Uniaxial Compressive Response and Constitutive Modeling of Selected Polymers Over a Wide Range of Strain Rates

Journal of Dynamic Behavior of Materials - Tập 1 - Trang 15-27 - 2015
Kenji Nakai1, Takashi Yokoyama1
1Department of Mechanical Engineering, Okayama University of Science, Okayama, Japan

Tóm tắt

The present work deals with constitutive modeling of the compressive stress–strain response of selected polymers at strain rates from 10−3 to nearly 103 s−1. Six different commercially available extruded polymers—ABS, HDPE, PC, POM, PP and PVC—are tested at room temperature. Cylindrical specimens with a slenderness ratio (=length/diameter) of 0.5 are used in high strain-rate tests, and those with the slenderness ratios of 1.0 and 2.0 are used in low and intermediate strain-rate tests. High strain-rate compressive stress–strain loops up to a strain of nearly 0.08 are obtained on a standard split Hopkinson pressure bar. Low and intermediate strain-rate compressive ones are measured on an Instron testing machine. By fitting experimental loading stress–strain data to a modified Ramberg–Osgood equation, material parameters are uniquely determined using a linear least-squares procedure. Experimental results indicate that all polymers tested exhibit intrinsic dynamic viscoelastic–plastic characteristics and a higher elastic after-effect following complete unloading. It is shown that the modified Ramberg–Osgood constitutive model is appropriate for describing the monotonic loading compressive stress–strain relations of the three semi-crystalline polymers over a wide range of strain rates. The advantages and limitations of the constitutive model are also discussed.

