Response of yarn systems to impact loading

RESPONSE OF YARN SYSTEMS TO IMPACT LOADING KOH CHIEN-PING, ADRIAN NATIONAL UNIVERSITY OF SINGAPORE 2009 RESPONSE OF YARN SYSTEMS TO IMPACT LOADING KOH CHIEN-PING, ADRIAN (BEng (Hons), National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2009 Acknowledgements This author wishes to express his sincere gratitude to his supervisors, Professor Victor Shim Phyau Wui and Professor Vincent Tan Beng Chye, for their patient and wise tutelage during the course of this study. They have been a great source of inspiration and knowledge. Their personal dispositions made the research an enjoyable undertaking. I would also like to thank laboratory officers Mr Joe Low Chee Wah and Mr Alvin Goh Tiong Lai who provided indispensible technical and logistical support. My special thanks to friends and colleagues of the Impact Mechanics Laboratory for their contributions on various research issues and for making my stay in the National University of Singapore a pleasant one. I would like to thank my parents for their unwavering support and encouragement in my pursuit of a higher degree. I am also grateful to the National University of Singapore for supporting me through a Research Scholarship and making available excellent academic services. Adrian Koh I Table of Contents Summary VII List of Tables X List of Figures XI Chapter - Introduction . 1.1. Objectives . 1.2. Scope Chapter - Literature Review . 2.1. Dynamic Tensile Testing of Yarns . 2.1.1. The Split Hopkinson Bar Method 2.1.2. Stress Uniformity in Split Hopkinson Bar Test Specimens 2.1.3. Radial Stress Uniformity in Split Hopkinson Pressure Bars . 2.1.4. The Transverse Impact Method . ® 2.2. Molecular Structure of Spectra . 2.3. Mechanical Properties of High-Strength Fibres . 11 2.3.1. Strain Rate Sensitivity . 11 2.3.2. Temperature Effects 12 2.4. Viscoelastic Constitutive Models . 13 2.4.1. Two-Element Viscoelastic Models 13 2.4.2. Three-Element Viscoelastic Model . 15 2.5. Armour-Grade Fabrics . 17 2.5.1. Effects of Impact Parameters . 18 2.5.2. Effects of Fabric Parameters 20 2.5.3. Effects of Inter-Yarn Slippage . 21 2.6. Numerical Modelling of Ballistic Impact on Fabric 22 Chapter - Tensile Response of Spectra® 900 Yarn 24 3.1. Experimental Investigation . 24 3.1.1. Quasi-Static Tensile Testing 24 3.1.1.1. Quasi-Static Testing at Higher Temperatures 26 3.1.2. Dynamic Tensile Test Arrangement 37 3.1.3. Dynamic Tests . 31 3.1.3.1. Dynamic Tensile Testing at Elevated Temperatures . 32 II 3.2. Experimental Results 34 3.2.1. Idealisation of Apparent Strain Rate Softening Behaviour using Three-Element Viscoelastic Model 36 3.3. Investigation of Validity of Results 39 3.3.1. Calculation of Adiabatic Heating 39 3.3.2. Finite Element Analysis of Effect of Specimen Grips 40 3.4. Correction of Spurious Data Generated by Specimen Grips 43 3.4.1. Correction of Input Bar Strain Signal 46 3.4.2. Correction of Output Bar Strain Signal . 50 3.4.3. Incorporation of Corrected Stresses into Hopkinson Bar Equations 54 3.5. Application of the Correction Method . 55 3.5.1. Application of Signal Correction to Finite Element Simulation of Hopkinson Bar Test 55 3.5.2. Validity of Correction Algorithm with Respect to Specimen–Grip Impedance Ratio 56 3.5.3. Application of Correction Algorithm to Data from Tests at 20°C . 58 3.5.4. Fitting of Three-Element Viscoelastic Model to Corrected Stress-Strain Data from Tests at 20°C . 59 3.5.5. Fitting of Wiechert Model to Corrected Stress-Strain Data from Tests at 20°C . 62 3.5.6. Design of Impedance-Matched Grips 64 3.5.7. Tests with Impedance-Matched Grips and Constitutive Modelling . 67 3.6. Application of Correction Algorithm to All Experimental Data 69 3.7. Analysis of Corrected Experimental Results 71 3.7.1. Fitting of Wiechert Model to Corrected Stress-Strain Data 71 3.7.2. Failure Data for Spectra® 900 Yarn . 