On the mechanics of localized necking in anisotropic sheet metals

Abstract

The ductility of sheet metals formed by cold rolling is often assessed by tension tests on long rectangular strips which are cut from a sheet at various angles to the direction of rolling. A strip typically deforms homogeneously to begin with, but eventually fails at a site where a narrow neck develops along a line that crosses the gauge section obliquely from side to side. The degree of obliquity depends on the material as well as on the cutting angle; so also does the stage of deformation at which a neck first appears. It has long been evident that material orthotropy and progressive hardening are crucial factors, but a theoretical analysis of the phenomenon that takes due account of both of these is apparently still lacking. Their joint influence is investigated here on the basis of the classical rigid/plastic constitutive model in its original form. Some pragmatic notions which were added later are excluded as being too simplistic and unnecessarily restrictive. The present analysis has been deliberately freed from ad hoc empiricism of any kind with a view to more realistic modeling in the future. Other than basic analytic requirements, there are no theoretical limitations on the path dependences of orthotropic parameters and the rate of strain hardening, nor on the evolving geometries of subsequent yield surfaces. It appears to the writer that, with well planned experiments and improved instrumentation, strip tests could be much more effective as a means to investigate orthotropic behaviour in metals.