Catastrophe Theory Models of Chip Formation

Abstract

The problem of describing variations in the deformation process in chip formation is considered by constructing two catastrophe theory models of the process. Shear plane chip formation models are studied, in which the shear energy as a function of shear plane orientation and work-piece deformation along a fixed shear angle is minimized. Both of these formulations result in cusp catastrophes represented as a folded minimum energy surface, i.e., the minimum energy surface is multivalued for some values of the chip formation model parameters. It is argued, that as deformation proceeds, changes in the work material properties move the chip formation state on the energy surface and can produce large-scale deformation behavior changes if the folded region of the surface is encountered.