Research on Phase-Field Model for Fatigue Fracture of Functionally Graded Materials
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摘要: 功能梯度材料参数的复杂性导致该材料具有复杂的应力场，给其疲劳断裂的数值分析带来了一定的困难. 相场模型不需要额外的断裂准则即能模拟复杂的断裂问题(如裂纹扩展等)，该文通过在相场模型中引入疲劳函数对其断裂能进行退化，将功能梯度材料的混合相场模型拓展至疲劳断裂问题，发展了功能梯度材料的疲劳断裂相场模型，并分析了其裂纹扩展驱动力. 揭示了相场模型下，功能梯度材料的疲劳裂纹扩展受控于应变能历程、临界能量释放率和疲劳退化函数的机制，为其结构设计提供了一定的指导意义.Abstract: The complex parameters of functionally graded materials (FGMs) lead to the complicated stress fields, which brings some difficulties for numerical analysis of their fatigue fracture. The complicated fracture problems such as crack propagation can be simulated with the phase-field model without additional fracture criteria. The hybrid phase-field model for FGMs was extended to fatigue fracture problems through introduction of the fatigue function to degrade the fracture energy. The phase-field model for fatigue fracture of FGMs was developed and the driving force for crack propagation was analyzed. The fatigue fracture mechanism that the crack propagation is controlled by the strain energy history, the critical energy release rate and the fatigue degradation function, was revealed. This work offers some guidance for the design of FGM structures.
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Key words:
- functionally graded material /
- phase-field model /
- fatigue /
- fracture
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图 2 单边裂纹板的载荷-位移曲线及最终裂纹路径
Figure 2. Load-displacement curves and the final crack path of the single-edge cracked plate
图 3 双层矩形板的计算模型及循环载荷
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 3. The computational model and the cyclic load of double-layer rectangular plate
图 5 中心裂纹板的计算模型及循环载荷
Figure 5. The computational model and the cyclic load of the plate with a center crack
图 6 中心裂纹板在不同循环周次下的裂纹扩展
Figure 6. Crack propagations at different numbers of cycles for the plate with a center crack
图 7 中心裂纹板的裂纹扩展驱动力分布
Figure 7. The distribution of crack propagation driving forces of the plate with a center crack
图 8 单边裂纹板的计算模型示意图(单位：mm)
Figure 8. Schematic diagram of the simulation model for the single-edge craked plate (unit: mm)
图 11 单边裂纹板的裂纹扩展驱动力分布
Figure 11. The distribution of crack propagation driving forces of the single-edge cracked plate
图 12 共线双裂纹板的计算模型及循环载荷
Figure 12. The computational model and the cyclic load of the plate with 2 collinear cracks
图 13 共线双裂纹板在不同循环周次下的裂纹扩展
Figure 13. Crack propagations at different numbers of cycles for the plate with 2 collinear cracks
图 14 共线双裂纹板的裂纹扩展曲线
Figure 14. Crack growth curves for the plate with 2 collinear cracks
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