Mathematical Analysis for Reduction of Thermal Stress in Functionally Graded Materials and Multi-objective Optimization of Material Composition

为了提高可重复使用火箭发动机和结构部件陶瓷涂层和接头的粘接强度，减小热应力，提出了功能梯度材料。今天，众所周知，这种对一种特性的持续控制可以扩展为一个更普遍的概念，可以通过逐渐改变材料的质地或成分来赋予任何材料新的特性和功能。金属/陶瓷FGM材料在使用前，必须基于温度和热应力分析进行材料成分设计，以便在预期热环境下进行热应力松弛。在加工后的冷却过程中，为了减小加热过程中的热应力，在FGM的富陶瓷层中也会产生严重的热应力导致裂纹的形成。在冷却过程中，除了控制材料成分外，还必须通过其他方法来减小热应力。在本研究中，采用部分稳定氧化锆（PSZ）在SUS304/PSZ FGM板中进行相变，以降低冷却过程中的热应力。控制板表面的冷却过程是有效利用体积膨胀相变的必要条件。然后利用Sugano的分段线性非齐次逼近方法和拉普拉斯变换的卷积定理，导出了具有任意热非齐次的FGM板的瞬态热传导问题的解析解。将Sugano导出的具有任意力学非均质性的非均匀板的热应力表达式进行扩展，得到了包含相变应变的热应力表达式。对不同厚度和冷却速度下陶瓷体积分数分布的数值计算结果表明，PSZ的相变对SUS304/PSZ FGM高温加工后冷却过程中的热应力降低非常有用。少

Functionally graded materials(FGM) was proposed in order to increase the adhesion strength and minimize the thermal stress in the ceramic coatings and joints being developed for the reusable rocket engine and structural elements. Today it is well known that this continuous control of a property could be extended to a more general concept that could be applied to impart new properties and functions to any material by gradually changing its texture or composition .Before using, material composition of metal/ceramic FGM must be designed based on the temperature and thermal stress analyses for the thermal stress relaxation under the expected thermal environment. During cooling after processing, the severe thermal stress lead to crack formation, also occurs in the ceramic-rich layer of the designed FGM for the reduction of the thermal stress during heating. The reduction of thermal stress during cooling must be accomplished by other method besides controlling material composition .In this r … More esearch, phase transformation of partially stabilized zirconia(PSZ) in SUS304/PSZ FGM plate was used for the purpose of the reduction of thermal stress during cooling. Controlling the cooling process of the plate surfaces is needful for the effective-use of the phase transformation with the volume expansion. Then an analytical solution was derived for the transient heat conduction problem in the FGM plate with arbitrary thermal nonhomogenieties by the piecewise-linear nonhomogeneous approximation method developed by Sugano and the convolution theorem of Laplace transformation. An expression of the thermal stress including phase transformation strain was obtained from an extension of thermal stress expression in nonhomogeneous plate with arbitrary mechanical nonhomogenieties derived by Sugano. The results of numerical calculation for the various cases of volume fraction distribution of ceramic through the thickness and cooling speed of the plate surfaces, has shown that phase transformation of PSZ is excellently useful for the reduction of thermal stress in SUS304/PSZ FGM during cooling after high-temperature processing. Less