Micromechanic analysis of fatigue band crossing grain boundary

Displacement of dislocations in metals causes plastic strain which is often highly localized and produces fatigue bands under cyclic loadings. Inside these bands, highly concentrated dislocation pile-ups develop at the grain boundary, causing severe resolved shear stress exceeding the critical shearing stress. This excessive stress is relieved either by nucleation of crack at the grain boundary or by forming another fatigue band in the neighboring crystal. Micromechanic analyses were performed on a fatigue band in a most favorably oriented crystal and an adjacent crystal with a slightly different orientation. Two cases were analyzed: (1) The most favorably oriented crystal with a sliding direction making 45° with the free surface in an aluminum polycrystal; and (2) Two adjacent crystals with sliding directions parallel to the free surface of a copper polycrystal subject to variable loadings. Results show that the amount of slip that propagates across the grain boundary reduces rapidly with the difference in orientations between the two crystals. In (2), two sequences of loadings were calculated: one is a low-amplitude loading followed by a high-amplitude loading (LH) and the other is a high-amplitude loading followed by a low-amplitude loading (HL). The LH sequence shows that the low-amplitude loading has no significant effect on the deformation in the subsequent high-amplitude loading. On the other hand, in the HL sequence, the high-amplitude loading has significant effect on the deformation in the low-amplitude loading. All these analytical results agree well with experimental observations.