Springback in cold metal-forming of AOOH steel: nonhomogeneous deformation

Abstract

The incremental theory of plasticity is applied in conjunction with finite elements to obtain the state of affairs in metal-forming. The allowable overforming for a AOOH steel sheet bent around a circular die is investigated numerically. For a 90° bend, the springback angle is found to be approximately 25%. That is, an overform of 25% is required if the sheet is to remain permanently deformed at 72°. The residual energy is found by comparing the energy states before and after spring back. The amount depends on the rate of forming. A modified theory of plasticity is also employed to find the nonhomogeneous character of the deformation field in the forming of metal sheets. Changes in the local strain rates and strain rate history are accounted for by deriving individual constitutive relations for each of the finite elements. Parameters assigned to describe material properties no longer remained constant but changed according to the loading rates. The strain rates at different locations were found to change by more than three orders of magnitude that could not have been adequately described by a single constitutive equation. Inhomogeneous deformation could play a significant role in metal-forming when local strain rates vary over a wide range, as demonstrated in this work.