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This paper is concerned with a comparative study of different, partly complementary micromechanical models for crack tip plasticity in polymer-rubber blends. It is experimentally well established that interspersion of micron-scale rubber particles into a polymer matrix can lead to a significantly enhanced toughness of the material. The last two decades have witnessed growing consensus about the underlying mechanisms: particle cavitation, void growth, crazing, and shear yielding. Cavitation of the particles followed by massive shear yielding of the matrix and the resulting dissipation of energy is believed to give blends their improved toughness. At the very microlevel, i.e. at length scales of the order of the micron-sized rubber particles, the key damage processes are well identified and largely understood. Their effect on the macroscopic scale may well be captured in a homogenized sense by continuum models, e.g. of the Gurson-type when focusing on void growth. However, at the scale of a crack, a complete and tractable model incorporating all relevant deformation mechanisms is not yet available. On the one hand, strong gradients of the stress fields violate the assumption of a sufficiently homogeneous material for a continuum representation to be valid, while on the other hand the length scale involved is too large in practice to model all particles individually. Therefore, in this paper several models for crack- tip plasticity in blends are combined and compared. Although none of the models introduced pretends to be the final answer, they all shed some light on parts of the solution

SUMMARYThe toughness of glassy polymers can be enhanced by blending with rubber particles. The consensus is that this toughening is due to massive plastic deformation of the matrix that takes place once the particles have cavitated. Micromechanical studies of regular stackings of particles in a polymer matrix have provided much insight into the localized plastic ow in blends at the microscale of individual particles (or voids, once cavitated). Even some steps towards macroscopic constitutive models have been made. However, at intermediate length scales (i.e. larger than several particles, but smaller than the scale at which the material may be regarded as homogeneous) the situation is unclear. It is this length scale that becomes important around crack tips, for example, where a thorough understanding of the toughening e ect has to be derived from. In this paper, we therefore present a novel approach to the analysis of distributed shear banding in polymer-rubber blends. A coarse-grain description, in which much of the morphology is retained but the local shear banding is idealized into 'shear surfaces', will enable us to analyse ensembles with large numbers of particles. The parameters of this model will be validated with results from detailed cell analyses.

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