Probabilistic Fracture of Functionally Graded Materials Using Multiscale Models

Abstract

This paper presents three multiscale models, including sequential, invasive, and concurrent models, for fracture analysis of a crack in a two-phase, functionally graded composite. The models involve stochastic description of the particle volume fractions, particle locations, and constituent material properties; a two-scale algorithm including microscale and macroscale analyses for determining crack-driving forces; and two stochastic methods for fracture reliability analysis. Numerical results indicate that the sequential and invasive multiscale models are the most computationally inexpensive models available, but they may not produce acceptable probabilistic characteristics of stress-intensity factors or accurate probability of fracture initiation. The concurrent multiscale model is su‐ciently accurate, gives probabilistic solutions very close to those generated from the microscale model, and can reduce the computational efiort of the latter model by more than a factor of two. In addition, the concurrent multiscale model predicts crack trajectory as accurately as the microscale model.