准脆性金属材料的Ⅰ-Ⅱ混合型裂纹扩展速率预测

PREDICTION OF CRACK GROWTH RATE BASED ON COUPLING FRACTURE WITH DAMAGE IN QUASI-BRITTLE MATERIALS

基于断裂与损伤力学方法,将裂纹的开裂和疲劳扩展两个过程结合起来考虑,研究准脆性金属材料内Ⅰ-Ⅱ混合型裂纹起裂后稳定扩展速率的预测问题。由于裂纹空间分布的复杂性及数学上的困难,将该裂纹简化为二维裂纹。首先分析裂尖构成,判定该裂纹的进一步扩展即分支裂纹的扩展问题,将Ⅰ、Ⅱ混合型裂纹等价地处理为起裂方向上的当量Ⅰ型裂纹;其次在断裂损伤耦合的基础上,对损伤(硬化)区的边界进行探讨;最后在损伤力学框架下,对该裂纹的扩展速率进行分析,初步导出一个Paris型的裂纹扩展速率公式。研究结论与有关文献及工程实际相吻合。在裂纹起裂和疲劳寿命预测研究方面具有一定的理论价值。

In order to predict crack propagation-rate within a quasi-brittle material,the expansion mechanism of a Ⅰ-Ⅱ mixed mode crack in quasi-brittle materials was investigated based on coupling the damage model with fracture mechanics.Due to complexity of calculation and the crack distribution in quasi-brittle materials,the mixed crack was simplified as a 2-D plane problem.Area around the crack tip was divided into four zones according to their deforming characters and the crack propagation was considered equivalent to the branched crack.So,the propagation-rate of the mixed crack was treated as one of the equivalent mode-Ⅰ branch crack.Boundary equations between damage zone and fracture zone were derived to determine the radial sizes of initial damage and fracture zones due to load on the crack.The crack propagation-rate was analyzed with damage model,and a Paris-formula was derived for the crack propagation here.This result manifests its important theoretical significance in predicting crack growth and fatigue life-span in cutting tool material.