26 (10): p. 2665-2675.  
67.  Shan, Z.W., et al., The effect of twin plane spacing on the deformation of copper 
containing a high density of growth twins. Jom, 2008. 60 (9): p. 71 -74.  
68.  Charit, I., S. Gollapudi, and K.L. Murty, Creep mechanisms in TI-3Al-2.5V alloy 
tubing deformed under closed-end internal gas pressurization. Acta Materialia, 
2008. 56 (10): p. 2406-2419. 
69. Savrun, E., W.D. Scott, and D.C. Harris, The effect of titanium doping on the 
high-temperature rhombohedral twinning of sapphire. Journal of Materials 
Science, 2001. 36 (9): p. 2295-2301. 
70.  Yoo, M.H., Twinning and mechanical behavior of titanium aluminides and other 
intermetallics. Intermetallics, 1998. 6 (7 -8): p. 597 -602. 
71.  Karthikeyan, S. and M.J. Mills, The role of microstructural stability on 
compression creep of fully lamellar gamma-TiAl alloys. Intermetallics, 2005. 
13 (9): p. 985 -992. 
72.  Chen, M.W., et al., Deformation twinning in nanocrystalline aluminum. Science, 
2003. 300 (5623): p. 1275 -1277.  
73.  Dorosinskii, L.A., et al., Kinetics of the Changes in the Twin Structure in 
Yba2cu3o7-X Single-Crystals. Jetp Letters, 1989. 49 (3): p. 182 -18 7.  
169 
 
74.  Dorosinskii, L.A., et al., Kinetics of Twin Boundary Migration in Yba2cu3o7-X 
Single-Crystals. Physica C, 1992. 203 (3-4): p. 342-346. 
75.  Salje, E.K.H., et al., Needle twins and right-angled twins in minerals: 
Comparison between experiment and theory. American Mineralogist, 1998. 83 (7 -
 8): p. 811 -822.  
76.  Gumbsch, P. and H. Gao, Dislocations faster than the speed of sound. Science, 
1999. 283 (5404): p. 965-968.  
77.  Zerilli, F.J. and R.W. Armstrong, Dislocation mechanics based analysis of 
material dynamics behavior: Enhanced ductility, deformation twinning, shock 
deformation, shear instability, dynamic recovery. Journal De Physique Iv, 1997. 
7 (C3): p. 637 -642. 
78.  Kalidindi, S.R., Incorporation of deformation twinning in crystal plasticity 
models. Journa l of the Mechanics and Physics of Solids, 1998. 46 (2): p. 267 -+.  
79.  Tome, C.N.e.a., Symposium on HCP Metals. TMS/AIME, 2001. New Orleans . 
80.  Bevis, M. and A.G. Crocker, Twinning Shears in Lattices. Proceedings of the 
Royal Society of London Series a-Mathematical and Physical Sciences, 1968. 
304 (1476): p. 123 -&.  
81.  Partridge, P.G., The crystallography of deformation modes of hexagonal close-
 packed metals. Metallurgical Reviews, 1967. 118 : p. 169-194  
82.  Pond, R.C., et al., The Crystallography and Atomic-Structure of Line Defects in 
Twin Boundaries in Hexagonal-Close-Packed Metals. Metallurgical Transactions 
a-Physical Metallurgy and Materials Science, 1991. 22 (6): p. 1185 -1196. 
83.  Serra, A., D.J. Bacon, and R.C. Pond, The Crystallography and Core Structure of 
Twinning Dislocations in Hcp Metals. Acta Metallurgica, 1988. 36 (12): p. 3183 -
 3203. 
84.  Yoo, M.H. and J.K. Lee, Deformation Twinning in Hcp Metals and Alloys. 
Philosophical Magazine a-Physics of Condensed Matter Structure Defects and 
Mechanical Properties, 1991. 63 (5): p. 987 -1000. 
85.  McCabe, R.J., et al., Quantitative analysis of deformation twinning in zirconium. 
International Journal of Plasticity, 2009. 25 (3): p. 454-472.  
86.  Crocker, A.G., Twinned Martensite. Acta Metallurgica, 1962. 10 (Feb): p. 113-&.  
87.  Crocker, A.G.a.B., M., The Science, Technology, and Application of Titanium, ed. 
R.I.J.a.N.E. Promisel. 1968, London.  
170  
 
