About residual stress

Residual stresses are mechanical stresses in a body, which is not experiencing external forces and which is in thermal equilibrium. They are caused by plastic deformation or thermal processes, such as welding or rapid cooling (quenching) after heating.

In general, three types of residual stresses are distinguished, which are referred to as stresses of the first, second and third kind [1]. Stresses of the first type are macrostresses, which can lead to distortion of a component. Stresses of the second type are stresses between grains, which are caused, for example, by plastic deformation and are balanced over a few grains. Stresses of the third type are stresses within the grains, caused for example by precipitates or dislocations. Stresses of the second and third type are referred to as microstresses. If diffraction methods are used to determine reflection shifts, then this includes all stresses leading to reflection shifts, independent of their nature [2]. In the simplest case, stresses of the third kind lead only to a symmetrical broadening of a diffraction reflection, but not to a shift of its position. The influence of stresses of the second kind can be minimized by selecting a suitable lattice reflection (for example for Al with fcc-lattice the (311)-reflection, for α-iron with with bcc-lattice the (211)-reflection). Thus, the values determined from the diffraction experiment often correspond in a good approximation to the macro residual stresses or stresses of the first kind.

Residual stress analysis using diffraction methods

Diffraction methods have been used for residual stress analysis for a long time. The measurement principle is essentially based on the Bragg equation,

λ = 2d sin θ

which relates the diffraction angle θ to the wavelength λ of the X-rays and the atomic lattice parameter d.

At a fixed wavelength, the diffraction angle can be used to directly measure atomic distances. If residual stresses, i.e. internal forces are present, the atomic distances are increased in comparison to a stress-free sample (tensile stresses) or reduced (compressive stresses).
The most widespread method is the use of a laboratory diffractometer with an X-ray tube. In this way, residual stresses on the surface can be determined, whereby, depending on the material, the penetration depth is around 10 μm, depending on the material. With high-energy X-ray radiation of a synchrotron (>50 keV), the penetration depth is considerably greater, so that the interior of the sample is also accessible.
The neutron diffraction method is based on the same principle, the largest penetration depths - several cm in most materials. By suitable selection of the neutrons’ a diffraction angle of about 90° is possible in most cases so that rectangular gauge volumes are obtained. A disadvantage of neutrons is the low flux density of the neutron beam compared to synchrotron radiation, which means that longer measurement times are necessary, and the lower spatial resolution [1, 2, 3].


To make assumptions on the strength and lifetime of a component, assessing of residual stresses important. The reason is the superposition principle, which means that in a first approximation a linear superposition (addition) of applied load during operation and residual stress distributions represent the total stress distribution within a workpiece or a component. Residual stresses have influence on many properties of a component, such as strength, fatigue behaviour, corrosion resistance and others. Failure of workpiece in most cases occurs due to plastic deformation or fracture when subjected to tensile loads. Here, e.g., because of notch effects, the near-surface area is critical. This means that compressive residual stresses in the near-surface zone can be beneficial with respect to workpiece or component lifetime. In some industrially produced components, such as generator shafts, or pressure vessels, terms of delivery often include specifications regarding maximum residual stress values and permissible residual stress distributions [2].

[1] Hauk, V.: Structural and Residual Stress Analysis by Nondestructive Methods, Elsevier, 1997
[2] Reimers, W.; Pyzalla, A. R.; Schreyer, A.; Clemens, H.: Neutrons and Synchrotron Radiation in Engineering Materials Science, Viley VCH, 2008, S. 115 ff.
[3] Lodini, A.; Fitzpatrick, M. E.: Analysis of Residual Stress by Diffraction Using Neutron and Synchrotron Radiation, CRC Press, 2003