Probabilistic investigation into brittle fracture of functionally graded materials using phase-field method

Modelling fracture using numerical techniques based on discrete modelling is complex as it requires tracking of progressing discontinuities in field parameters. Phase-field method for fracture is based on the variational framework and represents discontinuous crack surfaces by a damage variable that diffuses onto the crack surface. This approach offers the advantage of modelling crack where multiple crack nucleation, branching and coalescence can be determined without prior knowledge of the crack path. In this work, a probabilistic approach is used to predict the crack growth response in functionally graded material media when the mechanical properties and geometric parameters are random independent variables. Numerical implemen-tation based on the standard phase-field method is employed in a finite element framework to model crack growth in functionally graded brittle materials. Peak failure loads are estimated within acceptable limits due to dispersion in system properties. Benchmark problems are solved to demonstrate the applicability of this technique. The proposed approach is advantageous as no further intensive computations are needed after the initial evaluation of probabilistic measures for predicting dispersion in fracture propagation when material and geometric properties exhibit scatter.