88.  Oberson, P.G., An Experimental and Theoretical Investigation of the Low 
Temperature Creep Deformation Behavior of Single Phase Titanium Alloys, in 
Department of Materials Science and Engineering. 2006, University of Maryland: 
College Park, Maryland, USA. p. 208.  
89.  Cerreta, E., Gray, G.T., Lawson, A.C., Morris, C.E., Mason, T.A., Hixson, R.S., 
Rigg, P.A., The Influence of Oxygen Content on the Pressure Induced Phase 
Transformation and Shock Hardening of Titanium. Journal of Applied Physics, 
2006. 100 : p. 0135301-9. 
90. Cerreta, E., et al., The influence of interstitial oxygen and peak pressure on the 
shock loading behavior of zirconium. Acta Materialia, 2005. 53 (6): p. 1751 -1758.  
91. Khan, A.S., et al., Effect of oxygen content and microstructure on the thermo-
 mechanical response of three Ti-6Al-4V alloys: Experiments and modeling over a 
wide range of strain-rates and temperatures. International Journal of Plasticity, 
2007. 23 (7): p. 1105 -1125. 
92. Greene, C.A., PhD Dissertation:  Fundamental studies on ambient temperature 
creep deformation behavior of alpha and alpha-beta titanium alloys, in 
Department of Materials Science and Engineering. 1994, University of Maryland, 
College Park: College Park, MD. 
93. Conrad, H., Rate Controlling Mechanism during Yielding and Flow of Alpha-
 Titanium at Temperatures Below 0.4 Tm. Acta Metallurgica, 1966. 14 (11): p. 
1631-&.  
94. Capolungo, L., et al., On the interaction between slip dislocations and twins in 
HCP Zr. Materials Science and Engineering a-Structural Materials Properties 
Microstructure and Processing, 2009. 513 - 14 : p. 42-51. 
95. Xiao, G.H., N.R. Tao, and K. Lu, Effects of strain, strain rate and temperature on 
deformation twinning in a Cu-Zn alloy. Scripta Materialia, 2008. 59 (9): p. 975 -
 978.  
96. Lu, K., et al., Effect of the Zener-Hollomon parameter on the microstructures and 
mechanical properties of Cu subjected to plastic deformation. Acta Materialia, 
2009. 57 (3): p. 761 -772.  
97.  Li, B. and E. Ma, Atomic Shuffling Dominated Mechanism for Deformation 
Twinning in Magnesium. Physical Review Letters, 2009. 103 (3): p. -. 
98.  Porter, D.A. and K.E. Easterling, Phase Transformations in Metals and Alloys. 
Vol. 2nd ed. 1993, London: Chapman & Hall.  
99. Moriya, N., et al., Boron-Diffusion in Strained Si1-Xgex Epitaxial Layers. 
Physical Review Letters, 1993. 71 (6): p. 883 -886.  
171  
 
