Computer Simulation of Discrete Crack Propagation

Abstract

Although statistical methods are widely used to study a large amount o f phenomena ranging from random walk to percolation and particle charging, the application o f these methods to mechanics is limited. Nevertheless the use of senses like fractal dimension can be very handy to describe the mass o f a crack or the roughness of a surface. From this viewpoint subcritical crack growth is studied as a cluster growth process with the aid o f discrete computer experiments. A mechanical ballistic aggregation model motivated by a continuum theory of stress-assisted migration o f point defects is formulated and simulated on a square lattice. These defects move towards the crack tip under the action of the high stress gradients existing there. The crack grows by the inf lux of defects in the tip region with the rate of this process, which depends on the externally applied stress, determining the crack velocity and its dependence on the stress intensity factor. The crucial parameter of the model is the initial concentration of defect panicles. It is shown that there is a characteristic relation between critical stress and crack growth for different initial defect concentrations. The crack path is o f a fractal character and the crack velocity dependence on the stress intensity factor follows a power law relationship, in accordance with experimental trends. 1. I N T R O D U C T I O N Subcritical cracking /1, 2/ is a generic term used to indicate slow crack growth for applied loads below those causing dynamic fracture. Subcritical cracking may occur under creep, fatigue, hydrogen embrittlement