Science Update

in Vol. 13 - March Issue - Year 2012
Residual Stresses in Detail
Changes in stress cause changes in atomic lattice spacing "d" and an angular shift of the diffraction peak

Changes in stress cause changes in atomic lattice spacing "d" and an angular shift of the diffraction peak

Residual stresses from machining

Residual stresses from machining

Residual stress map of weld

Residual stress map of weld


Residual stresses are an integral part of manufactured components, whether they are introduced deliberately, as a part of the design, as a by-product of a process carried out during the manufacturing process, or are present as the product of the component’s service history. Residual stresses are additive with the stresses existing in the component as a result of service loads. Clearly, they may be considered beneficial to the component and therefore desirable, they may be irrelevant and can be ignored, or they are a potential detriment to the component and its continued service life. Given an adequate history, the magnitude of residual stresses in parts that are in service can be considered as indicators of the component’s deterioration.

Obviously, to realize the benefits of understanding the residual stresses in components and structures, tools are needed to measure them. Several techniques are available, with varying degrees of sophistication. Some of them are rather limited in their application, but one stands out as having widespread applications and being readily available.

X-ray diffraction is applicable to crystalline materials, which include virtually all metals and their alloys, and most ceramic materials. It is non-destructive in many applications, and is widely accepted by the engineering community, being the subject of SAE and ASTM publications, which provide reliable sources of information on methods to ensure repeatability and reliability in the results of measurements. Because individual measurements are non-destructive, they can be replicated to demonstrate their statistical reliability.

This article will look closely at the history of residual stress measurement by X-ray diffraction, explore the characteristics of measurements performed using modern X-ray methods, and offer a few practical examples.

Development History

X-rays were discovered in 1895 by Röntgen, but their nature was uncertain until X-ray diffraction was first recognized in 1912, when von Laue recorded the diffraction pattern of a single crystal on a photographic plate. This and subsequent work confirmed that X-rays have the properties of electromagnetic waves, and led to the Nobel Prize for Physics being awarded to von Laue in 1914.

The following year’s Nobel Prize for Physics was awarded to William Lawrence Bragg and his father, William Henry Bragg for their work on crystallography. Among their achievements was the statement of "Bragg’s Law", nλ = 2dsinθ, relating the deflection (θ) of X-ray beams by diffraction to the spacing (d) of parallel planes of atoms in crystals and integral multiples (n) of the X-ray wavelength (λ). While von Laue’s work on crystal structures is recognized most directly in the camera that carries his name (still used with the ‘white’ portion of the X-ray spectrum to determine the orientation of single crystals), the Bragg equation is most familiar in the field of powder diffraction.

With the sample in the form of a fine powder, all possible orientations are present. Using a single, known wavelength of X-rays, usually the characteristic K-alpha line, the X-rays appear to reflect from favourably oriented crystal planes, as if on the surface of a series of cones. Each cone corresponds to a single family of crystal planes. At high diffraction angles, a very small change in "d" generates a significant change in "θ". In fact, "θ" is so sensitive that changes in it can be used to measure elastic stress in the surface of the polycrystalline sample directly.

The simple relationship requires measurements of 2θ from planes parallel to the surface and at one other angle to the surface, and the experimental measurement of an appropriate constant, the "stress factor" ("K"). The stress equation in terms of diffraction angle is  = K (Δ2θ). "K" has to be determined using a material similar to the test material, and with precisely the same technique as will be used for measurements on the sample.

Use of the experimentally determined "K" is necessary because the X-ray measurements represent the surface of the material (where plane stress conditions are present), using a specific direction in a crystal lattice that is usually anisotropic. Published and measured values of elastic properties (Young’s Modulus and Poisson’s Ratio) are derived from all possible orientations within the crystals, in a three dimensional stress field. The surface and bulk measurements are reconciled in the experimental determination of "K" for the simple technique described above, and of the "X-ray Elastic Constant" for measurements performed with modern methods.

In 1925 the first residual stress measurements were performed with photographic film as the recording medium. Photographic techniques remain convenient and relatively rapid because the whole of the pattern is collected together, the film and its holder are light in weight, can be secured to the X-ray source’s supporting structure along with a collimator to define the beam of X-rays and, after development of the film, there is a permanent record of the diffraction pattern. Difficulties associated with photographic methods include the dimensional stability of the film itself (early types would shrink during processing), and locating the diffraction lines by eye or photo-densitometer is subjective, especially when they are broadened by fine grain size or deformation in the sample. Film for X-rays does not discriminate on the basis of wavelength, producing a monochrome image that includes a background consisting of radiation fluoresced in the specimen, and the "white" portion of the incident radiation.