100. Baumann, F.H., et al., Multilayers as Microlabs for Point-Defects - Effect of 
Strain on Diffusion in Semiconductors. Physical Review Letters, 1994. 73 (3): p. 
448 -451. 
101. Cowern, N.E.B., et al., Diffusion in Strained Si(Ge). Physical Review Letters, 
1994. 72 (16): p. 2585 -2588.  
102. Kuo, P., et al., Comparison of Boron-Diffusion in Si and Strained Si1-Xgex 
Epitaxial Layers. Applied Physics Letters, 1993. 62 (6): p. 612-614. 
103. Armstrong, R.W. and S.M. Walley, High strain rate properties of metals and 
alloys. International Materials Reviews, 2008. 53 (3): p. 105-128.  
104. Mostafa, M.M., Stress Enhanced Diffusion Process in Al-10wt-Percent Zn Alloy. 
Czechoslovak Journal of Physics, 1991. 41 (9): p. 865 -870.  
105. Nazarov, A.V. and A.A. Mikheev, Theory of diffusion under stress in interstitial 
alloys. Physica Scripta, 2004. T108 : p. 90-94. 
106. Aziz, M.J., et al., Pressure and stress effects on the diffusion of B and Sb in Si and 
Si-Ge alloys. Physical Review B, 2006. 73 (5). 
107.  Aziz, M.J., Pressure and stress effects on diffusion in Si. Defect and Diffusion 
Forum, 1998. 153 : p. 1-10. 
108.  Aziz, M.J., Thermodynamics of diffusion under pressure and stress: Relation to 
point defect mechanisms. Applied Physics Letters, 1997. 70 (21): p. 2810 -2812.  
109. Aziz, M.J., Stress effects on defects and dopant diffusion in Si. Materials Science 
in Semiconductor Processing, 2001. 4 (5): p. 397 -403. 
110. Salem, A.A., S.R. Kalidindi, and R.D. Doherty, Strain hardening of titanium: role 
of deformation twinning. Acta Materialia, 2003. 5 1 (14): p. 4225-4237.  
111. Salem, A.A., et al., Strain hardening due to deformation twinning in alpha-
 titanium: Mechanisms. Metallurgical and Materials Transactions a-Physical 
Metallurgy and Materials Science, 2006. 37A (1): p. 259-268.  
112. Salem, A.A., S.R. Kalidindi, and S.L. Semiatin, Strain hardening due to 
deformation twinning in alpha-titanium: Constitutive relations and crystal-
 plasticity modeling. Acta Materialia, 2005. 53 (12): p. 3495-3502. 
113. Mahajan, S., et al., Formation of annealing twins in f.c.c. crystals. Acta 
Materialia, 1997. 45 (6): p. 2633-2638.  
114. Pande, C.S., M.A. Imam, and B.B. Rath, Study of Annealing Twins in Fcc Metals 
and Alloys. Metallurgical Transactions a-Physical Metallurgy and Materials 
Science, 1990. 21 (11): p. 2891 -2896.  
172  
 
115. Follansbee, P.S. and G.T. Gray, An Analysis of the Low-Temperature, Low and 
High Strain-Rate Deformation of Ti-6al-4v. Metallurgical Transactions a-Physical 
Metallurgy and Materials Science, 1989. 20 (5): p. 863 -874.  
116. Wiezorek, J.M. K., et al., Deformation mechanisms in a binary Ti-48 at.%Al alloy 
with lamellar microstructure. Philosophical Magazine Letters, 1997. 75 (5): p. 
271 -280.  
117.  Bania, P.J., Beta-Titanium Alloys and Their Role in the Titanium Industry. Jom -
 Journal of the Mine rals Metals & Materials Society, 1994. 46 (7): p. 16 -19. 
118.  Brotzen, F.R., E.L. Harmon, and A.R. Troiano, Decomposition of Beta Titanium. 
Transactions of the American Institute of Mining and Metallurgical Engineers, 
1955. 203 (2): p. 413-419. 
119. Greene, C.A., Ankem, S., Beta Titanium Alloys in the 1990's, ed. D.B. Eylon, 
R.R., Koss, D.A. 1993, Warrendale, PA: TMS.  
120. Grosdidier, T., et al., Effect of microstructure variations on the formation of 
deformation-induced martensite and associated tensile properties in a beta 
metastable Ti alloy. Metallurgical and Materials Transactions a-Physical 
Metallurgy and Materials Science, 2000. 31 (4): p. 1095-1106. 
121. Karasevskaya, O.P., et al., Deformation behavior of beta-titanium alloys. 
Materials Science and Engineering a-Structural Materials Properties 
Microstructure and Processing, 2003. 354 (1-2): p. 121-132. 
122. Kim, H.S., et al., Stress-induced martensitic transformation of metastable beta-
 titanium alloy. Materials Science and Engineering a-Structural Materials 
Properties Microstructure and Processing, 2007. 4 49 : p. 322-325. 
123. Koul, M.K. and J.F. Breedis, Phase Transformations in Beta Isomorphous 
Titanium Alloys. Acta Metallurgica, 1970. 18 (6): p. 579 -&.  
124. Ling, F.W., E.A. Starke, and B.G. Lefevre, Deformation Behavior and Texture 
Development in Beta Ti-V Alloys. Metallurgical Transactions, 1974. 5 (1): p. 179 -
 187.  
125. Paris, H.G., B.G. Lefevre, and E.A. Starke, Deformation Behavior in Quenched 
and Aged Beta Ti-V Alloys. Metallurgical Transactions a-Physical Metallurgy and 
Materials Science, 1976. 7 (2): p. 273 -278.  
126. Sil, D., Greene, C.A., Ankem, S., Les Alliages Des Titane Beta, ed. A. Vassel, 
Eylon, D., Combres, Y. 1994: Soceite Francaise de Metallurgie et de Materiaux. 
127.  Weiss, I. and S.L. Semiatin, Thermomechanical processing of beta titanium alloys 
- an overview. Materials Science and Engineering a-Structural Materials 
Properties Microstructure and Processing, 1998. 2 43 (1-2): p. 46-65. 
173  
 
