An internal variable theory for isotropic visco-elastic-plastic solids : application to indentation of amorphous polymeric solids

Abstract

A significant advance in modeling the plastic deformation of amorphous polymers has been made by Parks, Argon, Boyce, Arruda, and their co-workers (e.g. Parks, Argon, & Bagepalli, 1985; Boyce, Parks, & Argon, 1998; Arruda & Boyce, 1993), and by Wu and Van der Giessen (1993). Although these models phenomenologically capture the large deformation elastic-viscoplastic response of these materials in a reasonably accurate manner, they do not adequately account for the creep response of these materials at stress levels below those causing "macro-yield", as well as the Bauschinger-type reverse yielding phenomena at strain levels less than ~ 30% associated with the macro-yield transient. Anand (2003) has recently generalized the model of Anand and Gurtin (2003) to begin to capture these important aspects of these material's mechanical response. In this work, we summarize Anand's three-dimensional theory and then specialize the constitutive equations to an approximate one-dimensional form. Also, we describe our monotonic, cyclic and creep experiments on the amorphous polymeric solid poly(methyl methacrylate) (PMMA), at ambient temperature and stress states under which this material does not exhibit crazing, and we outline detailed procedures for material parameter determination from these experiments. We have implemented the three-dimensional constitutive equations in the finite-element computer program ABAQUS/Explicit (ABAQUS, Inc., 2002), and using this finite-element program, we show numerical results to some representative problems in microindentation, and compare them against corresponding results from physical experiments.