IMPACT RESPONSE OF POLYURETHANE By JOHN ANDREW BRYSON A thesis submitted in partial fulfillment of The requirements for the degree of MASTERS OF SCIENCE IN MECHANICAL ENGINEERING WASHINGTON STATE UNIVERSITY School of Mechanical and Materials Engineering DECEMBER 2009 To the Faculty of Washington State University: The members of the Committee appointed to examine the thesis of JOHN ANDREW BRYSON find it satisfactory and recommend that it be accepted. ___________________________________ Lloyd V. Smith, Ph.D., Chair ___________________________________ Jow-Lain Ding, Ph.D. ___________________________________ David P. Field, Ph.D. ii Acknowledgments I would like to thank the many people who have made this work possible. First I would like to thank my wife Kelie she has been a great support to me. I would also like to thank my advisor Dr Lloyd V. Smith for his guidance and knowledge. Warren Faber has also been a great help to me in supplying the finite element data and figures for this thesis. iii IMPACT RESPONSE OF POLYURETHANE Abstract By John Andrew Bryson, M.S. Washington State University December 2009 Chair: Lloyd V. Smith The properties of polyurethane, the primary component of softballs, have been found to be rate sensitive. The impact response of softballs containing different rebound properties and stiffnesses were desired. Samples from five different softball models were tested at high and low strain rates. To test the polyurethane at high strain rates a split Hopkinson pressure bar with aluminum bars was designed and constructed. For comparison the polyurethane materials were also measured at low strain rates of 0.3 s-1 on a universal testing machine. An elastic modulus was measured during both the high strain rate and low strain rate tests. A viscoelastic model, obtained from numeric simulations, was compare to the measured high strain rate properties of the polyurethane. It was found that during impact a softball experiences a peak strain rate of 2500 s- 1 and strain magnitude of 0.2 strain. The average strain rate in the pressure bar tests was 2780 s-1. The stress measured at 0.2 strain increased 42% when the strain rate increased from 0.3 s-1 to 2780 s-1. On average the modulus was 33% high at 2780 s-1 compared to 0.3 s-1.The average modulus increase from the increase in strain rate was 33%. The viscoelastic model predicted stresses three times higher than the stresses observed during the high strain rate tests. iv Softballs with different stiffness and rebound properties were compared. The stress and modulus increased with ball stiffness in both the high strain rate and low strain rate tests. Hysteresis in the load-displacement response from the 0.3 s-1 tests was not sensitive to the measured ball COR. This suggests that rate effects are important to correctly characterize the ball. v Table of Contents Acknowledgments.............................................................................................................. iii Abstract .............................................................................................................................. iv List of Tables ...................................................................................................................... x List of Figures .................................................................................................................... xi 1 Introduction ............................................................................................................. 1 1.1 Introduction ........................................................................................ 1 2 Background ............................................................................................................. 4 2.1 Introduction ................................................................................................. 4 2.2 Physical Setup ............................................................................................. 4 2.2.1 Introduction ..................................................................................... 4 2.2.2 Instrumentation................................................................................ 6 2.2.3 Equations ......................................................................................... 7 2.3 Split Hopkinson Pressure Bar History ...................................................... 12 2.4 Soft Materials SHPB Testing .................................................................... 14 2.4.1 Introduction ................................................................................... 14 2.4.2 Problems Associated with Soft Material SHPB Testing ............... 15 2.4.3 Signal to Noise Ratio..................................................................... 15 2.4.4 Stress Distribution ......................................................................... 17 2.5 Softball Background ................................................................................ 19 vi 2.5.1 Softball Properties ......................................................................... 19 2.5.2 Softball Construction..................................................................... 20 2.5.3 Polyurethane Behavior .................................................................. 21 2.6 Summary ................................................................................................... 22 3 Apparatus .............................................................................................................. 24 3.1 Split Hopkinson Pressure Bar Setup ......................................................... 24 3.1.1 Introduction ................................................................................... 24 3.1.2 Pressure Bar Structure and Frame ................................................. 24 3.1.3 Pressure Bar Electronics................................................................ 26 3.1.4 Cannon Setup ................................................................................ 27 3.2 Pressure Bar Operation ............................................................................. 29 3.3 Problems and Solutions............................................................................. 31 3.3.1 Noise Problems ............................................................................. 31 3.3.2 Cannon Alignment ........................................................................ 35 3.4 Summary ................................................................................................... 36 4 Experiments .......................................................................................................... 38 4.1 Introduction ............................................................................................... 38 4.2 Verification ............................................................................................... 38 4.3 Capabilities ............................................................................................... 40 4.3.1 Amplitude and Duration ................................................................ 40 vii 4.3.2 Shaping .......................................................................................... 43 4.3.3 Polyurethane Specimen Size Effects ............................................. 45 4.4 Polyurethane Introduction ......................................................................... 47 4.4.1 Introduction ................................................................................... 47 4.4.2 Polyurethane Cell Comparison...................................................... 49 4.4.3 Finite Element Model .................................................................... 50 4.4.4 Viscoelastic Response ................................................................... 52 4.5 Low strain Rate Testing ............................................................................ 56 4.5.1 Low Strain Rate Test ..................................................................... 56 4.5.2 Stress Strain Results ...................................................................... 57 4.5.3 Modulus ......................................................................................... 59 4.5.4 Hysteresis ...................................................................................... 61 4.6 High strain Rate Testing ........................................................................... 65 4.6.1 Specimen Construction ................................................................. 65 4.6.2 Stress and Strain at High Strain Rates ........................................... 66 4.7 Discussion ................................................................................................. 73 4.7.1 Stress Increase with Strain Rate .................................................... 73 4.7.2 Modulus Increase with Strain Rate ............................................... 74 4.7.3 Viscoelastic Comparison ............................................................... 76 4.8 Summary ................................................................................................... 82 viii 5 Summary and Future Work ................................................................................... 85 5.1 Summary ................................................................................................... 85 5.2 Future Work .............................................................................................. 86 6 References ............................................................................................................. 88 Appendix A ....................................................................................................................... 91 Appendix B ....................................................................................................................... 95 Appendix C ....................................................................................................................... 97 ix List of Tables Table 4.1 Ball COR and Compression .............................................................................. 47 Table 4.2 Measured Average Ball Properties ................................................................... 48 Table 4.3 Ball Density ...................................................................................................... 49 Table 4.4 Polyurethane Parameters for Viscoelastic Model ............................................. 55 Table 4.5 Ball Modulus of Elasticity at 0.33s-1 Strain Rate .............................................. 59 Table 4.6 Strain Energy Density of Softballs at Constant Energy .................................... 63 Table 4.7 High Strain Rate Modulus ................................................................................ 72 Table 4.8 Stress Change at 0.2 Strain Between Strain Rates of 2780 s-1 and 0.33 s-1 ...... 74 Table 4.9 Modulus Percent Increase Due to Increased Strain Rate .................................. 76 Table 4.10 Viscoelastic Model Adjusted Parameters ....................................................... 79 x