128.  Xu, W., et al., Phase stability and its effect on the deformation behavior of Ti-Nb-
 Ta-In/Cr beta alloys. Scripta Materialia, 2006. 54 (11): p. 1943-1948.  
129. Zhao, Y.Q., S.W. Xin, and W.D. Zeng, Effect of major alloying elements on 
microstructure and mechanical properties of a highly beta stabilized titanium 
alloy. Journal of Alloys and Compounds, 2009. 481 (1-2): p. 190-194. 
130. Ivasishin, O.M., et al., Aging response of coarse- and fine-grained beta titanium 
alloys. Materials Science and Engineering a-Structural Materials Properties 
Microstructure and Processing, 2005. 405 (1-2): p. 296-305. 
131. Ankem, S. and H. Margolin, Alpha-Beta Interface Sliding in Ti-Mn Alloys. 
Metallurgical Transactions a-Physical Metallurgy and Materials Science, 1983. 
14 (3): p. 500-503. 
132. Ankem, S., et al., The Effect of Volume Per Cent of Phases on the High-
 Temperature Tensile Deformation of 2-Phase Ti-Mn Alloys. Materials Science 
and Engineering a-Structural Materials Properties Microstructure and Processing, 
1989. 111 : p. 51-61. 
133. Greene, C.A., Fundamental Studies on Ambient Temperature Creep Deformation 
Behavior of Alpha and Alpha-Beta Titanium Alloys, in Materials Science and 
Engineering. 1994, University of Maryland: College Park. 
134. Grewal, G. and S. Ankem, Isothermal Particle Growth in 2-Phase Titanium-
 Alloys. Metallurgical Transactions a-Physical Metallurgy and Materials Science, 
1989. 20 (1): p. 39-54. 
135. Jepson, K.S., Brown, A.R.G., Gray, J.A. The Science Technology and Application 
of Titanium. in Proceedings of the First International Conference on Titanium. 
197 0. London: Pergamon Press. 
136. Balcerza.At and S.L. Sass, Formation of Omega- Phase in Ti-Nb Alloys. 
Metallurgical Transactions, 1972. 3 (6): p. 1601-&.  
137.  Sass, S.L., Structure and Decomposition of Zr and Ti Bcc Solid-Solutions. Journal 
of the Less-Common Metals, 1972. 28 (1): p. 157 -&.  
138.  Silcock, J.M., An X-Ray Examination of the Omega-Phase in Tiv,Timo and Ticr 
Alloys. Acta Metallurgica, 1958. 6 (7): p. 481 -493. 
139. Kuan, T.S., R.R. Ahrens, and S.L. Sass, Stress-Induced Omega Phase-
 Transformation in Ti-V Alloys. Metallurgical Transactions a-Physical Metallurgy 
and Materials Science, 1975. 6 (9): p. 1767 -1774.  
140. Partridg.Pg and R.W. Gardiner, Indices of Planes and Directions in Hcp Crystals. 
Acta Metallurgica, 1967. 15 (2): p. 387 -&.  
174  
 
