Since the fracture toughness of materials in the ductile and brittle transition region presents obvious scatter, Weibull stress based on the local approach to fracture is widely used to clarify the randomness. A large number of detailed finite element analyses are necessary to be carried out for the calculation of Weibull stress, especially for the complex structures and loads. In order to simplify the calculation of Weibull stress, this paper derives Weibull stress solutions as functions of stress intensity factor or J integral for elastic and elastic–plastic materials under mode I-II loading. These solutions are verified by using modified boundary layer model and applied in the analysis of fracture toughness test results by four-point bending specimens. The relationship between failure probability P_f and SIF or J integral under mode I-II loading is derived and verified with experimental data. The result shows that the failure probability can predict the experimental data well.

由于材料在韧性和脆性过渡区的断裂韧性表现出明显的分散性，因此基于局部断裂方法的威布尔应力被广泛用于阐明随机性。为了计算威布尔应力，特别是对于复杂的结构和载荷，必须进行大量的详细有限元分析。为了简化Weibull应力的计算，本文推导了在I-II模式载荷下弹性和弹塑性材料的Weibull应力解作为应力强度因子或J积分的函数。这些解决方案通过使用改进的边界层模型进行验证，并应用于四点弯曲试样的断裂韧性测试结果分析。失效概率之间的关系推导了在模式I-II加载下的P _f和SIF或J积分，并用实验数据进行了验证。结果表明，故障概率可以很好地预测实验数据。