Stochastic failure analysis of an uncorrelated volume element using extended finite element method

Variability present in composite microstructures was characterized using image analysis techniques. The quantified variability was incorporated in computersimulated microstructures. Microstructures were generated at a length scale associated with an uncorrelated volume element, which is a mesoscale for multiscale analysis. Nearest neighbor and radial distributions were used to evaluate the statistics of the generated microstructures. Fiber locations in the generated microstructures were rearranged to enforce statistical equivalence between all generated and actual microstructures. To predict mechanical properties, image-based finite element models were developed by importing fiber center locations and their corresponding radii. Extended finite element method (XFEM) was implemented in ABAQUS to model matrix cracking under transverse tension. Cohesive surfaces were defined at fibermatrix interface to model debonding between the two constituents. The failure initiation and the evolution path were predicted without assigning a preexisting crack. An ensemble of statistically equivalent microstructures was simulated to determine the variability in transverse strength. To evaluate the variability in strength under biaxial loading, stochastic failure envelopes were developed.