141. Bowen, A.W., Omega Phase Embrittlement in Aged Ti-15 Percent Mo. Scripta 
Metallurgica, 1971. 5 (8): p. 709 -&.  
142. Bowen, A.W., Effect of Heat-Treatment on Fracture Toughness of a Ti-15mo 
Alloy. Metals Technology, 1978. 5 (Jan): p. 17 -23. 
143. Gysler, A., Lutjerin.G, and V. Gerold, Deformation Behavior of Age-Hardened 
Ti-Mo Alloys. Acta Metallurgica, 1974. 22 (7): p. 901 -909. 
144. Williams, J.C., B.S. Hickman, and H.L. Marcus, Effect of Omega Phase on 
Mechanical Properties of Titanium Alloys. Metallurgical Transactions, 1971. 
2 (7): p. 1913 -&.  
145. Greene, C.A., Ankem, S., Singh, S. The Effect of Morphology and Alloying 
Elements on the Ambient Temperature Creep of Alpha and Alpha-Beta Titanium 
Alloys. in Proceedings of the Eighth World Conference on Titanium. 1995. 
Birmingham, U.K.  
146. Gerland, M., et al., Deformation and damage mechanisms in an alpha/beta 6242 
Ti alloy in fatigue, dwell-fatigue and creep at room temperature. Influence of 
internal hydrogen. Materials Science and Engineering a-Structural Materials 
Properties Microstructure and Processing, 2009. 5 07 (1-2): p. 132-143. 
147.  Guo, Z., et al., Influence of stacking-fault energy on high temperature creep of 
alpha titanium alloys. Scripta Materialia, 2006. 54 (12): p. 2175 -2178.  
148.  Malakondaiah, G. and P.R. Rao, Creep of Alpha-Titanium at Low Stresses. Acta 
Metallurgica, 1981. 29 (7): p. 1263 -1275.  
149. Smith, D.J. and R.L. Jones, The Uniaxial Rate-Dependent Deformation-Behavior 
of Alpha-Titanium at Room-Temperature. Mechanics of Materials, 1989. 8 (2-3): 
p. 219-235. 
150. Seward, G.G.E., et al., In situ SEM-EBSD observations of the hcp to bcc phase 
transformation in commercially pure titanium. Acta Materialia, 2004. 52 (4): p. 
821 -832.  
151. Oka, M. and Y. Taniguchi, [332] Deformation Twins in a Ti-15.5 Pct-V Alloy. 
Metallurgical Transactions a-Physical Metallurgy and Materials Science, 1979. 
10 (5): p. 651-653. 
152. Ramesh, A., Effect of Stability and Grain Size on Ambient Temperature Tensile 
and Creep Behavior of Beta Titanium Alloys, in Materials Science and 
Engineering. 1998, University of Maryland: College Park. p. 162.  
153. Grosdidier, T. and M.J. Philippe, Deformation induced martensite and 
superelasticity in a beta-metastable titanium alloy. Materials Science and 
175  
 
Engineering a-Structural Materials Properties Microstructure and Processing, 
2000. 291 (1-2): p. 218 -223. 
154. Williams, B., Carter, CB, Transmission Electron Microscopy. Vol. II. 1996, New 
York: Plenum Press. 
155. Menon, E.S.K. and R. Krishnan, Phase-Transformations in Ti-V Alloys .1. 
Martensitic Transformations. Journal of Materials Science, 1983. 18 (2): p. 365-
 374.  
156. Jaworski, A. and S. Ankem, Influence of the omega phase on the tensile and creep 
deformation mechanisms of alpha-beta titanium alloys. Reviews on Advanced 
Materials Science, 2005. 10 (1): p. 11-20. 
157.  Ankem, S. and H. Margolin, The Role of Elastic Interaction Stresses on the Onset 
of Plastic-Flow for Oriented 2 Ductile Phase Structures. Metallurgical 
Transactions a-Physical Metallurgy and Materials Science, 1980. 11 (6): p. 963-
 972.  
158.  Ankem, S. and H. Margolin, Modeling Deformation in 2-Phase Alloys. Journal of 
Metals, 1986. 38 (4): p. 25-29. 
159. Greene, C.A. and S. Ankem, Modeling of Elastic Interaction Stresses in 2-Phase 
Materials by Fem. Materials Science and Engineering a-Structural Materials 
Properties Microstructure and Processing, 1995. 2 02 (1-2): p. 103-111. 
160. ANSYS Manual-Engineering Analysis System. 2005, Swanson Analysis Systems 
(SAS) Inc. 
161. Flowers Jr, J.W., Brien, K.C.O., McElency, P.C., Elastic Constants of Alpha-
 Titanium single crystals at 25C. Journal of Less Common Metals, 1964. 7 . 
162. Ikehata, H., et al., First-principles calculations for development of low elastic 
modulus Ti alloys. Physical Review B, 2004. 70 (17).  
163. Fisher, E.S., Dever, D., Jaffee, R.I. and Promisel, N.E. (eds.), The Science, 
Technology, and Applications of Titanium. 1968, New York: Pergamon Press. 
373.  
164. Greene, C.A., Finite Element Method (FEM) Modeling of Elastic Interaction 
Stresses in Two-Phase Materials, in Department of Materials Science and 
Engineering. 1992, University of Maryland, College Park: College Park, MD. p. 
94. 
165. Nye, J.F., Physical Properties of Crystals. 2nd ed. 1985, New York: Oxford 
University Press. 
 
