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考虑循环弹塑性效应的Ⅰ型裂纹疲劳扩展近场动力学计算方法

A PERIDYNAMIC COMPUTATIONAL METHOD FOR MODE I FATIGUE CRACK PROPAGATION CONSIDERING CYCLIC ELASTOPLASTIC EFFECTS

  • 摘要: 针对循环载荷作用下的Ⅰ型疲劳裂纹扩展行为, 基于键型近场动力学理论和键剩余寿命损伤模型, 引入Neuber法则与Ramberg-Osgood本构关系, 对裂尖局部循环键应变进行弹塑性修正, 并采用候选键群断裂比例的判据对单一核心键失效的裂纹推进机制进行改进, 建立了考虑裂尖循环弹塑性效应的近场动力学疲劳裂纹扩展模型, 通过铝合金裂纹板和Q345E钢材的疲劳试验验证了模型的适用性. 在此基础上, 分析了断键比例阈值和裂纹几何形状、初始裂纹长度比对裂纹扩展的影响, 并探讨了整体刚度演化的特征. 结果表明: 断键比例阈值是影响裂纹推进判定和寿命预测精度的关键参数, 当断键比例阈值ηc = 50%时, 模型预测精度高; 裂纹几何形状显著影响裂纹扩展速率, 双边裂纹板较中心裂纹板表现出更快的裂纹扩展, 主要因为二者裂尖循环键应变差异随裂纹扩展由4.0%增至12.7%; 初始裂纹比a0/w显著影响裂纹扩展, 且随着a0/w由0.3增至0.7, 裂尖循环键应变明显放大并促进裂纹加速扩展; 此外, 剩余整体刚度随疲劳过程呈非线性退化, 并与裂尖循环键应变演化表现出阶段性对应关系. 所建立模型为循环荷载作用下材料疲劳裂纹扩展行为模拟和寿命预测提供了一种新的分析方法.

     

    Abstract: For Mode I fatigue crack propagation under cyclic loading, a peridynamic fatigue crack growth model that accounts for crack tip cyclic elastoplastic effects was developed based on bond-based peridynamic theory and a bond residual life damage model. The Neuber rule and the Ramberg-Osgood constitutive relation were introduced to correct the local cyclic bond strain near the crack tip by considering elastoplastic effects, while a crack growth criterion based on the fracture ratio of candidate bond groups was adopted to improve the conventional crack propagation mechanism governed by the failure of a single critical bond. The applicability of the proposed model was validated against fatigue tests on cracked aluminum alloy plates and Q345E steel specimens. On this basis, the effects of the bond breaking ratio threshold, crack geometry, initial crack length ratio, and global stiffness evolution were investigated. The results show that the bond breaking ratio threshold is a key parameter governing crack growth determination and fatigue life prediction accuracy, and good agreement with experimental results is achieved when the threshold ηc is set to 50%. Crack geometry significantly affects the crack growth rate, with the double-edge cracked plate exhibiting faster crack propagation than the center-cracked plate, mainly because the difference in crack tip cyclic bond strain between the two configurations increases from 4.0% to 12.7% as the crack propagates. The initial crack length ratio a0/w also has a pronounced influence on crack growth; as a0/w increases from 0.3 to 0.7, the crack tip cyclic bond strain is substantially amplified, promoting accelerated crack propagation. In addition, the residual global stiffness exhibits nonlinear degradation during the fatigue process and shows a clear stage dependent correspondence with the evolution of crack tip cyclic bond strain. The proposed model provides a new analytical approach for simulating fatigue crack propagation and predicting fatigue life of materials subjected to cyclic loading.

     

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