A micromechanical model of texture induced orthotropy in planar crystalline polymers

Abstract

This paper proposes a self-consistent micromechanical description of orthotropic texture evolution in the context of a constrained single slip model for planar crystalline polymers. A micro-macro averaging scheme accounting for molecular chain inextensibility is proposed within the framework of tensor function representation theory. The chain axes of the crystals are described by an orientation distribution function that is expressible as a convergent series of irreducible tensors. The coefficients of this expansion are termed the moment tensors. The imposed macroscopic orthotropy enables us to derive explicit and self-consistent expressions for the second moment tensors. Recurrence formulae furnish explicit expressions for the higher order moment tensors. By an orientation average, the macroscopic plastic spin is expressed in terms of the second and the fourth moment tensors. We also propose a local constraint reaction approximation that is consistent with tensor function representation theory. The proposed model simulates the process of chain axes rotation toward the direction of maximum stretch. The texture hardening is illustrated for the cases of uniaxial stretching and simple shear.