Fracture mechanical character of small cracks in polycrystalline materials: concept and numerical K calculations

Abstract The impact of local variations in elastic modulus on the fracture mechanical character of “microstructurally small” cracks commonly encountered in early stages of fatigue in polycrystalline materials, is assessed. In particular, the stress intensity factor (SIF), K , variations along the crack front, influenced by the random crystallographic orientations of grains were numerically calculated for random variations of elastic moduli of grains. A conceptual framework for calculating the K variations due to local anisotropy was established on the basis of the weight function technique for three-dimensional cracks. As a model, an elliptical crack having sizes: three, five and twenty times the grain size, in polycrystalline Ni, Fe and Ti, was considered. Using patterns of random crystallographic orientations of grains, local inhomogeneous stresses that existed over the crack faces were determined on the basis of isostrain condition. These inhomogeneous stresses were used in the weight function-based calculations, to evaluate the effect of these stresses on the K variation along the crack front. It is shown that the effect of local anisotropy on the K variation is significant at small crack sizes and that the fracture mechanical character of microstructurally small cracks is quite different from that of large cracks in the isotropic environment. It is suggested that the local deviations in shapes of microstructurally small cracks, experimentally observed in many materials, are connected to the local K variations and their dependence on crack size, relative to the grain size.