平方主剪应力屈服准则

Yield Criterion of Square Principal Shear Stress

对各向同性材料在复杂应力状态下的屈服现象提出一新的物理解释。以菱形十二面体力滑移模型，即三组主剪应力的十二个作用面构成的应力单力体，并考虑到它的两个较小的主剪应力以反静力应力对材料屈服的影响，这一解释可称为平方主剪应力屈服准则。该准则认为当两个较小的主剪应力之平方和达到材料的某一极限值时，材料将开始屈服，而此极限值一般与静水应力成非线性关系。在三维主应力空间中，该准则在π－平面上的极限迹线满足Ｄｒｕｃｋｅｒ公设关于屈服面的外凸性条件，而极限速线的面积比Ｔｒｅｓｃａ屈服准则，Ｍｉｓｅｓ屈服准则和双剪应力屈服准则要大。

By using a rhombic dodecahedral body as a slip model which is formed by twelve sections acted in three groups of principal shear stresses on a stressed element,and by considering the influence of two smaller principal shear stresses and hydrostatic stress on the yielding of materials,a new physical interpretation of yield phenomena of isotropic materials under the complex stress state is made in this paper.It may be referred to as the yield criterion of the square principal shear.stress.It assumes that yielding begins when the square sum of two smaller principal shear stresses reaches a certain limit value which bears a non-linear relation with hydrostatic stress in general.Its cutting locus with π-plane in 3dimensional principal stress space satisfies the convexity condition of yield surface of Drucker's postulate and its area is larger than that of the Trescas yield,the Mises yield and the twin shear stress yield criteria,etc.In σ-τcombined stress state,some experimental data for mild steel made by Tayor and Quinney,the initial yield curve of an aluminum alloy made by Ivey and the test data of cast iron made by Cornet and Crassi are in good agreement with the yield criterion of square principal shear stress.