ABSTRACT Title of Dissertation: ENERGY ABSORBING CELLULAR STRUCTURES FOR CRASHWORTHINESS APPLICATIONS Colleen Marie Murray Doctor of Philosophy, 2024 Dissertation Directed by: Professor Norman Wereley Department of Aerospace Engineering Energy absorbing materials are utilized in many applications. Aircraft, automobiles, and helmets all use energy absorbing materials to ensure the safety of the individual during an impact event. The seats in aircraft are made from a material that can minimize the force that is transferred from the impact to the occupant. In a similar manner, the material in the front of an automobile is designed to absorb the energy from an impact event and redistribute it in a manner that minimizes the amount of energy experienced by the main cabin. Helmets perform in the same way: by taking the impact and distributing the load to protect the wearer. The materials used in these applications were tailored to meet the needs of the application, particularly the density and strength of the material. Using cellular structures allow for more control of the design for energy absorbing applications, particularly when looking to increase the performance of the material. There are three options for increasing the energy absorption in materials for crashworthi- ness applications: decrease the force with a constant mean crush stress, increase the mean crush stress with a constant force, or decrease the force while increasing the mean crush stress. In a force- displacement diagram, the area under the curve is the amount of energy that a material can absorb during an impact. By decreasing that initial force, the initial peak force will begin to equilibrate with the mean crush, resulting in a higher energy absorption. The structures that have been relied on throughout history for these applications are cellular structures. Cellular structures are described as any structure that is made of one phase composed of either air or fluid. As Lakes describes in his work, foams, honeycombs, and lattices are catego- rized as such; the voids allow the materials to reach physical limits beyond their previous. With the improvements of technology, it is important to re-asses these structures to determine whether they too can be manufactured and remain as effective in their original crashworthiness appli- cations as before. Throughout this work, different methods of additive manufacturing are used to create honeycomb structures specifically for energy absorption applications. Each of these studies focuses on a different attribute that additive manufacturing can help improve in energy absorption materials. In this dissertation, four case studies involving the out-of-plane compression of additively manufactured honeycomb will be discussed. The first chapter will center on the applications of visco-elastic theromplastic polyurethane (TPU) as a potential material of choice for energy absorption materials. TPU is a material that has the ability to achieve significant deformation and return to its original shape within a matter of minutes. This material is of interest due to the need to re-use helmet liners and other safety mechanisms before buying a new one. This work also focuses on the impact that adding buckling initiators will have to the structure in terms of energy absorption during quasi-static conditions. The next chapter is centered on the applications of these TPU honeycomb undergoing dy- namic testing. Crashworthiness materials experience impact velocities bordering on 10- 15 m/s (22- 35 mph). These tests differ from the previous due to the velocity no longer being constant. As the impactor falls, the velocity changes, while the quasi-static tests were completed under a constant velocity. This set of dynamic tests is most representative of long term applications, however the performance of these materials change drastically as discussed. In some applications, a visco-elastic plastic is not going to be able to absorb the energy from the impact. In these situations, a stiffer material would be necessary. To provide an alternative for these applications, acrylonitrile butadiene styrene (ABS) was studied since it is a commonly used plastic when additively manufacturing. Once again, honeycomb were manufactured and tested under out of plane, uni-axial quasi static compression. The samples were studied to determine the effects of buckling initiator location as well as the effect of the inscribed diameter. For this, samples were manufactured with an internal diameter of 10, 15, or 20 mm. The buckling initiators were located either 1/2, 3/4, or at the top of the samples to determine the design which enables the best energy absorption. The final study recognizes that traditional honeycomb has been manufactured using metals like aluminum and steel. By moving towards an additively manufactured honeycomb, this work has been focusing on polymeric honeycomb instead. The metallic additive manufacturing meth- ods require drastic safety precautions be taken. A safer alternative is proposed in this last study: combining stereolithography and electroplating. Here, an isotropic material can be the core of the structure, with a thin layer (about 150 µm) of metal creating the ductile layer. These sam- ples demonstrate a ductile failure as opposed to their plastic only counterparts who experience a brittle failure. The energy absorption performance is then characterized as a function of buckling initiator height as well. ENERGY ABSORBING CELLULAR STRUCTURES FOR CRASHWORTHINESS APPLICATIONS by Colleen Marie Murray 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 2024 Advisory Committee: Professor Norman Wereley, Chair/Advisor Professor Hugh Bruck Professor Abhijit Dasgupta Professor Amr Baz Professor Lourdes Salamanca-Riba © Copyright by Colleen Marie Murray 2024 Preface The following work includes previously published work: Chapter 3 was published in Polymers in August 2023 (https://doi.org/10.3390/polym 15163350). The author of this dissertation manufactured, tested, and analyzed all samples that were used in this publication. The author also prepared the manuscript and assisted with editing. Chapter 5 was previously published in SAMPE Journal in July 2024 (https://doi.org/ 10.33599/ SJ.v60no4.04). The author of this dissertation planned and executed the experiments using sam- ples manufactured by a colleague. The author also analyzed the data and prepared the manuscript. ii Acknowledgments I owe my gratitude to all of the people that have supported me through my graduate expe- rience. I have a deep appreciation for the time I have spent in the program and cannot begin to thank you enough for your encouragement. First, I would like to thank my advisor, Dr. Norman Wereley. The support, encouragement, and advice that he has granted me over the last 5 years has been incredible. My skills as a researcher, teacher, and writer have continued to grow while learning from him and his vast expertise in composites. I deeply appreciate the many hours of reviewing projects and career advice I have received. I can only hope to show my own students the extent of understanding and encouragement that he has provided me. I would like to recognize Dr. Hugh Bruck, Dr. Abhijit Dasgupta, Dr. Lourdes Salamanca- Riba, and Dr. Amr Baz for their willingness to serve on my thesis committee. Their knowledge and expertise led to a deeper understanding of the research I have completed. To my colleagues in the Composites Research Lab, who have been by my side throughout this process: thank you. Chris Clark, Gabrielle Schumacher, Grace Johnson, and Lane McDer- mott have provided invaluable feedback and encouragement throughout this process. I cannot begin to express the gratitude I have for sharing an office over four years with Frank Cianciarulo. He has always kept a positive attitude, making the difficult days bearable. The time spent with Drs. Jungjin Park and Young Choi have been incredibly eye opening and I am so grateful to have ii spent time working with these extraordinary individuals. The many hours of writing, analyzing, and developing test plans would have been much more challenging without the ongoing support from this incredible group. I would like to express my deepest appreciation for both my friends and family- Ed, Krista, Shannon and Lilith Murray who have always encouraged me. I know they thought I was crazy when I was in 8th grade and told them I wanted to be a composites engineer, but regardless, they have always provided me with the resources and support to reach this dream. I cannot express how grateful I am for their ongoing love and support. I cannot remember everyone who has supported me throughout this process, but I would like to especially recognize my friends and colleagues from the University of Delaware and the Center for Composite Materials along with the many connections I have made here, at the University of Maryland. I would be remiss if I did not acknowledge my dance family as well.The many teachers and friends that I have continuously supported my career and dance goals. To those I inadvertently left out and to all those mentioned above, thank you! iii Table of Contents Acknowledgements ii Table of Contents iv List of Tables vii List of Figures viii List of Abbreviations xii Chapter 1: Introduction 1 1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Analysis of Energy Absorption . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Energy Absorbing Structures . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.3 Honeycomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.1.4 Honeycomb Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2 Organization of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Chapter 2: Effect of Cell Size on Energy Absorption Properties of Additively Manu- factured Honeycomb at Low Strain Rate Events 21 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.1 Manufacturing and Testing . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.2 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.3 Computational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1 Preliminary Data Review . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.2 Validation of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.3 Design for Application . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chapter 3: Visco-Elastic Honeycomb for Low-Strain Rate Energy Absorption 45 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.1 Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.2 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 iv 3.2.3 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 Buckling Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.2 Quasi-Static Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3.3 Low Strain-Rate Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3.4 Repeated Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Chapter 4: Dynamic Crush of Visco-Elastic Honeycomb for Crashworthiness Applica- tions 75 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.3.1 Sample Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.3.2 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.3.3 Data Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.4.1 Quasi-Static and Constant Velocity Behavior . . . . . . . . . . . . . . . 85 4.4.2 Dynamic Impact Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.5.1 Strain Dependent Crush Efficiency . . . . . . . . . . . . . . . . . . . . . 90 4.5.2 Energy Absorbed Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 92 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Chapter 5: Electroplating Additively Manufactured Honeycomb Structures to Increase Energy Absorption Under Quasi-Static Crush 98 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Methods and Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2.1 Sample Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2.2 Testing Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2.3 Energy Absorption Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3.1 Effects of Plating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3.2 Effects of Buckling Initiators . