由Tresca和双剪应力两轨迹间误差三角形中线确定的屈服方程

在π平面上,取Tresca屈服轨迹与双剪应力屈服轨迹之间误差三角形的几何中线确定新的屈服轨迹,建立了该轨迹在HaighWestergaard应力空间上的应力方程,称此方程为几何中线屈服方程或简称GM屈服准则·证明了单位塑性功率表达式及其对Mises圆的逼近精度·精度分析与算例表明该准则与Mises准则的最大误差不超过2 9%,平均误差仅为0 95%,比MY(平均屈服)准则的逼近精度提高1%,且它是线性的,其轨迹为与Mises屈服轨迹相交的等边非等角十二边形·该准则的单位体积塑性功率表达式也是线性的·

New Yield Equation Based on Geometric Midline of Error Triangles Between Tresca and Twin Shear Stress Yield Loci

The geometric midlines of error triangles or gaps between Tresca and twin shear stress yield loci on π-plane were linked up together to form a third yield locus which reflects a new yield criterion called GM (geometric midline) yield criterion in Haigh Westergaard stress space. The mathematical relationship between the GM criterion and its yield locus on π-plane was given as well as an expression of the rate of plastic work done per unit volume. A precision analysis was made with an actually calculated example. It is showed that the GM criterion is a linear one of which the maximum error relative to Mises criterion is not greater than 2.9% with a mean relative error not greater than 0.95%, and its precision is 1% higher than that of MY criterion. As a linear one, its yield locus is a non-equiangular but equilateral dodecagon intersected with Mises locus. The expression of the rate of plastic work done per unit volume of the criterion is also linear.