A continuously distributed dislocation model for fatigue cracks in anisotropic crystalline materials

An elastic-plastic crack model is developed for anisotropic crystalline materials exhibiting elastic-perfect plastic behavior, using the continuously distributed dislocation theory (CDDT). The crack and its associated plastic zone are represented by an inverted pile-up of dislocations. The plastic zone size, the crack-tip opening displacement (CTOD) and the energy release rate of the crack are obtained in closed forms, in a fashion similar to the Bilby–Cottrell–Swinden–Dugdale model for isotropic materials, but in terms of material constants that are orientation dependent. Application of the model to the case of small-scale yielding, e.g., long fatigue cracks in Ni-base single crystal superalloys, is discussed.