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3.3 Performance Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.3.4 Comparison of Metrics for Plated Samples . . . . . . . . . . . . . . . . . 113 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Chapter 6: Conclusions 117 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.2 Original Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 v Bibliography 125 vi List of Tables 2.1 The average properties for the samples with varying BI location and inscribed diameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 The computational and experimental metrics for all three inscribed diameters. . . 35 2.3 The results of the analytical models in comparison with the experimental results. . 37 2.4 The minimum and maximum range over which each individual spoke is plotted. . 42 3.1 The average properties for the quasi-static strain rate samples. . . . . . . . . . . . 62 3.2 The average properties for the quasi-static strain rate samples. . . . . . . . . . . . 65 3.3 The decrease in the metrics when comparing the following tests to the first test. . 66 3.4 The properties of the experimental and computational quasi-static samples . . . . 71 4.1 Performance metrics for the quasi-static and constant velocity tests . . . . . . . . 87 5.1 Performance metrics of samples . . . . . . . . . . . . . . . . . . . . . . . . . . 108 vii List of Figures 1.1 A force-displacement curve as adopted from Niutta et al. Figure 4 showing the three stages that are characteristic of crashworthy materials . . . . . . . . . . . . 3 1.2 The collapse mode that Alexander assumed as adopted from Alexander et al. Figure 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 The glass fiber reinforced composite circular tubes with trigger mechanism Ozbeck et al. tested as shown in Ozbeck et al. Figure 3 . . . . . . . . . . . . . . . . . . . 8 1.4 A representation of the samples with trigger mechanism that were tested as adopted from Bhutada et al. in Figure 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 A sketch of the testing setup with no load and then with load as adopted from McGehee et al. Figure 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 A sketch of the two intersection methods used in tests as adopted from Jones et al. Figure 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.7 A demonstration of (top row) the different foam filling and (bottom row) the trigger mechanisms used as adopted from Wang et al. Figures 2 and 4 . . . . . . 12 1.8 A sketch of a honeycomb plane with the orientations identified . . . . . . . . . . 14 1.9 A sketch of a honeycomb under axial elastic buckling as adopted from Gibson et al. Figure 4.38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.10 A model where each color is representative of a different density of honeycomb as adopted from Liu et al. Figure 1 . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.11 The beetle and the intersection points that inspired the micro-circle and rib design for honeycomb application as adopted from Niu et al. Figure 1 . . . . . . . . . . 16 2.1 Computer aided design rendering of samples. (A) 0.00BI; (B) 0.50BI; (C) 0.75BI; (D) 1.00BI; (E) inscribed diameter varies, and (F) height and thickness of the sample are held constant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 The stress- strain behavior of the samples under quasi-static conditions. A) 10-, B) 15-, and C) 20-mm inscribed diameters. . . . . . . . . . . . . . . . . . . . . . 28 2.3 The strain dependent crush efficiency of the samples under quasi-static condi- tions. A) 10-, B) 15-, and C) 20-mm inscribed diameters. . . . . . . . . . . . . . 29 2.4 The energy absorbed efficiency of the samples under quasi-static conditions. A) 10-, B) 15-, and C) 20-mm inscribed diameters. . . . . . . . . . . . . . . . . . . 30 2.5 The metrics for the tested samples: A) peak stress, B) mean crush stress, C) maximum strain dependent crush efficiency, and D) maximum energy absorbed efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 viii 2.6 A computational analysis of 0.00BI and 1.00BI samples. A) 10 mm with 0BI; B) 15 mm with 0BI; C) 20 mm with 0BI; D) 10 mm with 1BI; E) 15 mm with 1BI; and F) 20 mm with 1BI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.7 The computational analysis metrics for the samples. A) The threshold strain de- pendent crush efficiency, B) the threshold energy absorbed efficiency as calcu- lated using a threshold of 40 MPa. C) The average and D) variance in crush efficiency from 2- 75% strain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.8 Analytical analysis of the experimental results for (a) peak stress and (b) plateau stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.9 Analyzing the samples for a given design application using a representative thresh- old stress value of 40 MPa where (A) is 10 mm, (B) is 15 mm, and (C) is 20 mm inscribed diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.10 The strain dependent crush efficiency of the quasi-static samples after the thresh- old has been applied for an inscribed diameter of A) 10-, B) 15-, and C) 20-mm. . 39 2.11 The energy absorbed efficiency of the samples tested quasi-static conditions after the threshold has been applied. A) 10-, B) 15-, and C) 20-mm inscribed diameters. 40 2.12 The design metrics as calculated using the threshold stress for (A) the threshold crush efficiency, (B) the threshold energy absorbed efficiency, (C) the average crush efficiency and (D) the variance in crush efficiency from 2- 75% strain. Any samples that had not met the threshold requirement are denoted with an ’X’. . . . 41 2.13 A radar plot of the samples that meet the threshold requirement for the design application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1 The unit cell of the tested honeycomb. (A) Accepted representative volume el- ement according to Gibson; (B) originally tested sheet of honeycomb; and (C) Walls with a free edge obstructed the view of the honeycomb walls during crush, so that all such free edges were eliminated in the unit cell shown here, which was used in this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2 The dimensions used to manufacture the honeycomb. (A) The buckling initia- tors are voids on the vertices in the isometric view of the representative volume element.(B) The thickness and cell dimensions are shown in the top view. (C) Diamond-shaped buckling initiator. (D) The remaining dimensions in the side view. The honeycomb was designed so that t = 0.85 mm, C = 30 mm, L = 18.3 mm, and H = 30 mm. In addition, the honeycomb had diamond-shaped buckling initiators, where B = 4 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3 Honeycomb stress–strain curves of the out of plane honeycomb compression.(a) Representative curve for the samples with no buckling initiators. (b) The rep- resentative curve of the samples with a single symmetric buckling initiator. For each curve, the peak stress, σpk, and its corresponding strain value, ϵpk, are iden- tified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4 The process of crushing the honeycomb results with (left) no buckling initiators and (right) buckling initiators. This was recorded at a time interval of 0.50 s to analyze the folding mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.5 A 0.0BI and 0.5BI sample rebounding after an initial uni-axial compression test. . 57 ix 3.6 The failure mechanism is dependent on the presence of buckling initiators in the honeycomb. (A) The isometric view shows the shear buckling panels forming after 3 cycles of testing. (B) A front view of the triangular buckling panel. (C) Model of the shear buckling. (D) Isometric view shows folding failure after 3 cycles of testing. (E) The front view shows that the folding failure aligns with the neighboring cells. (F) Model of the folding failure. . . . . . . . . . . . . . . . . 58 3.7 The stress-strain behavior of 0.0BI and 0.5BI samples. . . . . . . . . . . . . . . 60 3.8 The strain dependent crush efficiency at quasi-static strain rates. . . . . . . . . . 61 3.9 The stress–strain curves are plotted on the left axis with the energy-absorbed efficiency plotted on the right. The left-hand side shows the 0.0BI sample, and the graph on the right shows the 0.5BBI sample. The peak energy-absorbed efficiency strain corresponded with the threshold strain. . . . . . . . . . . . . . . . . . . . 62 3.10 The behavior of visco-elastic honeycomb tested under three different strain rates. Left column shows 0.0BI and right column shows 0.5BI. (A) and (B) show stress- strain curves, (C) and (D) show crush efficiency, and (E) and (F) show energy absorbed efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.11 The stress–strain curves during three different tests. The left column is for 0.0BI and the right column is for 0.5BI. The top row is for the quasi-static conditions, the middle is for 0.25 m/s, and the bottom is for 0.50 m/s. . . . . . . . . . . . . 67 3.12 The computational and experimental stress–strain curves for the samples tested at a quasi-static strain rate in the top row and the strain-dependent crush efficiency in the bottom row. The left column shows the 0.0BI samples and the right column shows the 0.5BI samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.13 The radar plot shows the performance of the quasi-static conditions with the 0.0BI and 0.5BI samples in regard to these particular metrics. . . . . . . . . . . . . . . 72 4.1 Samples that were used for testing. (A) is 0BI; (B) is 0.5BI; and (C) is 1BI. (D) shows the inscribed diameter, where D = 25 mm, while (E) shows the height, H, of the samples is 30 mm and the wall thickness, t, is 1.4 mm. . . . . . . . . . . . 80 4.2 Representative stress strain curve with idealized area shown in yellow. . . . . . . 84 4.3 The stress-strain curves for the quasi-static and constant velocity samples with 0BI and 0.5BIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4 The velocity- strain curves show how the presence of buckling initiators effect the strain range of the test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 The stress- strain curves for the dynamic impact tests. (A) 0BI; (B) 0.5BI; and (C) 1.0BI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.6 The displacement of the samples directly corresponds to the velocity of the test . 89 4.7 The strain dependent crush efficiency of the dynamic samples across the entire stroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.8 The data falls into three groups based on the studies that were conducted. The first is the quasi-static samples (VQS), which is an example of the second group: constant velocity, V0. The final group is the dynamic impact (∆V ) . . . . . . . . 93 4.9 The energy absorption efficiency for visco- elastic honeycomb during three differ- ent types of testing: quasi-static (green), constant velocity (yellow), and dynamic impact (grey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 x 4.10 The energy absorbed efficiency for visco-elastic TPU samples with a buckling initiator located midway up the height. . . . . . . . . . . . . . . . . . . . . . . . 95 5.1 The constant volume additively manufactured HC samples: (A, C) plastic HC via SLA; (B, D) plastic HC preform via SLA electroplated with CU, soft Ni, and hard Ni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.2 Stress vs. strain diagram for unplated and plated HC samples with no BIs . . . . 