75 3.7.3. Microscopic Observation of Ruptured Fibre Ends 78 3.8. Summary 81 III Chapter - Tensile Response of Spectra Shield® LCR 83 4.1. Spectra Shield® LCR 83 4.2. Tensile Testing of Spectra Shield® LCR 84 4.2.1. Quasi-Static Tests 84 4.2.2. Dynamic Tensile Tests 85 4.3. Experimental Results 87 4.4. Application of Correction Algorithm to Spectra Shield® Data 88 4.5. Analysis of Corrected Experimental Results 92 4.5.1. Fitting of Three-Element Viscoelastic Model to Corrected Stress-Strain Data . 92 4.5.2. Failure of Spectra Shield® LCR . 96 4.5.3. Microscopic Analysis of Ruptured Fibre Ends 98 4.6. Summary 106 Chapter - Transverse Impact on Spectra® 900 Yarn 107 5.1. Transverse Impact on an Elastic Yarn 108 5.1.1. Yarn with Pre-Tension . 108 5.1.2. Finite Element Analysis of Transverse Impact on an Elastic Yarn 111 5.1.2.1. Effect of Pre-Tension and Impact Velocity on Strain Rate . 115 5.1.2.2. Effect of Friction between Projectile and Yarn 116 5.2. Transverse Impact on a Viscoelastic Yarn . 117 5.2.1. Finite Element Analysis of Transverse Impact on Spectra® 900 Yarn . 117 5.2.2. Transverse Impact Experiments on Spectra® 900 Yarn 125 5.3. Summary 129 IV Chapter – Projectile Impact Tests and Simulations on Spectra® 903 Fabric 131 6.1. Experimental Investigation . 131 6.1.1. Ballistic Impact Tests 132 6.1.1.1. Minimisation of Slippage 134 6.1.1.2. Ballistic Limit . 135 6.1.1.3. Energy Absorption 135 6.1.2. High-Speed Imaging of Perforation Process . 136 6.2. Development of a Finite Element Fabric Model 139 6.2.1. Model Geometry 139 6.2.2. Fabric Model Material Properties (without Failure) 141 6.2.3. Fabric Model Interactions and Boundary Conditions 143 6.2.4. Refinement of Fabric Mesh . 146 6.2.5. Employment of Quarter Model for Parameter Testing 147 6.2.6. Development of Yarn Model to Incorporate Material Failure 149 6.2.6.1. Calculation of Young’s Modulus for Elastic Elements of Composite Model 153 6.2.6.2. Calculation of Parameters for Viscoelastic Elements of Composite Model 157 6.2.7. Fabric Model Failure Properties 160 6.2.7.1. Damage Initiation 160 6.2.7.2. Damage Evolution 162 6.2.8. FEM Verification of Composite Yarn Material Parameters . 164 6.3. Simulation of Impact Response of Spectra® 903 Fabric 167 6.3.1. Assignment of Failure Regions . 167 6.3.2. Prevention of Excessive Element Rotation at Yarn Ends 171 6.4. Validation of Fabric Model 172 6.4.1. Energy Absorption Characteristics Predicted by Model . 172 6.4.2. Analysis of FEM Results . 173 6.4.3. Alternating Arrangement of Elements . 177 6.5. Effect of Impact Velocity on Energy Absorption 179 6.6. Summary 180 V Chapter – Conclusions . 183 7.1. Summary of Findings . 183 7.2. Recommendations for Future Work . 187 References . 190 Appendix A – Tensile Split Hopkinson Bar Theory . 198 Appendix B – Stress Transmission in Discontinuous Shafts . 201 Appendix C – Theory of Transverse Impact on Fibres . 206 VI Summary Woven fabrics constructed from high-strength polymeric fibres are widely used in flexible personal protection systems. They are also effective in shielding critical components in aircraft and vehicles as part of rigid composites. The polymeric yarns they are made from have been shown to possess viscoelastic properties and exhibit strain rate hardening. There are now many polymeric fibres with exceptionally high elastic moduli and strength-to-weight ratios. Examples of materials that are commercially available include aramids (e.g. Kevlar®, Twaron®) and ultra high molecular weight polyethylene (e.g. Spectra®, Dyneema®). The employment of highstrength polymeric fibres in ballistic applications has motivated studies into their mechanical properties, involving experiments and theoretical modelling. This investigation is directed at furthering