INTERGRANULAR CRACK NUCLEATION IN BICRYSTALLINE MATERIALS UNDER FATIGUE

During cyclic deformation of polycrystalline materials, as substantiat ed by many experimental observations, due to existence of high stress concentration at the interfaces the preferential site of crack nucleat ion is intercrystalline. Accordingly, it is assumed that the highly lo calized cyclic deformation persistent slip band (PBS) occurs along the grain boundary (GB) which results in intergranular crack initiation. In the present work with irreversible accumulation of dislocations are used to characterize PSB by means of double pile-up which are compose d of vacancy and interstitial dipoles. We shall give the mechanism and a quantitative remedy of ratcheting of plastic deformation peculiar t o 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 en ergy of the system. The Gibbs free energy change Delta G increases wit h the fatigue cycle number due to cyclic increment of elastic strain e nergy which in turn stems from cyclic pile-up of dislocations along th e slip planes. The Gibbs free energy change attains its maximum value at a critical cycle number beyond which the state of dislocation dipol e accumulation becomes energetically unstable. In our theory we postul ate that this critical state is the onset of crack initiation. We shal l give a quantitative value for the fatigue limit and analyze the depe ndence of the S-N curve on several important physical parameters such as grain size; surface energy; yield strength; width of the PSB; and t he ratio of the shear modulus of the bicrystalline material.