Development of Polar Nonhomogeneous thermoelastic theory and its Application to Thermal Stress Analysis of Porous Functionally Graded Materials

基于功能梯度材料中气孔引起的热应力减小是由于偶应力的存在而产生的这一推论，利用Mindlin偶应力理论建立了非均质体的具有偶应力的平面应变热弹性问题。但是，由于功能梯度材料的热性能和力学性能的任意非均匀性以及偶应力理论的复杂性，控制微分方程组的解析解并未得到。然后，在本研究中，由于考虑了陶瓷100%层状垂直裂纹的萌生和垂直裂纹拼接引起的层裂，提出了一种只在厚度方向上具有温度变化和非均匀特性的功能梯度材料板中与竖直裂纹萌生和拼接有关的温度应力的近似三维分析方法。它是通过a…透露的对PSZ/SUS304功能梯度板的进一步分析和数值计算表明，受热表面100%陶瓷层的热应力降低与成分分布密切相关，富含陶瓷的成分分布对降低热应力非常有效。其次，得到了受表面间歇加热作用的功能梯度板的温度和热应力的解析解。用Vodicka方法分析了同一功能梯度板表面连续受热时的非稳态热传导问题，得到了非稳态温度场。热应力分析基于Rogers和Spencer的解，这些解表示为等效均质板的二维薄板近似控制方程的解。对PSZ/SUS304/PSZ功能梯度板中的瞬时温度和热应力分布进行了数值计算，揭示了富陶瓷成分分布在热循环加载过程中降低受热表面拉伸热应力的有效性。较少

Based on an inference that reduction of thermal stress due to pores in functionally graded materials (FGMs) is produced by the presence of couple stress, a plane-strain thermoelastic problem with couple-stress was formulated for nonhomogeneous bodies using Mindlin's couple-stress theory. But analytical solutions to the governing differential equations were not obtained because of arbitrary nonhomogeneities with respect to thermal and mechanical properties of functionally graded materials and complexity of couple-stress theory. Then, in the present research, because of consideration on initiation of vertical cracks of ceramics 100% layr and spallation caused by linking-up of verticalcracks, an approximate three-dimensional analysis method was proposed for thermal stresses related to the initiation and linking-up of vertical cracks in a functionally graded material plate with temperature variation and nonhomogeneous properties only in the thickness direction. It was revealedthrough the a … More nalysis and numerical calculation for PSZ/SUS304 functionally graded plate that the reduction of tensile thermal stresses in the ceramic 100% layr on the heated surface is significantly dependent on composional distribution, and that ceramics-rich compositional distribution is very effective for the thermal stress recuction. Secondary, analytical solutions was obtained for temprature and thermal stresses in a functionally graded plate subjected to intermittent heating on its surface. The transient temperature field was derived from the solution for a transient heat conduction problem in the same functionally graded plate heated continually on its surface that is analyzed by Vodicka's method. Thermal stresses were analyzed based on Rogers and Spencer's solutions which were expressed in terms of the solution to the approximate, two-dimensional, thin-plate, governing equations for an equivalent homogeneous plate. Numerical calculations for the transient temperature and thermal stress distributions in PSZ/SUS304/PSZ functionally graded plate revealed effectiveness of ceramics-rich compositional distribution for the tensile thermal stress reduction on the heated surface during thermal-cycle loading. Less