Measurement
of Residual Stress Using X-Ray Diffraction
X-ray diffraction (XRD) measures residual stress non-destructively by reading elastic lattice strain in crystalline materials, typically within the top few tens of micrometres of a surface. The stress is calculated from the shift of a diffraction peak, using the sin²ψ method and known elastic constants. This article covers the principle, geometry, preparation, procedure, accuracy limits, and applications.
Principle & mechanism
XRD stress measurement rests on elastic deformation of the crystal lattice. Every crystalline phase has a known interplanar spacing in the stress-free state. When a residual stress field exists, the spacing of a given set of lattice planes changes by a small elastic strain. Monochromatic X-rays are directed at the surface, and the diffraction peak is recorded at a Bragg angle. This gives the actual spacing of the selected planes. The shift of the peak position relative to the unstressed value is converted to strain through the Bragg equation. Strain is then related to stress through the elastic constants of the material. The diffraction angle is measured to high precision, so lattice strains on the order of 10⁻⁴ can be resolved. The method is non-destructive, surface-sensitive, and phase-selective. It reads the stress in a chosen crystalline phase rather than an averaged bulk value.
Principle of the sin²ψ method
The sin²ψ method is the standard geometry for converting peak shifts into stress. The specimen is tilted so that the angle ψ between the surface normal and the diffraction vector varies over several settings, commonly at least five to seven tilts. At each tilt, the peak position 2θ is recorded and the lattice spacing is calculated. For a biaxial surface stress state, the strain measured at each ψ varies linearly with sin²ψ. The slope of this line, multiplied by the X-ray elastic constant for the reflection used, yields the stress component along the measurement direction. Deviations from linearity — splitting of the ψ-positive and ψ-negative branches, or curvature — indicate shear stresses, stress gradients, or coarse-grain effects. The data should be treated accordingly. Rotating the specimen by 90° or through several azimuths allows the principal stress directions to be determined.
Sample preparation and surface treatment
Surface condition governs the validity of the result, because XRD samples only a shallow layer. Scale, oxide, coatings, paint, and heavily smeared or decarburized machining layers must be removed. Use gentle electrolytic polishing or chemical etching, not mechanical grinding, which introduces its own artifact stress. Where layer removal is needed for depth profiling, material is taken off incrementally, commonly in steps of a few to a few tens of micrometres. Stress correction is applied for the removed layer. Specimen geometry must permit access of the goniometer; curved or thin sections need special fixtures. Roughness above a moderate level scatters intensity and biases peak position, so surfaces are inspected visually befOre testing. For coated systems — for example, plasma-sprayed biomedical coatings as covered in hydroxyapatite coating thickness measurement work under ISO 13779 — the coating stress and substrate stress are separate measurements and should be reported distinctly.
Test procedure and instrument parameters
A routine measurement begins with material identification and selection of the radiation and reflection. Chromium Kα is used for steels on the (211) ferrite line; copper, cobalt, and manganese radiation are chosen depending on the alloy and expected peak position. A position-sensitive detector, or a point detector with step scanning, records the peak at each ψ tilt. A collimator of 1–2 mm or smaller defines the gauge area. Peak position is determined by fitting methods such as the centroid, parabola, or cross-correlation fit, after background subtraction and Lorentz-polarization and absorption corrections where applicable. Oscillation of the ψ or φ axis may be used on coarse-grained weld metal to improve statistical sampling. Counting time is set so that adequate intensity is collected at the highest tilt, where the path length is longest. Instrument alignment and a stress-free reference coupon are checked before each session. This practice is consistent with the metrology discipline reflected in equipment-safety frameworks such as IEC 61010-2-020.
Accuracy,
precision, and depth limitations
Uncertainty in XRD stress measurement comes from counting statistics, peak-fitting error, elastic constants, and instrument alignment. Precision is normally a few tens of MPa on well-prepared steel surfaces. Absolute accuracy depends chiefly on how representative the assumed X-ray elastic constants are for the material state. Penetration depth is shallow — typically 5–20 µm for common radiations on steel, contributing roughly half the diffracted intensity. The reported value is therefore a weighted near-surface average, not a bulk stress. Steep gradients, texture, large grains, and plastic anisotropy distort the sin²ψ linearity and require modified analysis or oscillation. Components with coarse columnar weld structures or strong preferred orientation should be flagged in the report. Depth profiles require electrolytic layer removal and correction, and each removed step adds uncertainty. These constraints parallel those seen in other fine-layer measurements such as resist thickness testing, where layer geometry and calibration likewise bound the reported accuracy.
Applications and applicable standards
The method is applied to welded structures, machined and ground surfaces, shot-peened and nitrided components, additive-manufactured parts, and heat-treated tooling — wherever surface stress controls fatigue life or distortion. It verifies peening effectiveness, qualifies weld repair procedures, and checks stress-relief treatments before parts enter service. It also serves coating and functional-layer development, including photovoltaic and hybrid-module work where interfacial stress affects reliability, an area touched by measurement documents such as IEC 63387-1. Widely used references include ASTM E915 (verification of the method with a stress-free reference), EN 15305 (non-destructive XRD stress measurement), and ISO/TS 21432 for hole-drilling comparison. National handbooks add radiation-selection tables. Reports should state the radiation, reflection, elastic constants, tilt set, and measurement direction so that results are traceable and comparable between laboratories.
Frequently Asked Questions
What
determines whether an X-ray diffraction residual stress result is acceptable?
Judgment rests on the linearity of the sin²ψ plot, the counting and fitting uncertainty, and verification against a stress-free reference per the method references cited above, such as ASTM E915 and EN 15305. Strong curvature or ψ-splitting signals shear or gradient effects. The result should be qualified accordingly rather than reported as a simple stress value.
Which
materials and products can be measured by XRD residual stress testing?
Any crystalline material that gives a distinct diffraction peak is measurable. This includes steels, aluminium and titanium alloys, nickel superalloys, and many ceramics. It suits welded joints, machined or ground surfaces, shot-peened parts, and add-on coated components. Amorphous materials and very coarse-grained sections are outside the normal scope without oscillation or special preparation.
What
does an XRD residual stress report contain and how is it used?
A report typically lists the radiation and reflection, elastic constants, tilt angles, measurement direction, stress value with uncertainty, and surface preparation history. Engineers use it to verify peening or stress-relief processes, qualify welding procedures, and assess fatigue-critical surfaces before assembly. It often serves as part of incoming or process-control inspection in an accredited laboratory.