105 5.3 Stress vs. strain for the uplated and plated samples with no buckling initiators (0BI), and with BIs at 50, 75, and 100% of the sample height (0.50BI, 0.75BI, and 1.0BI, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.4 Progression of crush as a function of strain: (Top Rows) Plated HC sample with- out BIs; (Bottom Rows) Plated HC sample with BI at 50% sample height (0.50BI) 109 5.5 Crush efficiency vs. strain for the uplated and plated samples without buckling initiators (0BI), and with BIs at 50, 75, and 100% of the sample height (0.50BI, 0.75BI, and 1.0BI, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.6 Energy absorbed efficiency vs. strain for the uplated and plated samples without buckling initiators (0BI), and with BIs at 50, 75, and 100% of the sample height (0.50BI, 0.75BI, and 1.0BI, respectively) . . . . . . . . . . . . . . . . . . . . . . 111 5.7 The performance metrics computed in this study for the unplated and plated HC samples without BIs (0BI) and with BIs at 50, 75, and 100% of the sample height (0.5BI, 0.75BI and 1.0BI, respectively). Here, peak values of crush efficiency and energy absorbed efficiency are used. . . . . . . . . . . . . . . . . . . . . . . . . 112 5.8 Performance metrics for plated samples displayed on a radar plot. . . . . . . . . . 114 xi List of Abbreviations α Internal angle A Area ABS Acrylonitrile butadiene styrene ABS-R Acrylonitrile butadiene sytrene- research AM Additive Manufacturing Auc Unit cell area Avg ηSD Average crush efficiency B Buckling initiator dimension BIs Buckling initiators C Inscribed diameter CAD Computer aided desing δϵ Change in strain δH Change in height ∆σ Change in stress (Peak stress- Mean crush stress) δσ Change in stress DED Direct energy deposition DI Inner diameter DO Outer diameter d Displacement across entire strain range ϵ Strain ϵd Densification strain ϵpk Peak strain ηEA Energy absorbed efficiency ηEA,T Theshold energy absorbed efficiency ηSD Crush efficiency ηSD,T Threshold crush efficiency Es Bulk modulus EA Strain energy density F Force FDM Finite Deposition Molding FEM Finite element model FFF Fused filament fabrication Fpk Peak Force F (x) Force at a given displacement xii H Height of sample HC Honeycomb K End constraint factor constant KE Kinetic energy L Length m Specific mass MTS Materials Testing System Pcrit Buckling load PBF Powder bed fusion PLA Polylactic acid σ Stress σpk Peak stress σmc Mean crush stress σys Yield strength σ2 ηSD Crush efficiency variance SEA Specific energy absorbed SLA Stereolithography t Wall thickness TPE Thermoplastic elastomer U(ϵ) Energy absorbed V Crush velocity vs Bulk Poisson’s Ratio x Displacement 0BI No buckling initiators 0.50BI Buckling initiator 50% height 0.75BI Buckling initiator 75% height 1BI Buckling initiator 100% height xiii Chapter 1: Introduction 1.1 Literature Review One critical consideration in engineering applications is improving structural crashworthi- ness. This requirement has constraints though, such as a limit on the force transmitted or an acceptable amount of deformation [1]. Applications of these constraints would be in automo- biles, trains, and aircraft, where in the case of an accident, there is a threat to the passengers’ life and safety [2, 3]. In train and aerospace applications, these materials would act as shock ab- sorbers since they increase the time over which the shock is applied to the vehicle by increasing the folds of the material [4]. The kinetic energy from the impact is transformed when it deforms the energy absorber into a plastic strain energy [4]. Cellular structures are commonly selected for these energy absorption applications due to their light-weight and high stiffness. The energy absorption properties are dependent on the material along with the geometric conditions [5–7]. As Deqiang, et al. show in their study, the ratios of the cell wall thickness of the honeycomb to the edge length will be directly related to the mean out of plane dynamic plateau stress [6]. Zou et al. experienced similar results while studying bamboo tubes. As the bamboo tubes were divided into sub-regimes, there was an increase in the initial force, however there was also a significant increase in the overall specific energy absorbed, or the energy absorbed per unit weight [7]. To better understand these terms, it is 1 important to understand what the force-displacement curve looks like for crashworthy materials. 1.1.1 Analysis of Energy Absorption Energy absorbing materials will experience a three stage force-displacement curve. The first stage shows an axial load increasing drastically in the elastic regime until the force reaches the initial peak force, Fpk, as seen in Figure 1.1 [8,9]. The second stage is the plateau or platform stage, where the force drops down to the plastic region and fluctuates in response to the progres- sive buckling, or folding, of the sample. In Figure 1.1, this corresponds to the second red box. This is the non-linear plastic regime where the majority of the energy absorption will occur [10]. The amount of fluctuation corresponds directly to the type of sample tested. Cellular structures, like honeycomb, lattices, and foam, experience a near constant stress, even with damage accumu- lation [11]. Once the sample can no longer buckle, the third stage, densification, begins. This is the region where the force rapidly increases since the sample is no longer viable [12]. This is the remainder of the force- displacement curve in Figure 1.1. From this curve, the energy absorption metrics can be determined. There are a series of commonly accepted parameters used to characterize the energy ab- sorption of materials during an impact collision. These parameters can be calculated from a force-displacement curve. To begin, the stress- strain curve must be calculated. σ = F A (1.1) Here, F is the the force being applied and A is the cross sectional area that is in contact with the 2 Figure 1.1: A force-displacement curve as adopted from Niutta et al. Figure 4 showing the three stages that are characteristic of crashworthy materials platen. The strain can be determined using the following: ϵ = δH H (1.2) Here, H is the height of the original sample and δH is the change in height. With these calcu- lations, the stress- strain curve can be determined and the energy absorption parameters can be calculated. The first crashworthiness parameter is the energy absorbed by the sample. The energy absorbed is the area under the force- displacement or stress-strain curve, which can be shown mathematically using the following [13]. EA = ∫ x 0 F (x)dx = ∫ ϵ 0 σ(ϵ)dϵ (1.3) 3 Here, x is the displacement and F(x) is the force at a given displacement. Knowing the energy absorbed, the specific energy absorption (SEA) can be determined. This is a ratio between the energy absorbed prior to densification divided by the material’s mass. [8, 12, 14] SEA = EA m = ∫ ϵ 0 σ(ϵ)dϵ m (1.4) where m is the mass of the sample. Throughout literature, there is disagreement as how the mean crush stress or plateau stress is calculated. Some sources find the average stress across the entire strain range, where d is the total displacement of the sample [8, 13, 15]. σmc = EA d = ∫ ϵ 0 σ(ϵ)dϵ d (1.5) This methodology is useful when the stress- strain curve does not experience a large stress vari- ation when comparing the peak stress to the plastic regions. For some materials, however, it becomes necessary to look at just the plateau region due to the peak stress skewing the mean crush stress. Niu et al. and others show this in their definition of the mean crush stress [16–18]. σmc = EA ϵd − ϵpk = ∫ ϵ 0 σ(ϵ)dϵ ϵd − ϵpk (1.6) Here, ϵd is the densification strain and ϵpk is the strain at the peak stress. This will remove any influence caused by the peak stress. For example, Yin et al. introduce Equation 1.5 as the mean crush stress in their work because the stress is relatively constant throughout the test, and thus it can be averaged from the beginning of compression until complete compaction [19]. 4 Once the general metrics have been determined, the efficiencies are used to determine the overall performance of the sample. Crush efficiency is the ratio of the energy absorption of the structure to the possible energy absorption of the material up to that strain. Mathematically it can be written as follows: ηSD = EA σpkϵ = ∫ ϵ 0 σ(ϵ)dϵ σpkϵ (1.7) This is a strain dependent crush efficiency because it determines how efficient the material has been at absorbing energy up to the strain. However it can also be useful to determine how efficient the material is at absorbing energy assuming there is complete densification of the material. To do so, the strain is set to 1 [20, 21]. ηEA = EA σpkϵ|ϵ=0 = ∫ ϵ 0 σ(ϵ)dϵ σpk (1.8) From this, the energy absorbed efficiency provides a quantitative value on how the sample per- formed. It is important to remember that the force-displacement curve, and thus the energy absorp- tion metrics are dependent on the geometry and material of the energy absorber that is selected. 1.1.2 Energy Absorbing Structures The original energy absorbers that were studied were metallic tubes. Tubes, by definition, have a constant cross-section throughout the length of the shape. Some common tubes that are studied within the energy absorption field have circular, square, or hexagonal cross sections. Due to the complexity of the later shapes, energy absorption analysis began with circular tubes. 5 Figure 1.2: The collapse mode that Alexander assumed as adopted from Alexander et al. Figure 1 As Alexander explained, circular tubes can collapse such that they form symmetrical folds similar to bellows, or they can form transverse and longitudinal waves [22]. When these tubes collapse in the symmetric folds, they are often called a concertina (Figure 1.2). In his model, Alexander was able to derive an equation where the collapse load for a tube can be approximated once the material constant is determined experimentally for tubes that experience concertina fold- ing [22]. Abramowicz modified Alexander’s theoretical approximation of the collapse load for con- certina deformations in circular tubes. The updated version included the effects of the effec- tive crushing distance, so that it further improved the accuracy of the model for static crushing 6 loads [23]. He also improved the mean dynamic crushing loads by including the effects of the the material strain rate sensitivity [23]. Similar theoretical models were also developed for square and rectangular cross section tubes. Wierzbicki et al. discuss how the mean crushing force is heavily dependent on the wall thickness of the tube for axially compressed rectangular tubes [24]. Abramowicz et al. contin- ued to modify the quasi-static mean axial crushing load equations to achieve results that agree reasonably well with the experimental results [25]. More recent studies like Wang et al. have moved away from studying metallic circular tubes, but instead implementing polymers to manufacture the tubes. As Wang found, the material can greatly effect the folding pattern as well as the mean crushing loads, so the models that exist cannot be used to predict the performance of polymer samples [26]. Ozbbeck et al. discuss how glass fiber reinforced composite pipes result in a more brittle fracture as opposed to the concertina folding that is associated with metallic tubes [27]. As a result, their study is focused on implementing other methods, such as trigger mechanisms, to improve the energy absorption (Figure 1.3). This concept of triggers were implemented in additional energy absorption samples, re- gardless of the bulk material. Triggers come in many different forms and shapes, however they all serve the same purpose: to decrease the peak stress and increase the mean crush stress. The most common types of triggers are buckling initiators. Buckling initiators are pur- poseful stress concentrators intended to control the failure mechanism of the sample. There are many types of these including holes, wall thickness