Limit strains in the sheet forming of strain and strain-rate sensitive materials

Abstract

Forming-limit diagrams are a convenient way of displaying the limits of performance of a sheet material in pressing and stamping: they represent the limiting combination of strains after which unacceptable necks are formed in the material. Although originally empirical, there is clearly much to be gained from the prediction of the limit curves using more readily measured material and process parameters; for example, the material prestrain and strain and strain-rate hardening indices, its degree of anisotropy, as well as the effects of die design, lubrication, etc. In this paper the growth of the neck through the development of strain gradients is explored. The neck is assumed to originate at pre-existing thickness imperfections or material inhomogeneities and has a continous, but accelerating, development resulting in a very localised defect which can be interpreted as failure: it is assumed that in the sheet-stretching region the neck lies perpendicular to the major in-plane strain whilst in the drawing region the neck lies along the direction of zero extension in the plane of the sheet. The strain-rate sensitivity of the material produces a delay in the growth of the neck, and the analysis can be extended to cover materials which show considerable rate effects resulting in superplastic behaviour. A comparison between forming-limit curves predicted on the basis of limiting strain gradients and published data is made for a number of sheet materials.