抄録
General concept of criterion for ductility is presented, and its applications to the prediction for cracking are shown: one is the formability in sheet metal forming as an example of plane stress problem, and the other is the centeral bursting in drawing and extrusion as an expmple of cracking in bulk specimens. Here, the criterion 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. 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 modes of which are consistent with the two modes required from the condition permitting strain rate discontinuity under the continuity of velocity. The general treatment about these criteria and the mode of planes permitting strain rate discontinuity is discussed. Next, two examples for application of the proposed criterion are showm: one is the prediction for the formability of sheet metal, deforming according to the assumed process proceeding from statical instability to kinematical one, and another shows the die angle reduction combination on which a chevron crack occurs in drawing and extrusion under plane strain, where statical instability coincides with kinematical one. These forming limits predicted are compared with several experimental results published in the literature, and they are in very good agreement.
