Materials Science and Engineering, A 125 (1990) 129-140 129 An Analysis of Residual Stress Formation in Whisker-reinforced M-SiC Composites G. L. POVIRK, A. NEEDLEMAN and S. R. NUTT Division of Engineering, Brown University, Providence, R102912 (U.S.A.) (Received June 14, 1988; in revised form November 7, 1989) Abstract The effects of fiber spacing, volume fraction and aspect ratio on the residual stresses in metal-matrix composites are analyzed numeri- cally. The composite is modeled as a periodic array of cylindrical cells, each consisting of the matrix alloy with a whisker embedded in the cen- ter. Account is taken of thermoelasticity both in the fiber and in the matrix and of temperature-depen- dent plasticity in the aluminum matrix. A general formulation, valid for finite strains and rotations, is discussed. Quenching is simulated by imposing a temperature history obtained from a macroscopic solution of the heat equation for a cylindrical bar to the surface of a cell. The resulting residual stress fields are calculated. The results show that the side- to-side spacing of fibers is the most important microstructural parameter affecting the distribu- tion of residual stress and plastic deformation in the matrix. The overall level of plastic deformation in the matrix, measured by the volume average of effective plastic strain, depends primarily on fiber volume fraction. The fiber aspect ratio has little effect, apparently because the residual fields become essentially independent of axial position a short distance from the fiber corner. 1. Introduction The addition of silicon carbide whiskers to aluminum results in a material that has increased stiffness, tensile strength and creep resistance in comparison with an unreinforced aluminum alloy [1-3]. Whiskers of SiC are relatively inexpensive, and the composite can be processed using con- ventional metal-forming techniques [3]. Thus, AI-SiC whisker composites show promise for use as a relatively low cost structural material with improved mechanical properties. Unfortunately, the composites also exhibit low ductility and consequently low fracture toughness [1]. A better physical understanding of metal-matrix compo- sites is essential if these problems are to be resolved. Residual stresses are inherent in AI-SiC com- posites because of the mismatch in thermal expansion of aluminum and silicon carbide. The stresses develop upon cooling after thermo- mechanical processing of the material. In situ high voltage electron microscopy (HVEM) observa- tions by Vogelsang et al. [4] showed that disloca- tions emanated from the fiber-matrix interface upon cooling and found a particularly high density of matrix dislocations near the interface. Christman and Suresh [5] found that the presence of residual stresses and the resulting high disloca- tion density in the matrix affected the microstruc- tural development of the alloy. Specifically, they found that the dislocations acted as nucleation sites for precipitates, thus altering the aging characteristics of the composite when compared with an unreinforced alloy. In addition, previous analyses of void nucleation in metal-matrix com- posites have assumed that the material is initially stress free. More realistic models would include the effect of residual stresses. Thus, a quantitative description of residual stresses would constitute an important step towards understanding the behavior of these materials. The approach used here is to model the material as a periodic array of cylinders, each consisting of an aluminum alloy with a SiC whisker embedded in the center. A temperature history is applied to the cylinder surface, and the temperatures in the cylinder are found via solu- tion of the heat equation with a coupling term due to the heat generated by plastic deformation. The intent is to include in the analysis the possibility of thermal softening because of intense plastic 0921-5093/90/$3.50 © Elsevier Sequoia/Printed in The Netherlands