含Ⅰ型边缘裂纹离心叶轮的应力强度因子预测方法

离心叶轮叶片在高速旋转时容易因裂纹扩展出现断裂破坏。由于叶片几何形状和载荷均很复杂，采用公式法计算I型裂纹的应力强度因子不可避免地存在着误差。扩展有限元法分析应力强度因子虽精度较好，但一般要花费大量的计算时间且有时收敛困难。首先基于ABAQUS软件扩展有限元法模块，仿真分析了不同的裂纹起始位置和裂纹长度下的叶片裂纹尖端应力强度因子，得到其与裂纹长度和起始位置的关系。接下来，基于断裂力学理论知识，检验了公式法估算应力强度因子的准确度。最后，以扩展有限元法的仿真结果为训练数据，以叶片裂纹位置和裂纹长度为输入参数，建立了裂纹尖端应力强度因子的多层反向传播人工神经网络(back propagation artificial neural network, BP-ANN)。算例表明，BP-ANN的预测精度优于公式法，并可有效减少扩展有限元法的仿真次数，推进断裂力学在离心叶轮可靠性设计中的应用。

Prediction Methods for Stress Intensity Factor of Centrifugal Impeller with Mode I Edge Crack

The blades of centrifugal impellers are prone to fracture and damage due to crack propagation when rotating at high speed. Due to the complex geometry and load of the blade, computational error can occur in the evaluation of the stress intensity factor of the Mode-I crack by the formula method. Despite of the satisfactory accuracy achieved through the extended finite element method (XFEM), the computation of the stress intensity factor can be expensive and sometimes difficult to converge. In this paper, , the stress intensity factor of the blade crack tip under different crack initiation positions and crack lengths is analyzed based on the ABAQUS XFEM module, and the relationship between the factor and the crack length and initiation position is obtained. Next, based on the basic theory of fracture mechanics, the accuracy of the formula method to estimate the stress intensity factor is tested. Finally, taking the simulation results of the extended finite element method as the training data, a multilayer BP-ANN artificial neural network was constructed carrying the crack position and length as input parameters, and the stress intensity factor of the Mode-I crack was predicted with different starting positions and different lengths parameters. Through numerical example, it is demonstrated that the BP-ANN not only provides more accurate predictions than the formula method, but also effectively reduces the number of simulations of the extended finite element method.