We have constructed a model of the growth of a fatigue crack in a thin, isotropic plate, taking the two-stage evolution of the fracture process into account. The model is based on concepts of the mechanics of a continuous defective state and on a schematic representation of the neighborhood of the tip of a fatigue crack as a plastic zone moving together with the crack. The model takes into account the influence of the cumulative defective state (damage level) along the crack propagation front on the speed of propagation.
We have formulated solutions for the cases when the length of the plastic zone is constant and when it varies during the growth of fatigue cracks. We have established the fact that the plastic zone at the crack tip tends to disrupt the stability of the motion immediately at the time of inception or opening of the crack. The speed of crack propagation decreases as the plastic zone grows in size.
We have shown that the problem of estimating the kinetics of fatigue cracks in thin plates can be reduced to calculating the growth rate as a function of the peak-to-peak amplitude of the stress intensity factor while preserving the structure of the governing equations of the model. We have also shown that the concept of a plastic zone of constant length induces a power-law dependence of the crack rate on ΔK, the power exponent varying from 2 to 10–12. The Dugdale model gives a square-law dependence of the crack rate on ΔK, which for the most part is applicable to plastic materials.
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Golub, V.P., Plashchinskaya, A.V. Fatigue fracture model for thin isotropic plates with cracks in axial loading. Int Appl Mech 30, 520–529 (1994). https://doi.org/10.1007/BF00847247
- Fatigue Crack
- Stress Intensity Factor
- Fatigue Fracture
- Plastic Zone