Tài liệu tham khảo

Wada Y, Kasahara T (1967) Relation between impact strength and dynamic mechanical properties of plastics. J Appl Polym Sci 11:1661–1665 Brown HR (1973) A critical examination of the impact test for glassy polymers. J Mater Sci 8:941–948 Allen G, Morley DCW, Williams T (1973) The impact strength of polycarbonate. J Mater Sci 8:1449–1452 Oshinski AJ, Keskkula H, Paul DR (1996) The role of matrix molecular weight in rubber toughened nylon 6 blends: 2. room temperature Izod impact toughness. Polymer 37:4909–4918 Davies EDH, Hunter SC (1963) The dynamic compression testing of solids by the method of the split Hopkinson pressure bar. J Mech Phys Solids 11:155–179 Chiu SS, Neubert VH (1967) Difference method for wave analysis of the split Hopkinson pressure bar with a viscoelastic specimen. J Mech Phys Solids 15:177–193 Chou SC, Robertson KD, Rainey JH (1973) The effect of strain rate and heat developed during deformation on the stress–strain curve of plastics. Exp Mech 13:422–432 Chase KW, Goldsmith W (1974) Mechanical and optical characterization of an anelastic polymer at large strain rates and large strains. Exp Mech 14:10–18 Briscoe BJ, Nosker RW (1984) The influence of interfacial friction on the deformation of high density polyethylene in a split Hopkinson pressure bar. Wear 95:241–262 Walley SM, Field JE, Pope PH, Safford NA (1989) A study of the rapid deformation behaviour of a range of polymers. Philos Trans R Soc Lond A 328:1–33 Dioh NN, Leevers PS, Williams JG (1993) Thickness effects in split Hopkinson pressure bar tests. Polymer 34:4230–4234 Walley SM, Field JE (1994) Strain rate sensitivity of polymers in compression from low to high rates. DYMAT J 1:211–227 Tay TE, Ang HG, Shim VPW (1995) An empirical strain rate-dependent constitutive relationship for glass-fibre reinforced epoxy and pure epoxy. Compos Struct 33:201–210 Buckley CP, Harding J, Hou JP, Ruiz C, Trojanowski A (2001) Deformation of thermosetting resins at impact rates of strain. Part I: experimental study. J Mech Phys Solids 49:1517–1538 Li Z, Lambros J (2001) Strain rate effects on the thermomechanical behavior of polymers. Int J Solid Struct 38:3549–3562 Chen W, Lu F, Cheng M (2002) Tension and compression tests of two polymers under quasi-static and dynamic loading. Polym Test 21:113–121 Song B, Chen W (2004) Loading and unloading split Hopkinson pressure bar pulse-shaping techniques for dynamic hysteretic loops. Exp Mech 44:622–627 Trautmann A, Siviour CR, Walley SM, Field JE (2005) Lubrication of polycarbonate at cryogenic temperatures in the split Hopkinson pressure bar. Int J Impact Eng 31:523–544 Siviour CR, Walley SM, Proud WG, Field JE (2005) The high strain rate compressive behaviour of polycarbonate and polyvinylidene difluoride. Polymer 46:12546–12555 Mulliken AD, Boyce MC (2006) Mechanics of the rate-dependent elastic-plastic deformation of glassy polymers from low to high strain rates. Int J Solid Struct 43:1331–1356 Jordan JL, Siviour CR, Foley JR, Brown EN (2007) Compressive properties of extruded polytetrafluoroethylene. Polymer 48:4184–4195 Garg M, Mulliken AD, Boyce MC (2008) Temperature rise in polymeric materials during high rate deformation. ASME J Appl Mech 75:011009–1–011009–8 Nakai K, Yokoyama T (2008) Strain rate dependence of compressive stress–strain loops of several polymers. J Solid Mech Mater Eng 2:557–566 Naik NK, Shankar PJ, Kavala VR, Ravikumar G, Pothnis JR, Arya H (2011) High strain rate mechanical behavior of epoxy under compressive loading: experimental and modeling studies. Mater Sci Eng A 528:846–854 Okereke MI, Buckley CP, Siviour CR (2012) Compression of polypropylene across a wide range of strain rates. Mech Time-Depend Mater 16:361–379 Nakai K, Yokoyama T (2012) High strain-rate compressive properties and constitutive modeling of selected polymers. J Solid Mech Mater Eng 6:731–741 El-Qoubaa Z, Othman R (2014) Volume change in polyetheretherketone under compression loads over wide ranges of strain rate and temperature. J Strain Anal 49:315–324 Acharya S, Mukhopadhyay AK (2014) High strain rate compressive behavior of PMMA. Polym Bull 71:133–149 Kendall MJ, Siviour CR (2014) Experimentally simulating high-rate behaviour: rate and temperature effects in polycarbonate and PMMA. Philos Trans R Soc A 372:20130202 Shim VPW, Yuan J, Lee S-H (2001) A technique for rapid two-stage dynamic tensile loading of polymers. Exp Mech 41:122–127 Rae PJ, Brown EN (2005) The properties of poly(tetrafluoroethylene) (PTFE) in tension. Polymer 46:8128–8140 Gilat A, Goldberg RK, Roberts GD (2007) Strain rate sensitivity of epoxy resin in tensile and shear loading. J Aerosp Eng 20:75–89 Sarva SS, Boyce MC (2007) Mechanics of polycarbonate during high-rate tension. J Mech Mater Struct 2:1853–1880 Naik NK, Perla Y (2008) Mechanical behaviour of acrylic under high strain rate tensile loading. Polym Test 27:504–512 Fu S, Wang Y, Wang Y (2009) Tension testing of polycarbonate at high strain rates. Polym Test 28:724–729 Fleck NA, Stronge WJ, Liu JH (1990) High strain-rate shear response of polycarbonate and polymethyl methacrylate. Proc R Soc Lond A 429:459–479 Kolsky H (1949) An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc B 62:676–700 Tardif HP, Marquis H (1963) Some dynamic properties of plastics. Can Aeronaut Space J 9:205–213 Briscoe BJ, Hutchings IM (1976) Impact yielding of high density polyethylene. Polymer 17:1099–1102 Hamdan S, Swallowe GM (1996) The strain-rate and temperature dependence of the mechanical properties of polyetherketone and polyetheretherketone. J Mater Sci 31:1415–1423 Roland CM, Twigg JN, Vu Y, Mott PH (2007) High strain rate mechanical behavior of polyurea. Polymer 48:574–578 Rae PJ, Brown EN, Orler EB (2007) The mechanical properties of poly(ether-ether-ketone) (PEEK) with emphasis on the large compressive strain response. Polymer 48:598–615 Furmanski J, Trujillo CP, Martinez DT, Gray GT III, Brown EN (2012) Dynamic-Tensile-Extrusion for investigating large strain and high strain rate behavior of polymers. Polym Test 31:1031–1037 Millett JCF, Bourne NK (2000) The deviatoric response of polymethylmethacrylate to one-dimensional shock loading. J Appl Phys 88:7037–7040 Millett JCF, Bourne NK (2004) The shock induced equation of state of three simple polymers. J Phys D Appl Phys 37:2901–2907 Chen W, Zhou B (1998) Constitutive behavior of Epon 828/T-403 at various strain rates. Mech Time-Depend Mater 2:103–111 Sadd MH, Morris DH (1976) Rate-dependent stress–strain behavior of polymeric materials. J Appl Polym Sci 20:421–433 Khan A, Zhang H (2001) Finite deformation of a polymer: experiments and modeling. Int J Plast 17:1167–1188 Porter D (1995) Group interaction modelling of polymer properties. Marcel Dekker, New York Buckley CP, Dooling PJ, Harding J, Ruiz C (2004) Deformation of thermosetting resins at impact rates of strain. Part 2: constitutive model with rejuvenation. J Mech Phys Solids 52:2355–2377 Porter D, Gould PJ (2009) Predictive nonlinear constitutive relations in polymers through loss history. Int J Solid Struct 46:1981–1993 Richeton J, Ahzi S, Daridon L, Rémond Y (2005) A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures. Polymer 46:6035–6043 Richeton J, Ahzi S, Vecchio KS, Jiang FC, Adharapurapu RR (2006) Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: characterization and modeling of the compressive yield stress. Int J Solid Struct 43:2318–2335 Richeton J, Ahzi S, Vecchio KS, Jiang FC, Makradi A (2007) Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates. Int J Solid Struct 44:7938–7954 Khan AS, Lopez-Pamies O, Kazmi R (2006) Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures. Int J Plast 22:581–601 ASTM E9-89a (1995) Standard test methods of compression testing of metallic materials at room temperature. American Society for Testing and Materials, Philadelphia Gray GT III, Blumenthal WR (2000) Split-Hopkinson pressure bar testing of soft materials. In: ASM Handbook®, Vol. 8, Mechanical Testing and Evaluation. ASM International, Materials Park Yokoyama T, Ogawa K (2003) Impact tensile properties of 6061 aluminium alloy to SUS 304 stainless steel friction-welded butt joints. Weld Int 17:514–523 Lindholm US (1964) Some experiments with the split Hopkinson pressure bar. J Mech Phys Solids 12:317–335 Bernatskii AD, Rabinovich AL (1964) Strain in certain crosslinked polymers. Polym Sci USSR 6:1166–1175 Dieter GE (1988) Mechanical metallurgy. McGraw–Hill, London Swallowe GM (1999) Mechanical properties and testing of polymers: an A-Z reference. Kluwer Academic Publishers, Dordrecht Brinson HF, Brinson LC (2008) Polymer engineering science and viscoelasticity: an introduction. Springer, New York Ghorbel E (2008) A viscoplastic constitutive model for polymeric materials. Int J Plast 24:2032–2058 Malatyński M, Klepaczko J (1980) Experimental investigation of plastic properties of lead over a wide range of strain rates. Int J Mech Sci 22:173–183 Ramberg W, Osgood WR (1943) Description of stress–strain curves by three parameters. Technical note 902; National Advisory Committee for Aeronautics, Washington DC McLellan DL (1967) Constitutive equations for mechanical properties of structural materials. AIAA J 5:446–450 Hight TK, Brandeau JF (1983) Mathematical modeling of the stress strain–strain rate behavior of bone using the Ramberg–Osgood equation. J Biomech 16:445–450 Nunes RW, Martin JR, Johnson JF (1982) Influence of molecular weight and molecular weight distribution on mechanical properties of polymers. Polym Eng Sci 22:205–228 Hallam MA, Cansfield DLM, Ward IM, Pollard G (1986) A study of the effect of molecular weight on the tensile strength of ultra-high modulus polyethylenes. J Mater Sci 21:4199–4205 Talbott MF, Springer GS, Berglund LA (1987) The effects of crystallinity on the mechanical properties of PEEK polymer and graphite fiber reinforced PEEK. J Compos Mater 21:1056–1081 Lee LH, Vanselow JJ, Schneider NS (1988) Effects of mechanical drawing on the structure and properties of PEEK. Polym Eng Sci 28:181–187 Hoy RS, Robbins MO (2006) Strain hardening of polymer glasses: effect of entanglement density, temperature, and rate. J Polym Sci Part B Polym Phys 44:3487–3500 Vorselaars B, Lyulin AV, Michels MAJ (2009) Microscopic mechanisms of strain hardening in glassy polymers. Macromolecules 42:5829–5842 Bouvard JL, Ward DK, Hossain D, Marin EB, Bammann DJ, Horstemeyer MF (2010) A general inelastic internal state variable model for amorphous glassy polymers. Acta Mech 213:71–96