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This paper presents numerical solutions of axisymmetric sheet stretching employing an experimentally determined stress-strain curve and measured overall coefficient of friction along the punch-sheet interface. Experiments have been conducted on thin sheet metals such as mild steel, aluminum and brass with a hemispherical steel punch. Predicted values of loads, deflections, strain distributions and other relevant data are favorably compared with experimental values of these same quantities. NOTATION ciju fourth order material constant tensor D~j rate of deformation tensor p uniform normal pressure P punch load rc radius of contact boundary r ratio width to thickness strain average r value R orthogonal rotation tensor R t transpose of orthogonal rotation tensor x~ current coordinates X~ reference coordinates equivalent strain 0 arc angle of punch rate of rotation tensor # coefficient of friction r shear stress p punch radius # equivalent stress a* rotated Cauchy stress a v stress rate tensor ~b angle with rolling direction.

In this paper a numerical solution of strip rolling based on finite element method is presented. The material behavior in the form of a stress-strain curve obtained from a plane-strain compression test and measured interfacial velocities as prescribed boundary conditions are used as input data to the numerical model of strip rolling. Numerical results such as distributions of roll pressure, frictional stress, and coefficient of friction in the contact region are presented.

Experimental results are presented for carefully controlled plane-strain strip drawing experiments. Transparent aluminum oxide (sapphire) dies have been used to make direct observations of the die-work interface in strip drawing, including the distortion of scribed lines which were used for estimating velocity profiles at the interface. Such profiles can be used as input to theoretical models (Appleby et al., 1984), thus permitting the calculation of interface friction rather than requiring its assumption. Experiments were conducted with tungsten carbide, as well as sapphire, dies in which process parameters such as reduction, speed, die angle, lubricant, and back tension were varied, and die separating forces and drawing loads were measured. In general the frictiot~ was lower for the sapphire dies, but the variation with process parameters was similar. For one experiment, residual stresses in the product strip were measured. The results are believed to be documented in sufficient detail to be of general use in evaluating theoretical models.

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