Computational simulation of woven fabric subjected to ballistic impacts

COMPUTATIONAL SIMULATION OF WOVEN FABRIC SUBJECTED TO BALLISTIC IMPACTS CHING TUAN WOON (B.Eng.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2005 ACKNOWLEDGEMENTS I will like to thank my supervisor, Dr Vincent Tan BC, for his most wonderful guidance throughout my project. His patience and willingness to accommodate me as a part-time student is very much appreciated. Thanks, Dr Tan. Special thanks too to Eng Kit, Dr Yuan JM, and others, for without their experimental results, there wouldn’t be anything for me to validate my numerical model with. I’ll also like to thank Xuesen for his most valuable help regarding numerical modelling of woven fabric. Will also like to thank the staff of LSTC for providing me with an academic license of LS-DYNA for me to start my simulation work, as well as being so helpful in answering my technical queries concerning the software. Thanks too to Alvin and Joe, for all the help ever rendered to me in the Impact Laboratory. And finally, a big thank you to the people of the Impact Laboratory, without whom the time I spent in the laboratory will be dreadful and boring. Here’s wishing all of you the best in your future endeavours! i TABLE OF CONTENTS ACKNOWLEDGEMENTS i TABLE OF CONTENTS ii SUMMARY iv LIST OF TABLES v LIST OF FIGURES vi LIST OF SYMBOLS x 1. INTRODUCTION 1 2. LITERATURE REVIEW 3 3. 4. 5. 2.1. Yarn And Fabric Properties 3 2.2. Analytical Models 8 2.3. Numerical Models 9 METHODOLOGY 12 3.1. Experimental Details 12 3.2. Woven Fabric Material Properties 14 3.3. Finite Element Model 20 TWARON® CT716 WOVEN FABRIC RESULTS 25 4.1. Single Ply Model 25 4.2. Friction Effects 41 4.3. Fabric Weave Effects 43 4.4. Multiple Plies Model 52 KEVLAR® 218440 WOVEN FABRIC RESULTS 59 5.1. Single Ply Model 59 5.2. Multiple Plies Model 68 ii 6. 7. DISCUSSION 71 6.1. Multiple Plies Effects 71 6.2. Fabric Thickness Effects 73 6.3. Mesh Density Effects 77 RECOMMENDATIONS 79 7.1. Material Properties 79 7.2. Boundary Conditions 79 8. CONCLUSIONS 80 9. BIBLIOGRAPHY 83 APPENDIX A: LS-DYNA INPUT FILE FOR TWARON® CT716 FABRIC 88 APPENDIX B: LS-DYNA INPUT FILE FOR KEVLAR® 218440 FABRIC 92 iii SUMMARY This project proposes a novel numerical method to simulate the ballistic impact of woven fabric by small projectiles. The model takes into account various yarn and fabric properties that affects the performance of fabric armour. These properties include the rate-dependent property of the yarns, the fabric woven structure and crimp, as well as inter-yarn friction. The model also takes into account projectileyarn friction, and can simulate oblique impacts and different projectile geometries. The model uses only 1D elements for the modelling of the fabric, and allows for multiple plies of fabric to be modelled. The spacing between the plies of the fabric can also be adjusted. The model runs on a commercially available finite-element analysis software. Agreement with experimental results was achieved for 2 different types of woven fabric. Insights to the influences of various parameters to the woven fabric penetration process were also obtained. iv LIST OF TABLES Table 1. Nominal material properties of Twaron® CT716 14 Table 2. Values of viscoelastic model parameters of Twaron® CT716 15 Table 3. Measured material properties of Kevlar® 218440 19 Table 4. Values of viscoelastic model parameters of Kevlar® 218440 19 Table 5. Numerical Results for Twaron® CT716 clamped on all sides 30 Table 6. Numerical Results for Twaron® CT716 clamped on 2 sides 36 Table 7. Ballistic Limits Obtained For Different Projectile-Yarn COF 42 Table 8. Ballistic Limits Obtained For Different Yarn-Yarn COF 42 Table 9. Numerical Results for 4x4 twill weave Twaron® CT716 clamped on all sides 45 Table 10. Comparisons of projectile displacement and velocities for clamped-onall-sides model 46 Table 11. Numerical Results for 4x4 twill weave Twaron® CT716 clamped on 2 sides 49 Table 12. Comparisons of projectile displacement and velocities for clamped-on2-sides model 50 Table 13. Ballistic Limits Obtained For Multiple Plies 57 Table 14. Numerical Results for Kevlar® 218440 clamped on 2 sides 63 Table 15. Numerical Results for Kevlar® 218440 clamped on all sides 68 Table 16. Numerical Results for 2-ply Kevlar® 218440 clamped on all sides 69 Table 17. Numerical Results for 3-ply Kevlar® 218440 clamped on 2 sides 70 v LIST OF FIGURES Figure 1. 3-element linear viscoelastic model 3 Figure 2. Fabric fully clamped on all sides (from [35]) 13 Figure 3. Fabric fully clamped on 2 sides (from [35]) 13 Figure 4. Axial force (N) against time (ms) graph showing relaxation behaviour of Twaron® CT716 17 Figure 5. Axial force (N) against strain graph showing response of Twaron® 18 CT716 to different strain rates (ms-1) Figure 6. Mesh of Twaron® CT716 woven fabric 21 Figure 7. Mesh of Kevlar® 218440 woven fabric 22 Figure 8. Entire numerical model. 