Stochastic model of crack paths in composites based on the Langevin equation

A stochastic model based on the Langevin equation was used to describe crack paths in composites. A single crack path in a fiberglass reinforced epoxy matrix composite was used to predict Langevin parameters quantifying architectural drift and material variability. The predicted Langevin parameters were consistent with moderate architectural drift (Langevin drift parameter of 0.04 ± 0.02) and moderate material variability (Langevin variability parameter of 0.05 ± 0.03). These Langevin parameters were then used to predict a family of crack paths exhibiting the same stochastic characteristics as the original crack path. Architectural drift was qualitatively related to the orientation of the reinforcing phase. A strong correlation between the predicted and experimental crack path suggests the utility of the Langevin model to quantify crack paths.