Intergranular Crack Nucleation in Bicrystalline Materials Under Fatigue

During cyclic deformation of polycrystalline materials, as substantiated by many experimental observations, due to existence of high stress concentration at the interfaces the preferential site of crack nucleation is intercrystalline. Accordingly, it is assumed that the highly localized cyclic deformation persistent slip band (PSB) occurs along the grain boundary (GB) which results in intergranular crack initiation. In the present work the irreversible accumulation of dislocations are used to characterize PSB by means of double pile-up which are composed of vacancy and interstitial dipoles. We shall give the mechanism and a quantitative remedy of ratcheting of plastic deformation peculiar to fatigue deformation. In a manner conceptually analogous to Griffith theory (1921), the critical number of cycles to failure and hence the S-N curves for crack initiation is obtained by considering the free energy of the system. The Gibbs free energy change ΔG increases with the fatigue cycle number due to cyclic increment of elastic strain energy which in turn stems from cyclic pile-up of dislocations along the slip planes. The Gibbs free energy change attains its maximum value at a critical cycle number beyond which the state of dislocation dipole accumulation becomes energetically unstable. In our theory we postulate that this critical state is the onset of crack initiation. We shall give a quantitative value for the fatigue limit and analyze the dependence of the S-N curve on several important physical parameters such as grain size; surface energy; yield strength; width of the PSB; and the ratio of the shear modulus of the bicrystalline material.