24 Figure 9. Fabric deformation of Twaron® CT716 clamped on all sides for impact velocity = 110ms-1 26 Figure 10. Fabric deformation of Twaron® CT716 clamped on all sides for impact velocity = 400ms-1 27 Figure 11. Pyramidal shape deformation of fabric (from [34]) 27 Figure 12. “Wedge-through” effect 28 Figure 13. Residual velocity (ms-1) against impact velocity (ms-1) for Twaron® CT716 clamped on all sides 29 Figure 14. Energy absorbed (J) against impact velocity (ms-1) for Twaron® CT716 clamped on all sides 29 Figure 15. Fabric deformation of Twaron® CT716 clamped on 2 sides for impact velocity = 110ms-1 32 Figure 16. Fabric deformation of Twaron® CT716 clamped on 2 sides for impact velocity = 400ms-1 33 Figure 17. Deformation of fabric clamped on 2 sides (from [34]) 34 Figure 18. “Yarn pull-out” effect of fabric (from [34]) 34 Figure 19. Unravelling of yarns at the free edges of fabric (from [9]) 34 vi Figure 20. Residual velocity (ms-1) against impact velocity (ms-1) for Twaron® CT716 clamped on 2 sides 35 Figure 21. Energy absorbed (J) against impact velocity (ms-1) for Twaron® CT716 clamped on 2 sides 35 Figure 22. Residual velocity (ms-1) against impact velocity (ms-1) for different boundary conditions 38 Figure 23. Perforation time (ms) against impact velocity (ms-1) for different boundary conditions 39 Figure 24. Percentage improvement in perforation time (ms) against velocity (ms-1) for the clamped-on-2-sides model Figure 25. Fabric deformation of Twaron® CT716 for impact velocity = 110ms-1 and time = 20ms 40 Figure 26. Ballistic limit (ms-1) against projectile-yarn COF 41 Figure 27. Ballistic limit (ms-1) against yarn-yarn COF 42 Figure 28. Residual velocity (ms-1) against impact velocity (ms-1) for different fabric weaves for clamped-on-all-sides model 44 Figure 29. Energy absorbed (J) against impact velocity (ms-1) for different fabric weaves for clamped-on-all-sides model 44 Figure 30. Deformation plot for different fabric weaves for clamped-on-all-sides model at impact velocities of 110ms-1 (at 0.2ms) 46 Figure 31. Deformation plot for different fabric weaves for clamped-on-all-sides 47 model at impact velocities of 400ms-1 (at 0.05ms) Figure 32. Residual velocity (ms-1) against impact velocity (ms-1) for different fabric weaves for clamped-on-2-sides model 48 Figure 33. Energy absorbed (J) against impact velocity (ms-1) for different fabric weaves for clamped-on-2-sides model 49 Figure 34. Deformation plot for different fabric weaves for clamped-on-2-sides model at impact velocities of 200ms-1 (at 0.14ms) 51 Figure 35. Deformation plot for different fabric weaves for clamped-on-2-sides model at impact velocities of 400ms-1 (at 0.05ms) 51 Figure 36. 3-ply stacked system 53 Figure 37. 3-ply system spaced 5mm apart 53 impact 39 vii Figure 38. Sequence of fabric deformation for Twaron® CT716 3-ply stacked system 54 Figure 39. Sequence of fabric deformation for Twaron® CT716 3-ply system with 5mm spacing 55 Figure 40. Residual velocity (ms-1) against impact velocity (ms-1) for different ply systems 56 Figure 41. Fabric deformation of Kevlar® 218440 clamped on 2 sides for impact velocity = 100ms-1 60 Figure 42. Fabric deformation of Kevlar® 218440 clamped on 2 sides for impact velocity = 400ms-1 61 Figure 43. Residual velocity (ms-1) against impact velocity (ms-1) for Kevlar® 218440 clamped on 2 sides 62 Figure 44. Energy absorbed (J) against impact velocity (ms-1) for Kevlar® 218440 clamped on 2 sides 62 Figure 45. Fabric deformation of Kevlar® 218440 clamped on all sides for impact velocity = 160ms-1 65 Figure 46. Fabric deformation of Kevlar® 218440 clamped on all sides for impact velocity = 400ms-1 66 Figure 47. Residual velocity (ms-1) against impact velocity (ms-1) for Kevlar® 218440 clamped on all sides 67 Figure 48. Energy absorbed (J) against impact velocity (ms-1) for Kevlar® 218440 clamped on all sides 67 Figure 49. Sequence of fabric deformation for Kevlar® 218440 2-ply system with 5mm spacing 69 Figure 50. Sequence of fabric deformation for Kevlar® 218440 2-ply system with 10mm spacing 71 Figure 51. Disintegration of the Twaron® CT716 fabric with actual dimensions 74 Figure 52. Modifications made for Twaron® CT716 fabric 75 Figure 53. “Wedge-through” effect for 2nd modification model 76 Figure 54. Residual velocity (ms-1) against impact velocity (ms-1) for both modified models 76 Figure 55. Energy absorbed (J) against impact velocity (ms-1) for both modified models 77 viii Figure 56. Refined mesh density 78 Figure 57. Original mesh density 78 ix LIST OF SYMBOLS σ Fabric yarn stress ε Fabric yarn strain K1, K2 Stiffness parameters of 3-element linear viscoelastic model μ Viscosity parameter of 3-element linear viscoelastic model K0 Initial stiffness of 3-element linear viscoelastic model K∞ Long-term stiffness of 3-element linear viscoelastic model β Decay constant of 3-element linear viscoelastic model x 1. INTRODUCTION The use of body armour by man for protection from injury in combat has been prevalent since ancient times. The type of materials used to make such body armour has progressed with the advancement of technology from animal skins in ancient times to metals in the Middle Ages, and to composites made from various types of materials (natural and man-made) in modern times. Aromatic polyamide fibres, better known as Aramid fibres, is one example of manmade materials that is commonly used in making today’s body armour. Details of this fibre is described by Chiao et al. in [1]. Kevlar® and Twaron® are 2 examples of such fibres. These fibres are used to make yarns which are then woven into fabric. Woven fabric is commonly used in today’s body armour due to their excellent impact resistance, high strength-to-weight ratio and drapability. It has been determined that the deformation and perforation process of the woven fabric during ballistic impact are influenced by various yarn and fabric properties. A review of these properties is given by Cheeseman and Bogetti [2]. The design of protective clothing to optimize these properties is typically based on extensive ballistic impact tests. These tests consist of firing projectiles of various shapes and sizes into clamped specimens of the fabric. The impact and exit velocities of the projectile are measured, and the deformation of the fabric is captured with highspeed cameras. 