Analysis of Strain-Hardening Viscoplastic Wide Sheets Subject to Bending under Tension

The present paper provides an accurate solution for finite plane strain bending under tension of a rigid/plastic sheet using a general material model of a strain-hardening viscoplastic material. In particular, no restriction is imposed on the dependence of the yield stress on the equivalent strain and the equivalent strain rate. A special numerical procedure is necessary to solve a non-standard ordinary differential equation resulting from the analytic treatment of the boundary value problem. A numerical example illustrates the general solution assuming that the tensile force vanishes. This numerical solution demonstrates a significant effect of the parameter that controls the loading speed on the bending moment and the through-thickness distribution of stresses.

Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

Plastic Bending at Large Strain: A Review

Finite plastic bending attracts researchers’ attention due to its importance for identifying material properties and frequent occurrence in sheet metal forming processes. The present review contains theoretical and experimental parts. The theoretical part is restricted to analytic and semi-analytic solutions for pure bending and bending under tension. The experimental part mainly focuses on four-point bending, though other bending tests and processes are also outlined.