Plastic Instability and Forming Limits in Anisotropic Sheet Metal

Abstract

A new nonquadratic yield function recently proposed by the author to describe the anisotropic behaviour of rolled sheets under biaxial states of stress is applied here to define the plane stress yield locus when the principal stresses act in arbitrary directions with respect to the direction of rolling. The condition for plastic instability in plane stress is established for the special case of normal anisotropy, which corresponds to a constant strain ratio R throughout the sheet. Numerical results for the principal surface strains at the onset of instability are presented in graphical form on the basis of the Ludwik power law for the effective stress-strain curve. The nonquadratic yield function is also used in the present work to estimate the limit strains in sheet metal forming, using a theoretical model that provides some physical justification to the customary assumption of the initial existence of a localized groove across the direction of the greatest principal stress in the stretching process. It is shown that the estimated limit strain is less sensitive to the R-value of the sheet metal than that predicated on the basis of an inhomogeneity factor that is independent of the R-value.