Resolved shear stress in elastically anisotropic polycrystals

Kneer’s analysis was used to calculate the fraction of a tensile stress applied along the rolling or transverse direction, which is resolved as a shear stress on the various slip systems of an α titanium crystallite as a function of crystallite orientation. The crystallite was assumed to be imbedded in a sheet for which the crystallite orientation distribution had been previously determined. The maximum resolved shear stress was found to increase in the order \(\left\{ {10\bar 10} \right\} - \left\langle {1\bar 210} \right\rangle \) , \(\left\{ {10\bar 11} \right\} - \left\langle {1\bar 210} \right\rangle \) , \(\left\{ {0001} \right\} - \left\langle {1\bar 210} \right\rangle \) in the ratio 1∶1.04∶1.17 for the material studied. This seems to be a direct consequence of single crystal anisotropy, and should be relatively insensitive to changes in crystallite orientation distribution. For a given slip system, the maximum resolved shear stress was found to be higher for a tensile stress applied along the rolling direction than for an equivalent stress along the transverse direction in the ratio 1.04∶1 for the material studied. This is a result of the type of preferred orientation present, which is typical for titanium sheet continuously rolled in the α phase.