热冲击下温度相关物性对热弹性响应的渐进分析

Effect of Temperature Dependency on Thermoelastic Response During Transient Thermal Shock

计及材料物性与温度的相关性,基于Green-Naghdi能量无耗散广义热弹性理论(G-N II理论),对热冲击下具有变物性特征材料的热弹性响应进行了求解分析.借助Laplace正、反变换技术以及Krichhoff变换,在热物性参数随真实温度呈线性规律的前提下,推导了半无限大体受热冲击作用时热弹性响应的解析表达式,通过求解分析,得到了热冲击下热波、热弹性波的传播规律,位移场、温度场以及应力场的分布情况,以及物性随温度相关性对热弹性响应的影响效果.结果表明:当考虑材料物性随温度的变化时,热波、热弹性波的传播以及各物理场的分布均受到不同程度的影响,且物性随温度相关性对热弹性响应的作用效果将受到材料热-力耦合特性的影响.

The thermoelastic behavior induced by transient thermal shock varies significantly due to temperature dependency of material properties. Research on the thermoelastic response of materials with variable properties, especially the prediction of thermal stresses, is very important to evaluate material lives in some circumstance with extreme heat supply. The thermoelastic response of materials with temperature- dependent properties suffering transient thermal shock is studied in this paper. The equations with variable material properties are proposed in the context of generalized theory of thermoelasticity without energy dis- sipation （Green-Naghdi II model）. The analytical solutions of the problem for a semi-infinite body subjec- ted to a sudden thermal shock on its boundary are derived by means of the Laplace transform technique and the Krichhoff transform,where the variable thermal material properties are assumed to be a linear function of real temperature. The explicit expressions of two waves,i, e. the thermal wave and thermoelastic wave, are obtained from these analytical solutions, which clearly reveal the propagation of the two waves and their connections with the characteristic parameters, such as the thermo-mechanical coupling coefficient and tem- perature factor. The distributions of displacement, temperature and stress, associated with the finite propa- gation velocity of heat signal, are obtained and plotted. Meanwhile, comparisons with the results obtained from the case with constant material properties are also made to reveal the effect of temperature dependen- cy of material properties on them. The results show that when variations in thermal material properties are taken into account, the propagation of two waves changes, so does the distribution of each physical field; and these changes are dependent on the value of thermo-mechanical coupling coefficient.