Calculation of lattice strains in oblate inclusions embedded in an isotropic matrix with variable elastic moduli: Consequences for X-ray stress analysis

The stress σijI inside spherical and oblate inclusions (“I”) is calculated as a function of Young's modulus EM and Poisson's ratio νM of the enclosing infinite isotropic matrix (“M”), which is subjected to an uniaxial tension σ11M. σijI yield the “transfer X-ray elastic compliances” S1IM and (1/2)S2IM which relate average lattice strains of the inclusions obtained by X-ray diffraction to σijM. The larger (1/2)S2IM the more sensitive is the method of X-ray stress analysis (XSA).On decreasing EM/EI, (1/2)S2IM increases and finally reaches a plateau. The effect is stronger if the inclusions become flatter, but decreases with their increasing volume fraction. Flat instead of spherical inclusions might be helpful in XSA of polymers where the lattice strains of added crystalline filler particles are investigated. For flat cubic single-crystals with well-defined crystallographic orientation strong variation of the lattice-plane spacings is observed for special permutations of the Miller indices.