Relation of elastic strain distributions determined by diffraction to corresponding stress distributions

The problem of converting elastic strain distributions determined by diffraction measurements to stress distributions is discussed. The relation of mean strains measured by powder diffraction to the corresponding mean stresses is well known and regularly employed in residual stress measurements. However, the relation between strain variance and stress variance is not so straightforward. The elastic strain distribution depends on both the variation of strain from point to point in a given direction in a volume, and in all directions at each point in the same volume. In this paper, relations between the strain variance and corresponding stress variance are developed in both two and three dimensions for the case of microstress variations in particulate systems. The two components cannot be separated from a diffraction measurement of the strain distribution but the relations developed provide upper and lower limits on the variance in the stress distribution and are useful for relating diffraction results to models of the material. The results are applied to elastic strain distributions obtained in composite systems from measurements of diffraction peak breadths and modeled using two-dimensional finite element methods.