Abstract: The stress expressed in the integral form was obtained based on analytical analysis of the flange for axisymmetrical deep drawing process under certain assumptions. After an appropriate substitution of variable, analytical expressions of radial stress have been simplified by using the integral mean value theorem and Taylor series expansion method respectively according to the linear variation of integral function. The radial stress distributions of the flange at any deformation moments and the stress at the entrance of the die at different moments during the process can be directly calculated by using the simplified formula. The calculated results by using the two simplified methods match well ones by integration. Some given examples show that the maximum relative errors of the radial stress at the entrance of the die during the deep drawing process are less than 0.6%, and relative errors of maximum stress less than 0.15%. In cases of deep drawing of cylindrical cup, the limiting drawing coefficient calculated by the simplified analytical formula was calculated considering friction in the flange area and the die fillet area and sheet metal bending deformation in the die fillet area. The results are in good agreement with the experimental ones.

Key words: Deep drawing, Integral mean value theorem, Sheet metal forming, Stress solution, Taylor series