Anisotropy in stress-strain relationship in commercially pure titanium enhanced by deformation incompatibility

While work hardening mechanism of metals has been studied mainly focused on the dislocation theory, effects other than dislocations may affect the work hardening. When a polycrystal metal deforms, grains potentially deform in different shapes with each other due to the plastic anisotropy. The gaps generated between grains are so-called deformation incompatibility, which increases the work hardening rate. This hardening is generally attributed to the accumulation effect of geometrically necessary dislocations (GNDs). However, the elastic deformation to fill the gap explained by continuum mechanics also directly increases the stress. This study focused on the effect of not GND density but elastic deformation induced by deformation incompatibility on work hardening, and tensile tests of commercially pure titanium (CP-Ti) with a basal split texture were conducted by experiments and crystal plasticity finite element (CPFE) analyses. The results obtained showed that stress-strain curves changed depending on tensile direction, and the anisotropy was closely related to the difference in deformation incompatibility which varied depending on crystallographic orientations and active slip systems. A simple constitutive law was also proposed as a function of degree of deformation incompatibility, and could be used to quantify the effect of change in the deformation incompatibility due to the activation of slip systems on work hardening. These results, for the first time, indicate the possibility of controlling the work hardening rate of polycrystalline metals by the deformation incompatibility. • ▪The reason for the anisotropy of stress-strain curves in CP-Ti was investigated by experiments and numerical analyses. • It has been revealed for the first time that deformation restraint between grains, namely deformation incompatibility strongly influences the anisotropy of stress-strain curves. • ▪Deformation incompatibility changes depending on the type of slip systems and its timing of activation. • ▪Work hardening rates in CP-Ti can be controlled by controlling the deformation incompatibility.