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Kinematic hardening represents the anisotropic component of strain hardening by a shift of the center of the yield surface in stress space. The current approach in stress analysis at finite deformation includes rotational effects by using the Jaumann derivatives of the shift and stress tensors. This procedure generates the unexpected result that oscillatory shear stress is predicted for monotonically increasing simple shear strain. A theory is proposed that calls for a modified Jaumann derivative based on the spin of specific material directions associated with the kinematic hardening. This eliminates the spurious oscillation. General anisotropic hardening is shown to require a similar approach.

A complete stress analysis of a metal-forming process is necessary in order to assess the onset of metal-forming defects such as the initiation of internal or surface cracks or the generation of residual stresses. This demands elasticplastic analysis. A program to evaluate complete stress distributions has been developed and applied to the extrusion process. Such solutions have not previously been obtained for general two-and threedimensional problems encompassing the technologically important steady state processes. although these solutions are essential for the rational assessment of limits on process variables which will ensure a satisfactory metal-forming procedure. The stress fields obtained for the extrusion process exhibit features which are consistent with the known development of extrusion defects, such as the appearance of surface cracks.

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