Explicit method for calculating the effective properties and micromechanical stresses: An application to an alumina-SiC composite

Abstract

Abstract High-temperature processing induces large internal stresses at room temperature in composites because of the difference between the thermal coefficients of the matrix and of the reinforcing particles. In this work we develop a theoretical scheme to calculate the strains in the particles by using the Eshelby equivalent method. The interaction between the inhomogeneous inclusions (fibres) is evaluated by means of a mean-field model given by Mori and Tanaka, and full anisotropy of fibres and matrix is taken into account within an explicit approach by which the problem is solved as a function of the deformation field instead of the thermoelastic properties. The model is applied to the thermoelastic moduli and residual stresses in biphase composites. We analyse the influence of the orientation distribution function of fibres, its volume fraction and elastic inhomogeneity factor on Young's modulus, Poisson's ratio and the thermal coefficients. We calculate the thermal residual stresses in an Al2O3-SiC composite as a function of direction, and the results are compared with the neutron measurements made by Majundar et al. As the non-uniform crystal structure of SiC whiskers complicates the interpretation of experimental data collected from whisker-reinforced composites, a general equation based on the fractions of cubic and hexagonal polytypes is incorporated in the model. We demonstrate that the residual stresses cannot easily be explained on the basis of elastic interactions and distribution of fibre orientations, even accounting for the elastic and thermal anisotropy of fibres. Correct interpretation and comparison of residual stresses with the measured values requires analysis of the peak shift and broadening stemming from the residual stresses.