The conceptual physical framework of stochastic fracture kinetics

Abstract

Physically based, rational, constitutive laws are developed by analysis or synthesis: the second represents the maturity of deformation and fracture science. The basic processes are thermally activated discrete steps, each controlled by the elementary rate constant derived rigorously by rate theory considerations of statistical mechanics. The rate constants are combined by the laws of kinetics, leading to the constitutive relations which express the rate of the process as a function of the applied load, component geometry, temperature, and microstructure. The physical process is stochastic and the appropriate mathematics is expressed by the Markov chain or by the Fokker-Planck transport differential equation: both are the appropriate forms of the random walk process. The constitutive laws can lead to direct engineering applications and have critical significance at the threshold conditions.