Slip rotations occurring during rolling are considered to be due to a triaxial stress system, in which the three stresses are σ, a compressive stress normal to the rolling plane, −nσ, a tensile stress parallel to the rolling direction and (1−n)⁄2·σ, a compressive stress parallel to the transverse direction. If the direction cosines of each stress axis with respect to the slip plane normal and slip direction are represented, the total resolved shear stress acting on the slip system is given by: τ=σ{cosφ_1 cosλ_1+(1-n)/2 ·cosφ_3 cosλ _3-n cosφ_2 cosλ_2}.
In case of the triaxial stress system where two compression axes exist, displacements of the rolling plane normal in a standard stereographic projection will depend on the ratio of component of resolved shear stresses owing to the two compressive stresses. When the effect of the tensile stress can be ignored, the trarsverse compressive stress causes the transverse direction to move to the slip plane normal and the normal compression rotations lead the rolling plane normal towards the slip plane normal. In consequence, the displacements of the rolling plane normal will be composed of those which arise from two compressive stresses.
When a lateral spread occurs at cosφ₃cosλ₃<0, it will be necessary to operate the slip system which accommodates the lateral spread. In case that cosφ₃cosλ₃ is nearly zero, the slip rotations on the triaxial stress system will be consistent with that on the biaxial stress system, since the effect of the transverse compressive stress can be ignored.
It can be concluded that the three stress axes should be considered to act together in order to investigate the texture development from slip rotations occurring during rolling.