1 There have also been numerous attempts, noticeably in the last decade, to numerically model the ballistic impact of woven fabric by small projectiles. The effects of the yarn and fabric properties on the ballistic impact performance of woven fabric have also been numerically studied. These have been made possible with the great advancement made in computing technology. The present study proposes a novel method of numerically modelling the ballistic impact of woven fabric by small projectiles using a commercially available software. This method allows for various important yarn and fabric properties that affect the penetration process of the woven fabric to be modelled while using only simple 1D elements for the fabric. Various other parameters that affect the penetration process can also be included. Numerical models of 2 types of woven fabrics with different weaving patterns were investigated and compared with experimental results. Having successfully validated the models, some parameters were then varied to study their effects on the penetration process. 2 2. LITERATURE REVIEW 2.1. Yarn And Fabric Properties A brief description of some of the yarn and fabric properties that past researchers have found to influence the deformation and perforation process of woven fabric during ballistic impact is reported in this section. 2.1.1. Yarn Material Properties Shim et al. [3,4] performed high-speed tensile tests on Twaron® yarns to investigate their response to dynamic loads. The experimental results indicate that Twaron® yarns are highly strain-rate dependent. A 3-element linear viscoelastic constitutive model (Figure 1) was found to describe the experimental stress-strain response reasonably well. This constitutive model was also used by Lim et al. [5] in the numerical modelling of Twaron® fabric. Figure 1. 3-element linear viscoelastic model 3 The stress-strain response of this model can be described by (1 + K2 & = K2 + & ) + K2 K1 (1) where K1, K2 (both representing spring stiffness) and μ (representing viscosity) are constants pertaining to the yarn material. The stiffness varies in the following manner K = K ∞ + (K 0 − K ∞ ) exp (− t) with K ∞ = (2) K + K2 K 1K 2 , K 0 = K1 , = 1 K1 + K 2 where K∞ is the long-term stiffness, K0 is the initial stiffness, and β is the decay constant. As explained by Shim et al. [3], this 3-element linear viscoelastic constitutive model is able to represent the primary bond of the fabric fibres with the K1 spring, and the secondary bond of the fabric fibres with the K2 spring and dashpot. As the extension of the K2 spring is affected by the dashpot, its behaviour during high strain rate loading will be very limited. Thus at high strain rate loading, the behaviour of this 3element linear viscoelastic constitutive model will be governed mostly by the K1 spring, while the K2 spring will also influence the behaviour of the 3-element linear viscoelastic constitutive model at low strain rate loading. The strain-rate dependent properties of Kevlar® yarns were also investigated by Wang and Xia [6,7]. 4 2.1.2. Fabric Woven Structure Several important effects obtained during the deformation and perforation process of the woven fabric are dependent on its woven structure. The type of weave of a fabric was found to affect the performance of the fabric by Cunniff [8]. He found that an unbalanced weave resulted in an asymmetric transverse deflection of the fabric. This resulted in less material being strained in the fabric, and a corresponding decrease in its performance. The plain cross woven structure is commonly used in the construction of the fabric of protective clothing. This woven structure will result in the fabric being orthotropic, with the principal directions in the warp and weft directions. Cheeseman and Bogetti [2] noted a “wedge-through” effect during the fabric penetration process. During this process, some yarns are pushed aside while some are broken by the projectile, allowing the projectile to slip through. The formation of a hole smaller than the projectile diameter, obtained in experiments done by Shim et al. [3], Tan et al. [9], and others bears claim to this effect. Cheeseman and Bogetti [2] attribute the yarn mobility to be a cause of this “wedge-through” effect, with loosely woven fabric being more susceptible to it. The “yarn pull-out” effect, also mentioned by Cheeseman and Bogetti [2], is the pulling out of the yarns from the free edges by the projectile. This happens to fabric specimens that are clamped on only 2 sides. It was noted that this also resulted in more energy absorption by the fabric. This effect was observed to occur in different degrees with projectiles of different shapes by Tan et al. [9]. In particular, conical 5 and ogival projectiles gave rise to the least yarn pull-out, compared to hemispherical and flat-head projectiles. Crimp is the undulation of the yarns due to their interlacing in the woven structure. The straightening and realignment of these yarns during ballistic impact will result in higher fabric deflection, as mentioned by Shim et al. [3,4]. It was mentioned by Zeng et