Stochastic Computational Mechanics in Brittle Fracture and Fatigue

Abstract

The probabilistic finite element method (PFEM), which is based on a second-order perturbation is developed for non-linear problems. In order to incorporate the probabilistic distribution for the compatibility condition, constitutive law, equilibrium, domain, and boundary conditions into the PFEM, the probabilistic Hu-Washizu variational principal is applied. The first- and second- order moments of the response variable are determined from the statistics of the random parameters and loads. The fusion of the PFEM and the first order reliability analysis provides a means for determining fatigue life and its stochastic nature which results from the randomness in the load, crack length, crack location and orientation, and crack growth parameters. A stochastic damage model is employed to explore the brittle fracture of advanced materials. The model, based on the macrocrack-microcrack interaction, incorporates uncertainties in locations and orientations of microcracks. The statistical nature of the fracture toughness is compared with the Neville function, which gives correct fits to sets of experimental data from advanced materials. Finally, a stochastic approach to the curved fatigue crack growth reliability is outlined.