Markov Process Model for Fatigue Crack Growth

Abstract

Crack propagation analysis is a major task in the design and life prediction of fatigue‐critical structures, yet experimental tests indicate that fatigue crack propagation involves a large amount of statistical variation and is not adequately modeled deterministically. A method of analysis based on Markov process theory is presented for the investigation of fatigue crack propagation. A new fracture mechanics based, lognormal random process model is developed, and without approximation, a boundary value problem is formulated for the statistical moments of the random time to reach a given crack size. A Petrov‐Galerkin finite element method is then used to obtain solutions to the boundary value problem. A parametric study of the power‐law fatigue crack growth model is conducted, and a numerical example is given in which excellent agreement is found between the finite element results and experimental data. The model and problem formulation are consistent with physical phenomena, overcome many objections to previous analyses, and eliminate the need for costly Monte Carlo simulation.