Plastic shear deformation of a thin strain-hardening disc: variational principles

Abstract

An analytical solution is derived for the problem of shearing of a thin disc of incompressible rigid, plastic strain-hardening material. The solution is obtained by a methodology introduced by the author in previous publications, relying fundamentally on continuity of the rotation-rate vector field. A variational theorem is derived which shows that the velocity vector field is unique if the boundary values are properly prescribed. The derived solution is compared to experiments, with which it shows good agreement.

Keywords:

• plasticity
• metal
• work-hardening
• deformation mechanism
• stress analysis
• variational principles

Acknowledgements

The author would like to thank Patricia Irene Bish (née Field) for her invaluable assistance with the figures. Helpful suggestions from the referee(s) are gratefully acknowledged.