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

The stress σ i j I inside spherical and oblate inclusions (“I”) is calculated as a function of Youngʹs modulus EM and Poissonʹs ratio νM of the enclosing infinite isotropic matrix (“M”), which is subjected to an uniaxial tension σ 11 M . σ i j 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 i j M . The larger ( 1 / 2 ) S 2 IM the more sensitive is the method of X-ray stress analysis (XSA). reasing EM/EI, ( 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.