Prediction of the limiting drawing ratio and the maximum drawing load in cup-drawing

Abstract

A new, simple and practically applicable equation, including the normal anisotropy value R and the strain hardening exponent n, for estimating the limiting drawing ratio LDR in cup-drawing of a cylindrical cup with a flat-nosed punch is derived. The normal anisotropy is based on Hill's theory of an anisotropy sheet that is isotropic in its plane. Whiteley's equation for estimating the LDR, and Hill's upper limit value of LDR, are two special cases of the new equation. Compared with the published experimental work, good agreement between the calculation and the experiment is obtained. The new equation shows that the most important parameter for LDR is the normal anisotropy value R, the strain hardening exponent n has also some influence on the LDR, and clearly explains the real interaction between the normal anisotropy value R and the strain hardening exponent n on the LDR. It is different from other equations, which are functions of the normal anisotropy value R only. A new equation, incorporating the value of LDR derived as above and the critical drawing load Pc based on the maximum load principle for localization of plastic flow, for estimating the maximum drawing load Pc at a certain drawing ratio DR in cup-drawing with a flat-nosed punch is developed. This equation is simple and supplies an accurate estimation of the maximum drawing load Pd. A comparison between the calculation and the experiment shows that good agreement is also obtained. It is thereby possible to better understand and control the cup-drawing behavior of sheet metal.