Thickness reduction rate of plastically compressed metal plate by hardened rollers

The rate at which a solid deforms permanently depends on the load history, geometry and material properties. When a metal plate is compressed between two hardened rollers, its thickness reduces continuously if the material elements are deformed beyond their elastic limits. Those near the region of contact will experience more distortion as compared with those interior to the plate. This effect is analyzed incrementally in time by the theory of plasticity coupled with the strain energy density criterion. Failure is examined by assuming that the location of crack initiation coincides with the maximum of the minimum strain energy density function, (dW/dV)_min^max, when reaching its critical value. This is found to occur at the center of the plate depending on the rate of deformation. An increase in plate thickness reduction without failure can be achieved by taking smaller loading steps. Displayed graphically are numerical results for five different load histories that provide useful insights into the rate dependent process of metal forming.