Analysis of diffuse plastic stability in tubes and sheets

The diffuse plastic instability in tubes and sheets under biaxial stress conditions is examined by the use of perturbation methods. Very general constitutive relationships for material properties are used. This requires the inclusion of first order changes in the strain directions inside the patch and also treatment of the material anisotropy and strain rate sensitivity in addition to strain hardening. The inclusion of variations in strain direction is found to alter the form of the characteristic equation for stability from first order to second order but both roots are real for all cases investigated. The value of strain hardening at which the largest root becomes significantly positive is almost the same as that reached when changes in strain directors are ignored. However the strain hardening at which this root becomes formally zero can be very different. The former condition is considered to be of more practical importance than the latter. By this test the stability increases rapidly above a strain rate sensitivity of about 0.1.