Review of Stress, Linear Strain and Elastic Stress-Strain Relations

Abstract

In metal forming and machining processes, the work-piece is subjected to external forces in order to achieve a certain desired shape. Under the action of these forces, the work-piece undergoes displacements and deformation and develops internal forces. A measure of deformation is defined as strain. The intensity of internal forces is called stress. The displacements, strains and stresses in a deformable body are interlinked. Additionally, they all depend on the geometry and material of the work-piece, external forces and supports. Therefore, to estimate the external forces required for achieving the desired shape, one needs to determine the displacements, strains and stresses in the work-piece. This involves solving the following set of governing equations: (i) strain-displacement relations, (ii) stress-strain relations and (iii) equations of motion.