Failure maps for sheet metal

Possible stress and the strain states atfailure in sheel metalforming processes are illustrated in diagrammatic form. Simple plane-stress proportional loading processes are considered, and the well known forming-limit diagram is presented as a particular example; other diagrams in different stress and strain spaces are presented, including the stress deviator space and the π plane. Various ductilefracture criteria are illustrated in stress and strain space, and a mapping concept is outlined in which the curves from different criteria are superimposed. The inner envelope of these curves forms a failure-limit diagram which indicates the failure mode most likely to terminate a process defined by a given stress or strain ratio. These maps illustrate that various failure criteria can be applied to a single material and in a given forming process; the performance of the material will depend on both the process and the competition between the various failure modes.