The thermal expansion and bulk modulus of composites consisting of arrays of spherical particles in a matrix, with body- or face-centred cubic symmetry

Source abstract

Abstract A method is described of calculating the thermal expansion coefficient and the bulk modulus for composite materials consisting of regular cubic arrays of isotropic spherical particles in an isotropic matrix. The method consists of using symmetry-adapted harmonic vectors in Kelvin’s solution of the problem of the sphere. Harmonics up to 11th order are used but the method allows the use of harmonics of any order. Results for the expansion coefficient and the bulk modulus are given for silicon carbide spheres in an aluminium matrix, and are compared with the results obtained by other methods. The method of this paper allows simple calculation of the stresses and displacements anywhere in the composite and also, by extension, in a composite consisting of coated particles. Such calculations are not simple using any other existing method. Large variations of stress are found at the interface between particles and matrix both in thermal expansion and in bulk deformation. Such stresses may exceed the mean value (corresponding to dilute concentrations) by up to 20% for some composites. The maximum stress concentrations are at the positions of nearest neighbours, that is along [111] directions in the body-centred cubic packed particles and along [110] directions where the packing is face-centred.