Development of Supporting System of Design of the Functionally Graded Materialsand its Constitutional Equations

本课题包括两部分内容：[1]研究功能梯度材料在热载荷作用下的本构方程；[2]开发基于有限元法的功能梯度材料热应力释放系统。[1]部分：热载荷作用下功能梯度材料（fgm）的本构方程研究。功能梯度材料是由陶瓷和金属的组分组成的。因此，可以将fgm视为一种复合材料，其组成成分依赖于位置。提出了考虑热负荷的功能梯度材料的本构方程。基于椭球夹杂的Eshelby解和Mori-Tanaka关于有限浓度颗粒在热载荷作用下的平均应力-应变的概念，采用增量理论建立了描述颗粒增强复合材料热弹塑性行为和损伤行为的方程。[2]部分：用有限元方法释放含裂纹和不含裂纹的fgm中热应力的编程系统的开发。(1)利用所提出的本构方程，我们可以开发编程系统来讨论fgm中的热应力。(2)利用所提出的本构方程计算了基体和颗粒的应力应变曲线。即使平均应力为零，在基体中也会产生较大的可压应力，而在颗粒中则会产生较大的拉应力。应力应变曲线在很大程度上取决于fgm的制造工艺。(3)从冷热循环供热条件下带边裂纹的功能梯度板应力强度因子的时间变化计算结果可以得到如下结果：应力强度因子较大的区域被限制在极薄的层内，裂纹扩展长度被限制在板厚的十分之一内。fgm组分的最佳组成是从陶瓷到金属呈线性分布。少

This research project consists of two parts : [1] Study of constitutional equations of the functionally graded materials (FGMs) under thermal load, [2] Developments of programming system to release the thermal stresses in FGMs with and without a crack by Finite Element Methods (FEM).PART [1] : Study of constitutional equations of the functionally graded materials (FGMs) under thermal load. The functionally graded materials (FGMs) are consisted by compositional components of the ceramics and metals. Then, FGMs can be considered as one of the composite materials which its compositional components dependent on the position. The constitutional equations are proposed for the functionally graded materials taking into consideration of thermal load. The equations are developed by an incremental theory which describes the thermal elasto-plastic behavior and damage behavior of particulate-reinforced composites, based on Eshelby's solution of an ellipsoidal inclusion and Mori-Tanaka's conception … More of average stress-strain for the finite concentration of particles under thermal load.PART [2] : Developments of programming system to release the thermal stresses in FGMs with and without a crack by Finite Element Methods (FEM).(1) We could develop programming system to discuss the thermal stresses in the FGMs by used of the proposed constitutional equations.(2) The stress-strain curves are calculated for the matrix and the particle by used of the proposed constitutional equations. Even if the average stress is zero, large compressible stress occurs in the matrix, but large tensile stress occurs in the particle. The stress-strain curves largely depend on the manufacturing process of the FGMs.(3) From the results of calculation for the time variation of the stress intensity factor of the functionally graded plate with an edge crack under heating-cooling cycle heat supply, we obtained the following results. The region of the large stress intensity factor is restricted within a very thin layr, and length of crack growth is restricted within one time tenth of the thickness of the plate. The optimal composition of the component of FGMs is linear distribution from the ceramics to the metal. Less