一种后继屈服函数及其在弹塑性有限元中的应用

Elliptical Subsequent Yield Function and Its Application to Elastic-Plastic Finite Element Analysis

构造了一种在π平面上为椭圆的后继屈服函数 ;并将其应用于干涉孔及冷胀孔问题的弹塑性有限元分析当中。从分析结果来看 ,该屈服函数的应用 ,不仅在冷胀孔问题方面取得了较好的分析结果 ,而且在干涉孔问题方面 ,分析结果也出现了和试验结果更为接近的趋势。本文提出的这种椭圆型后继屈服函数是通过改变屈服函数以解决弹塑性问题的大胆尝试 ,为改进弹塑性问题的求解方法提供了又一新的思路。

The yield function put forward by Misses is a circle in π plane. It is based on the hypothesis that metal materials always are isotropy during subsequent yield, but this is not always true. We put forward an elliptical subsequent yield function (eq.3) which takes into account metal materials′ anisotropy in subsequent yield. In section 2, we applied the elliptical subsequent yield function to the elastic plastic finite element calculations of holes′ cold expansion and inference. Figs.4 through 6 show the comparison of test data with computed results of the holes′ inference. They show that the tendencies of stress, strain and the ratio between radial and tangential strain around the hole obtained by the elliptical yield function are more similar to the test than those by Misses yield function. Fig.7 shows the comparison of the test data with computed results of the holes′ cold expansion. The dotted curve and the bold solid curve are computed results, while the solid curve is the test data. It shows that the computed results are quite satisfactory.