Abstract
The deformation zone approach to the solution of practical deformation processing problems in the workshop introduced by Hill and elaborated by Green et al. is a very useful concept based on two-dimensional (plane strain) slip line field theory. A key element of this approach is an estimate of the intensification of die pressure due to inhomogeneous strain as the ratio of die contact separation ( h) to die contact length ( L) increases above one. Since this estimate is based on slip line field theory that assumes the work material to be rigid where it is not plastic and to act in plane strain, it cannot be used to answer questions concerning residual elastic stresses or brittle fracture (such as the central burst problem). A new approach to deformation zone geometry based on elastic rather than rigid-plastic behavior is presented and compared with slip line field results. Unlike the slip line field technique, the new approach is applicable to 3-D (axisymmetric) as well as 2-D problems and in addition, provides a limit of safety beyond which a central burst or centerline residual tensile stresses may be expected to present a problem.
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