Macrostresses, Microstresses and Stress Tensors

Residual stresses are commonly classified as residual stresses of the first kind (macro residual stresses), second and third kind (micro residual stresses) according to the length scale over which they are nearly constant in magnitude and direction. Diffraction methods are sensitive to all three kinds of residual stresses, thus giving more detailed information on the stress state of a material than any other technique. On the other hand, this complicates the evaluation of diffraction data considerably. An overview is given how to detect the presence of microstresses and how to separate them from macrostresses.At any particular point, the stress state can be characterized by a stress tensor from which the magnitude and the direction of the three principal stresses can be calculated. In case that the directions of the principal stresses cannot be inferred from the sample geometry, a complete characterization of the stress state requires the determination of lattice strains in at least six directions. The stresses can then be evaluated from the strains via a tensor calculus using tabulated or specifically determined elastic constants. Appropriate elastic constants, which describe the elastic response of the material for macroscopic dimensions or single grains, allow the determination of both macro-and microstresses.