耦合宏微观效应的约束应力区疲劳裂纹模型的求解与应用

ANALYTICAL SOLUTION AND APPLICATION OF RESTRAINING STRESS ZONE FATIGUE CRACK MODEL WITH COUPLING THE MACROSCOPIC AND MICROSCOPIC EFFECTS

用约束应力区描述材料损伤状态,建立耦合宏微观效应的跨尺度疲劳裂纹模型,可描述材料疲劳破坏从微观缺陷到宏观断裂的整个过程。约束应力的分布取决于材料的损伤状态。假定约束应力为线性分布,在远场均匀拉应力作用下,应用Muskhelishivili方法,对跨尺度裂纹模型进行了解析求解,得到了裂纹张开位移与跨尺度应变能密度因子的解析解。以跨尺度应变能密度因子作为疲劳裂纹从微观到宏观扩展的控制参量,对疲劳破坏全过程进行了数值模拟计算。以LC4铝合金板为例,利用模型精确再现出不同疲劳荷载作用下的实验S-N曲线。由于模型考虑了微观因素的影响,疲劳实验数据的发散特性也精确再现出来。另外,通过数值计算,分析了微观效应对疲劳裂纹扩展行为的影响。

Material damage state can be depicted by a restraining stress zone. A trans-scale fatigue crack model with coupling the macro / micro effects is developed. The proposed model can describe the whole process of fatigue failure from a microflaw（ fatigue source） to the final fracture. The distribution of restraining stresses depends on the material damage state in the restraining stress zone. A linear distribution of restraining stresses is assumed. Under the remotely applied uniform tension,the trans-scale crack model is analytically solved using Muskhelishivili approach. Analytical expressions of crack opening displacement and trans-scale strain energy density factor are obtained. The trans-scale strain energy density factor serves as the controlling parameter of fatigue crack growth from micro-scale to macro-scale. Numerical simulations for the whole process of fatigue failure are completed. By application of the present model,the experimental S-N curves of LC4 aluminum alloy plates under the different loading conditions are accurately re-produced. The scatter of fatigue test data owing to the microscopic effects is also reflected by the present model. Moreover,the influences of microscopic effects on the fatigue crack growth are also discussed.