A new continuum approach to the coupling of shear yielding and crazing with fracture in glassy polymers



Over the past decades, several constitutive models accounting for finite viscoplasticity and failure in glassy polymers were developed. However, depending on thermal and loading rate conditions, the response might change from ductile to brittle. This brittle response is characterized by inelastically deformed zones, so-called crazes, having the thickness of micrometers and spanning at some fractions of a millimeter, containing a dense array of fibrils interspersed with elongated voids, detailed discussion e.g. [1]. The shear yielding and crazing are not completely independent excluding each other. Present models introduce crazing either discrete by cohesive surfaces, e.g. [2], or continuous, see [3]. In this work, we outline an extension of a ductile plasticity model towards (i) the description of volumetric directional plasticity effect due to crazing and (ii) the modeling of the local failure due to fracture. The ultimate amount of volumetric plastic craze strain is bounded by a limiting value, where failure occurs. In a second step, the modeling of subsequent failure mechanisms is realized by introducing a fracture phase field, characterizing via an auxiliary variable the crack. Here, we adopt structures of a continuum phase field model of fracture in brittle solids [4], and modify it for a fracture driving term related to the volumetric plastic deformation of the crazes. We demonstrate the performance of proposed formulation by means of a representative boundary value problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)