Lattice strains at cracks in single crystal titanium: Elastic distortion and GND contributions

There is evidence from diffraction experiments that significant peak broadening is measured local to crack tips and this has been attributed to the development of geometrically necessary dislocations (GNDs) which are retained upon unloading. This is reasonable due to the stress singularity found locally at the crack which is expected to activate slip on favourably oriented slip systems, potentially resulting in plastic strain gradients and geometrically necessary dislocation development. Hence, a systematic study is presented here to ascertain the contributions of both elastic distortional strain and GND density to lattice deformation local to the crack at loaded and subsequently unloaded states. The results show that whilst elastic strains dominate lattice distortion in comparison to GNDs at the loaded state i.e. at the peak load applied, these strains are largely recovered upon unloading and the contribution from GND development subsequently dominates the broadening seen. Two initial crystallographic configurations were considered. In the example in which the crystal c-axis was oriented parallel to the loading direction, the pyramidal systems contributed most to slip with basal slip system contributing to a lesser extent. However, in the example where the c-axis was oriented perpendicular to the loading direction, the pyramidal and prismatic systems were the more significant contributors to slip and the basal contributing to a lesser extent. However, basal, prismatic and c+a pyramidal slip systems were found to be active in both examples and this was attributed to significant lattice rotation driven by locally high stresses which enabled otherwise badly oriented slip systems to become favourable for slip. Finally, increases in GND density were seen upon unloading for c-axis orientation parallel with loading. This was attributed to the influence of pyramidal slip on reverse plasticity leading to diffuse GND density distributions and significant resulting lattice strains compared to that from prism slip loading.