Technique of statistical validation of rival models for fatigue crack growth process and its identification

The development of suitable models of stochastic crack growth process is important for the reliability analysis of fatigued structures as well as the scheduling of inspection and repair/replacement maintenance. Based on modifications of the solution of the deterministic differential equation for the crack growth rate, where a stochastic nature of this rate is expressed by a random disturbance embedded in the solution of the differential equation, the simple stochastic models are presented for practical applications. Each of these models represents a stochastic version of the solution of the Paris-Erdogan law equation. The models take into account the random disturbance parameters while maintaining the simplicity and advantages of the Paris-Erdogan law equation. A technique is proposed in order to find the appropriate model for crack growth behavior from the family of rival models and test its validity in the light of experimental results. The model analysis technique can be implemented easily using deterministic crack growth analysis results and estimates of the statistics of the crack growth behavior. The solution of the deterministic differential equation associated with the stochastic model gives us the crack exceedance probability as well as the probability of random time to reach a specified crack size. Once the appropriate stochastic model is established, it can be used for the fatigue reliability prediction of structures made of the tested material. An illustrative example is given.