al. [10] that the warp and weft yarns have different degrees of crimp due to the weaving process, as higher tension is applied to the weft yarns then. 2.1.3. Friction Experiments done by Tan et al. [9] showed that frictional effects are more prominent at lower impact velocities. Small patches of fibre breakage at the yarn crossover points could be seen near the impact region for lower impact velocities compared to the cleaner breakage for higher impact velocities. It was thought that this was due to more yarns being broken on contact for higher impact velocities. Frictional effects are also dependent on the shape of the projectile. Three fabric failure mechanisms – fibrillation (the splitting of fibres along its length), flattening and rupturing of the fibres, were also identified. Bazhenov [11] found a decrease in ballistic impact performance for wet Aramid laminates. A projectile could successfully perforate a wet 20-ply laminate, but not a dry 14-ply laminate. It was noticed that less energy was transferred to yarns away from the impact zone and the width of the yarn pull-out zone was very much reduced for wet laminates. It was thought that the presence of water led to a 6 reduction of friction between the projectile and fabric, resulting in the sliding of the projectile between the fabric yarns. In a study of the effects of inter-yarn friction on ballistic performance of fabric, Tan et al. [12] varied the inter-yarn friction of their fabric samples by impregnating them with varying concentrations of silica-water suspension. It was found that the ballistic limits of their fabric ply systems increased when the concentrations of silica-water suspension was increased, up till a certain weight concentration. 2.1.4. Boundary Conditions Zeng et al. [10] investigated how different types of boundary conditions of fabric targets will affect their ballistic impact response. They found that fabrics that were clamped only on 2 opposing sides showed better energy absorption (up to 90%) than fabrics clamped on all sides for lower impact velocities. This is due to the large amount of kinetic energy transferred to the fabrics clamped only on 2 opposing sides, brought about by the “yarn pull-out” effect. However, for higher impact velocities, the fabrics clamped on all sides could absorb more energy than fabrics that were clamped on 2 opposing sides. This is because nearly as much kinetic energy as well as much more strain energy was transferred to the fabrics clamped on all sides at such high velocities. They attribute the shorter perforation time of fabrics clamped on all sides to the faster failure of yarns brought about by the reflection of stress waves from the clamped boundaries. 7 2.1.5. System Effects Of Multiple Plies The system effects of a 2-ply system were investigated by both Cunniff [8] and Lim et al. [13]. Cunniff [8] found that a spaced system armour would absorb more energy than a plied system armour. Lim et al. [13] found that the response of these 2 systems varied with different projectile geometries and impact velocities. In particular, a spaced system absorbed more energy than a plied system at high impact velocities for a spherical projectile. 2.2. Analytical Models Analytical models for predicting the ballistic impact response of fabric have been developed by a number of researchers [14–17]. General continuum mechanics equations are typically used in these models for the study of penetration mechanics. These models typically make a number of simplifications and assumptions. While the simplicity of these models makes them very attractive, such models typically predict only the ballistic limit of the fabric for a given configuration. These models very often do not or cannot take into account all the factors that affect ballistic impact. The model of Parga-Landa and Hernandez-Olivares [14] does not include rateeffects of the fabric material during impact. It also does not take into account projectile geometry, and accounts for fabric woven structure by making the wave velocity of the fabric a fixed fraction of the wave velocity in a single fibre. The model of Walker [15] models fabric as an extended system of linear elastic springs. 8 While it takes into account the mass of the projectile and number of fabric layers, it does not model projectile geometry, friction, and interaction between fabric layers. It also assumes no slippage between the fibres. Similarly, the model of Billion and Robinson [16] neglects friction and interaction between fabric layers. The model of Gu [17] models fabric as crossed non-woven yarns. Although this model does consider strain-rate effects, it does not consider friction nor projectile geometry. 2.3. Numerical Models The Finite Element Method (FEM) is a mathematical tool developed by academic and industrial researchers during the 1950s and 1960s. It is used for simulating the response of a physical system when the system is subjected to a set of loads and boundary conditions. For this method, the system is discretized into small elements that are connected to each other by nodal points, and their behaviour is represented by a system of equations. For simulation of dynamic cases, the equations are solved incrementally at each time-step. Various results, such as displacement and stress, are then derived from the solution. The real system with infinite unknowns is thus approximated with a finite number of unknowns. With the advance of computing power, FEM has become a powerful design tool. Today’s personal computer is able to solve some practical problems within minutes. New capabilities have also been added to the method. Today’s FEM software are able to solve structural, thermal, fluid flow, electromagnetic, and even coupled-field problems. It has also been used for the simulation of ballistic impact by several researchers. 