考虑热-力耦合效应的形状记忆合金疲劳断裂相场模型研究
PHASE FIELD MODELLING OF FATIGUE FRACTURE IN SHAPE MEMORY ALLOYS CONSIDERING THERMO-MECHANICAL COUPLING EFFECT
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摘要: NiTi形状记忆合金(SMA)因其特殊的宏观力学行为及优异的弹热效应, 在众多新兴工业领域得到了广泛应用. 然而, 该合金在服役过程中较差的疲劳寿命及复杂的断裂行为成为其大规模应用过程中的主要阻碍. 本文在热力学框架下推导了SMA的宏观热-力耦合本构模型以及疲劳断裂相场模型, 保证了热力学一致性. 使用断裂相场模型对SMA考虑热-力耦合效应的疲劳断裂行为展开了模拟研究, 尤其是宏观尺度上裂纹扩展过程中SMA裂尖温度场的振荡行为. 本文使用断裂相场模型从理论上深入分析了SMA裂尖的温度振荡与马氏体相变行为之间的关联, 阐释了循环载荷下裂尖热滞回效应的成因, 揭示了由加载频率升高所引发的热累积机制, 并探明了不同温度对疲劳裂纹扩展行为的影响规律. 数值实现方面, 完成了SMA疲劳断裂相场模型的有限元移植, 采用了一种残差控制交错迭代求解算法, 避免了相场模型能量泛函非凸性问题, 并通过设置收敛条件提高计算收敛性. 模拟结果表明, 循环加载下, SMA裂尖发生马氏体相变并释放潜热, 与温度场进行热交换, 引起热滞回效应. 在不同加载频率下, SMA裂尖释放潜热与热交换之间存在时间尺度上的差异, 出现热累积现象. 本文提出的模型为后续SMA宏观疲劳断裂行为的进一步研究提供了理论工具.Abstract: NiTi shape memory alloys (SMAs) have found extensive application across numerous emerging industrial fields due to their unique macroscopic mechanical behaviour and exceptional thermoelastic effects. However, the poor fatigue life and complex fracture behaviour exhibited by these alloy materials during service represent major obstacles to their large-scale development. This work presents a unified derivation within a thermodynamic framework for both the macroscopic thermo-mechanically coupled constitutive model and the fatigue fracture phase field model for SMAs, ensuring the thermodynamic consistency. Employing the fatigue fracture phase field model, this study conducts an in-depth investigation into the fatigue fracture behaviour of SMA under thermo-mechanical coupling, particularly focusing on the oscillatory temperature field at the crack tip during crack propagation at the macroscopic scale. The fracture phase-field model is employed to theoretically investigate the relationship between temperature oscillations at the crack tip and martensitic phase transformation behavior in SMAs, along with the thermal hysteresis effect observed during cyclic loading, the thermal accumulation effect emerging with increased loading frequency, and the fatigue crack propagation behavior at different temperatures. Regarding numerical implementation, this study completed the finite element adaptation of the fatigue fracture phase field model of SMAs. A residual-controlled staggered algorithm is employed to circumvent the non-convexity issue of the phase field model's energy functional, with convergence conditions set to enhance computational stability. Simulation results indicate that under cyclic loading, martensitic phase transformation occurs at the SMA crack tip, releasing latent heat. This latent heat undergoes thermal exchange with the temperature field, inducing a thermal hysteresis effect. At different loading frequencies, temporal discrepancies arise between the latent heat release at the SMA crack tip and the thermal exchange process, leading to thermal accumulation phenomena. The model proposed herein provides a theoretical tool for subsequent research into the macro-fatigue fracture behaviour of SMAs.
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