Modelling non-linear stress–strain behaviour of rubber toughened plastics

Abstract

An elastic–plastic model has been developed for describing the non-linear, stress–strain curves of rubber toughened plastics. Following a linear elastic response at low strains, it is assumed that the material undergoes plastic deformation which, for dilatational stress states, is enhanced by the generation and growth of cavities within the rubber particles. The model is based on Gurson's theory of plasticity in porous materials and follows the developments proposed by Bucknall and co-workers. Parameters are included that allow for the effect of pressure on the yield stress of the matrix material between the cavities and for the influence of void interactions on matrix shear banding. Account is also taken of the change in matrix composition, and hence the matrix yield stress, during void nucleation. The nucleation is assumed to occur over a critical range of volumetric strain ε_V and to involve the replacement of rubber particles by an equal volume of effective cavities. Two different nucleation functions have been investigated to describe the dependence of the effective void fraction on ε_V.

Equations that govern the elastic, yield and flow behaviour under multiaxial stress states have been solved to determine required material parameters and to predict behaviour in tension and compression from shear hardening data. The predicted and observed behaviour show good agreement, indicating that the model may be applied with some confidence to stress analyses using finite element calculations.