reduction, grooves, notes, beads, and corru- gation [28]. As Bhutada et al. describes, removing material symmetrically on a metallic circular tube surface can modify the deformation mode so that a long tube that traditionally deforms un- 7 Figure 1.3: The glass fiber reinforced composite circular tubes with trigger mechanism Ozbeck et al. tested as shown in Ozbeck et al. Figure 3 Figure 1.4: A representation of the samples with trigger mechanism that were tested as adopted from Bhutada et al. in Figure 3 der Euler buckling will experience a more stable collapse [29]. Figure 1.4 shows the 3D models of the samples that were investigated. With the numerical studies, it was determined that the location and size of the cut-outs will determine the deformation pattern of the metallic tubes [29]. Additional cross-sections have been studied to determine what the effects of buckling initia- tors are. Arnold et al. implemented circular buckling initiators on opposing walls in an aluminum square tube and studied the effect of the diameter of the buckling initiators on the collapse of the tube and the energy absorption [30]. In this work, Arnold et al. determined that collapse mode 8 and energy absorption were dependent on the presence of buckling initiators, not necessarily the geometry [30]. Cheng et al. conducted similar studies, however in their work, either a circular, elliptical, or slotted discontinuities was machined into the sample [31]. In their studies, it was determined that the dimensions and geometric shape of the discontinuity do not effect the energy absorption if the discontinuity was smaller then a critical dimension [31]. Dionisius et al. also studied the effects of circular buckling initiators, but this time in square steel tubes, while quanti- fying the effects that the wall thickness, diameter, and angle of the buckling initiators have on the energy absorption [28]. A function model was generated using numerical simulation methods to quantify these effects [28]. Similar to the previously reported studies, there have been trigger mechanisms imple- mented in composite pipes as well. Ozbeck et al. analyzed the effects of the number, location, and size of circular trigger mechanisms in a glass fiber reinforced composite pipe [27]. To im- prove energy absorption, the trigger mechanisms should be located closer to the impacted edge for laminates. It was also reported that as the diameter became too large, the energy absorption decreased, so the buckling initiator size must be optimised [27]. Another type of initiator that has been reported throughout literature is designing the end of the sample to match the collapsing mode shape. As Kim describes, the simplest collapsing mode is designed to match the first elastic buckling mode shape [32]. The study focuses on how the simple trigger mode compares to the complex trigger mode in aluminum square tubes, where the end of the sample is designed to take the shape of a plastic quasi-inextensible fold [32]. By implementing the the complex trigger mode, the complex mode of crushing occurs for just the first fold, and crushing for the remainder, providing an increased stability in the progressive collapse [32]. Ma et al. also provide examples of pre-folding the structure so that the collapse of 9 Figure 1.5: A sketch of the testing setup with no load and then with load as adopted from McGe- hee et al. Figure 2 the structure can be controlled and tailored to the design application [33]. If the application of the material allows for a permanent attachment, a cap or hat can be implemented to encourage a controlled failure. McGehee et al. describe this process as a tapered tube coming into contact with a die that has an edge with a radius as shown in Figure 1.5 [34]. The fragmenting that occurred when the circular aluminum tube came into contact with the die results in a stress that can fluctuate as load is being applied. The fluctuations were found to decrease when the ratio of the internal diameter of tube to the die forming radius increased [34]. Depending on the final application of the energy absorption structure, it is possible to im- 10 Figure 1.6: A sketch of the two intersection methods used in tests as adopted from Jones et al. Figure 2 plement a radius as an initiator between the structure and the structure applying to load. In Jones et al. the location where the longitudinal subfloor beams and the lateral bulkheads meet were analyzed to increased energy absorption [35]. For this reason, it was crucial to include the top and bottom plates since the load is distribute over these surfaces. In this study, the intersection between the longitudinal and lateral beams was open to design, so a radius was applied to the end of the beams as a crush initiator, while also varying the joint in the middle of the beam (Figure 1.6). From the study, it was determined that using a tapered design to attach the intersections improves the energy absorption parameters the most [35]. Another method that is used to help stabilize the force- displacement curve of energy ab- sorbing materials is by implementing a foam filler. Goel studied the effect of filling both square and circular aluminum tubes with an aluminum closed cell foam for a varying number of concen- tric tubes [36]. From this work, it is noted that having a foam-filled structure greatly improves the energy absorption abilities of the structure and that when experiencing dynamic loading, having multiple tubes, allows for the stress wave propagation to dissipate, all while maintaining a light 11 Figure 1.7: A demonstration of (top row) the different foam filling and (bottom row) the trigger mechanisms used as adopted from Wang et al. Figures 2 and 4 weight structure. There are ways though to combine buckling initiators with foam filled boxes though. Wang et al. studied crash boxes that are used in vehicles. To do so, the study was composed of four different foam filling scenarios: no foam, completely filled, double filled, and corner filled (Figure 1.7). From each, three different trigger mechanisms were tested: folds on the long side, folds on the short side, and cut outs. Wang et al. found that using the foam in the corners was able to improve the energy absorption parameters while still balancing other objectives like maintaining a lightweight structure and increasing the load carrying abilities. Although these energy absorption strategies have been implemented on circular and tubular structures, they can also be implemented on another familiar tubular structure: honeycomb. 12 1.1.3 Honeycomb Honeycomb is an array of repeating prismatic cells that nest together to form a plane [11, 37]. Honeycomb is most often designed as a 2D lattice structure, with cells that can be hexagonal, but can also be triangular, square, or rhombic [18, 37]. Hexagonal honeycomb is based in a triangle unit cell, where each edge length is constant as it is spread 120◦ around the vertex. Six of these triangular unit cells are joined to create a hexagon, resulting in additional locations to continue the pattern. Due to the triangle at each vertex, there is a sharp corner where a stress concentration can occur. Nazir et al. showed that by rounding these corners, the stiffness and energy absorption increase [20]. Honeycombs can be compressed in one of two ways: in plane and out of plane. Figure 1.8 shows an example of a honeycomb plate. If this honeycomb were to be compressed in the X1−X2 plane, this would be in plane compression [13]. As the load is applied the cell walls bend due to linear elastic deformation before collapsing [37]. The reason for collapse is dependent on the material of the honeycomb, but it could be elastic buckling, plastic yielding, creep, or brittle fracture [37]. If the sample experiences plastic yielding, there will be a region of plasticity deforming the sample, but for brittle samples, they can be identified by fracturing. Regardless of the mode of collapse, the cells will collapse until they touch each other, resulting in the structure densifying as the stiffness increases [37]. When a sample is compressed in the out of plane direction, the load would be applied in the X3 direction. When this happens, the load is applied parallel to the cell walls, resulting in either extension or compression of the walls [37]. As a result, the modulus and collapse stress are higher than those experienced during an in plane compression. The linear elastic deformation 13 Figure 1.8: A sketch of a honeycomb plane with the orientations identified Figure 1.9: A sketch of a honeycomb under axial elastic buckling as adopted from Gibson et al. Figure 4.38 is controlled by the buckling of the cell walls as seen in Figure 1.9, so both axial and bending contribute to the plastic collapse strength [37]. Due to the complexity of these honeycomb, numerical analysis was developed to predict the performance of these structures. Beginning in 1961, McFarland produced an equation that provided the average compression force for the out of plane quasi static compression of metallic hexagonal honeycomb [38]. By 1983, Wierzbicki et al. modified McFarland’s work using the principle of energy conservation. The updated results provided a solution for the static average 14 Figure 1.10: A model where each color is representative of a different density of honeycomb as adopted from Liu et al. Figure 1 compression force for an out of plane compression test of hexagonal aluminum honeycomb [39]. Gibson and Ashby used the previous work to determine the displacement of a honeycomb sample subjected to out of plane quasi static compression [37]. The methodology for deriving all moduli needed to calculate the displacement is provided in Section 4.5 in Cellular Solids: Structure and Properties [37]. The traditional hexagon honeycomb structure has three main reinforcement designs that will improve the energy absorption: the negative Poisson’s ratio structural design, the functionally graded design, and the bio-inspired hierarchical design [40]. Anni et al. implemented the functionally graded design in a thermoplastic polyurethane (TPU) honeycomb by changing the density of different sections as the height of the honeycomb increased [41]. Liu et al. conducted a similar experiment, however each section of the sheet of honeycomb was a different thickness (Figure 1.10) [17]. These samples are also known as auxetic because they have a negative Poisson’s ratio. Liu et al. describe the process of designing a bio-inspired re-entrant honeycomb [42]. The 15 Figure 1.11: The beetle and the intersection points that inspired the micro-circle and rib design for honeycomb application as adopted from Niu et al. Figure 1 reinforcements that were added were similar to those used in plants to support the forces they encounter. Niu et al. implemented a bio-inspired hierarchical design by using a unit cell with a central micro-circle and a varying number of ribs, similar to the cellular structure of beetles [16]. The simplified microstructure shown in Figure 1.11 was implemented in a hexagon for the studies. Similar to Niu et al., Sharma et al. were inspired by another living organism: a sea sponge. It is a cylindrical skeleton that consists of small square units cells which are composed of two open and two closed cells [21]. This same unit cell was replicated in the lab using PLA and TPU. The samples with TPU for the horizontal and vertical struts and the PLA for the diagonal struts were found to have the highest energy absorption parameters. Others insist that by using materials with different properties, the combination of strength and toughness will be similar to that of bone and nacre [43]. Another method used to improve the energy absorption properties of honeycomb is through the use of hierarchical honeycombs. A hierarchical honeycomb is created when a cell wall of the hexagon is replaced with a series of smaller hexagonal honeycomb [14]. There are examples of this micro- meso scale structural hierarchy in bone, tendon, nacre, and coconut shell [9, 44, 45]. 