the dynamic testing methodology for high-strength polymeric fibres based on the tensile split Hopkinson bar method and the transverse impact method, to identify the dynamic mechanical properties and failure modes of Spectra® 900 yarn and of Spectra Shield® flexible laminated composite at rates of loading corresponding to impact. Another objective is to establish a computational model for fabric that incorporates viscoelastic material properties, inter-yarn interactions and fabric architecture features in order to describe the penetration response of Spectra® 903 woven fabric. Quasi-static tests on Spectra® samples are performed using universal testing machines, while dynamic tension is applied by means of a split Hopkinson bar arrangement. The grips used to hold the specimens are found to interrupt stress wave VII propagation, thereby producing inaccuracies. Consequently, a correction method based on one-dimensional stress wave theory is proposed. The corrected results show that there is an increase in the material modulus and failure stress, accompanied by a decrease in failure strain, as the strain rate is increased for both Spectra® 900 yarn and Spectra Shield® flexible composite. An increase in temperature for Spectra® 900 yarn has the opposite effect on these properties. The experimental data are described by the Wiechert spring-dashpot constitutive model. Scanning electron microscopy (SEM) is used to examine the broken filament ends of tested specimens in order to deduce the relationship between strain rate and failure mechanisms. The images indicate that both Spectra® 900 yarn and Spectra Shield® composite exhibit a transition from ductile failure at quasi-static strain rates to mixed ductile failure and brittle fracture modes at dynamic strain rates. However, at high strain rates, Spectra Shield® demonstrates an increase in the proportion of filaments that fail in a ductile manner or by shearing, although brittle fracture continues to dominate. This is postulated to be caused by frictional or adiabatic heating and insufficient time for alignment of filaments in the direction of loading. Computer simulations and experiments involving transverse projectile impact on single viscoelastic yarns show that the stress and strain at the elastic and transverse wave fronts decay with time, resulting in a decrease in the transverse wave velocity. 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Amsterdam: North-Holland Publishing Co., 1967. p. 219. 197 Appendix A Tensile Split Hopkinson Bar Theory [12] εr As εi l0 εt A Fig. A1: Schematic diagram of specimen, input and output bars and strain pulses in tensile Hopkinson apparatus The incident tensile strain pulse is εi = vi c (A1) The reflected compressive strain pulse is εr = − vr c (A2) The transmitted pulse in the output bar is εt = vt c (A3) where v denotes the particle velocity and c is the stress wave velocity. 198 Therefore, the displacements at interfaces and are given by t u1 (t ) = c ∫ (ε i (t ) − ε r (t ))dt (A4) t u (t ) = c ∫ ε t (t )dt (A5) The average strain in the specimen is εs = u1 − u l0 ε s (t ) = (A6) t c (ε i (t ) − ε r (t ) − ε t (t ))dt l ∫0 (A7) The forces at the ends of the interfaces are F1 = EA(ε i + ε r ) (A8) F2 = EAε t (A9) Assuming that wave propagation effects within the specimen are negligible and that F1 = F2, εr = εt − εi (A10) Substituting Equation (A10) into Equation (A7), ε s (t ) = t 2c (ε i (t ) − ε t (t ))dt l0 ∫0 (A11) 199 The specimen strain rate is therefore ε&s (t ) = 2c (ε i (t ) − ε t (t )) l0 (A12) Assuming F1 = F2, the stress in the specimen is σs = F1 F2 = As As (A13) Substituting Equation (A9) into Equation (A13), σ s (t ) = A Eε t (t ) As (A14) Summarising, the specimen stress, strain and strain rate are given by the following expressions: σ s (t ) = A Eε t (t ) As