基于二阶组构张量的各向异性屈服准则

将四个屈服准则:Tresca准则、Mises准则、Mohr-Coulomb准则以及Drucker-Prager准则归类为剪切屈服准则。Tresca准则和Mohr-Coulomb准则是关于最不利截面的剪切屈服准则,而Mises准则和Drucker-Prager准则是关于各方向截面的剪应力和正应力的某种综合度量的八面体剪应力和八面体正应力的剪切屈服准则。从方向函数(ODF)的概念入手,将各方向截面的剪应力和正应力综合度量直接取为所有方向截面上的剪应力和正应力的平均。对各向同性材料,提出了平均剪切屈服度准则:当平均剪应力和平均正应力的组合达到某一极限值时,材料开始屈服。研究表明,平均剪切屈服准则与Drucker-Prager准则具有相同的形式,当不考虑平均正应力对屈服的影响时,它与Mises准则具有相同的形式。针对由各向异性损伤导致的材料各向异性强度问题,定义截面上的有效正应力和有效剪应力则分别为截面上的法向力和切向力与有效承载面积之比,基于截面上的有效应力提出了各向异性材料的平均剪切屈服准则。各向异性损伤引起的截面上有效应力放大系数为方向函数,可以采用二阶组构张量来近似表示,在任意坐标系中,各向异性屈服准则为应力分量的二次齐次式,导出了其中的系数与二阶组构张量之间的显式关系式。在二阶组构张量的主轴坐标系内,各向异性屈服准则与殷有泉的拓展Hill准则形式完全相同,当不考虑正应力对屈服的影响时,它与Hill准则具有相同的形式。

AN ANISOTROPIC YIELD CRITERION BASED ON THE TWO-ORDER FABRIC TENSOR

In this paper, four yield criteria, i.e. Tresca yield criterion, Mises yield criterion, Mohr-Coulomb yield criterion and Drucker-Prager yield criterion are categorized into shear yield criteria. Tresca yield criterion and Mohr-Coulomb yield criterion belong to the shear yield criterion for the shear stress and the normal stress at the critical plane of a given material point. Mises yield criterion and Drucker-Prager yield criterion belong to the shear yield criterion for the comprehensive measurement of shear stress and normal stress of all planes of a given material point. Based on the concept of ODF (Orientation Distribution Function), mean shear stress and mean normal stress are taken as a comprehensive measurement of shear stress and normal stress at all planes, which are defined as the average shear stress and the average normal stress at all planes respectively. For virgin isotropic materials, mean shear yield criterion states that the material will yield if the linear combination of mean shearstress and mean normal stress reaches an utmost value. It is shown that mean shear yield criterion has the same form as the Drucker-Prager yield criterion. Particularly, it has the same form as the Mises yield criterion if the effect of mean normal stress on yield is not considered. For anisotropic damaged materials, the mean yield criterion is the linear combination of the mean effective normal stress and the mean effective shear stress. The amplification ratios of the effective normal stress and the effective shear stress to their nominal counterparts are approximated by two-order fabric tensors. The mean yield criterion for the anisotropic damage material is expressed as quadratic equation of stress tensor components. For coordinates that coincide with the principal axes of the fabric tensors, it has been proved that the anisotropic yield criterion has the same form as the extended Hill anisotropic yield criterion. Particularly, if the effect of mean normal stress on yield is not considered,the anisotropic yield criterion has the same form as the Hill anisotropic yield criterion.