How to measure residual stresses?

There are many methods to measure residual stresses. The methods are commonly grouped as non-destructive, semi-destructive, and destructive. Or diffraction-based, strain relaxation-based, and other methods. However, they all have the same common point, being indirect. Yes, there is no direct method to measure stresses; they are calculated or derived from a measured quantity such as elastic strain or displacement. Let’s briefly look at the most common methods now.

Diffraction based methods

In diffraction-based methods, the elastic strain is measured using Bragg’s law. The stress calculation is done with Hooke’s law and elastic modulus (E) and Poisson’s ratio (ν).

Bragg´s law is expressed as

In a stressed material, the wavelength is known, d is unknown, theta is observed at several angles, and stress causes small changes in theta’s d shift. In crystalline materials, grain structure atoms are arranged with periodic symmetry.

Hooke’s law is used for the measured strains’ conversion to stresses and expressed as

The deformation which is the change in the length of the stressed material and is expressed as

The strain is the non-dimensional deformation can be expressed as

Poisson’s ratio is needed for the stress calculation and is expressed as

Stress is the force per unit area to external load that is applied to a body, which is expressed as

An elastically stressed material’s strains will be uniform in all grains. Any stress will cause a change in the strain, which will cause a shift of the diffraction peaks since we know the diffraction peaks of stress-free material has any residual stress in it. For example, a stressed body’s surface will have biaxial stresses parallel to the surface.

Stress calculation is affected by material based parameters such as differences in lattice parameters, precipitations, interstitial occupation, and micro-stresses.

In a polycrystalline structure with disordered crystals at the grain boundaries, precipitation, and lattice defects, the line widens and forms a Gaussian-like peak. The peak width is measured as Full Width at Half Maximum (FWHM), a measure of the dislocation density and micro stress.

X-ray diffraction

X-ray diffraction (XRD) is one of the fastest and the most accurate method to investigate the residual stress levels on the surface layer. X-ray diffraction for residual stress measurements is relatively cheap and widely available with mini, portable, stationary, and robotic diffractometers for both in situ and laboratory testing. XRD measurement is useful for stress analysis when the below conditions are met:

  • The material must have a crystalline structure.
  • The material should have small grains.
  • Grains should be randomly orientated to avoid the texture problem.
  • Diffraction peaks should occur with high back reflections.
  • Elastic constant (XEC) needs to be known.

Non-destructive measurement depth for steel and aluminum is about 0.02 mm. Destructive measurement depth, with electropolishing, is about 0.5 mm, and with a combination of grinding and electropolishing, it is about 10 mm.

Relevant standards for XRD

  • ASTM E2860–12 Standard Test Method for Residual Stress Measurement by X-Ray Diffraction for Bearing Steels
  • ASTM E915–16 Standard Test Method for Verifying the Alignment of X-Ray Diffraction Instrumentation for Residual Stress Measurement
  • ASTM E1426–14 Standard Test Method for Determining the X-Ray Elastic Constants for Use in the Measurement of Residual Stress Using X-Ray Diffraction Techniques
  • BS EN 15305:2008 Non-destructive testing. Test method for residual stress analysis by X-ray diffraction
  • A National Measurement Good Practice Guide, Determination of Residual Stresses by X-ray Diffraction — Issue 2, National Physical Laboratory, UK

Neutron diffraction

Neutron diffraction (ND) provides full residual stress tensor, σ11 (parallel to the surface), σ22 (parallel to the surface), and σ33 (normal to the surface), analyses on thick components. As in XRD, ND is as well measures the elastic strain using Bragg’s law and calculates the stress with Hooke’s law together with the elastic modulus (E) and Poisson’s ratio (ν). Neutron diffraction for residual stress measurements is not widely available and easy to access due to expensive stationary diffractometers for neutron generation.

Non-destructive measurement depth for steel is about 40 mm, and aluminum is about 50 mm. Especially in the aircraft manufacturing industry, neutron diffraction is used as a non-destructive method to investigate the residual stress distribution.

The spatial resolution is not very high in neutron diffraction. It is in the range of millimeters.