9 A popular method of modelling fabric with finite elements is to represent them as networks of 1D elements. Shim et al. [3], Roylance et al. [18], Ting et al. [19], and Cunniff and Ting [20] modelled yarns using such elements pin-jointed at the nodes. Crimp was represented by Shim et al. [3] by discounting a fraction of the total strain of the elements as due to the straightening of the yarns. The model of Roylance et al. [18] accounts for crimp and fabric weave structure by providing a means to scale the mass of the fibre elements accordingly. Multiple plies were also represented by increasing the numerical density of the fabric, although it was admitted that this approach ignores the interaction between different plies. The projectile geometry was also not considered as the projectile impact velocity was applied only to a node. Ting et al. [19] and Cunniff and Ting [20] modelled the 1D elements in a noncoplanar fashion with kinks to represent crimped yarns. The nodes of the warp and weft yarns are coupled together with spring elements in their models. Ting et al. [19] modelled multiple plies by coupling different plies with compression elements. Their model assumes the plies to be laterally uncoupled, and does not check for contact between consecutive plies. The models of Shim et al. [3], Roylance et al. [18], Ting et al. [19], and Cunniff and Ting [20] do not account for the slippage of yarns. Johnson et al. [21] and Shahkarami et al. [22] also used pin-jointed 1D elements to model the yarns of the fabric. They used shell elements to provide contact surfaces for interactions between the projectile and different fabric layers. Johnson et al. [21] modelled crimp by using a bilinear stress-strain relation for the 1D elements. The simple idealization of fabrics as 2D shells or membranes were done by Lim et al. [5], Simons et al. [23], Brueggert and Tanov [24], and Tabiei and Ivanov [25,26]. 10 A disadvantage of using these types of elements is the inability to account for the slippage and unravelling of yarns. Inter-yarn friction, as well as crimp, could also not be represented. Detailed full-scale discretization of the yarns with solid elements was done by Shockey et al. [27], Blankenhorn et al. [28], Borovkov and Voinov [29], Gu [30], and Duan et al. [31,32]. The advantage of modelling the yarns with solid elements is that the orthotropic material properties of fabric, inter-yarn friction and crimp can be realistically modelled. However, as acknowledged by Blankenhorn et al. [28], the increased cost due to the large numbers of elements required is a major drawback of this method. The software used by a number of researchers [5,22–32] for their simulations is LSDYNA (Hallquist [33]). LS-DYNA is a commercially available non-linear, explicit, finite-element analysis software. It has been used to successfully simulate various types of impact phenomena. 11 3. METHODOLOGY Two different types of woven fabric made from different Aramid fibres, Twaron® CT716 and Kevlar® 218440, were modelled in this project. The Twaron® CT716 woven fabric is a product of Teijin Twaron, while the Kevlar® 218440 woven fabric is a product of Barrday. 3.1. Experimental Details The numerical models are based on actual ballistic tests done on 1-ply Twaron® CT716 woven fabric specimens (Tham [34]); as well as 1-ply, 2-ply and 3-ply systems for the Kevlar® 218440 woven fabric (Yuan and Tan [35]). The fabric specimen is constrained in 2 different ways during the ballistic tests. It is either fully clamped on all sides (Figure 2) or fully clamped only on 2 opposing sides (Figure 3). The fabric specimens had dimensions of 120mm by 120mm, and the projectile was a steel sphere of diameter 12mm and mass 7g. The projectile is propelled normally onto the centre of the fabric target by a high-pressure gas gun, with impact velocities ranging from 80ms-1 to 520ms-1. The experimental setup is similar to that of Shim et al. [3]. 12 Figure 2. Fabric fully clamped on all sides (from [35]) Figure 3. Fabric fully clamped on 2 sides (from [35]) 13 3.2. Woven Fabric Material Properties The present study uses the 3-element linear viscoelastic constitutive model used previously by Shim et al. [3,4] and Lim et al. [5] to model the strain-rate dependent properties of both types of woven fabric. For the modelling performed in this project, this constitutive model is adopted using one of LS-DYNA’s constitutive material model for discrete springs and dampers (*MAT_SPRING_MAXWELL). 