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

摘要

The stress σ_(ij)~I inside spherical and oblate inclusions ("I") is calculated as a function of Young's modulus E~M and Poisson's ratio v~M of the enclosing infinite isotropic matrix ("M"), which is subjected to an uniaxial tension σ_(11)~M. σ_(ij)~I yield the "transfer X-ray elastic compliances" S_1~(IM) and (1/2)S_2~(IM) which relate average lattice strains of the inclusions obtained by X-ray diffraction to σ_(ij)~M. The larger (1/2)S_2~(IM) the more sensitive is the method of X-ray stress analysis (XSA). On decreasing E~M/E~I, (1/2)S_2~(IM) 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.