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应用于复合型断裂的三种主要准则（Ｇ－准则，σθ－准则及Ｓ－准则）都假定断裂核区是一个圆域，其圆心在裂纹类端。某个适当的力学参量沿半径为ｒ的圆周计算，并认为在此圆周上这一力学参量的数值决定裂纹的扩展。但是精确的，值至今未被严格地定量确定。本文根据Ｔｈｅｏｃａｒｉｓ［１］提供的方法，应用Ｍｉｓｅｓ屈服准则，引入初始弹－塑性边界来确定断裂核区，并将裂纹尖端的切向应力σθ沿初始弹－塑性边界计算，对σθ－准则进行修正。修正后的σθ－准则可以应用于准脆性断裂。
The three main criteria (G-criteria, σθ-criteria and S-criteria) applied to composite fractures all assume that the fracture nucleus is a circular domain with its center at the crack end. An appropriate mechanical parameter is calculated along a circle of radius r and the value of this mechanical parameter on this circle determines the expansion of the crack. But precisely, values have so far not been rigorously quantified. According to the method provided by Theocaris [1], the Mises yield criterion is introduced to introduce the initial elastic-plastic boundary to determine the fracture nuclei. The tangential stress σθ at the crack tip is calculated along the initial elastic-plastic boundary to correct the σθ-criterion . The modified σθ-criterion can be applied to quasi-brittle fracture.