3.2.1. Twaron® CT716 Woven Fabric The nominal material properties of Twaron® CT716 are listed in Table 1. The values of the 3 different parameters of the viscoelastic model used in this study for Twaron® CT716 are listed in Table 2. Table 1. Nominal material properties of Twaron® CT716 Specific density (g/mm3) 1.44e-3 Fibre tenacity (N/dtex) 0.23 Fibre modulus (MPa) 9e4 (N/dtex) 6.25 Elongation at break (%) 3.3 Count (warp / weft) (dtex) 1100 / 1100 Density (warp / weft) (ends/mm) 1.22 / 1.22 Areal density (g/mm2) 2.8e-4 Thickness (mm) 0.40 (1 dtex = 1e-7 g/mm) 14 Table 2. Values of viscoelastic model parameters of Twaron® CT716 K0 (N/mm) 8387.5 K∞ (N/mm) 4193.8 β (/ms) 4.62 The value of K0 is based on the nominal fibre modulus of Twaron® CT716. Its derivation is as follows Yarn modulus = 6.25 N/dtex × 1100 dtex = 6875 N/strain K 0 = 6875 N/strain × 1.22 ends/mm (3) = 8387.5 N/mm The relationship between K∞ and K0 was derived from Equation (2) with the values of K1 and K2 (which had similar values) used by Shim et al. [3]. K∞ = K1 K 2 K1 + K 2 1 K1 2 1 = K0 2 = 4193.8N/mm = (4) 15 Equation (2) was also used to estimate the value of β from the constants used by Shim et al. [3]. The derivation of β is as follows = K1 + K 2 6930 N/mm + 6930 N/mm 3000 N ms/mm = 4.62/ms = (5) where the values of K1, K2 and μ are used by Shim et al. [3]. The following figures (Figures 4 and 5) demonstrate the response of the 3-element linear viscoelastic constitutive model used to model Twaron® CT716. Figure 4 shows the relaxation behaviour of Twaron® CT716. This figure shows how the force required to extend a unit length of Twaron® CT716 by a constant strain of 1 will decrease exponentially from 8386N to a constant value of 4194N. Figure 5 shows the response of Twaron® CT716 subjected to varying strain rates. It can be seen that for very high strain rates, the stiffness of Twaron® CT716 (represented by the gradient of the curves) remains fairly constant. As the strain rates decreases, there is an increase in the rate at which the stiffness decreases. The stiffness of Twaron® CT716 will thus be lowest for the smallest strain rate. 16 Figure 4. Axial force (N) against time (ms) graph showing relaxation behaviour of Twaron® CT716 17 90.00 80.00 70.00 Force (N) 60.00 50.00 40.00 30.00 20.00 10.00 0.00 0.000 0.002 0.004 0.006 0.008 0.010 0.012 Strain 3000 2000 1000 500 300 200 100 50 Figure 5. Axial force (N) against strain graph showing response of Twaron® CT716 to different strain rates (ms-1) 18 3.2.2. Kevlar® 218440 Woven Fabric The measured material properties of Kevlar® 218440 [35] are listed in Table 3. The values of the 3 different parameters of the viscoelastic model used in this study for Kevlar® 218440 are listed in Table 4. Table 3. Measured material properties of Kevlar® 218440 Yarn modulus (N/strain) 12616 Density (warp / weft) (ends/mm) 0.9 / 0.9 Areal density (g/mm2) 6.25e-4 Thickness (mm) 0.627 Table 4. Values of viscoelastic model parameters of Kevlar® 218440 K0 (N/mm) 11350 K∞ (N/mm) 5680 β (/ms) 5 The value of K0 is based on the measured yarn modulus of Kevlar® 218440. Its derivation is as follows K 0 = 12616 N/strain × 0.9 ends/mm = 11350 N/mm (6) The value of K∞ is also estimated to be ½K0, and the value of β is estimated simply as a rounded-up value of that used for Twaron® CT716. 19 3.3. Finite Element Model The 3-element linear viscoelastic constitutive model found in LS-DYNA (*MAT_SPRING_MAXWELL) is for discrete springs and dampers elements, and models only the stress-strain response. The mass and volume of the fabric yarns are accounted for by using truss elements modelled using a null material model. This type of 1D element has 3 degrees of freedom at each node and carries only an axial force. It was used as it was deemed the most appropriate for modelling fabric yarns. The truss elements were assigned a circular cross-sectional area as the fabric yarns were simplified as being cylindrical in shape. Every fabric yarn element modelled thus consists of a truss element superimposed onto a discrete springs and dampers element. The truss element will account for the mass and contact surface of the fabric yarns, while the discrete springs and dampers element will account for the strain-rate dependent stiffness. The warp and weft yarns of the fabric are not tied to each other, and are free to interact and slide along one another. Another important reason for using LS-DYNA to model the ballistic impact of fabric (besides it having the 3-element linear viscoelastic constitutive model) is that one of its contact algorithms checks the entire length of 1D elements for penetration. This feature allows yarns to be modelled by 1D elements efficiently, and is extensively used in this study. The fabric yarn elements are modelled using a length consistent with the actual spacing of the fabric yarns. The nodes of the warp and weft yarns elements will thus 20 be vertically aligned at the crossover points of the fabric. This length was used as it is the longest length that can still accurately account for the fabric structure. The horizontal spacing of the fabric yarn elements is also similar to that used by Shim et al. [3]. A total of 84680 1D elements (42340 discrete springs and dampers elements and 42340 truss elements) were used to model the fabric. The Twaron® CT716 woven fabric has a plain cross woven structure, as can be seen in Figure 6. The Kevlar® 218440 woven fabric has a more complicated woven structure, that of a 4x4 twill. A diagram of the fabric mesh for the Kevlar® 218440 woven fabric can be found in Figure 7. 