A theory of amorphous polymeric solids undergoing large deformations: application to micro-indentation of poly(methyl methacrylate)

Abstract

Although existing continuum models for the elasto-viscoplastic response of amorphous polymeric materials phenomenologically capture the large deformation response of these materials in a reasonably acceptable 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 [1] has recently generalized the model of Anand and Gurtin [2] to begin to capture these important aspects of the mechanical response of such materials. In this work, we summarize Anand’s constitutive model and apply it to the amorphous polymeric solid poly(methyl methacrylate) (PMMA), at ambient temperature and compressive stress states under which this material does not exhibit crazing. We describe our compression-tension and creep experiments on this material from which the material parameters in the model were determined. We have implemented the constitutive model in the finite-element computer program ABAQUS/Explicit [3], and using this finite-element program, we show numerical results for some representative problems in micro-indentation of PMMA, and compare them against corresponding results from physical experiments. The overall predictions of the details of the load, P, versus depth of indentaion, h, curves are very encouraging.