Better methods were developed to detect X-rays with the recognition that they can be considered as photons, and diffractometers take advantage of these detectors. Diffractometers find and locate diffraction lines by scanning or stepping through a range of angles while the detector outputs the count rate to a strip-chart recorder or to a rate-meter. Most significantly, the data from the diffractometer is numerical, and mathematical techniques can be applied to the data to refine the results. Scintillation counters and proportional counters respectively provide much higher count rates than the original Geiger counters, and some energy discrimination. Despite these improvements, collecting the diffraction pattern sequentially remained time consuming.
A breakthrough for X-ray diffraction occurred with the development of position sensitive detectors. A portion of the diffraction pattern large enough to contain a whole peak profile and the associated background could be collected at once. A development of the Position Sensitive Scintillation Detector by Ruud and Barrett has a coherent fibre-optic bundle between the scintillator (a thin layer of material that emits light when absorbing an X-ray photon) and the photocathode (a thin layer of material that emits electrons when absorbing light). The scintillator is small enough to replace the film in a simple residual stress camera, the rest of the detector and its amplifiers could be placed elsewhere. The output of the instrument is fully compatible with the digital processing requirements of software installed on a PC. The result is an instrument with the simplicity and robustness of the residual stress camera, and the power and speed of the computer to calculate and interpret its data and to control its functioning.

One of the benefits of the current generation of instruments is in the abundance of data one instrument can generate. Each residual stress measurement now requires only a few minutes to complete (compared to hours by conventional diffractometer), and the presence of the computer allows a more sophisticated analytical approach to the data than is possible by manual calculation. It is now normal to consider the relationship between d-spacing and the square of the sine of the tilt angle (psi) rather than the difference between two diffraction angles. The sine-squared-psi method takes several measurements of d-spacing over the available range of tilts and fits an ellipse (rather than a straight line) to a graph of d-spacing vs. sine-squared-psi. Supported by a more complete treatment of stress and strain as tensors, the tensile stresses are represented by the slope of the major axis of the ellipse, while the minor axis represents the shear stresses. Multiple measurements of the stress in different directions at the same surface location allows the stress tensor at the surface to be calculated and the Principal Stresses to be estimated, using a Mohr’s Circle calculation.


Characterization of machined surfaces

The development of machining processes for difficult-to-machine materials is a problematic area. The potential to reduce manufacturing costs by adopting new practices is attractive to companies, but there is a responsibility to ensure that component life is not compromised by process changes. Demonstrating component life by mechanical testing is often expensive, particularly where the potential failure mechanism is subject to statistical scatter, as is the case in fatigue crack initiation. Simulated service testing in a rig is possible, but is usually reserved to demonstrate that goals have been met, not to monitor progress during development. Normal quality control methods, measuring traditional parameters such as dimensional accuracy, surface roughness and topography can be augmented by enhanced NDT, but these do not address the material affected by changed machining methods.

The near-surface region most likely to be altered in some way by a changed machining process is the same area that is the home of fatigue crack initiation sites. Residual stress profiles associated with machining processes are created by mechanical distortion and adiabatic heating of the near-surface material, and the thermal effects of friction between tool, work piece and chip. These are not constants, but vary with other conditions at the tool’s cutting edge, such as a tool geometry changed by wear, or altered coolant flow. If the objective is to create a surface similar to that of a legacy process, one should expect the residual stress profiles to reflect that similarity.

X-ray diffraction in conjunction with electro-polishing offers a rapid method of measuring both the residual stress profile and the damage to the material’s crystal structure with a depth resolution that is fine enough to capture the complex effects of machining processes. These "fingerprints" are characteristic of the surface, and if significant differences are found, the surface should be evaluated for other forms of microscopic damage, as well as being assessed analytically for the effects of the new residual stress distribution added to the overall mechanical stress pattern of the part in service.

Characterization of peened surfaces

Like machining methods, shot peening processes are subject to change as equipment is replaced and modified. Residual stress measurement offers an excellent tool to demonstrate intensity on test parts in areas that cannot be simulated by Almen strip placement, or that necessarily present an oblique surface to the shot stream. Areas for measurement do not need to be flat, but they do have to be accessible to the X-ray beam.

Characterization of welds

Welds are particularly sensitive areas of assemblies. They are created by heating the material locally to its melting point, and then allowing the molten bead to solidify and cool. Thermal contraction in the bead and surrounding material causes complex three dimensional stress fields in the vicinity of the weld, where the material properties are also likely to be modified by exposure to the heat of the welding process. The small beam diameter available in modern X-ray stress measuring systems provides the spatial resolution needed to capture the steep stress gradients found close to welds. The relatively small size of current X-ray tubes and detector assemblies contribute to successful measurements in confined spaces, such as inside holes, or deep inside pipes.


As X-ray diffraction celebrates its centenary, the developments that have affected one successful area of the science have been reviewed. The future for X-ray diffraction continues to look bright, as further developments in X-ray detectors are needed in medical imaging to improve resolution and reduce exposure. Research in high energy and particle Physics, and increasing interest in X-ray telescopes for space applications will also promote the development of improved X-ray detectors. These improvements will in turn benefit residual stress measurement, with better ability to discard photons that are not part of the diffraction pattern, and greater count rates. Meanwhile, the existing database of residual stress measurements will continue to grow, as will awareness of residual stress and its role in the life and safety of components around us.

For Information:
Proto Manufacturing Ltd.
2175 Solar Crescent, Oldcastle,Ontario
Canada, N0R 1L0
Tel. +1.519.737.6330
Fax +1.519.737.1692
E-mail: proto@protoxrd.com