t ε s (t ) = 2c (ε i (t ) − ε t (t ))dt l0 ∫0 ε&s (t ) = 2c (ε i (t ) − ε t (t )) l0 200 Appendix B Stress Transmission in Discontinuous Shafts [49] Consider a stationery prismatic bar of cross-sectional area A0 subjected to a sudden compressive stress of magnitude σ0 at its free end (x = 0) such that a sudden velocity v is imparted to the particles at this end. The stress at the free end is σ xx = −σ (B1) and the particle velocity is v = u& x ( x = 0, t = 0) (B2) where ux is the displacement at the free end and the negative (−) sign for σxx denotes compression. If the stress is maintained, then at some time t = ∆t, the disturbance (stress wave) would have propagated a distance c∆t into the bar, where c is the stress wave speed. All the particles within this original bar length of l0 = c∆t would have acquired a velocity of v. The impulse applied up to this instant is I = (σ A0 )Δt = −σ xx A0 Δt (B3) 201 The momentum imparted is FΔt = mv (B4) − σ xx Ao Δt = ρAo (cΔt )v (B5) where F is the force at the free end, m is the mass of bar with particle velocity v and ρ is the bar material density. Therefore, the relationship between normal stress, stress wave speed and the particle speed imparted in an elastic medium of density ρ is σ xx = − ρcv (B6) Strictly speaking, the above expression should be [σ ] = − ρc~[v ] (B7) where [σ] is the change in stress. c~ is the wave velocity which takes account of the direction of propagation, i.e. c~ = +c if the wave velocity is in the positive x-direction and c~ = −c if it is propagating in the negative x-direction. [v] is the change in particle velocity, taking into consideration the sign of the velocity change, i.e. a stress-free bar can be travelling in the positive x-direction when a sudden but small restraining pull in the negative x-direction is given. The resultant particle velocity could still be positive but of a smaller magnitude. However, [v] is negative. 202 Note that for tensile stress waves, the direction of wave propagation is always opposite to that of the change in particle velocity; for compressive stress waves, they are in the same direction. The elastic engineering strain induced by the stress wave is ε xx = Δl vΔt =− l0 cΔt [v ] ε xx = − ~ c (B8) (B9) This is a case of uniaxial stress. Hence, from Hooke's law and Equations (B7) and (B9), the Young’s modulus E is E= σ xx − ρc~[v] = [v ] ε xx − ~ c E = ρc (B10) (B11) From Equation (B11), the elastic longitudinal wave speed for normal stress in terms of material properties is c= E ρ (B12) The above equation indicates that in materials of the same density, longitudinal stress waves travel faster when the elastic modulus E is higher. In materials of similar stiffness, the wave speed is higher if the density is smaller. (However, in many materials, density and elastic stiffness vary in the same way.) In rigid-body mechanics, material is assumed to be perfectly rigid (E = ∞); hence the wave speed is 203 infinite, the body is loaded up instantly throughout and there is no deformation. (Note that the preceding simple analysis neglects the Poisson's ratio effect; i.e. compression causes a transverse expansion of the bar and tension produces a transverse contraction.) σI, VI A2 A1 σT, VT ρ1 c1 σR, VR ρ2 c2 Fig. B1: Stress wave transmission in discontinuous shafts Consider a stepped bar made by joining two bars of different materials and cross-sectional areas (Fig. B1). On encountering the interface, an incident tensile stress σI will be both partially transmitted and reflected. Assume that both the transmitted σT and reflected σI components are tensile. These may be analysed by noting that at the interface: I. The force on both bars is common II. The particle velocities in both bars are common since no separation occurs From Equation (B7) but considering only magnitudes, σI