An energy-based peridynamic model for fatigue cracking

Fatigue design assessment is a crucial step in the design process of ships and offshore structures. To date, the stochastic approach is commonly used to calculate the total lifetime accumulated fatigue damage and the probability of fatigue failure for the structures. Meanwhile, the details of damage initiation and propagation are infrequently investigated. In terms of predicting crack growth, the traditional approaches face conceptual and mathematical difficulties in terms of predicting crack nucleation and growth, especially for multiple crack paths because the equations in classical continuum mechanics are derived by using spatial derivatives. Peridynamics is a nonlocal theory using the integral equations rather than differential equations which makes it suitable for damage prediction. In this study, a novel energy-based peridynamic model for fatigue cracking is proposed. The definition of cyclic bond energy release rate range and the energy-based peridynamic fatigue equations for both phases crack initiation and crack growth phases are introduced. For validation, first, a problem of mode-I fatigue crack growth is investigated. Next, different mixed-mode fatigue damages are also investigated and the peridynamic results are compared with the experimental results.