Kinematic Hardening Applied to Non-Proportional Loading
ARMY MATERIALS AND MECHANICS RESEARCH CENTER WATERTOWN MA
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A series of critical experiments in the determination of a plastic flow rule is re-examined using kinematic hardening. Non-proportional loading experiments on thin-walled, aluminum tubes were conducted by Budiansky, Dow, Peters, and Shepherd in 1951 to determine whether plastic flow exhibits behavior consistent with the physical, slip theory of plasticity or with the phenomenological, J sub 2 flow and deformation theories. Their results were mixed since none of these theories predict the full range of exhibited, material behavior. Pan and Rice have sparked recent interest in these experiments by introducing a slight rate dependence into slip theory. Through a judicious choice of a strain rate sensitivity parameter they match the experiments reasonably well. This article reports on the comparison of these experiments against the predictions of a flow rule based on the PragerZiegler kinematic hardening theory. Both shear and axial strains are predicted for a variety of load histories. Results show good agreement between theory and experiment. The implications to buckling and instability analysis are briefly discussed.
- Numerical Mathematics