MODELING OF GROWTH OF 3-DIMENSIONAL CRACKS BY A CONTINUOUS DISTRIBUTION OF DISLOCATION LOOPS

This paper is concerned with a numerical simulation of growth of fatig ue cracks in a three-dimensional geometry. A continuous distribution o f infinitesimal dislocation loops is employed to model the crack faces , so that the crack problem can be formulated as a set of singular int egral equations. A numerical procedure based on an analytical treatmen t of the associated finite part integral is developed to solve the sin gular integral equations. The Paris law is then used to predict the ra te of crack growth, so that the evolution of the crack shape under fat igue can be traced by a step-by-step algorithm. Various crack growth p roblems, e.g., the growth of a subsurface crack in a surface treated s pecimen, are analyzed using the technique, providing new data for seve ral cracks of practical interest.