Building models for crack propagation under fatigue loads: Application to macrocrack growth

This paper deals with the problem of building crack growth models. First, some inconveniences of existing models are described. Next, a general methodology is presented starting by identifying the set of variables involved in the crack growth problem obtaining a minimum subset of dimensionless parameters with the help of the Buckingham theorem, and imposing some consistency and compatibility conditions in terms of functional equations. These functional equations, once solved, provide the subset of crack growth models satisfying the required deterministic and stochastic compatibility conditions, which, in addition to providing mean values of the crack sizes as a function of time, as alternative models do, also give densities of the crack sizes. The main elements required to build a crack growth model, such as the initial crack size distribution, the crack growth function and a loading effect function, have been identified. The methodology is illustrated with some examples, including crack growth for different load histories. Finally, some models proposed in the past are shown to satisfy these conditions and one numerical example is given.