Residual stresses in cubic materials with orthorhombic or monoclinic specimen symmetry: influence of texture on ψ splitting and non-linear behaviour

A quantitative formulation is given of the X-ray diffraction determination of (elastic) lattice deformation in a direction determined by two angles ψ and φ with respect to the specimen frame: the so-called sin²ψ method giving full credit now to crystallographic texture. In most cases of practical X-ray stress analysis, (residual) stresses are evaluated by the traditional sin²ψ, method using quasi-isotropic X-ray elastic constants depending on the lattice plane {hkl} chosen for the measurement but not on the directions φ and ψ. For the case of a textured specimen, however, the single-crystal elastic bitensor components should be coupled to the orientation distribution function (o.d.f.). At variance with most papers published on this subject, which describe the texture using ideal texture components, a general method is developed making full use of relevant o.d.f. theory. It is demonstrated that for orthorhombic specimen symmetry no ψ splitting occurs in contrast with the case of monoclinic specimen symmetry. The theory developed is used to explain some experimental results published previously. All calculations use Reuss's theory of elasticity which neglects the mutual coupling of the crystallites.