Ductile Forming Limit Stress in Sheet Forming Processes with Nonlinear Strain Path Involving Out-of-plane Forming

Abstract

The ductile forming limit in nonlinear strain paths which include out-of-plane forming such as rolling was investigated for a 11% Cr steel sheet. For strain paths with only a plane stress state, e.g., in-plane strain, the forming limit stress diagram (FLSD) has been proven to be effective, even if the paths are nonlinear. In this research, a method of extending the FLSD theory to strain paths which include out-of-plane strain is investigated experimentally and theoretically. An experimental procedure is used to measure directly the stresses at the onset of diffused and localized necking and at the onset of separation with rolling-stretching loading paths. Theoretically, an assumption is introduced to consider out-of-plane strain in the M-K theory. The experimental and theoretical results of the forming limit stress show good agreement. When large rolling strain is induced in first-stage loading paths, this research demonstrated that there are cases where the FLSD theory is not effective for predicting the ductile forming limit. Those cases are characterized by a stress state of the re-yielding point in the final loading stage. If the point is outside the FLSD curve, the forming limit stress is not on the FLSD curve but located near the subsequent yield surface. Thus, a modified FLSD curve can be defined by the lines connecting the outer line of the conventional FLSD curve and the subsequent yield surface of the loading path under consideration. With this extension, it is possible to demonstrate the applicability of the FLSD method to processes which include out-of-plane loading paths such as rolling.