Inverse first-order reliability method for probabilistic fatigue life prediction of composite laminates under multiaxial loading

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is based on a novel small timescale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics based on the geometric relationship between the crack-tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single-degree-of-freedom and multiple-degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated by using coupon testing data from open literature. Following this, the methodology is demonstrated by using a steel girder bridge. The proposed methodology shows that concurrent structural dynamics and material fatigue crack growth analysis can be achieved. Cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels shows a satisfactory accuracy by using the proposed coupled state-space model.