Scripta METALLURGICA Vol. 25, pp. 2279-2284, 1991 Pergamon Press plc et MATERIALIA Printed in the U.S.A. All rights reserved TEMPERATURE CHANGE INDUCED PLASTICITY IN METAL MATRIX COMPOSITES: EFFECT OF REINFORCEMENT MORPHOLOGY Glenn S. Daehn, Peter M. Anderson, and Hongyan Zhang Department of Materials Science and Engineering The Ohio State University 116 W. 19th Ave., Columbus, OH 43210 (Received June 5, 1991) (Revised August 5, 1991) Introduction It iswell known that suffidenfly large temperature changes can induce plastic deformation in the matrices ot metal based composites. This is driven by the difference between the coefficients of thermal expansion (CTE) of the maffix and reinforcing phase. Thermally induced matrix plasticity plays an important role in a number of related phenomena: it produces dimensional instability (1,2), it is thought to produce a strength differential between tensile and compressive flow behavior (~-6) and both recent analyses (7,8) and experiments (7,9-11) show that composite creep is accelerated by thermal cycling conditions which induce plastic deformation in the matrix. ~In thermalcycling creep, this low resistance to deformation can be readily predicted by modeling plastic flow at yield using the Levy-vonMises equations (12). Such analyses show that if temperature excursions are sufficiently small so that plasticity is not introduced by thermal expansion mismatch, composites should maintain good strength under changing tem. perature, conditions. . . . . . . . For all the above reasons it is important, to estimate the temperature excursion reqmred to reduce slgnlhcant plastic deformation m the matrix of a reinforced metal matrix composite. Furthermore, it is desirable to understand how changes in the reinforcement geometry will vary the temperature excursion needed to induce matrix plasticity. Recent work by Klipfel et aL (6) examined the residual stresses and plastic strains developed in the cooling of idealized f~er and particle reinforced composites. In this work, they used the 41astic- plastic solutions derived by Hill et al. for an internally pressurized thick-walled tube (13) and a pressurized thick-walled splierical shell (14). These solutiofis were applied to composites by matching force and displacement conditions imposed by the CTE mismatch at the inner surface of the cylindrical tube or spherical shell. One conclusion that could be drawn from their work, as it is presented, is that it would typically require a larger temperature excursion to render the matrix fullyplastic for a composite reinforced with continuous fibers than one reinforced with spherical particles. For example, Klipfel et al. (6) examine a composite with 25 volume percent reinforcement with material properties shown in Table I which approximate an AI-SiC composite. Their analysis indicates that for spherical reinforcements the thermal mismatch strain, A~AT, must be 2.5 times the matrix uniaxial yield strain for the matrix to become fully plastic. However, they report a corresponding value of 3.4 times the matrix yield strain for an aligned fiber reinforced composite. This result counters intuition, as one may expect the deviatoric stresses to be relativelyhigher in a composite reinforced with aligned fibers. This discrepancy occurs because the analysis by Hill et al. (13) assumes plane strain along the tube axis. This is reasonable in some cases for a pressurized pipe, as Hill analyzed, but longitudinal strains play a central role in fiber reinforced composites. We will show that the consideration of longitudinal strains makes significant changes to the fiber reinforced composite analysis. For particle reinforced composites, the stress state is accurately represented with Hill's analysis. This note will consider three exact models to determine the thermal expansion mismatch strain needed to plastically deform the matrix of idealized reinforced deformable matrix composites. These models consider idealizations of fiber reinforced composites, laminated composites and particulate (spherical reinforcement) composites. The idealized cell geometries considered are illustrated in Figure 1. In all of the analyses that ~ollow we shall assume that the reinforcement is an isotropic elastic solid that is perfectly bonded to an isotropic, linear elastic, perfectly plastic matrix. Furthermore, for simplicity, we shall consider the case in which the composite is being cooled and the coefficient of thermal expansion of the matrix, ~m, is greater than that of the fiber, czf,by an amount, Act. However, field quantities such as stress and strain simply change in sign for the heating case, or if the fiber has a larger CTE than the matrix. The details of the derivation of the exact solution for the fiber reinforced composite may be found in (15). 2279 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc