STRAIN-HARDENING AND RATE EFFECTS IN PLASTICITY
MEI, LU-TSUEN DANIEL
Doctor of Philosophy
In this study the effects of strain-hardening and rate sensitivity in plasticity theory are investigated. Because the method of characteristics cannot be applied to problems involving rate dependent yield conditions (65) therefore a different procedure is developed. In this investigation of large plastic deformation, the displacement field of the wedge indentation and inverted plane strain extrusion problem can be specified by following the trajectory of each element during deformation processes. Therefore, the unit diagram, introduced by Hill, et al (50), and the trajectory equations, derived by Hill (51), are utilized to specify the strain, strain rate fields for wedge indentation and extrusion problem, respectively. The plane strain inverted extrusion with 50% reduction in area is employed in this study because a complete solution has been given by Alexander (3) and the relative motion between the die and billet is prevented. Finite element and finite difference schemes are used to calculate the total work required to produce indentation and extrusion processes; work is then converted to the pressure or force. Atlan and Boulger (4), Adams and Beese (1), and Holzer (54) have presented the empirical equations for describing the strain-hardening and rate dependent characteristics of metals. Due to the simplicity and accuracy power law equations are employed to describe the material properties presented by Dugdale (34, 35) and the author. These material constitutive equations are then used to calculate the stress field which is the basis for the corrections of strain hardening or rate effects for the solutions based on the perfectly plastic theory. The agreement between the published experimental results and the theoretical predictions based on the analyses described in this study indicates the method proposed in this investigation is appropriate in modifying the slip line solutions for rigid, perfectly plastic material when strain hardening and rate effects are involved. Aspects of the theory which demand further investigation in future studies are pointed out.