Stochastic Modeling of Crack Initiation and Short-Crack Growth Under Creep and Creep-Fatigue Conditions

A simplified stochastic model is proposed for crack initiation and short-crack growth under creep and creep-fatigue conditions. Material inhomogeneity provides the random nature of crack initiation and early growth. In the model, the influence of microstructure is introduced by the variability of (1) damage accumulation along grain boundaries, (2) critical damage required for crack initiation or growth, and (3) the grain-boundary length. The probabilities of crack initiation and growth are derived by using convolution integrals. The model is calibrated and used to predict the crack density and crack-growth rate of short cracks of 304 stainless steel under creep and creep-fatigue conditions. The mean crack initiation lives are predicted to be within an average deviation of about ten percent from the experimental results. The predicted cumulative distributions of crack-growth rate follow the experimental data closely. The applicability of the simplified stochastic model is discussed and the future research direction is outlined.