热惯性对热流冲击半无限体热应力波影响的研究

Study on the Dynamical Thermal Stresses for the Half-Space Shocked by Heating Flux With Thermal Inertia Boundary Condition

考虑超快速热流加热引起传热过程的非傅立叶效应,基于线性热弹性理论和表面热惯性特性,建立了带惯性热流加热条件的半无限体的动态温度场、热应力场方程组.用拉普拉斯变换法对方程组进行求解.结果表明,快速加热在半无限体内产生温度场和应力场,且热和应力呈波动输运机制.讨论了不同热惯性对半空间温度场和应力场的影响,比较弹性波波速与热波波速之比对动态热应力的影响.

Based on the modified Fourier law and linear thermalelastic theory with surface thermal inertia, the equation groups on the dimensionless thermal stress and dimensionless temperature field for the halfspace with thermal inertia heat flux boundary condition are built. The results obtained by the Laplace Transfer Method show that the two kinds of stress waves are produced simultaneously inside the halfspace. The following different characteristics are drawn compared with unit step heat flux boundary condition: (1) The temperature distributions inside the body with thermal inertia at any time are continuous and the any local temperature rises from zero; (2) The less the surface thermal inertia is, the slower the temperature variable rates; (3) The thermal stress distributions inside the body with thermal inertia at any time are continuous and the any local temperature rises from zero; (4) The Less the surface thermal inertia is, the greater the thermal stress shock; (5) The vertex stresses with the expanding wave velocity greater than the thermal waves′ are greater than those with the expanding wave velocity less than the thermal waves′; (6) Shocking stresses at the beginning with surface thermal inertia are zero in comparison with the final vertex stresses without surface thermal inertia.