一个与Mises轨迹覆盖面积相等的线性屈服条件  

A Linear Yield Criterion with Equal Covered Area to Mises Yield Locus' Coverage in Haigh Westergaard Stress Space

作　　者：赵德文[1] 方琪[1] 刘相华[1] 王国栋[1] 

机构地区：[1]东北大学轧制技术及连轧自动化国家重点实验室,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2005年第3期248-251,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(50474015);国家重点基础研究发展规划项目(G2000067208 4).

摘　　要：在π平面上,取Mises屈服轨迹覆盖面积与其相交十二边形覆盖面积相等的方法确定十二边形6个顶点,顶点与内接点连线为新的屈服轨迹,建立该轨迹在HaighWestergaard应力空间上的直线方程,证明了此方程确定的屈服准则为Mises屈服准则的最大程度的线性逼近,其偏差应力矢量模长与Mises准则模长在π平面上平均误差为零;给出了十二边形内接点顶角为159 836°,圆外顶角为140 164°;以及单位体积塑性功率表达式·Let the area covered by Mises yield locus on the π-plane be equal to the area coverage of a non-equiangular but equilateral dodecagon and the two areas be overlapping to determine the six apexes of the new yield locus. Then, the lines connecting these apexes and six inscribed points are defined as the new yield criterion loci or locus as a whole. The linear equation of the new locus in Haigh Westergaard stress space has been deduced. It is proved that the new yield locus is approximate upmost to that of Mises yield criterion and is called MA (most adjacent) yield criterion for short, and the apex angle of the new dodecagon is 159.836° with the apex angle of circumscribed hexagon equal to 140.164°. The mean error of deviator stress vector modulus on the π-plane between Mises and MA criterions is zero. Furthermore, the plastic power rate for unit volume is also given.

关 键 词：线性逼近 Mires屈服准则 π平面 积分中值定理 最高精度 塑性功率 

分 类 号：TG301[金属学及工艺—金属压力加工]