Relevant standards for ND

  • ISO/TS 21432:2005 Non-destructive testing -Standard test method for determining residual stresses by neutron diffraction

Synchrotron diffraction

Synchrotron diffraction is a higher energy version of x-ray diffraction, which provides full residual stress tensor, σ11 (parallel to the surface), σ22 (parallel to the surface), and σ33 (normal to the surface), analyses with even a higher resolution than neutron diffraction. It is possible to use synchrotron diffraction for components with complex geometries, but the component's size is usually limited. There are only several synchrotron facilities worldwide, making the method not portable and leads time to have the results way too long.

Non-destructive measurement depth for steel is about 25 mm, and aluminum is about 100 mm. However, the spatial resolution is not as good as the XRD method.

Mechanical strain relaxation based methods

ESPI with hole drilling

Prism (Precision Real-Time Instrument for Surface Measurement) is a residual stress measurement system developed by Stresstech Group.

Prism is based on three principles,

Traditional hole drilling

Hole drilling removes a volume of material from the workpiece hence changes the stress equilibrium in part. The remaining material rebalances its stress fields, and near the hole, the surface distorts slightly.

Distortion measurement

Prism measures surface distortion optically using laser light with a technology based on Electronic Speckle Pattern Interferometry (ESPI). The measured surface displacements are correlated with planar stresses.

Residual stress calculation

The residual stress calculation requires ESPI images of the measurement surface before and after each drilling increment. This allows the determination of surface displacements as a fraction of the wavelength. The stress calculation algorithm is compatible with the requirements described in the strain-gage hole-drilling ASTM standard.

Prism provides a speedy stress depth profile, and it requires little sample preparation. The system does not use a strain gauge, which is one of the main disadvantages of the deep hole drilling method. With Prism, steels, aluminum, titanium, copper, composites, and many other materials are measured.

Relevant standards for ESPI with hole drilling

Deep-hole drilling

Deep-hole Drilling (DHD) method provides bi-axial residual stress measurement for many different material types and even complex geometries.

Semi-destructive measurement depth could be up to 750 mm.

In addition to the above methods, Incremental Center-hole Drilling, Contour, Slitting, Block Removal, Splitting and Layering, Sach’s Boring, Inherent Strain, Ring-core, and Indentation are known and used destructive methods for residual stress measurements.

Other methods

Barkhausen noise snalysis

Barkhausen Noise Analysis (BNA) is based on a concept of inductive measurement of a noise-like signal, generated when a magnetic field is applied to a ferromagnet.

In this article, more details about the phenomena of Barkhausen noise can be found. Two main material characteristics will directly affect the intensity of the Barkhausen noise signal.

The presence and distribution of elastic stresses influence domains to choose and lock into their magnetization’s easy direction. This phenomenon of elastic properties interacting with the material’s domain structure and magnetic properties is called “magnetoelastic interaction.”

As a result of magnetoelastic interaction, in materials with positive magnetic anisotropy (iron, most steels, and cobalt), compressive stresses will decrease Barkhausen noise intensity while tensile stresses increase.

This fact can be exploited so that by measuring the intensity of Barkhausen noise, the amount of residual stress can be determined. The measurement also defines the direction of principal stresses.

Processes, as cold rolling and shot peening, which is used to create complex compressive residual stress distributions at the surface layer, can be characterized by Barkhausen noise.

The effective depth of signal penetration is between 0.01 mm and 1 mm.

Relevant standards for BNA

  • SAE ARP 4462 — Barkhausen Noise Inspection for Detecting Grinding Burns in High Strength Steel Parts


The ultrasonic analysis could be used to determine the stress levels. In this method, the time of the ultrasonic wave’s flight between the sensor and the transition zone is calculated. The stress calculation is based on the velocity measurement of the ultrasonic wave. However, the velocity of the ultrasonic waves is also affected by microstructure and defects. Several studies and even specifically designed hardware (both laboratory and portable) for ultrasonic measurement of residual stresses. The ultrasonic method offers a nondestructive measurement possibility of 150 mm depth. Calibration of the stress measurement requires a stress-free sample, which is the disadvantage of this method.

The above methods, Photoelastic and Thermoelastic, are not commonly used non-destructive methods for residual stress measurements.

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