0.828mm Figure 6. Mesh of Twaron® CT716 woven fabric 21 1.11mm 1.15mm Figure 7. Mesh of Kevlar® 218440 woven fabric As can be seen in both Figures 6 and 7, the fabric yarn elements are modelled in a non-coplanar manner with kinks to represent crimp. It was assumed that the crimp in the warp and weft directions are the same. The thickness of the actual Kevlar® 218440 woven fabric is 0.6mm. Hence the yarns were modelled with cylindrical truss elements of 0.15mm radius. This meant that the yarns at the crossover points will initially be in contact with one another. Given that the weave density is 0.9x0.9 ends/mm, the length of each yarn segment between crossover points shown in Figure 7 works out to be 1.11mm for the straight elements and 1.15mm for the kinked elements. A similar way of modelling the Twaron® CT716 woven fabric shown in Figure 6 was attempted. The Twaron® CT716 woven fabric has a thickness of 0.4mm and weave density of 1.22x1.22 ends/mm. Hence it was initially modelled with 22 cylindrical truss elements of 0.1mm radius, so that the yarns at the crossover points will also initially be in contact with one another. However, this model seemed to display an extremely “brittle” characteristic, with the fabric disintegrating in a very unrealistic manner on impact. Two other models with modified dimensions were subsequently generated and tried. The model that was eventually chosen has cylindrical truss elements of 0.05mm radius with crossover points initially in contact with one another. The length of each yarn segment between crossover points works out to be 0.828mm. More details of these Twaron® CT716 woven fabric numerical models can be found in Section 6.2. It should be noted that the densities of the fabric yarns for both woven fabrics were adjusted to account for the correct fabric mass. In order to allow for fabric perforation, the truss elements were modelled with individual nodes joined together with spot-weld constraints. These constraints were defined to fail when the truss elements of the fabric experience a tensile strain of 5% in the axial direction of the fabric yarns. No shear failure was defined. This type of constraint allows the truss elements to rotate freely about the constrained nodes. The failure strain of 5% was based on the fabric fibres primary bond failure strain used by Shim et al. [3]. The fabric fibres primary bond failure strain, which is equivalent to the high strain rate failure strain as explained in Section 2.1.1, was chosen as it was found by Shim et al. [3] to be the cause of fabric fibres failure during ballistic impact due to the high strain rates experienced. 23 Friction was introduced between the projectile and fabric, as well as between the warp and weft yarns of the fabric. A value of 0.2 was used for the coefficient of friction between yarns as well as the coefficient of friction between fabric and steel for both types of yarns. This value is an estimate of the friction coefficient based on the measured value of 0.22 for the friction coefficient of Kevlar® 49 yarns [36]. Two different sets of boundary conditions were used for the simulations. One set has the fabric perfectly clamped on all sides, while the other set has the fabric perfectly clamped on 2 opposing sides. The projectile was simply modelled as a rigid sphere, and assigned the mechanical properties of steel. The projectile was modelled to impact the centre of the fabric in a normal direction. A plan view picture of the entire numerical model is shown in Figure 8. Figure 8. Entire numerical model. 24 4. TWARON® CT716 WOVEN FABRIC RESULTS 4.1. Single Ply Model 4.1.1. Clamped-On-All-Sides Model The deformation plots of the clamped-on-all-sides model subjected to impacts at velocities of 110ms-1 and 400ms-1 can be found in Figures 9 and 10. These 2 velocities are chosen because they represent low impact velocity and high impact velocity loading respectively. The impact velocity is considered low if the transverse wave reached the fixed edges prior to complete penetration, as can be seen in Figure 9, while it is considered high if complete penetration of the fabric was achieved before the transverse wave could reach the fixed edges, as can be seen in Figure 10. The plots also show that the pyramidal shape deformation observed in high-speed photographs of the ballistic impact experiment (Figure 11) is also obtained by the numerical model. It can be seen that for both impact velocities, tearing of the fabric yarns occurs only at the projectile impact region. 25 0.05ms 0.10ms 0.15ms 0.20ms 0.25ms Figure 9. Fabric deformation of Twaron® CT716 clamped on all sides for impact velocity = 110ms-1 26 0.01ms 0.03ms 0.05ms Figure 10. Fabric deformation of Twaron® CT716 clamped on all sides for impact velocity = 400ms-1 Figure 11. Pyramidal shape deformation of fabric (from [34]) 27 The deformation plots of Figure 12 show that as the projectile penetrates the fabric, some of the yarns are broken while some are pushed aside by the projectile. It can be seen that the pushing aside of the yarns allows the projectile to slip pass through. The “wedge-through” effect can clearly be seen in this numerical model. 0.035ms 0.040ms 0.045ms 0.050ms 0.055ms 0.060ms Figure 12. “Wedge-through” effect Figure 13 shows a plot of the residual velocity of the projectile against its impact velocity. This plot also includes experimental data (Tham [34]). A similar plot, for energy absorbed by the fabric (calculated by the loss in kinetic energy of the 28 projectile) against impact velocity of the projectile, can be found in Figure 14. The results are listed in Table 5. 