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本文在４种材料３０ＣｒＭｎＳｉＡ，４０ＣｒＮｉＭｏＡ，４５钢和２０钢宏观与细观试验结果的基础上，对韧性细观断裂的随机性和模糊性进行了研究。以基于孤立空洞长大模型基础上的临界空穴扩展比模型为例，指出细观空穴形核半径和临界半径可以用对数正态分布描述，其它模型参量可以用正态分布描述。具体分析了这４种材料在不同应力状态和应变水平下的断裂特征，结果表明，考虑参数的随机性，即采用概率断裂力学方法，所得结果比传统的确定性断裂模型接近实验结果。文中进一步讨论了断裂状态的模糊性，提出了考虑断裂状态随机模糊失效慨率的计算模型，算例分析表明，断裂状态的模糊性是事物的本质特性，基于专家经验基础上的模糊断裂分析方法能较全面描述材料及试样的断裂问题。本文建立的方法也适用于其它断裂模型的分析．
Based on the macroscopic and microscopic experimental results of 30CrMnSiA, 40CrNiMoA, 45 and 20 steels, the randomness and fuzziness of ductile mesoscopic fracture are studied in this paper. Taking the critical cavity expansion ratio model based on the model of isolated cavity growth as an example, it is pointed out that the nucleation radius and critical radius of the mesopore can be described by a logarithmic normal distribution, and the other model parameters can be described by the normal distribution. The fracture characteristics of these four materials under different stress states and strain levels are analyzed in detail. The results show that the results obtained are close to the experimental results when compared with the traditional deterministic fracture model, considering the randomness of the parameters, that is, using the method of probabilistic fracture mechanics. In the paper, the fuzziness of the fracture state is further discussed and a calculation model considering the stochastic fuzzy failure rate of the fracture state is proposed. The case study shows that the fuzziness of the fracture state is the essential property of the thing. Based on the expert’s experience, Can more fully describe the fracture of the material and the sample. The method established in this paper is also applicable to the analysis of other fracture models.