Residual Stress Measurement Techniques: XRD and Hole-Drilling

Residual stress measurement is essential wherever locked-in stress from welding, machining, heat treatment, or surface engineering influences fatigue life, distortion, or cracking risk. This guide develops the two most widely used practical measurement techniques, XRD sin-squared-psi and ASTM E837 hole-drilling, in depth, and positions them against neutron diffraction, contour, slitting, and magnetic methods for selecting the right technique for a given application.

What Is Residual Stress and Why Measure It?

Residual stress is stress that remains locked within a component after all external loads have been removed, generated by non-uniform plastic deformation, thermal gradients, or phase transformation during manufacturing processes such as welding, machining, casting, rolling, or heat treatment. Because residual stress superimposes directly on applied service stress, tensile residual stress can significantly reduce fatigue life and promote cracking, as discussed in our spalling failure and reheat cracking guides, while compressive residual stress, deliberately introduced by shot peening or similar treatments, can substantially improve fatigue performance. Quantifying residual stress is therefore essential for both root-cause failure analysis and for validating manufacturing processes intended to control it.

XRD Residual Stress Measurement: The Sin-Squared-Psi Method

X-ray diffraction residual stress measurement relies on the fact that elastic lattice strain, caused by residual or applied stress, produces a measurable shift in diffraction peak position relative to the strain-free interplanar spacing. The sin-squared-psi (sin²ψ) method measures this shift for a chosen lattice plane across a series of sample tilt angles, psi, relative to the diffraction plane normal, a technique developed in more depth in our dedicated XRD for metallurgical analysis guide.

Sin-squared-psi method (biaxial stress state, isotropic material):

sigma_phi = (E / (1+nu)) * (1/d0) * (d(d)/d(sin^2 psi))

where:
  d0     = strain-free interplanar spacing
  E, nu  = X-ray elastic constants
  sigma_phi = residual stress at the surface in direction phi

Because the technique relies on a diffracted beam that travels into and back out of the material, it samples only a shallow near-surface volume, typically a few to a few tens of microns depending on the X-ray source and material absorption. This shallow, non-destructive sampling makes XRD particularly well suited to fine-resolution mapping of near-surface stress variation, for example across a weld toe, a shot-peened surface, or a ground component, without physically altering the part.

Hole-Drilling Residual Stress Measurement: ASTM E837

Principle and Procedure

ASTM E837 specifies a well-established, general-purpose method for determining near-surface residual stress in isotropic, linearly elastic material. A specialized three-element strain gauge rosette is bonded to the component surface, and a small hole, commonly with a nominal diameter around 2 mm, is drilled at the rosette’s geometric centre using a high-speed air turbine or orbital milling technique specifically to minimize additional machining-induced stress. Removing stressed material from the hole location allows the surrounding material to relax, and this relaxation produces small but measurable strain changes at each of the three gauges, oriented at different angles around the hole to fully resolve the in-plane stress state.

Calculation Method

The relieved strains measured at each gauge are converted into the original residual stress using calibration coefficients, denoted a and b, that are tabulated in ASTM E837 for standard rosette geometries (Types A, B, and C) and were derived from finite element calculations. For a uniform stress field through the hole depth, the calculation reduces to a closed-form relationship between the three measured strains and the principal in-plane stresses and their orientation; for stress fields that vary with depth, the standard’s incremental method processes the strain readings collected at each successive drilling step to reconstruct a depth-resolved stress profile.

Uniform-stress hole-drilling relation (conceptual form):

e_j = (1/E) * [ a_jk * (sigma_x + sigma_y)/2
              + b_jk * (sigma_x - sigma_y)/2 * cos(2*theta)
              + b_jk * tau_xy * sin(2*theta) ]

where:
  e_j        = relieved strain measured at gauge j
  a_jk, b_jk = tabulated calibration coefficients (ASTM E837)
  sigma_x, sigma_y, tau_xy = in-plane residual stress components
  theta      = gauge angular position around the rosette

Blind-Hole vs. Through-Hole Drilling

Blind-hole drilling is the more commonly applied approach in practice, since incremental depth stepping allows a subsurface stress profile, valuable for characterizing shot-peened, case-hardened, or machined surface layers where stress varies significantly with depth, a topic connected to the hardening mechanisms covered in our quenching and tempering guide.

XRD vs. Hole-Drilling: Choosing the Right Method

Neither method is universally superior; the choice depends on the depth and spatial resolution the application requires. Many weld residual stress assessment programmes, including those relevant to the restrained joint behaviour discussed elsewhere on this site, apply both techniques together: XRD to finely map near-surface stress variation across the weld toe and adjacent HAZ, and hole-drilling to establish the shallow subsurface depth profile beneath any surface treatment or decarburized layer.

Other Residual Stress Measurement Techniques

XRD and hole-drilling are the two most widely used practical techniques, but several others fill specific niches where deeper penetration, full destructive validation, or particularly rapid screening is required.

Industrial Significance

Accurate residual stress measurement underpins fatigue life prediction, distortion control, and the qualification of stress-relief and surface treatment processes across welding, machining, and heat treatment operations. XRD and hole-drilling remain the two most widely deployed techniques precisely because they balance practical accessibility, reasonable cost, and adequate accuracy for the vast majority of near-surface residual stress questions encountered in fabrication quality control and failure investigation, reserving neutron diffraction and destructive methods for the smaller set of cases that genuinely require bulk or full-depth characterization.

Frequently Asked Questions

Recommended Reference Reading

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