双相延迟非傅里叶热传导及相关的热冲击断裂理论研究

Classic Fourier law assumes thermal disturbance propagates with an infinite speed. This does not necessarily to be correct for certain problems of practical interest in contemporary engineering. To overcome the limitations of classic Fourier law, the single-phase-lag model was developed to include a delayed response between the heat flux vector and the temperature. However this model still assumes an immediate response between the temperature gradient and the energy transport. The dual-phase-lag model allows a delayed response between the temperature gradient and the temperature, which is the result of the microstructural effect in high-rate heat transfer and has been demonstrated by experiments. In this project, the dual-phase-lag model is used to investigate the heat conduction and associated fracture mechanics problems under high-rate heating. A finite element numerical method corresponding to the dual-phase-lag model will be developed. The dynamic thermo-mechanical coupling fracture behavior of the materials will be explored. A method for predicting the thermal shock resistance of materials will be established. Due to essential differences between the dual-phase-lag model and the classic heat conduction model and the single-phase-lag model, new rules and phenomena are expected to be obtained from the proposed research.

经典傅里叶定律认为热量传递是速度无限的扩散行为，在一些极端情况下并不能完全反映真实的热传导现象。单相延迟热传导模型考虑了热流矢量和温度之间的延迟响应，但其应用仍然具有一定的局限性。双相延迟模型认为在急速传热过程中，温度梯度和温度之间也存在时间上的延迟。这一模型已被一些实验现象所证实，同时也符合量子力学的基本规律。本项目以双相延迟热传导模型为基础，系统地研究材料在瞬态热载荷作用下的热传导及其相关的断裂力学问题，建立基于双相延迟导热模型的有限元素法，探索材料内部的动态热-力耦合断裂行为，构造材料的热冲击阻力评价的理论模型。由于双相延迟导热模型与经典傅里叶热传导模型和单相延迟热传导模型具有本质的差别，因此本项研究将会在热-力耦合断裂力学方面获得一些新的现象和规律。

固体材料的热迟滞行为在描述微尺度或超急速等极端条件下的热传导现象时是非常重要的。双相延迟模型通过引入两个不同的时间弛豫参数来描述热流矢量、温度梯度、和能量输运之间的迟滞效应。这两种不同的迟滞行为分别是：热流矢量的传播和温度之间的迟滞行为，与热流梯度和温度之间的迟滞行为（实验证明：在超急速传热中，声子-电子在微观尺度上的相互作用将会导致温度梯度和热流矢量之间也存在延迟）。如果仅考虑热流矢量的传播和温度之间的迟滞行为，那么归一化的双相延迟热传导模型将退化为双曲型热传导模型；如果两种迟滞行为都不考虑，那么归一化的双相延迟热传导模型将退化为经典傅里叶热传导模型。本项目以双相延迟热传导模型为基础，系统地研究了材料在瞬态热载荷作用下的热传导及其相关的断裂力学问题，建立了基于双相延迟导热模型的有限元素法，利用有限差分法求解了关于时间变量三阶导数的微分方程组，探索了材料内部的动态热-力耦合断裂行为，构造了材料的热冲击阻力评价的理论模型。由于双相延迟导热模型与经典傅里叶热传导模型和单相延迟热传导模型具有本质的差别，因此本项研究在热-力耦合断裂力学方面获得了一些新的现象和规律。