ABSTRACT
Most investigations have been conducted based on the assumption that selected crystallographic reflections could be used as simple monitors of the macroscopic strain much like a strain gauge: just using the ever-present crystallographic lattice as an embedded atomic strain gauge. Furthermore, most investigations have been based on the assumption that strains measured on this microstructurally relevant scale represented the tensorial quantity of strains in the continuum mechanics sense. As a consequence stresses have been deduced simply by a conversion of the lattice strains through a continuum mechanics formalism into stress tensors. Both stress and strain tensors have been taken to behave like ordinary second rank tensors with the associated characteristic transformation rules. Consequently, experimenters conducting diffraction-based investigations have adopted the concept of principal stresses and strains and the associated definition of principal directions along which no shear components are present. In the general sense, at least six independent measures of strain are required for a complete characterization of a strain tensor; however, when considering the inherent measurement errors, it requires an over-determination with more like 8-12 independent measures in order for errors on the stresses not to grow unacceptably large [12]. Typically it is, however, not feasible either for technical or for economic reasons to perform enough measurements to derive the full tensor, and most experimental characterizations have in fact been based on assumptions of principal directions, and strain measurements have been limited to three orthogonal directions. In short the basic concepts of continuum mechanics have been adopted and stress/strain relations have been based on the generalized Hooke’s law.