16 1.1.4 Honeycomb Manufacturing The need for faster and cheaper honeycomb manufacturing has increased with many in- dustries looking to implement honeycomb as an energy absorber in their respective fields. The material will dictate what manufacturing methods can be used. With the increased understanding of additive manufacturing, there are many new manufacturing options that are available. The preliminary manufacturing methods that were developed focused on manufacturing metallic honeycomb. The first method of these is the stamp forming method. In this process, a punch and die are used to transfer the desired pattern onto a metal plates [46]. The internal structure is then free to be removed. If necessary, a secondary step can be used to bend the structure if needed, prior to welding [46]. Stretch mesh folding is another option that can be used to manufacture a flat plate with the desired design. Here, a punch is used to remove the excess material [47]. At this point, the flat plate goes through a roller to flatten it and deform the honeycomb to the correct dimensions [47]. Another example of the manufacturing process is taking long, thin sheets of metal and applying an adhesive strip in the desired locations. A second thin sheet of metal is placed on top while additional adhesive is applied. The process repeats to create flattened honeycomb. The structure is expanded through the use of compressed air. The final example of metallic honeycomb manufacturing is Gypsum pressure percolation. A low-melting polymer model is manufactured and placed in a mold. A gypsum slurry is used to fill the mold before leaving the gypsum to dry [48]. Once dried, the polymer model is removed and liquid aluminum is used to fill the mold. This is placed in a vacuum to ensure the aluminum fully penetrates the mold [48]. The final mold can be rinsed with water to remove the aluminum part. 17 Although these methods are consistent, they cannot be used to manufacture complex hon- eycomb, such as a constant wall thickness honeycomb or a honeycomb with buckling initiators. These individual processes must be combined with welding or subtractive manufacturing. Weld- ing though, can cause stress concentrations at the weld bead, therefore weakening the entire structure [18]. Another material choice is a polymeric honeycomb. Two processes will be highlighted for manufacturing non-metallic honeycomb. The first is the laser cutting method. Depending on the material, the material is laid out and a laser probe is used to remove the excess material in the plate [49]. The consistency of this process is dependent on the accuracy of the stage that the material is placed on as well as the stiffness of the material [49]. Another similar process is water jet cutting. Here, a water jet is used to cut the honeycomb pattern into the material. Once completed, multiple pieces are stacked together and attached to the face plates so that a sandwich structure is manufactured [50]. There is still room for improvement when manufacturing large pieces of honeycomb though [18]. Additive manufacturing was developed as an alternative to subtractive manufacturing. Sub- tractive manufacturing begins with a large block of material and removes what is unnecessary, whereas additive manufacturing adds material only to the areas where it is needed. There are seven families in which additive manufacturing technology falls into: binder jetting, material extrusion, powder bed fusion, vat polymerization, direct energy deposition, material jetting, and sheet lamination. Of these families, only two will be reviewed in the following. Material extrusion is the form of additive manufacturing that most individuals think of when they hear the phrase ”additive manufacturing.” Finite deposition modelling (FDM) is the process of melting, extruding, and depositing thermoplastic polymer to manufacture the desired geometry [51]. The raw material, or filament, is kept on a spool which is fed fed into the nozzle. 18 The filament is heated to above the glass transition temperature to allow for the ability to place the material as needed in a layer by layer process [21]. The most common polymers used in FDM are as follows: polylactic acid (PLA), polycarbonate (PC), polyethene terephthalate (PET), TPU, ABS, and Nylon 6 [52]. The main concerns with FDM is the build orientation or the placement on the part relative to the build platform [53]. As Anni et al. explain, it is necessary to determine the material properties relative to the testing orientation [41]. Additional work has been conducted to quantify the mechanical properties [13, 54]. Vat Polymerization encompasses any additive manufacturing process that uses a photosen- sitive liquid. For both processes that follow, the structure being manufactured is sliced into 2D layers. The first process is Stereolithography (SLA). This is a process where a photo-curable resin is placed in a transparent container to allow a laser to point cure the resin per the design [55]. SLA is commonly used because it has high precision, however there is a limit on available resins and there is an extensive post processing step. The second vat polymerization process that is commonly used is digital light processing (DLP). Here, a light is projected over the entire bath of resin so that the entire layer of the print is cured at once [56]. This process continues until all layers of the print have been cured [57]. Both of these methods create a solid-body object with no concerns regarding anisotropy. 1.2 Organization of Dissertation The following dissertation is organized by topic area. Each chapter consists of a unique set of studies that were completed. Chapter 2 discusses the effects of cell size and buckling initiator location in an ABS hon- 19 eycomb. Here, three inscribed diameters are tested under uni-axial quasi- static compression while the effect of buckling initiator is quantified. Three unique buckling initiator locations were studied: located at the top of the sample, 3/4 up the height of the sample, and at the midpoint of the sample. These samples were compared to the performance of the samples without buckling initiators. Chapter 3 is focused on a series of studies involving a visco-elastic honeycomb. For this set of studies, thermoplastic polyurethane (TPU) was used to manufacture a honeycomb unit cell with either no buckling initiators or buckling initiators located halfway up the height of the sample. This study quantified the effects of buckling initiators and cross head velocity on the energy absorption properties. The repeatability of the testing is also quantified. Chapter 4 continues on the previous study to further quantify the performance of the visco- elastic honeycombs when subjected to dynamic impact events. Here, the TPU samples with buckling initiators located at the top and midpoint of the sample along with samples having no buckling initiators were subjected to a series of impact velocities. These results were compared to those of the constant velocity and quasi- static tests that were conducted in the previous chapter to determine if there is a simpler test method that could predict the energy absorption of the dynamic samples. In Chapter 5, a series of uni-axial quasi-static compression tests were conducted on both electroplated and no plated resin honeycomb. Due to the increased safety concerns and cost of additively manufacturing metallic honeycomb, a set of stereolithography samples were studied to determine if electroplating the mandrel would result in a more ductile performance. Here, a set of SLA printed honeycomb with and without buckling initiators were tested and compared to their electroplated counterparts. 20 Chapter 2: Effect of Cell Size on Energy Absorption Properties of Additively Manufactured Honeycomb at Low Strain Rate Events Honeycomb materials are being used for energy absorption applications in aerospace and automotive industries due to their high strength to weight ratio. In this work, additively manufac- tured honeycomb with different inscribed diameters were tested in quasi-static compression on a servo-hydraulic material test system to determine how the geometry effects the energy absorption properties. Samples were manufactured with buckling initiators, or small triangle cutouts, located at various positions vertically up the height of the sample, while others had no modifications. As this study showed, the strain dependent crush efficiency and energy absorbed efficiency increase as the inscribed diameter decreases. When the inscribed diameter is 10 mm, the crush efficiency is 62%, while it is 3 times smaller when the inscribed diameter increases to 20 mm (20.29%). The energy absorbed efficiency is 45% for the 10 mm sample while it decrease to 16.70% when the diameter is 20 mm (36% decrease). Similarly, the presence of buckling initiators will increase the crush efficiency and energy absorbed efficiency of the samples when compared to their no buckling initiator counterparts, regardless of the size of the honeycomb. 21 2.1 Introduction Additive manufacturing has been incorporated into industries such as automotive, con- struction, aerospace, medical, and others in recent years [58]. The reduction in cost and time to manufacture complex geometries, along with minimal capital investment and versatile produc- tion has resulted in more of an interest in the field [58, 59]. The most common and affordable additive manufacturing technique is finite deposition molding or FDM [60, 61]. Here, an object is manufactured by depositing material layer by layer on a build plate [58]. The concern with this method is it will result in high anistropy and weak interlayer bonding [60, 62]. The aerospace, automotive, and defense industries have been increasingly interested in the use of additively manufactured honeycomb for sandwich panels in energy absorption applications [63, 64]. When printed in the out-of-plane direction and loaded like such, the highly anisotropic layers would allow for the honeycomb to absorb more energy. These honeycomb cores are of great interest due to the high strength-to-weight ratio, high stiffness-to-weight ratio, and high energy absorption capabilities [65]. As Habib et al. explains, when designing a honeycomb for energy absorption applications, a significant amount of time must go into selecting the correct cell geometry to keep the transmitted force below the force threshold that can cause damage [64]. Manufacturing these honeycomb cores using finite deposition molding allows for greater control of the geometries. Previously, honeycomb structures could not be modified beyond the cellular dimensions due to the manufacturing methods, however honeycomb structures can now be tailored to create stronger and more efficient structures [20]. One example of this is varying the wall thicknesses. Honeycomb used to have varying wall thicknesses due to the manufactur- ing method, however using FDM allows for the cores to be manufactured to final dimension and 22 thus have a constant wall thickness. The following study shows how the use of FDM can create an ABS honeycomb core with integrated buckling initiators. To date, literature does not docu- ment the correlation between the buckling initiator performance as the honeycomb core geometry changes. In this study, a series of honeycomb cores were tested under out of plane quasi-static com- pression with buckling initiators in a variety of locations. Each of these honeycomb cores had a different inscribed diameter, increasing from 10 to 20 mm in increments of 5 mm. As the in- scribed diameter increased, the crush efficiency was found to decrease, however the cores with buckling initiators always out performed their counterparts without buckling initiators. 2.2 Materials and Methods 2.2.1 Manufacturing and Testing For this study, a series of additively manufactured honeycomb of varying inscribed diam- eters were tested to identify the energy absorption properties. These samples were manufac- tured using acrylonitrile butadiene styrene (ABS-R), which has a tensile strength and modulus of 41 and 2400 MPa respectively (Makerbot, New York, NY). The samples are composed of six hexagons surrounding a central hexagon. For the study, there were three types of samples man- ufactured: those with inscribed diameters of 10, 15, and 20 mm respectively. The samples kept all other geometric values constant by using a height of 30 mm and a wall thickness of 0.7 mm. Each type of sample were designed to include buckling initiators (BIs), or small diamond cutouts located at the vertices. There were four unique locations of the buckling initiators: a) no buckling initiators; b) buckling initiators located halfway up the height; c) buckling initiators located 3/4 23 Figure 2.1: Computer aided design rendering of samples. (A) 0.00BI; (B) 0.50BI; (C) 0.75BI; (D) 1.00BI; (E) inscribed diameter varies, and (F) height and thickness of the sample are held constant. up the height; and d) buckling initiators located at the top. These buckling initiators are 4 mm in length and 4 mm in height. This created a total of 24 different types of samples (Figure 2.1). The samples were modeled using Solidworks and then sliced using Makerbot’s CloudPrint software. The Method X was used to print the samples due to the accuracy and precision (Maker- bot, New York, NY). ABS-R was selected as the filament of choice due to thewell- understood material properties. The samples were tested in uni-axial compression on a servo-hydraulic material test system in the out of plane orientation (MTS, Eden Prairie, MN). The samples were tested at 1E-3 s−1 or a cross head velocity of 0.03 mm/s. The samples were imaged using a Nikon every 10 seconds so that the failure could be documented and reviewed later. 24 2.2.2 Metrics Energy absorption metrics have been identified from literature to assist in the assessment of these samples. The stress must be determined first. σ = 2F 21L2 √ 3 (2.1) Here σ is the stress, F is the force, and L is the length of the side wall. Because the sample is composed of seven independent hexagons, the area was determined using: A = 21 √ 3 2 L2 (2.2) From this, the energy absorbed can be determined. U(ϵ) = ∫ ϵ 0 σ(ϵ)dϵ (2.3) The strain dependent crush efficiency can be determined when the idealized energy absorption is compared to the energy absorption. ηSD(ϵ) = U(ϵ) max[σ(0), σ(ϵ)]ϵ = σmc max[σ(0), σ(ϵ)] (2.4) In this equation, σmc is the mean crush stress and it can be found using: σmc = U(ϵ) ϵ (2.5) 25 The mean crush stress provides a representative value of the stress throughout the entire strain range of the sample. When the energy absorbed is compared to the idealized energy absorbed across the entire strain range, the energy absorbed efficiency can be determined. Mathematically, it would be the following: ηEA(ϵ) = U(ϵ) max[σ(0), σ(ϵ)]ϵ|ϵ=1 = U(ϵ) max[σ(0), σ(ϵ)] (2.6) 2.2.3 Computational Analysis In order to investigate the honeycomb behavior under uni-axial quasi-static compression, a finite element model (FEM) was developed to simulate the out of plane compression in ABAQUS. The dimensions, cell shape, and overall geometry of the honeycomb including buckling initiators and wall thickness were represented using the shell elements model. To explore the advantages of honeycomb structures with buckling initiators, the FEM model of the structure without buckling initiators was also simulated. The shell element thickness of both model was set to be 0.7 mm. Two plates (modeled as rigid bodies) were added to the honeycomb to represent the MTS test fixture and facilitate the load being applied. In the uni-axial compression simulation, the bottom and top plates were modeled as a general surface-to-surface contact with the honeycomb block bottom and top surfaces with a friction coefficient of 0.6. The bottom plate was fixed and a displacement of 24 mm was applied to the top plate to mimic testing. The dynamic explicit solver in ABAQUS was adopted with a simulation time period of 0.02 s and the compression displacement was ramped from 0 to 24 mm in this period. The material properties of the ABS-R adopted in the FEM simulations are: an effective 26 elastic modulus of 1702 MPa, a Poisson’s ratio of 0.193, and a yield stress of 71.79 MPa. For simplicity, a linear isotropic hardening plastic model after yielding was used in the simulation with a yield stress of 71.79 MPa at a plastic strain of 0 and 82 MPa at a plastic strain of 0.3. In addition, shear failure with an initiation value of 1.4 was added in the analysis. 2.3 Results 2.3.1 Preliminary Data Review As the buckling initiator height increases, the peak stress was found to decrease as Fig- ure 2.2A shows. This occurs regardless of the inscribed diameter. The peak stress is found to decreases as the inscribed diameter increases due to the increase in contact area over which the load is being applied (Figure 2.2A-C). The peak stress also experiences a shift from a later strain range to an earlier strain as the buckling initiator height increases. The crush efficiency of these samples show a consistent trend. The samples experience an initial increase in crush efficiency until it plateaus before decreasing once densification initiates. Figure 2.3A-C show that the maximum crush efficiency decreases as the inscribed diameter in- creases. Regardless of the inscribed diameter, the samples with the buckling initiators located at the top result in the highest crush efficiency across the usable strain range. This is followed by the samples without buckling initiators for the samples with an inscribed diameter of 15- and 20-mm. When the inscribed diameter is smaller, having buckling initiators are found to increase the crush efficiency across the usable strain range. The energy absorbed efficiency describes the ability of the sample to absorb the energy, thus protecting the occupant. Regardless of the inscribed diameter, the maximum energy absorbed 27 Figure 2.2: The stress- strain behavior of the samples under quasi-static conditions. A) 10-, B) 15-, and C) 20-mm inscribed diameters. 28 Figure 2.3: The strain dependent crush efficiency of the samples under quasi-static conditions. A) 10-, B) 15-, and C) 20-mm inscribed diameters. 29 Figure 2.4: The energy absorbed efficiency of the samples under quasi-static conditions. A) 10-, B) 15-, and C) 20-mm inscribed diameters. efficiency is achieved by the samples with buckling initiators located at the top, followed by 0.00BI, 0.75BI, and 0.50BI respectively (Figure 2.4). The samples also densify in the same order, so the 1.00BI sample has the shortest usable strain range, about 70% strain, compared to 0.50BI, which is usable up to 85% strain. The metrics for these quasi-static tests are summarized in Figure 2.5. The peak stress is found to decrease as the height of the buckling initiator increases with the exception of the sample without buckling initiators. The peak stress decreases from over 90 MPa to less than 40 MPa by moving the buckling initiator from the midpoint to the top of the sample (Figure 2.5A). Also, increasing the inscribed diameter of the sample results in a decrease of the peak stress. For the samples with the buckling initiator at the midpoint, the peak stress decreases from about 90 to 50 30 Figure 2.5: The metrics for the tested samples: A) peak stress, B) mean crush stress, C) maximum strain dependent crush efficiency, and D) maximum energy absorbed efficiency. MPa by increasing the inscribed diameter from 10 mm to 20 mm. The mean crush stress is a metric that reports the average stress value over the full strain range. According to this metric, the 0.50BI sample has the highest average stress for both the 10- and 20-mm inscribed diameter samples (Figure 2.5B). The lowest reported mean crush stress for all samples is the 1.00BI samples. The maximum strain dependent crush efficiency is highest for the 1.00BI samples for all tested diameters by 5-10%. This is followed by the samples without buckling initiators. Regard- less of the situation, it will be more beneficial to use no buckling initiators before implementing buckling initiators 50 or 75% of the way up the sample. The maximum energy absorbed efficiency is dominated by the 1.00BI samples regardless of the sample’s diameter. These 1.00BI samples absorbed are almost 10% more efficient then the 31 Table 2.1: The average properties for the samples with varying BI location and inscribed diame- ters. D BI σpk σmc ∆σ ηSD ηEA [mm] [-] [MPa] [MPa] [MPa] [%] [%] 10 0.00 47.09 31.09 16.00 72.37 40.10 0.50 91.62 34.66 56.96 65.96 34.49 0.75 55.83 30.92 24.92 64.11 42.65 1.00 33.26 28.11 5.15 78.57 54.64 15 0.00 34.11 20.21 13.90 63.20 45.72 0.50 61.48 21.25 40.24 55.92 28.60 0.75 49.92 27.47 22.45 57.77 41.62 1.00 25.63 18.77 6.86 73.31 51.53 20 0.00 28.10 16.02 12.08 65.92 38.97 0.50 50.94 20.63 29.32 57.83 34.31 0.75 33.64 17.02 16.62 56.90 38.64 1.00 21.24 14.31 6.93 73.40 49.82 next most efficient samples (Figure 2.5D). The quantitative vales are provided in Table 2.1. 2.3.2 Validation of Results 2.3.2.1 Computational Analysis A computational analysis was completed on the 0.00BI and 1.00BI samples to determine whether the experimental results could be predicted. These two classes of samples were selected due to their promising outcomes with regards to the metrics. The computational analysis shows agreement with the experimental results for the 0.00BI stiffness results. The initial increase in slope matches well, reaching a peak stress of similar values at the same strain (Figures 2.6B and C). The mean crush stress is over-predicted by the computational analysis by approximately 5 MPa in the three inscribed diameters. This will likely result in an over-prediction of the crush efficiency. 32 Figure 2.6: A computational analysis of 0.00BI and 1.00BI samples. A) 10 mm with 0BI; B) 15 mm with 0BI; C) 20 mm with 0BI; D) 10 mm with 1BI; E) 15 mm with 1BI; and F) 20 mm with 1BI. Reviewing Figures 2.6 D, E, and F shows the computational analysis over predicts the stress in the 0 - 20% strain range. Although the strain at the peak stress is correct, the increase in stiffness results in a higher peak stress value. Each of the metrics were computed for the computational and experimental sets of data (Figure 2.7). The computational analysis shows strong agreement between the metrics for the exper- imental and computational samples. Figure 2.7A shows the crush efficiency decreases as the inscribed diameter increases. Similarly, it shows the maximum crush efficiency decreases when there are buckling initiators located at the top of the sample as compared to having no buckling initiators. Similarly, the maximum reported energy absorbed efficiency is found to decrease as the inscribed diameter increases (Figure 2.7B). Likewise, the maximum energy absorbed efficiency value decreases with the presence of buckling initiators. 33 Figure 2.7: The computational analysis metrics for the samples. A) The threshold strain depen- dent crush efficiency, B) the threshold energy absorbed efficiency as calculated using a threshold of 40 MPa. C) The average and D) variance in crush efficiency from 2- 75% strain. The average crush efficiency across the strain range of 2 to 75% strain shows a different set of trends. The samples with buckling initiators have a higher average crush efficiency than those without buckling initiators (Figure 2.7C). The samples maintain a relatively consistent crush ef- ficiency across the range of inscribed diameters studied. The variance in this crush efficiency is found to be significantly larger in the samples with buckling initiators, however the computa- tional analysis does not capture this response. Figure 2.7D shows the disagreement between the computational analysis and the experimental study. With the exception of the variance in the crush efficiency, the computational analysis pro- vides the ability to predict the performance of the samples. The behavior of the computational analysis will allow for the ability to design future samples without extensive testing. The table below includes the values for each metric that was analyzed in this study, as determined by the computational model and the experiments (Table 2.2). The difference between these values are 34 reported to provide additional insight into the precision of the model. Table 2.2: The computational and experimental metrics for all three inscribed diameters. Diameter σpk σmc ηSD,T ηEA,T avg ηSD σ2 ηSD [mm] [MPa] [MPa] [%] [%] % [-] 10 0.0BI Measured 8.00 5.28 41.35 1.86 50.90 0.0040 Computed 50.30 30.99 58.34 2.10 57.99 0.0005 % Change 528.8 998.3 41.08 12.90 13.93 87.5 0.5BI Measured 5.93 5.01 60.01 47.79 72.84 0.0079 Computed 36.73 28.96 72.39 54.96 74.17 0.0022 % Change 519.4 478.0 20.63 15.00 1.83 72.15 15 0.0BI Measured 4.66 2.84 51.40 40.44 54.40 0.0026 Computed 39.13 27.13 67.82 49.41 63.32 0.0010 % Change 739.7 855.3 31.95 22.18 16.40 61.59 0.5BI Measured 3.38 3.10 49.57 38.15 65.62 0.0072 Computed 34.32 24.40 60.99 45.30 66.98 0.0011 % Change 915.4 687.1 23.04 18.43 2.07 84.72 20 0.0BI Measured 2.92 1.77 40.37 30.20 46.87 0.0029 Computed 28.74 21.82 54.55 37.00 64.58 0.0026 % Change 884.2 1132 35.13 22.52 37.78 10.34 0.5BI Measured 2.27 1.72 38.21 30.64 61.61 0.0041 Computed 27.08 20.46 51.16 37.92 70.88 0.0012 % Change 1092 1089 33.89 23.76 15.05 70.73 2.3.2.2 Mathematical Analysis The analytical analysis for honeycomb materials have existed for well over 50 years. The original buckling load within a single panel of a honeycomb was derived by Timoshenko and Gere in 1961 [66]. In their work, Timoshenko et al. determined that the buckling load is Pcrit = KEs (1− v2s) t3 l (2.7) 35 where K is a constant for the end constraint factor, Es is the modulus of the material, vs is the Poisson’s Ratio, and the remaining variables correspond to geometric dimensions of the honey- comb. The honeycomb in this study have a singular wall thickness, t, so the elastic buckling stress must be re-derived slightly, since Roark’s equation (originally derived from Timoshenko et. al) assumes walls of varying thicknesses [67]. For this study, the elastic buckling stress was derived knowing that all six walls have a singular thickness, t, and thus will maintain the same load after they reach a collapse load of Pcrit [67]. The elastic buckling load is the sum of the individual loads that each walls carries, so the elastic collapse stress or peak stress is: σ3 = 6Pcrit 2cosα(1 + sinα)l2 = 3KEs (1− v2s)cosα(1 + sinα) t3 l3 (2.8) This equation requires knowing the material properties of the honeycomb. From data sheets, the modulus was determined to be 2400 MPa with a yield stress of 41 MPa and a Pois- son’s ratio of 0.25 [Ultimaker]. To determine the predicted value, it is important to identify the end constraint factor. When the ends are rigidly clamped, literature has shown that K = 6.2, however this is not always the case [66, 67]. A conservative estimate is K = 3.29 because each wall is simply supported along the edges. These two values will provide an upper and lower bound, respectively, for the elastic collapse stress of the tested honeycomb [67]. To analyze the behavior of these honeycomb, the end constraint factor chosen for this analysis was K = 5.73 because it is preferential to a clamped setup, but is not rigidily clamped [66]. As Figure 2.8A shows, the experimental peak stresses fall within the upper and lower bounds that was derived using the modified Roark analysis. Each of these points is an average 36 Figure 2.8: Analytical analysis of the experimental results for (a) peak stress and (b) plateau stress. Table 2.3: The results of the analytical models in comparison with the experimental results. Diamater Upper Bound Analytical Experimental Lower Bound [mm] [MPa] [MPa] [MPa] [MPa] σpk 10 22.05 20.38 8.00 0.31 15 6.84 7.41 4.66 0.13 20 3.33 1.92 2.92 0.05 σpl 10 - 5.48 5.28 - 15 - 2.99 2.56 - 20 - 1.92 1.53 - peak stress for the given inscribed diameter, with the error bar denoting the standard deviation of the measurements. The analytical analysis is an appropriate fit for this data, confirming the experimental tests (Table 2.3). Wierzbicki derived another relationship to describe the behavior of honeycomb. This one determines the plastic buckling stress of honeycomb using the geometric and material proper- ties [39]. Ashby and Gibson provide an overview of the derivation for regular hexagons with a uniform wall thickness [37]. This plastic buckling stress or mean crush stress is defined as σ3 = 5.6σys( t l )5/3 (2.9) 37 This is the region during which the buckling occurs. Figure 2.8B shows the analytical equation is a good predictor of the mean crush stress of the experimental samples for the ABS-R honeycomb, once again confirming the experimental results. 2.3.3 Design for Application Due to the application of these materials, the materials must not exceed a threshold stress value. If they do, the energy would not be absorbed and therefore the occupant would be dam- aged. For this study, the representative threshold stress selected was 40 MPa. Figure 2.9 shows the threshold stress marked on the stress-strain curves. Any of the samples that exceed this threshold stress are considered in-effective for this application. Reviewing Figure 2.9A, 0.00BI, 0.50BI, and 0.75BI are unable to meet the threshold requirement. Similarly, 0.75BI and 0.50BI are unable to meet the threshold requirement for the 15 mm diameter samples and the 0.50BI sample is unable to meet the requirement for the 20 mm diameter samples. The strain dependent crush efficiency shows the performance of these samples taking into account the restricted threshold stress of 40 MPa. In Figure 2.10, the 1.00BI sample reaches a crush efficiency of 65% by 10% strain and maintains it over the full strain range. Similarly, at 15 mm, the 0.00BI and 1.00BI samples reach a consistent crush efficiency of 45% by 25% strain and hold that value until densification is achieved. The energy absorbed efficiency is also plotted in Figure 2.11. For all samples, it is shown to be constantly increasing. As the inscribed diameter increases, the maximum energy absorbed efficiency is found to decrease. None of the samples are found to densify in the given strain range 38 Figure 2.9: Analyzing the samples for a given design application using a representative threshold stress value of 40 MPa where (A) is 10 mm, (B) is 15 mm, and (C) is 20 mm inscribed diameter. Figure 2.10: The strain dependent crush efficiency of the quasi-static samples after the threshold has been applied for an inscribed diameter of A) 10-, B) 15-, and C) 20-mm. 39 Figure 2.11: The energy absorbed efficiency of the samples tested quasi-static conditions after the threshold has been applied. A) 10-, B) 15-, and C) 20-mm inscribed diameters. either, indicating the occupant would be injured before the sample fully densifies. The performance metrics are reported in Figure 2.12. Any sample that did not meet the threshold requirement was denoted with an ’x’ of the respective color. Although the maximum reported crush efficiency was the lowest for the samples with 1.00BI at all diameters, the average crush efficiency was highest for these samples. The energy absorbed efficiency and variance of crush efficiency further confirm why these 1.00BI samples are a good candidate for this end application. 2.4 Discussion As discussed throughout this Chapter, the geometry of the honeycomb cell will effect the energy absorption properties. To demonstrate the effects of the metrics selected, a series of radar 40 Figure 2.12: The design metrics as calculated using the threshold stress for (A) the threshold crush efficiency, (B) the threshold energy absorbed efficiency, (C) the average crush efficiency and (D) the variance in crush efficiency from 2- 75% strain. Any samples that had not met the threshold requirement are denoted with an ’X’. plots are presented in Figure 2.13 to assist in the decision making process. Each spoke portrays a different crashworthiness metric of interest. Beginning with the topmost spoke, the change is stress is shown using a range shown in Table 2.4. The change in stress is the difference between the peak stress and the plateau stress. This spoke has been inverted such that the smallest value (3 MPa) is on the exterior, indicating best performance. The less deviation between the peak and plateau stress, the more area under the curve and thus an increase in crashworthiness. The next spoke portrays the maximum strain dependent crush efficiency recorded for the thresholded data. The spoke is designed to have the maximum crush efficiency on the exterior and the minimum crush efficiency shown on the interior. The third spoke analyzes a similar characteristic called the threshold energy absorbed efficiency. Once again, it shows the maximum efficiency on the exterior of the radar and the minimum efficiency on the interior of the radar. The final two spokes 41 Table 2.4: The minimum and maximum range over which each individual spoke is plotted. ∆σ ηSD,T ηEA,T Avg ηSD σ2 ηSD [MPa] [%] [%] [%] [-] Minimum 3 35 30 30 2 Maximum 18 65 50 75 15 return to analyzing the initial data without thresholding it. The first shows the average crush efficiency recorded between 2 and 75% strain. This is representative of the efficiency across the full impact event. Similarly, on the final spoke, the variance of the crush efficiency is provided. This is intended to provide additional information regarding the relative error seen with this sample. Figure 2.13 shows all three geometries as radar plots. Each plot consists of the five met- rics that have been studied throughout this work. The values most suited for energy absorption applications are listed furthest from the center of the radar plot. Each of these three plots show the 1.00BI sample encompasses the entire 0.00BI and 0.75BI samples when applicable. This is indicative of the 1.00BI sample outperforming in all metrics, regardless of the geometry of the cell. When looking at the individual radar plots, it is evident that the 1.00BI sample with the smallest inscribed diameter (Figure 2.13A) is the best or second best choice in all metrics except the peak crush stress. For this reason, the 10 mm inscribed diameter honeycomb with buckling initiators will perform the best in crashworthiness applications. 42 Figure 2.13: A radar plot of the samples that meet the threshold requirement for the design application. 2.5 Conclusions During the course of this study, honeycomb with three different inscribed diameters were manufactured using ABS-R to study the influence of buckling initiators on changing geometries. The following conclusions can be drawn from this work. 1. The peak stress and mean crush stress will decrease with the increasing inscribed diame- ter, regardless of the presence of the presence of buckling initiators. Similarly, the crush and energy absorbed efficiency will decrease as the inscribed diameter increases. For all metrics, except the peak stress, the presence of buckling initiators will increase the perfor- mance compared to their counterparts. As mentioned, the peak stress will decrease with the presence of buckling initiators. 2. The performance of these samples have been validated through the use of a finite element model in ABAQUS. The same trends are apparent: as the inscribed diameter increases, the peak and mean crush stress and energy absorbed and crush efficiencies will decreases regardless of the presence of buckling initiators. 