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Firstly, it is not generally valid for crack initiation. The model is unable to predict the very small (sub-micron) crack sizes which are of great interest in fatigue crack growth. Secondly, the model assumes that the relationship between crack length and crack growth is independent of the stress state. This is not realistic, as crack nucleation is a non-linear process and the crack can be arrested and reversed in the early stages of fatigue crack growth. Thirdly, the model ignores the possibility of crack intersection.
To overcome these problems, a more general fatigue crack growth model was proposed by Röhrle and Kurz (1987). The model is based on a strong power law dependence of the crack growth rate on the stress level. The crack is assumed to grow at the same rate for any stress level, and a final state is obtained by considering all possible crack paths and their contribution to the crack growth rate. All of these assumptions are well-justified and have been tested by Meng and Blythe and by Röhrle and Kurz. The new model, like the Meng and Blythe's model, is based on a straight line approximation to the crack front and has the same deficiencies as the Meng and Blythe's model.
Fatigue crack growth rates are strongly dependent on the cyclic stress amplitude, and the crack is often only marginally retarded by the cyclic stress field. Nevertheless, it is possible to obtain a reasonable estimate of the fatigue crack growth rate by fitting a simple model to the fatigue data, and the approach is simple and convenient to apply.
The fatigue crack growth model proposed by Meng and Blythe (1987) is based on a straight line approximation to the crack front and a power law dependence of the crack growth rate on the applied stress. This model is now of long standing, and is well illustrated by the data of ERS'87, Figure 2. Meng and Blythe's model has some obvious deficiencies.
The crack growth model of Röhrle and Kurz is based on a lattice formulation and will now be briefly described in the context of a plane strain beam. The plane strain assumption is justified for the present analysis, as crack growth rates are only weakly dependent on the stress level.
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