Criterion and mode of the forming limit in sheet forming

Abstract

In this paper, the forming limit of sheet metals is examined, with respect to the collapse of the unique solution. In general, there are two cases bringing about multiplicity: one is statically-admissible multiplicity and the other is kinematically-admissible multiplicity. The multiplicities are considered to correspond to plastic instability. After the appearance of statical instability, the strain path cannot be controlled as freely as would be preferred. Ultimately, localized necking occurs when the process satisfies the condition of kinematical instability, the mode of which is consistent with one of the two modes required from the condition permitting strain-rate discontinuity under the continuity of velocity. These instabilities are compared with the diffuse necking of Swift and with the localized necking of Hill from the standpoints of criterion and mode. The dependency of formabilities on the strain path is discussed in terms of several assumed strain paths. © 1992.