Effect of stress concentrators on a stochastic model of crack paths in composites based on the Langevin equation

Fracture mechanics used to quantify stress concentrations and crack propagation mechanisms in materials is based on the assumption of material properties as a continuum. These continuum models are problematic in the analysis and design of composite materials because they do not capture the anisotropic behavior associated with the architecture of a composite material, particularly a composite containing a woven fabric. In this work the Langevin Equation was used to construct a stochastic model to describe crack paths in composites containing stress concentrators. Single ply 0°/90° plain weave fiberglass reinforced epoxy matrix composites were fabricated and tested to determine the Langevin drift and variability parameters. Two different sizes of stress concentrators (holes) were examined. The first was a 9/64 inch hole and the second was a 9/32 inch hole. For composite plies containing a 9/64 inch hole, Langevin drift parameters ranging from 0.02 +/- 0.02 to 0.04 +/- 0.04 and Langevin variability parameters ranging from 0.09 +/- 0.04 to 0.2 +/- 0.1 were observed. For composite plies containing a 9/32 inch hole, Langevin drift parameters ranging from 0.01 +/- 0.01 to 0.13 +/- 0.03 and Langevin variability parameters ranging from 0.07 +/- 0.08 to 0.234 +/- 0.006 were observed. These Langevin parameters were then used to predict stochastic crack paths for the composites and compared to the actual crack paths. The predicted crack paths show that a stochastic model based on the Langevin Equation is an effective first order approximation to relate composite architecture and stress concentrators to crack paths.