Modelisation of strains measured by X-ray diffraction in composites with spherical particles

In a particle composite, elaboration residual stresses have two main origins: differences between thermal expansion coefficients of particles and matrix on the one hand, and volume changes induced by reactions at particles / matrix interface on the other hand. We have compared calculated thermal stresses, and experimental measures on two composites, one presenting an interface reactivity and the other none. The two composites with a nickel matrix and spherical particles either of silica or of alumina have been sintered at 1400 °C and analyzed between room temperature and 240 °C by X-ray diffraction (Cu Ka radiation). In the semi-infinite composite model, spherical particles have been distributed at the points of a simple cubic lattice. Modelised thickness is larger in comparison of the thickness analyzed by X-ray diffraction. Calculations are based on elastic theory and the difference of coefficients of thermal expansion between the matrix and the particles. Materials are supposed isotropic. At a given temperature, the strain to be observed by X-ray diffraction in a given directions calculated from the distribution of strains in matrix; absorption phenomena are taken into account. Effects of the free surface and of interfacial reactivity are thus shown off.