Bulk strain and grain strain in axisymmetric deformation

Bulk strain, defined in terms of original and final dimensions of a specimen, correlates well with the logarithm of the average number of intercepts per unit length on test lines parallel to axes of symmetry after uniaxial deformation of an axisymmetric specimen. This suggests a definition of principal grain strain based on the mean linear intercepts before and after deformation, measured along principal directions. Results of type 304 stainless steel strained to varying amounts between necking and fracture support the hypothesis that the axial gradient of the total grain boundary area projected onto any cylindrical surface coaxial with the axis of deformation remains unchanged as deformation progresses. Although the behavior of the grain boundary network leads to simple correspondences between grain and bulk strains, they are not numerically equal for this type of deformation