Stochastic Modeling of Progressive Damage and Its Scaling in Polymer Composites

Abstract

This study proposes a novel stochastic framework for the modeling of damage initiation and propagation at the microscale in the matrix of polymer composites. The model builds on recent experiments and computational simulations which have shown a significant energetic-statistical size effect on the strength and fracture energy of thermoset polymers. In fact, the microscale strength of thermosets was shown to be from six to ten times larger than the values estimated from macroscopic tests whereas the microscale fracture energy was found to be one fortieth of its macroscopic value. To capture this significant size effect, the computational framework proposed in this work combines a two-scale cohesive model and an autocorrelated random field of material strength. The two-scale traction separation law, featuring two distinct characteristic length scales, accounts for the energetic size effect on the average fracturing process due to the stress redistribution in the crack Fracture Process Zone (FPZ).