ρ1c1 σ vR = R ρ1c1 σ vT = T ρ 2c2 vI = (B13) 204 From Figure B1, the interface velocity is vT = vI − vR (B14) Substituting Equation (B13) into Equation (B14), σT σ σ = I − R ρ 2c2 ρ1c1 ρ1c1 (B15) From Figure B1, the interface force is given by A1 (σ I + σ R ) = A2σ T (B16) Substituting Equation (B15) into Equation (B16) yields σT = A1ρ 2c2 σI A2 ρ 2c2 + A1ρ1c1 (B17) σR = A2 ρ 2c2 − A1ρ1c1 σI A2 ρ 2c2 + A1ρ1c1 (B18) 205 Appendix C Theory of Transverse Impact on Fibres [3] y Fixed boundary Cl W Cs Wdt Y [(1 + ε)U]t [(1 + ε)U − W]t x Vdt Vt Fig. C1: Configuration of a yarn after impact [3] This analysis is based on that of Smith et al. [19, 20]. The configuration of the fibre at a time t after impact is shown in Figure C1. After impact, a point on the fibre does not experience any effects until the longitudinal wave front reaches it at time t. At this instant, the strain suddenly increases and the particle starts to move downwards towards the point of impact. The longitudinal stress wave velocity is given by Cl = (1 / M )∂T / ∂ε = (1 / ρ )∂σ / ∂ε = E / ρ (C1) 206 where T is the tension, ε is the strain, σ is the stress, M is the mass per unit length of the unstrained yarn, E is the elastic modulus and ρ is the material density. The particle flow velocity is given by W = Cl ε (C2) The material flows downwards with a velocity W along the fibre until time t = Y/U; this is the time of arrival of the transverse wave front. At this instant, the particle acquires sudden motion in the horizontal direction at the impact velocity V. The velocity of the transverse wave U, relative to the points on the unstrained fibre, is given by U = T M (1 + ε ) (C3) The tension in the fibre T is given by [63] T = T0 + MCl ε (C4) where T0 is the initial tension in the fibre before impact. Consider the movement of the fibre from the standpoint of an external observer; at time t after impact, the outer portions of the fibre are vertical and motionless. In the region between the longitudinal wave front at y = Clt and the transverse wave front at y = Cst, the fibre has a strain ε and a particle velocity W. The transverse wave front propagates with velocity U relative to the unstrained fibre, but because of the strain and movement of the fibre, the velocity of the transverse wave front with respect to the laboratory coordinate system is Cs, which is given by [64] 207 C s = (1 + ε )U − W (C5) Using trigonometry, from Figure C1, we can find the following relationship: V = (1 + ε ) 2U − [(1 + ε )U − W ]2 (C6) The impact velocity V and the velocity of the transverse wave Cs, which is relative to the laboratory coordinate system, can be determined from high-speed photographic images. The mass per unit length M, the material density ρ and the cross-sectional area A = M/ρ can be obtained separately. From the Equations (C1–C6) we can obtain the following: W = C s [ + V / C s − 1] (C7) B = C s / W + 2C s − T0 / μW (C8) C1 = [ B + B − 4T0 / M ] / (C9) ε = W / Cl (C10) U = C l (C s + W ) /(C l + W ) (C11) E = ρCl = ( M / A)Cl (C12) where B is an intermediate value. 208 [...]... Calculation of yarn properties from FE simulation of transverse impact on a pre-tensioned elastic yarn (m0 = 500g, V = 100m/s) Table 5.3 Yarn properties used in FE simulation of transverse impact on Spectra® 900 viscoelastic yarns Table 5.4 123 Calculation of instantaneous modulus from transverse impact test on Spectra® 900 yarn (m0 = 500g, V = 109.6m/s) Table 5.7 122 Calculation of instantaneous... helps to rapidly dissipate the energy of impacting projectiles to a larger area of the material Theoretical analysis of 1 ballistic impact processes involving fabric is difficult due to complexities arising from the textile structure, physics of penetration, and the viscoelastic nature of fibres A knowledge of the dynamic mechanical