Review of approximate analyses of sheet forming processes

Approximate models are often used for the following purposes: in on-line control systems of metal forming processes where calculation speed is critical; to obtain quick, quantitative information on the magnitude of the main variables in the early stages of process design; to illustrate the role of the major variables in the process; as an initial check on numerical modelling; and as a basis for quick calculations on processes in teaching and training packages. The models often share many similarities; for example, an arbitrary geometric assumption of deformation giving a simplified strain distribution, simple material property descriptions - such as an elastic, perfectly plastic law - and mathematical short cuts such as a linear approximation of a polynomial expression. In many cases, the output differs significantly from experiment and performance or efficiency factors are developed by experience to tune the models. In recent years, analytical models have been widely used at Deakin University in the design of experiments and equipment and as a pre-cursor to more detailed numerical analyses. Examples that are reviewed in this paper include deformation of sandwich material having a weak, elastic core, load prediction in deep drawing, bending of strip (particularly of ageing steel where kinking may occur), process analysis of low-pressure hydroforming of tubing, analysis of the rejection rates in stamping, and the determination of constitutive models by an inverse method applied to bending tests.