43 3. The analytical analysis validated the performance of the samples as well. The re-derived version of Roark’s equation allows for the peak stress to be accurately predicted. The peak and mean crush stress decrease with increasing inscribed diameters. 44 Chapter 3: Visco-Elastic Honeycomb for Low-Strain Rate Energy Absorption Energy-absorbing materials have extensive applications in aerospace and automotive appli- cations. Research has shown buckling initiators, or triggers, in energy-absorbing tubular struc- tures increase the energy absorbed by encouraging the side panels to fold when loaded out of plane in compression conditions. Additively manufactured TPU honeycombs were designed in this study to include these buckling initiators, which introduced a slight decrease in initial weight, as well as initial stress concentrations, while improving crashworthiness characteristics. The samples with buckling initiators located 50% up the height (0.5BI) showed an increase in crush efficiency when directly compared to their no buckling initiator (0.0.0BI) counterparts. The 0.5BI samples maintained an increased crush efficiency regardless of the strain rate used. The samples with 0.5BI were able to better equilibrate the peak stress with the plateau stress. These honeycomb samples were found to maintain their crush efficiency, even after multiple rounds of compression testing. The quasi-static 0.0BI samples experienced a 23.4% decrease in the peak stress after multiple rounds of compression testing, while the 0.5BI samples saw approximately a 23.0% decrease. The 0.5BI samples averaged a decrease in crush efficiency of 0.5%, while the 0.0.0BI samples saw a decrease in crush efficiency of 5%. As the strain rate increased, the crush efficiency for the 0.5BI samples showed an increase in performance, with a smaller degra- dation in crush efficiency over multiple uses. Visco-elastic honeycomb with buckling initiators 45 has a higher energy absorption than samples with no buckling initiators when exposed to multiple impact cycles. This research was published in Polymers [68]. 3.1 Introduction Crashworthiness and energy-absorbing materials are of great interest to both automotive and aerospace industries due to the need for occupant protection. Work to date has shown that foam and honeycomb materials have a promising future in regard to energy absorption [69, 70]. Using a controlled failure mechanism in a honeycomb will allow for a further increase in the energy absorption of the material. Buckling initiators, sometimes referred to as trigger mechanisms, have been a commonly studied mechanism through which to introduce the controlled failure of a material structure. Two methods are typically used to introduce controlled failures [71]. For the purpose of this paper, they will be differentiated by the names buckling initiators and trigger mechanisms. Buckling initiators are voids introduced into the structure via a subtractive manufacturing method [72,73]. These initiators are purposeful stress concentrations intended to fail first, thus encouraging the structure to begin folding [74, 75]. Traditionally, the part is completed before a drill is used to remove a portion of the material along the vertices. This method can be difficult to use due to the lack of control when implementing the buckling initiators. If the buckling initiator is implemented too high on the wall of the structure, there is the potential for the structure stiffness to decrease, causing the energy absorption to decrease [72]. Similarly, machining may introduce residual stresses into the part, potentially reducing the repeatability of the buckling performance. 46 On the other hand, an external trigger mechanism can also lead to controlled failures. These trigger mechanisms tend to be a plate placed at either the top or bottom of a tube [76–78]. These plates have a rectangular protuberance, so that when a compressive load is applied, the walls of the tube will experience a localized stress regime until failure occurs [79–81]. These plates, or trigger mechanisms, are easier to implement in a laboratory setting; however, they can be more difficult to implement in a large-scale setting. External trigger mechanisms also add weight to the structure; and so they are less desirable in vehicle applications. Buckling initiators and trigger mechanisms have been extensively studied in tubular sam- ples. There is extensive literature available regarding the behavior of tubes having different forms of defects. The most common cross-sections are circular and square tubes [82–84]. This con- cept has been studied in metals in the literature as far back as the 1960s, but the focus has been primarily on aluminum and its alloys [22, 85–88]. Researchers saw the potential of combining lightweight aluminum with the high-strength, low-density design of the honeycomb [89–92]. Aluminum honeycomb is typically manufactured by gluing strips of aluminum together and inflating them to obtain the final structure [37,93,94]. The location of these strips of glue will increase the honeycomb wall thickness at those interfaces, causing the honeycomb to fail due to those interfaces as opposed to failing in buckling [95]. The thickness of the honeycomb walls will not be consistent using this manufacturing method. The varying wall thickness increases computational complexity, so consistent wall thickness has been assumed for simplicity [96, 97]. Honeycomb can be designed to have various core shapes, including rectangular, triangular, and hexagonal [98–104]. Although aluminum is a common honeycomb material, honeycomb has been manufactured out of many materials, including—but not limited to—steel, fiber glass, paper, acrylonitrile butadiene sytrene (ABS), polylactic acid 47 (PLA), and thermoplastic elastomer (TPE) [105–110]. Additively manufactured honeycombs like ABS, PLA, and TPU provide numerous bene- fits. The need for glue strips, unlike aluminum honeycomb, is eliminated. When oriented prop- erly on the print bed, the fused filament fabrication (FFF) process will maintain the strength of the material, as many additive manufacturing studies have shown [111, 112]. Additive manu- facturing enables the precise fabrication of honeycomb geometry, especially with respect to a constant wall thickness. BIs can be introduced in any location and in any shape during print- ing so that residual stress from subtractive machining can be eliminated. Even with all of these benefits, additively manufactured honeycomb structures have not been extensively studied due to their brittle nature [59, 113, 114]. ABS and PLA exhibit brittle failure and high stiffness where it might be desirable to have buckling failure and low stiffness with the potential for shape re- covery, which would suggest the use of a softer, visco-elastic material. Moreover, if a flexible, lighter weight visco-elastic material is identified, a honeycomb could be manufactured that could include buckling initiators and still be crashworthy [115]. Extensive research on honeycomb materials has been reported in the literature, including research on metallic honeycombs (ductile materials) and polymer material-based honeycombs (brittle materials). The original contributions of this current work are focused on: (1) the use of low shore hardness visco-elastic polymers with a goal of creating a low-pressure honeycomb that is suitable for occupant protection, (2) the introduction of buckling initiators (diamond-shaped holes) that are integrated into the structure to encourage the folding of the honeycomb faces and to improve the crush efficiency of the honeycomb structure, (3) to exploit the deformation recovery that may be possible when using buckling initiators of this type so that protection against multiple impacts can be provided (albeit with reduced effectiveness), and (4) to exploit additive 48 manufacturing to fabricate these visco-elastic honeycomb structures with these buckling initiator features. To achieve these goals, this study focuses on the influence of buckling initiators in a ther- moplastic polyurethane (TPU) honeycomb structure (or a visco-elastic honeycomb structure). The buckling initiators are expected to increase the crush efficiency due to the controlled buck- ling of the honeycomb faces (sides). Using an additive manufacturing process should minimize stress concentrations prior to testing, while ensuring that all walls are of the same thickness. Ad- ditive manufacturing enables the precise fabrication of cell size, as well as the location, shape, and size of the buckling initiators. The low shore hardness TPU should allow for the honeycomb to maximize the energy absorbed at low stroking loads as well. We will compare the energy absorption characteristics of visco-elastic honeycomb structures with buckling initiators located on the vertices (0.5BI samples) to those without buckling initiators (0.0BI samples) in order to assess their relative merits as crashworthy structures. 3.2 Materials and Methods 3.2.1 Manufacturing Honeycomb materials are commonly provided in sheets and have a repeating pattern. As explained in [37], the unit cell of a honeycomb structure may be represented as a vertex with its three adjoining walls (Figure 3.1A). Because of this lack of additional vertices, the interaction be- tween cell BIs could not be easily observed in the experiment. As a result, preliminary tests were conducted on the samples that were square in shape; however, there were multiple free-standing walls (Figure 3.1B). When these honeycomb were tested, the walls collapsed in unrepeatable 49 manners that were not representative of the honeycomb. These walls also blocked the view of the buckling initiators. Figure 3.1: The unit cell of the tested honeycomb. (A) Accepted representative volume element according to Gibson; (B) originally tested sheet of honeycomb; and (C) Walls with a free edge obstructed the view of the honeycomb walls during crush, so that all such free edges were elimi- nated in the unit cell shown here, which was used in this study. Because the goal of this study was to analyze the effects that BIs have on visco-elastic honeycomb, it was imperative that the BIs were visible. To maintain the representative perfor- mance of a full sheet of honeycomb and ensure that the BIs were visible, a representative volume element of six hexagonal cells surrounding a central hexagonal cell was selected (Figure 3.1C). Samples were manufactured using the Pro Series Flex TPU filament (MatterHackers, Lake Forest, CA, USA, 2018). The TPU had a Shore hardness of 98A. Samples were manufactured using a Diabase H-Series 3D Printer (Diabase Engineering, Longmont, CO, USA). This fused deposition modeling printer was selected for its proprietary extruders, which are compatible with flexible filaments with a Shore hardness ranging from 83D down to 60A. All samples had an overall height of 30 mm, with individual cells having a wall thickness of 0.85 mm, and an in- scribed circle diameter of 30 mm (Figure 3.2). The samples with buckling initiators (0.5BI) had the BI half way up the wall at all vertices. The diamond shape was defined by a point-to-point interior dimension of 4 mm in each direction (Figure 3.2C). Honeycomb samples without buck- 50 ling initiators (0.0BI) were also manufactured, for the purpose of comparison with the samples that had 0.5BIs, to assess how BIs affect performance. Figure 3.2: The dimensions used to manufacture the honeycomb. (A) The buckling initiators are voids on the vertices in the isometric view of the representative volume element.(B) The thickness and cell dimensions are shown in the top view. (C) Diamond-shaped buckling initiator. (D) The remaining dimensions in the side view. The honeycomb was designed so that t = 0.85 mm, C = 30 mm, L = 18.3 mm, and H = 30 mm. In addition, the honeycomb had diamond-shaped buckling initiators, where B = 4 mm. 3.2.2 Testing All testing was conducted using an