An Efficient Method for Describing Plane Strain Bending of Viscoplastic Sheets at Large Strains

Abstract

AbstractAn efficient method for describing plane strain bending of wide rigid viscoplastic sheets at large strains is developed. Both pure bending and bending under tension are considered. The approach is based on the transformation equations between Eulerian and Lagrangian coordinates. In addition, it is shown that it is advantageous to use the equivalent strain rate as an independent variable instead of the space coordinate. Due to this change in the independent variable, a uniform treatment of an arbitrary dependence of the yield stress on the equivalent strain rate is possible. The solution reduces to an ordinary differential equation that should be solved numerically. However, one term of this equation reduces to the expression 0/0 at the initial instant. Therefore, analytic treatment of the differential equation is required to describe an initial stage of the process. An illustrative example is provided. This example illustrates the effect of the parameter involved in the Bingham model on the through-thickness distribution of stresses and the bending moment. It is shown that the thickness of the sheet decreases as the deformation proceeds.KeywordsBending under tensionViscoplasticityLarge strainsAnalytic solution