Development of Supporting System of Design to Release Thermal Stresses in the Functionally Gradient Materials with a Crack

本研究由两部分组成：[I]梯度功能材料热应力理论研究，[II]含裂纹梯度功能材料热应力有限元释放程序系统的开发。利用一种新的变量变换和摄动法可以求解非线性一维热传导方程。在冷却初期，功能梯度板的陶瓷表面产生较大的拉应力。但这种大的应力区被限制在很薄的一层内。(2)我们可以解决含有内部裂纹的功能梯度材料的稳态和非稳态热应力问题，其所有的材料性能都是一个变量的指数函数。当年轻的mod…更多的ULU和线膨胀系数在功能梯度材料中变化很大，应力强度因子K_i和K_t；II&gt；如果能优化选择FGM的组成，使陶瓷的杨氏模数高于金属，而导热系数和线膨胀系数低于金属，则应力强度因子K_i和K_t；PART[II]开发了含裂纹功能梯度板热应力的有限元释放程序系统。(1)开发了含裂纹功能梯度板热应力的有限元释放程序系统。(2)通过对含边裂纹功能梯度板应力强度因子随时间变化的有限元计算，得到了以下结果。陶瓷表面有很大的应力强度因子K_i。应力强度因子K_i较大的区域被限制在很薄的一层内。裂纹的扩展长度被限制在非常薄的一层内。较少

This research project consists of two parts : [I] Theoretical treatises of thermal stresses in the functionally gradient materials(FGMs), [II] Developments of programming system to release the thermal stresses in FGMs with a crack by Finite Element Methods(FEM).PART[I] Theoretical treatises of thermal stresses in the functionally gradient materials.(1) The governing equation of transient heat conduction for the functionally gradient materials is nonlinear. We could solve the nonlinear transient one dimensional heat conduction equation by use a new transformation of a variable and the perturbation method. The large tensile stress occurs on the ceramic surface of the functionally gradient plate at the earlier stage of cooling. But this large stress region is restricted within a very thin layr.(2) We could solve the steady and unsteady thermal stress problems of the FGMs with an internal crack whose all material properties are some exponential functions of a variable. When the Young's mod … More ulus and the coefficients of linear thermal expansion in the FGMs largely change, Stress intensity factors K_I and K_<II> vary drastically. If we can optimally select the composition of FGM such that the Young's modulus of ceramic in FGM is higher than that of metal, but the heat conductivity and the coefficients of linear thermal expansion are lower than that of metal, the stress intensity factors K_I and K_<II> decrease drastically.PART[II] Developments of programming system to release the thermal stresses in the FGMs with a crack by FEM.(1) We could develop programming system to release the thermal stresses in the FGMs with a crack by FEM.(2) From the results of calculation for the time variation of the stress intensity factor of the functionally gradient plate with an edge crack by FEM, we obtained the following results. A very large stress intensity factor K_I occurs on the ceramic surface. The region of the large stress intensity factor K_I is restricted within a very thin layr. A length of crack growth is restricted within a very thin layr. Less