On modeling the deformation and fracture response of glassy polymers due to shear-yielding and crazing

Abstract

We have developed a constitutive model and failure criteria, which account for the competition between shear-yielding and crazing, and provide a framework for the quantitative prediction of the deformation and fracture response of glassy polymers. To represent shear-yielding we use the model of Boyce et al. (e.g. [Mech. Mater. 7 (1988) 15]), which has been recently re-formulated by Anand and Gurtin [Int. J. Solids Struct. 40 (2003) 1465]. To model crazing, we introduce a continuum constitutive relation which contains the three ingredients of crazing: initiation, widening, and breakdown. We allow for local inelastic deformation due to shear-yielding in possible concurrence with that due to crazing, and introduce a craze-initiation criterion based on the local maximum principal tensile stress reaching a critical value which depends on the local mean normal stress. After crazing has initiated, our continuum model represents the transition from shear-flow to craze-flow by a change in the viscoplastic flow rule, in which the dilational inelastic deformation associated with craze-plasticity is taken to occur in the direction of the local maximum principal stress. Finally, for situations in which the local maximum tensile stress is positive, craze-breakdown and fracture is taken to occur when a local tensile plastic craze strain reaches a critical value. We have implemented our constitutive model in a finite-element computer program. This finite-element program permits the modeling of failure by an element-removal technique. We have calibrated the constitutive parameters in our model for the important glassy polymer, polymethylmethacrylate (PMMA) under normal dry conditions. We show that our model, when suitably calibrated and implemented, is able to reasonably-well predict the macroscopic load–displacement curves, and local aspects of the craze-flow and fracture processes in (a) a thin plate with a circular hole under tension, and (b) a notched beam in four-point bending.