Fatigue Crack Growth Analysis and Damage Prognosis in Structures

Abstract

This chapter describes a computational methodology for fatigue crack growth analysis and damage prognosis in structures. This methodology is applicable to a variety structural components and systems with complicated geometry and subjected to variable amplitude multi-axial loading. Finite element analysis is used to address complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading conditions are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. Crack growth under variable amplitude loading is modeled using a modified Paris law that includes retardation effects. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis, thereby significantly improving computational effort. The effect of different types of uncertainty – physical variability, data uncertainty and modeling errors – on crack growth prediction is investigated. The various sources of uncertainty include, but not limited to, variability in loading conditions, material parameters, experimental data, model uncertainty, etc. Three different types of modeling errors – crack growth model error, discretization error and surrogate model error – are included in analysis. The different types of uncertainty are incorporated into the framework for calibration and crack growth prediction, and their combined effect on crack growth prediction is computed. Finally, damage prognosis is achieved by predicting the probability distribution of crack size as a function of number of load cycles, and this methodology is illustrated using a numerical example of surface cracking in a cylindrical component.