Sheet-Metal Forming

Abstract

The stress-state is said to be plane when the direction normal to the plane is a principal stress direction and the magnitude of the stress in this direction is zero. This situation occurs when a sheet is loaded along its edges in the plane of the sheet. In-plane deformation of sheet metal, such as bore expanding and flange-drawing, is an example of plane-stress problems. For out-of-plane deformation of sheet metals, such as punch stretching, sheet bending, and cup drawing, a simple analytical method is the use of membrane theory. This theory neglects stress variations in the thickness direction of a sheet and considers the distribution of stress components only in the plane of the sheet. Thus, the basic formulations for the analysis of both in-plane and out-of-plane deformations contain only the stress components acting in the plane of the sheet. However, the analysis of out-of-plane deformation requires consideration of large deformation, while the infinitesimal theory is applicable for in-plane deformation analysis. Many materials employed in engineering applications possess mechanical properties that are direction-dependent. This property, termed anisotropy, stems from the metallurgical structure of the material, which depends on the nature of alloying elements and the conditions of mechanical and thermal treatments. Metal sheets are usually cold-rolled and possess different properties in the rolled and transverse directions. Therefore, in sheet-metal forming in particular, the effect of anisotropy on the deformation characteristics may be quite appreciable and important. In the past the calculation of the detailed mechanics of large plastic deformation of metal sheets has been achieved with some success by numerical methods. However, without exception, these studies have dealt with deformations that possess a high degree of symmetry, and were concerned with the anisotropy existing only in the direction of sheet thickness (normal anisotropy). Methods that are capable of solving nonaxisymmetric problems in forming of anisotropic sheet metal are still being sought. The finite-element method is one of those methods. It was applied to the elastic-plastic analysis of nonaxisymmetric configurations of sheet stretching with normal anisotropy by Mehta and Kobayashi.