600 Experiment Simulation Residal velocity (ms-1) 500 400 300 200 100 0 80 120 160 200 240 280 320 360 400 440 480 520 560 Impact velocity (ms-1) Figure 13. Residual velocity (ms-1) against impact velocity (ms-1) for Twaron® CT716 clamped on all sides 70 Experiment Simulation Energy absorbed (J) 60 50 40 30 20 10 0 80 120 160 200 240 280 320 360 400 440 480 520 560 Impact velocity (ms-1) Figure 14. Energy absorbed (J) against impact velocity (ms-1) for Twaron® CT716 clamped on all sides 29 Table 5. Numerical Results for Twaron® CT716 clamped on all sides Impact Velocity (ms-1) Residual Velocity (ms-1) Energy Absorbed (J) 100 0.0 35.0 105 43.9 31.8 110 50.5 33.4 120 65.9 35.2 125 75.7 34.6 150 113.2 33.9 175 139.8 38.8 200 165.6 44.0 250 227.3 38.0 300 278.2 44.0 350 332.8 41.1 400 379.7 55.5 450 431.1 58.4 500 485.0 51.9 525 514.5 38.2 The plots of residual velocity against impact velocity (Figure 13) and the energy absorbed against impact velocity (Figure 14) show that the numerical model is in good agreement with the experimental results, particularly in the lower impact velocity range ([...]... used to model the fabric The Twaron® CT716 woven fabric has a plain cross woven structure, as can be seen in Figure 6 The Kevlar® 218440 woven fabric has a more complicated woven structure, that of a 4x4 twill A diagram of the fabric mesh for the Kevlar® 218440 woven fabric can be found in Figure 7 0.828mm Figure 6 Mesh of Twaron® CT716 woven fabric 21 1.11mm 1.15mm Figure 7 Mesh of Kevlar® 218440 woven. .. Details of this fibre is described by Chiao et al in [1] Kevlar® and Twaron® are 2 examples of such fibres These fibres are used to make yarns which are then woven into fabric Woven fabric is commonly used in today’s body armour due to their excellent impact resistance, high strength -to- weight ratio and drapability It has been determined that the deformation and perforation process of the woven fabric. .. was transferred to yarns away from the impact zone and the width of the yarn pull-out zone was very much reduced for wet laminates It was thought that the presence of water led to a 6 reduction of friction between the projectile and fabric, resulting in the sliding of the projectile between the fabric yarns In a study of the effects of inter-yarn friction on ballistic performance of fabric, Tan et al... of the fabric for a given configuration These models very often do not or cannot take into account all the factors that affect ballistic impact The model of Parga-Landa and Hernandez-Olivares [14] does not include rateeffects of the fabric material during impact It also does not take into account projectile geometry, and accounts for fabric woven structure by making the wave velocity of the fabric. .. velocities of the projectile are measured, and the deformation of the fabric is captured with highspeed cameras 1 There have also been numerous attempts, noticeably in the last decade, to numerically model the ballistic impact of woven fabric by small projectiles The effects of the yarn and fabric properties on the ballistic impact performance of woven fabric have also been numerically studied These have been... crossover points works out to be 0.828mm More details of these Twaron® CT716 woven fabric numerical models can be found in Section 6.2 It should be noted that the densities of the fabric yarns for both woven fabrics were adjusted to account for the correct fabric mass In order to allow for fabric perforation, the truss elements were modelled with individual nodes joined together with spot-weld constraints... technology The present study proposes a novel method of numerically modelling the ballistic impact of woven fabric by small projectiles using a commercially available software This method allows for various important yarn and fabric properties that affect the penetration process of the woven fabric to be modelled while using only simple 1D elements for the fabric Various other parameters that affect the... number of unknowns With the advance of computing power, FEM has become a powerful design tool Today’s personal computer is able to solve some practical problems within minutes New capabilities have also been added to the method Today’s FEM software are able to solve structural, thermal, fluid flow, electromagnetic, and even coupled-field problems It has also been used for the simulation of ballistic. .. explicit, finite-element analysis software It has been used to successfully simulate various types of impact phenomena 11 3 METHODOLOGY Two different types of woven fabric made from different Aramid fibres, Twaron® CT716 and Kevlar® 218440, were modelled in this project The Twaron® CT716 woven fabric is a product of Teijin Twaron, while the Kevlar® 218440 woven fabric is a product of Barrday 3.1 Experimental... behaviour of the 3-element linear viscoelastic constitutive model at low strain rate loading The strain-rate dependent properties of Kevlar® yarns were also investigated by Wang and Xia [6,7] 4 2.1.2 Fabric Woven Structure Several important effects obtained during the deformation and perforation process of the woven fabric are dependent on its woven structure The type of weave of a fabric was found to affect ... different types of woven fabric Insights to the influences of various parameters to the woven fabric penetration process were also obtained iv LIST OF TABLES Table Nominal material properties of Twaron®... And Fabric Properties A brief description of some of the yarn and fabric properties that past researchers have found to influence the deformation and perforation process of woven fabric during ballistic. .. 218440 woven fabric has a more complicated woven structure, that of a 4x4 twill A diagram of the fabric mesh for the Kevlar® 218440 woven fabric can be found in Figure 0.828mm Figure Mesh of Twaron®