Approximation of Nonlinear Unloading Effects in the Strain Rate Dependent Deformation Analysis of Polymer Matrix Materials Utilizing a State Variable Approach
Publication: Journal of Aerospace Engineering
Volume 21, Issue 3
Abstract
An experimental and analytical program is carried out to explore key behaviors in the loading and unloading behavior of polymers. Specifically, the effects of strain rate and hydrostatic stresses on the nonlinear portions of the deformation response are examined. Tension, compression, and shear load only and load/unload tests are conducted on a representative polymer across a range of strain rates, and key features of the experimental results are identified. To conduct a preliminary exploration of how the key features of the deformation response could be simulated analytically, a previously developed set of constitutive equations, which were developed to analyze the strain rate dependent, nonlinear deformation of polymers including the effects of hydrostatic stresses, were modified in order to approximate key features of the nonlinear unloading behavior observed in the polymer. The constitutive relations are based on state variable constitutive equations originally developed for metals. The nonlinear unloading observed in the experiments is approximated by reducing the unloading modulus of the material as the effective inelastic strain is increased. The effects of the hydrostatic stress state on the unloading modulus are also simulated analytically. To examine the revised formulation, the loading and load/unload responses of the representative polymer in tension, compression, and shear are examined at several strain rates. Results computed using the developed constitutive equations were found to correlate reasonably well with the experimental data.
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References
ASTM. (2004). “Standard test method for tensile properties of plastics.” D638, Philadelphia.
Bodner, S. R. (2002). Unified plasticity for engineering applications, Kluwer Academic/Plenum, New York.
Bordonaro, C. M. (1995). “Rate dependent mechanical behavior of high strength plastics: Experiment and modeling.” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, N.Y.
Brusselle-Dupend, N., Lai, D., Feaugas, X., Guigon, M., and Clavel, M. (2001). “Mechanical behavior of a semicrystalline polymer before necking. Part I: Characterization of uniaxial behavior.” Polym. Eng. Sci., 41, 66–76.
Brusselle-Dupend, N., Lai, D., Feaugas, X., Guigon, M., and Clavel, M. (2003). “Mechanical behavior of a semicrystalline polymer before necking. Part II: Modeling of uniaxial behavior.” Polym. Eng. Sci., 43, 501–518.
Chang, W. J., and Pan, J. (1997). “Effects of yield surface shape and round-off vertex on crack-tip fields for pressure-sensitive materials.” Int. J. Solids Struct., 34, 3291–3320.
Cheng, J. (2006). “Material modeling of strain rate dependent polymer and 2D tri-axially braided composites.” Ph.D. thesis, Univ. of Akron, Akron, Ohio.
Colak, O. U. (2005). “Modeling deformation behavior of polymers with viscoplasticity theory based on overstress.” Int. J. Plast., 21, 145–160.
Daniel, I. M., Hsiao, H. M., and Cordes, R. D. (1995). “Dynamic response of carbon/epoxy composites.” High strain rate effects on polymer, metal, and ceramic matrix composites and other advanced materials, Y. D. S. Rajapakse and J. R. Vinson, eds., AD-Vol. 48, ASME, New York, 167–177.
Gilat, A., Goldberg, R. K., and Roberts, G. D. (2007). “Strain rate sensitivity of epoxy resin in tensile and shear loading.” J. Aerosp. Eng., 20, 75–89.
Goldberg, R. K., Roberts, G. D., and Gilat, A. (2005). “Implementation of an associative flow rule including hydrostatic stress effects into the high strain rate deformation analysis of polymer matrix composites.” J. Aerosp. Eng., 18, 18–27.
Hasan, O. A., and Boyce, M. C. (1995). “A constitutive model for the nonlinear viscoelastic viscoplastic behavior of glassy polymers.” Polym. Eng. Sci., 35, 331–344.
Hsu, S.-Y., Vogler, T. J., and Kyriakides, S. (1999). “Inelastic behavior of an AS4/PEEK composite under combined transverse compression and shear. Part II: Modeling.” Int. J. Plast., 15, 807–836.
Khan, A. S., and Huang, S. (1995). Continuum theory of plasticity, Wiley, New York.
Kolling, S., Haufe, A., Feucht, M., and Du Bois, P. A. (2006). “A constitutive formulation for polymers subjected to high strain rates.” Proc., 9th Int. LS-DYNA Users Conf., Vol. 15, Livermore Software Technology Company, Livermore, Calif., 55–74.
Krempl, E., and Ho, K. (2000). “An overstress model for solid polymer deformation behavior applied to Nylon 66.” Time dependent and nonlinear effects in polymers and composites, ASTM STP 1357, R. A. Schapery and C. T. Sun, eds., ASTM, West Conshohocken, Pa., 118–137.
Lai, D., Yakimets, I., and Guigon, M. (2005). “A nonlinear viscoelastic model developed for semicrystalline polymer deformed at small strains with loading and unloading paths.” Mater. Sci. Eng., A, 405, 266–271.
Li, F. Z., and Pan, J. (1990). “Plane-stress crack-tip fields for pressure-sensitive dilatant materials.” J. Appl. Mech., 57, 40–49.
Littell, J. D., Ruggeri, C. R., Goldberg, R. K., Roberts, G. D., and Binienda, W. K. (2007). “Measurement of epoxy resin tension, compression, and shear stress-strain curves over a wide range of strain rates using small test specimens.” J. Aerosp. Eng., submitted.
Stouffer, D. C., and Dame, L. T. (1996). Inelastic deformation of metals: Models, mechanical properties, and metallurgy, Wiley, New York.
Sun, C. T., and Chen, J. L. (1991). “A micromechanical model for plastic behavior of fibrous composites.” Compos. Sci. Technol., 40, 115–129.
Ward, I. M. (1983). Mechanical properties of solid polymers, Wiley, New York.
Wineman, A. S., and Rajagopal, K. R. (2000). Mechanical response of polymers, Cambridge University Press, New York.
Xia, Z., Hu, Y., and Ellyin, F. (2003). “Deformation behavior of an epoxy resin subject to mechanical loadings. Part II: Constitutive modeling and predictions.” Polym. Eng. Sci., 43, 734–748.
Yoon, K. J., and Sun, C. T. (1991). “Characterization of elastic-viscoplastic properties of an AS4/PEEK thermoplastic composite.” J. Compos. Mater., 25, 1277–1296.
Zhang, C., and Moore, I. D. (1997). “Nonlinear mechanical response of high density polyethylene. Part II: Uniaxial constitutive model.” Polym. Eng. Sci., 37, 414–420.
Zheng, X. (2006). “Nonlinear strain rate dependent composite model for explicit finite-element analysis.” Ph.D. thesis, Univ. of Akron, Akron, Ohio.
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© 2008 American Society of Civil Engineers.
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Accepted: Nov 21, 2007
Received: Nov 27, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
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