Thermal stress and strain in a metal matrix
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I.
INTRODUCTION
A S metal matrix composites (MMCs) technology matures, new applications keep arising, and MMCs are anticipated to be used as structural materials in severe environments. One such example is the use of MMCs, especially intermetallics matrix composites, in aircraft at elevated temperatures. At elevated temperatures, even intermetallics matrix composites lose some of their roomtemperature properties. Moreover, the loss becomes much worse and results in material deterioration under thermal cycling or thermal fatigue. Thermal fatigue has been reported to occur in various MMCs: tungsten fiber/copper, 11,zl tungsten fiber/ superalloys, 131 boron fiber/aluminum, t4,5,61 A1203 (FP) fiber/aluminum, tTl FP fiber/magnesium, tSl SiC fiber/ titanium, t91 SiC whisker/aluminum, tl~ and graphite fiber/ aluminum ull composites. Thermal fatigue is associated with the thermal stress and strain induced by repeating constraints of free thermal expansion and contraction. The constraints can be grouped into two categories: external and internal. The external constraint is due to boundary forces applied to the surface of the component which is being heated or cooled. The internal constraint is produced by the difference in coefficients of thermal expansion (CTEs) of the constituent phases in the component material, CTE mismatch, and/or nonuniform temperature distribution in the component thermal gradient. Coefficient of thermal expansion mismatch-induced thermal fatigue is a characteristic with MMCs, since this mismatch for most of MMCs is large. Thermal stress and strain have been analyzed extensively for continuous fiber H2-281 and whiskerreinforcedt29,3~ MMCs. However, such analysis has been very limited for particulate M M C s . 131'321 This article analyzes thermal stresses and strains caused by CTE mismatch between the spherical reinforcement particle and the matrix in an MMC. The stresses and strains are derived as functions of CTE and temperature range. In particular, the critical pressure for plastic deformation in the immediate vicinity of a reinforcement particle is derived as a function of CTE, temperature range, Poisson's ratio, EUN U. LEE, Materials Engineer, is with the Aircraft Division, Naval Air Warfare Center, Warminster, PA 18974-5000. Manuscript submitted September 19, 1991.
METALLURGICAL TRANSACTIONS A
yield stress, and elastic constant. This analytical approach is different from the others. In this analysis, the assumptions are similar to those used for the analysis of elastic-plastic problems. [31,33-371These assumptions are (1) The reinforcement particle is a sphere in an infinite matrix of an MMC. (2) The matrix has elastic-perfectly plastic behavior. (3) The stress-strain behavior is independent of strain rate and stress orientation. (4) The temperature in the MMC is uniform at all times. Therefore, there is no thermal gradient in the MMC. II.
ANALYSIS
The thermal stresses and strains, induced by CTE mismatch, are analyzed under purely elastic conditions first and then under plastic conditio
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