主应力空间等向强化数学方程与几何描述

来源期刊：有色金属科学与工程2011年第6期

论文作者：赵德文 章顺虎 李灿明 王国栋

文章页码：12 - 15

关键词：主应力空间；等向强化；三元二次曲面；稳定材料；比例加载

Key words：principal stress space; isotropic hardening; ternary quadric; stabilizing materials; proportional loading

摘    要：

对等向强化给出在主应力空间的具体强化曲面方程，绘出了比例加载条件下稳定材料相应的屈服轨迹及后续强化曲面证明初始屈服后，若后续屈服三轴强化系数不等并逐渐减小时则强化曲面不再是圆台面而是椭球面；但当强化半径相等即三轴强化系数相等时为球面，两轴应力且强化系数不等时为椭圆若材料无包辛格效应，承受相等的负平均应力硬化曲面与前述图形沿等倾几何轴线oH成对称该结论仅适合满足Drucker公设材料。

Abstract:

A specific isotropic hardening quadric equation for stabilizing materials is proposed and derived in principal stress space, and the corresponding locus and subsequent yield surface are drawn up in proportional loading. After the initial yielding the subsequent yield surface is no longer a circular truncated cone but a ellipsoid when triaxial hardening exponents are diversity and diminution. However, if triaxial hardening exponents are equal, namely hardening radius are the same, the subsequent yield surface is a sphere, or is an ellipse with unequal hardening exponents at biaxial space. If there is no Bauschinger effect, the hardening quadric is symmetrical about equally inclined geometric axis oH with equal negative mean normal stress. The conclusion is suitable only to the stabilizing materials according to Drucker postulation.