The diffuse and local instability criteria associated with sheet metal forming limits are investigated for materials having a wide range of properties. The results are compared with available experimental data. An alternate method based on the pre-existence of an initial inhomogeneity or weakness within the material is developed. The straining paths which are dependent upon the particular applied stress ratio are presented and the results correlated with experimental limit strains obtained from the hydrostatic bulging of aluminum diaphragms in circular and elliptical dies.

A method based on the finite difference technique is deve loped for the construction of slip-line fields when the material has a defined deg ree of anisotropy. Solutions for the indentation of semi-infinite and finite depth anisottopic media are developed and compared with the results obtained from the indentation of aluminum specimens for which the deg r ee of anisotropy is evaluated from yield stress considerations. The solutions are extended to include the extrusion of anisotropic materials and the approximate, but simpler, upper bound limits. The analogue between plane strain slip-line field solutions and the collapse loads associated with flat plates are investigated for anisotropic materials.