Overload failure of structural components under random crack propagation and loading – a random process approach

In this paper, the problem of overload failure of a structural component under random loading and under random crack propagation is addressed. The problem is formulated by combining the first passage failure model with stochastic models of crack propagation. Disadvantages of the standard random variable approach to the problem are discussed, and an alternative random process approach is developed. The developed solution addresses both overload and critical crack growth failure modes, requires a single mean crack growth computation, allows the consideration of non-destructive inspections and significantly speeds life-time analysis. The random process approach leads to a first passage problem involving crossings of a random barrier level, which is solved by means of the ensemble up-crossing rate approximation. Limitations of this approximation are addressed and related to typical problem parameters. The concept of barrier failure dominance is discussed, and extended to the case of a barrier-defined failure. Sensitivity studies involving different problem variables are performed, helping to identify the appropriate solution method for specific problems.