 
Zane W. Wyatt 
10141 Tanfield Ct.                                   zane.w.wyatt@gmail.com Mobile: (443) 844-0185 
Ellicott City, MD  20142 
United States Citizen 
 
Education: 
? University of Maryland, College Park, MD. 
Ph.D. Materials Science and Engineering, GPA:  3.91/4.00 November 2011 
 ?The ?ffect of ?hase Constitution and ?orphology on Room Temperature Deformation Behavior 
of Two-?hase Titanium ?lloys? 
? University of Maryland, College Park, MD. 
M.S. Materials Science and Engineering, GPA: 3.90/4.00                                 May 2010 
?The ?ffect of ?etastability on Room Temperature Deformation Behavior of Beta and ?lpha + 
Beta Titanium ?lloys? 
? University of Utah, Salt Lake City, UT.                                              
B.S. Metallurgical Engineering, GPA: 3.80/4.00 May 2007 
??n ?nvestigation into the Ballistic ?erformance of a Titanium-Boride (TiB) Personal Body 
?rmor ?aterial? 
 
Employment Experience: 
? Materials Engineering Intern May ? August 2006 
Caterpillar Inc. (CAT: NYSE), Peoria, IL 
Performed statistical reliability study on debris damage of alloyed titanium turbocharger 
compressor wheels for large displacement engines 
Developed a 1E Spec to dictate internal manufacturing requirements for high-temperature enamel 
exhaust manifold coatings 
? Bicycle Mechanic/Ski Tuner April 2009 - Current 
Princeton Sports, Columbia, MD 
? Ski-Lift Operator Winter 2004-05/2006-07 
Park City Mountain Resort, Park City, UT 
? Farm Hand Summer 2003/2004 
Idaho Trout Co., Buhl, ID 
 
Publications and Awards: 
1) ?yatt, ?.?., ?hu, D., ?nkem, ?., ?Deformation mechanisms and kinetics of time-dependent 
twinning in an alpha-titanium alloy?, ?ubmitted to the International Journal of Plasticity . 
2) ?berson, ?.?., ?yatt, ?.?., ?nkem, ?., ??odeling interstitial diffusion controlled twinning in 
alpha titanium during low-temperature creep?, Scripta Materialia 65 (2011) 638 ? 641. 
3) ?yatt, ?.?., ?nkem, ?., ?Advances in low temperature (<0.25Tm) creep deformation 
mechanisms of alpha, alpha + beta, and beta titanium alloys?, The Conference Proceedings of the 
12th World Conference on Titanium (Ti-2011). 
4) ?yatt, ?.?., ?nkem, ?., ?Recent developments in mechanisms and the kinetics of deformation 
twinning in titanium alloys?, Materials Science Forum 654 ? 656 (2010) 863 ? 866.  
5) Wyatt, ?.?., ?nkem, ?., ?The effect of metastability on room temperature deformation behavior 
of beta and alpha + beta titanium alloys?, Journal of Materials Science  45(18) (2010) 5022 ? 
5031. 
 
? Oblad Silver Medal of Excellence for Outstanding Research, University of Utah, May 2007 
? College of Mines & Earth Sciences Top Ranked Student, University of Utah, May 2005, 2006, 
2007 
 
Other Pertinent Experience: 
? ANSYS Finite Element Method simulations of phase interaction stresses in two-phase titanium 
alloys