properties of the material has a direct bearing on the accuracy of predictions... The dynamic response of fabric systems when they are subjected to ballistic impact is not dependent solely on the response of individual yarns, but also on the way yarns interact with one another because they are woven together into a fabric system In addition to materials selection, the design parameters for flexible fabric armour include weave architecture, weave density, surface treatment of the constituent... Idealised yarn weave pattern 140 XV Fig 6.13 3D model of a fabric 140 Fig 6.14 Close-up of fabric model 141 Fig 6.15 FEM model of projectile impact on Spectra® 903 fabric (100m/s impact velocity, no failure incorporated) 145 Fig 6.16 Close-up view of spline yarn model 146 Fig 6.17 Simulation of Spectra® 903 fabric consisting of spline yarns showing slip-through of projectile... constitutive models of these materials Another objective is to establish a computational model of Spectra® 903 woven fabric that incorporates the material model derived for Spectra® 900 yarn, together with realistic structural features and inter -yarn interactions This fabric model enables the prediction of the fabric response to projectile impact 3 1.2 Scope A literature review of studies related to the dynamic... thermocouple 33 Fig 3.11 Yarn grips placed within temperature chamber 33 Fig 3.12 Apparent stress-strain responses of Spectra® 900 yarn at 20°C 34 Fig 3.13 Apparent stress-strain responses of Spectra® 900 yarn at 40°C 35 Fig 3.14 Apparent stress-strain responses of Spectra® 900 yarn at 60°C 35 Fig 3.15 Three-element spring-dashpot model 36 Fig 3.16 Apparent variation of modulus at 2% strain... Schematic diagram of projectile 126 Fig 5.13 Transverse impact experimental setup 126 Fig 5.14 Photographs of transversely impacted Spectra® 900 yarn 127 Fig 5.15 Ultranac high-speed camera used to capture yarn specimen images 127 Fig 6.1 Schematic diagram of ballistic impact test setup 132 Fig 6.2 Gas gun pressure chamber and barrel 132 Fig 6.3 3D model of fabric clamping... FEM of transverse impact on Spectra® 900 yarn (m0 = 500g, V = 150m/s) Table 5.6 119 Calculation of instantaneous modulus from FEM of transverse impact on Spectra® 900 yarn (m0 = 500g, V = 100m/s) Table 5.5 113 128 Calculation of instantaneous modulus from transverse impact test on Spectra® 1000 yarn (m0 = 500g, V = 109.6m/s) 129 Table 6.1 Spectra® 903 fabric specifications 131 Table 6.2 Yarn. .. results for variation of stress with time at locations 10mm, 100mm and 500mm above the impact point (transverse impact on Spectra® 900 yarn, m0 = 500g, V = 100m/s) 120 Fig 5.10 FEM results for variation of stress with strain at locations 10mm, 100mm and 500mm above the impact point (transverse impact on Spectra® 900 yarn, m0 = 500g, V = 100m/s) 121 Fig 5.11 Schematic diagram of transverse impact test arrangement... various striker velocities and yarn- to- grip impedance ratios obtained from corrected input/output bar strain histories 57 ® Fig 3.27 Stress-strain responses of Spectra 900 yarn at 20°C based on corrected input/output bar data 58 Fig 3.28 Comparison of fitted to experimental stress-strain curves when only dynamic data is fitted 60 Fig 3.29 Comparison of fitted to experimental stress-strain . RESPONSE OF YARN SYSTEMS TO IMPACT LOADING KOH CHIEN-PING, ADRIAN NATIONAL UNIVERSITY OF SINGAPORE 2009 RESPONSE OF YARN SYSTEMS TO IMPACT LOADING . Verification of Composite Yarn Material Parameters 6.3. Simulation of Impact Response of Spectra ® 903 Fabric 6.3.1. Assignment of Failure Regions 6.3.2. Prevention of Excessive Element Rotation at Yarn. stress-strain responses of Spectra ® 900 yarn at 20°C 34 Fig. 3.13 Apparent stress-strain responses of Spectra ® 900 yarn at 40°C 35 Fig. 3.14 Apparent stress-strain responses of Spectra ® 900 yarn