基于非局部和非傅里叶理论的微纳米材料热冲击断裂力学理论研究

In recent years, micro/nano materials is more and more used in high-speed missiles, astronautics and high-speed aircraft and so on, and they are always used under thermal shock. So thermal shock fracture mechanics of micro/nano materials is becoming more and more important. Considering the spatial size effect of micro/nano materials and time size effect of thermal shock load, the nonlocal elasticity and non-Fourier heat conduction theories were developed and received much attention. However, to obtain more reliable theoretical result in the study of thermal shock fracture mechanics of micro/nano materials, both of the two theories should be considered simultaneously. Therefore, in this project, both the nonlocal elasticity and non-Fourier heat conduction theories are introduced to the study of thermal shock fracture mechanics micro/nano materials. A new temperature-stress constitutive equation will be established, and the dynamic thermo-mechanical coupling behavior of micro/nano materials will be investigated. The fracture mechanics behaviors of micro/nano materials under thermal shock load will be explored. A method for predicting the thermal shock resistance of micro/nano materials will be presented. Due to the essential differences between the model combining the nonlocal elasticity and non-Fourier heat conduction theories and classical model/ pure nonlocal model/ pure non-Fourier model, new phenomena and rules are expected to be obtained from the proposed research.

近年来微纳米材料在高速导弹，宇宙航行，高速飞机等方面的应用越来越多，而且常常被应用于热冲击环境中，因此微纳米材料的热冲击断裂力学研究日益显出其重要性。前人针对微纳米材料的空间尺度效应和热冲击荷载的时间尺度效应，分别提出了非局部弹性理论和非傅里叶热传导理论，受到广泛的关注。但是在研究微纳米材料热冲击断裂力学问题时，有必要同时考虑空间和时间尺度效应以得到更可靠的理论结果。因此本项研究将非局部弹性理论和非傅里叶热传导理论统一引入到微纳米材料的热冲击断裂力学研究中，建立新的温度-应力本构方程，研究微纳米材料内部的动态热-力耦合问题，探索微纳米材料的热冲击断裂力学行为，提出微纳米材料的热冲击阻力评价方法。由于非局部弹性理论和非傅里叶热传导理论结合模型与传统模型/单纯非局部模型/单纯非傅里叶模型有本质的差别，因此本项研究将会在微纳米材料的热冲击断裂力学方面获得一些新的现象和规律。

微纳米材料在高速导弹，宇宙航行，高速飞机等方面的应用越来越多，而且常常被应用于热冲击环境中，因此微纳米材料的热冲击断裂力学研究日益显出其重要性。本项目求解了微纳米梁、板、圆柱模型的非傅里叶热传导温度场方程解析解，求解了热-力耦合、热-力-电耦合、热-力-电-磁耦合的热应力、电位移和磁感应强度及其裂纹问题的热应力强度因子、电位移强度因子和磁感应强度因子，研究了材料性质的温度相关性、半椭圆型表面裂纹、热冲击时间和裂纹长度对微纳米材料热冲击断裂行为的影响。基于最大应力准则和断裂力学准则计算了微纳米压电圆柱模型的热冲击阻力，并给出适合工程应用的最小热冲击阻力公式。以上结果与傅里叶热传导结果进行对比，发现非傅里叶热传导模型更准确。本项目的研究结果为微纳米材料的热冲击断裂力学设计提供一定的理论指导。