Multi-scale homogenization-based modeling of semi-crystalline polymers

Abstract

This paper presents a finite-strain, multi-scale constitutive model for semi-crystalline polymers, accounting explicitly for the current state and evolution of the underlying crystallographic, lamellar and morphological texture. Specifically, a semi-crystalline polymer is modeled as a two-scale composite, assumed to be, at the larger length scale, an aggregate of randomly distributed grains that, at the smaller length scale, are made up of alternating layers of an amorphous and a crystalline phase. The model incorporates finite elasticity for the amorphous phase and crystallographic hardening for the crystalline phase. The instantaneous effective response of this composite is determined by means of multi-scale homogenization methods, consisting in the use of a “linear comparison composite” (LCC) with the same internal structure as the actual nonlinear composite, with local properties that are optimally chosen via suitably designed variational principles. The effective properties of the resulting two-scale LCC are obtained through a “sequential” homogenization procedure, involving the exact solution for the effective behavior of the lamellar grains and a self-consistent estimate for the aggregate. The latter results are also used to establish evolution laws for the appropriate internal variables in the material. The predictions of the model for the macroscopic response and texture evolution in high-density polyethylene are confronted with available experimental results and compared with those of earlier models.

Keywords:

• heterogeneous materials
• granular materials
• mechanical properties
• microstructure change
• polycrystalline
• texture

Acknowledgements

This material is based in part upon work supported by the National Science Foundation under Grant Number CMMI-0654063. We are grateful to Dr. R. Lebensohn for providing his VPSC code. Certain parts of this code, and in particular the parts dealing with the computation of the second moments, were suitably adapted and used in the calculations of the effective response and microstructure evolution of the semi-crystalline polymers using the linear comparison homogenization model.