Equilibrium conditions for the average stresses measured by X-rays

True macro-stresses are measured with X-rays after material processing, only if there is auniform plastic deformation in the sampled volume that is different from that in the rest of the material. In this stress-field the components in the direction of the surface normal are usually negligible over the depth penetrated by X-rays (for example, peening). However, pseudo-macrostresses, or backstresses, arise when this condition is violated, for example, if there are second phase particles and there is a gradient of plastic deformation from particle to matrix. This pseudo-macrostress field is three-dimensional, and the stresses in the direction of the surface normal can be measured with X-rays. Equations are presented which allow estimates to be made of the magnitudes of the two kinds of stress fields.