Complete Numerical Solution of the Axisymmetrical Deep-Drawing Problem

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Abstract
The present study introduces a finite difference method to obtain the complete numerical solution of the axisymmetrical deep-drawing of a circular blank. The theory includes nonlinear strain-hardening, normal plastic anisotropy, prestrain, variable coefficient of friction as a function of deformation, an approximation to the thickness stress, and an instability criterion. Using a computer program, distributions of any variable such as stress or strain can be obtained at any stage. Theoretical solutions are in good agreement with experimental ones. The method of solution slightly overestimates the limiting drawing ratio, which can be improved by adding the effects of bending and unbending at the die.

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