Thermo±elasto±plastic stresses in functionally graded materials under consideration of the fabrication process Y. M. Shabana, N. Noda Summary The present study analyzes elasto±plastic thermal stresses in some particle-rein- forced functionally graded material plates FGP) by taking into consideration residual stresses of the fabrication process. For the FGP, the region near the cooling metal surface consists of distributed ceramic particles in a metal matrix, while the region near the heating ceramic surface contains distributed metal particles in a ceramic matrix. We use the thermo±elasto± plastic constitutive equation of a particle-reinforced composite, taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Elasto±plastic thermal stresses are discussed here with the goal of reducing the thermal stresses. Two kinds of particle-reinforced FGP are considered: the ®rst kind FGP1) represents distributed ceramic particles in the metal matrix, and the second one FGP2) represents distributed metal particles in the ceramic matrix. We modify the thermo±elasto±plastic constitutive equation of a particle- reinforced composite for the FGP2 by taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Using the temperature-dependent material properties, three cases of temperature conditions are studied. The ®rst one is the cooling from the fabrication temperature to the room temperature, the second one is the heating from the room temperature, and the last one is the heating after cooling from the fabrication temper- ature. The particle volume fraction is assumed to vary according to a power function in the thickness direction of the FGPs. Using the ®nite element method, the effects of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix and the stress in the particle in the FGPs are discussed. Also, the effects of the particle volume fraction and the fabrication temperature on the maximum tensile matrix stress are discussed. Keywords Thermal stress, functionally graded material plate, elastoplasticity, incremental theory, temperature-dependent properties 1 Introduction The components of a space vehicle are subjected to ultra-high temperatures, ultra-high tem- perature gradients and cyclical changes of the temperatures due to a number of take-offs and landings. One of the most important problems in the development of a space vehicle is how to make an advanced high-temperature resistant material. The initial concept of functionally graded materials FGMs) was proposed as an advanced high-temperature-resistant material. The FGMs have been the subject of intense research in the recent years, and their mechanical and mathematical modeling is currently an active research area. FGMs are, generally, two-phase composites with volume fractions continuously varying from one surface of the material to the other. These continuous changes result in gradient material properties. Since ceramic has Archive of Applied Mechanics 71 2001) 649 ± 660 Ó Springer-Verlag 2001 649 Received 22 November 2000; accepted for publication 24 April 2001 Y. M. Shabana &) Graduate School of Science and Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561, Japan e-mail: yasser_shabana@hotmail.com N. Noda Mechanical Engineering Department, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561, Japan