residual stress

Residual stress is stress that stays locked inside a part even when nothing is pushing or pulling on it from outside. It is left behind by processes that deform the material unevenly — welding, machining, grinding, quenching, or depositing a coating. Because the atomic planes themselves end up slightly stretched or squeezed, X-ray diffraction can measure the change in plane spacing and read the stress straight from it. In effect the crystal lattice becomes its own built-in strain gauge.

The mechanism runs through peak position. Stress strains the d-spacings, and by Bragg's law that shifts the peaks. The standard sin-squared-psi method measures the spacing d (or the peak angle) for a chosen set of planes at several sample tilt angles psi. Plotting d against sin^2(psi) gives a straight line whose slope, combined with the material's elastic constants (Young's modulus E and Poisson's ratio nu), yields the stress. A tensile residual stress pulls apart the planes lying parallel to the surface and shifts the peak one way; a compressive stress closes them and shifts it the other.

This matters because residual stress quietly governs fatigue life, cracking, and warping. A compressive stress deliberately put into a surface — by shot peening, for instance — closes up incipient cracks and can dramatically extend fatigue life, so measuring it is routine in aerospace, welds, and hard coatings. Be honest about the limits: X-rays penetrate only a few micrometres, so the method probes a thin near-surface layer, not the bulk; it needs the correct elastic constants and assumes a particular stress model; and strong texture or coarse grains break the simple straight-line sin-squared-psi analysis.