X-Ray diffraction

As in all diffraction methods, X-ray diffraction can measure residual stress using the distance between crystallographic planes, d spacing, as a strain gauge. When the material is in tension the distance between crystallographic planes increases compared to the unstressed condition. The lattice spacing is calculated from the diffraction angle, 2θ, and the known x-ray wavelength using Bragg's Law. The strains are measured by placing the sample in a X-ray diffractometer. The specimen is then exposed to an X-ray beam that interacts with the crystal lattice and cause diffraction patterns. Suitable X-ray diffractometers are available for both laboratory and “on-site” measurements.

X-ray diffraction residual stress measurement

Because the x-ray penetration is very shallow (less than 10 µm) it is reasonable to assume that only surface stresses are measured and hence a condition of plane stress exists and that stress normal to the surface is zero.  However, the strain perpendicular to the surface is not zero and can be measured by comparing the stressed d-spacing in the normal direction and unstressed d-spacing.  The benefit of measuring surface stresses using x-ray diffraction technique is that unstressed d-spacing is not required.  A number of d-spacings (in ∅ direction) are measured at different tilts (φ  angle), see Figure 3.  The plot of measured d-spacing versus Sin2φ should be linear. The stress in ∅ direction is directly related to the slope of this linear line:

Where m is the slope of the d versus φ plot. This method of analysis is based on plane stress assumption is usually referred to as the Sin2φ technique.

Plane stress at a free surface showing the change in lattice spacing with tilt for a uniaxial stress parallel to one edge.


  • non-destructive for surface measurements.
  • Available on site at the StressMap Laboratory.
  • Good spatial resolution (gauge volume of 1mm2 can be achieved practically in most engineering material).
  • Suitable for residual stresses of high magnitude.
  • Bi-axial and shear stress obtainable.


  • For measurements below the surface, layer removal is required and the technique becomes semi-destructive.
  • Reliability affected by crystallite size and texture.
  • Only suitable for polycrystalline material.
  • Highly sensitive to surface treatments such as polishing or scratching which may mask the desirable information.