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

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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