Residual stress measurement using X-ray diffraction (XRD) is now widely adopted in both industry and academia. However, a growing disconnect has emerged between instrument operation and foundational understanding, driven by oversimplified tools that limit data collection to two-tilt or single-exposure techniques, insufficient training, and fragmented education. The triaxial nature of the stress field, including out-of-plane shear components, is often overlooked, and the component’s stress distribution is not adequately characterized. Additionally, some instrument manufacturers promote simplified measurement approaches that can yield erroneous results, as many operators and equipment purchasers have not been provided with sufficient information to recognize the inherent limitations of these methods.

This article examines the challenges facing XRD-based residual stress analysis, including significant gaps in theoretical knowledge and the risks of treating instruments as opaque “black boxes.” It ultimately advocates for renewed emphasis on education, thorough documentation, and methodological transparency to uphold the scientific rigor of XRD techniques.

Residual stress measurements rely on a range of techniques developed over several decades. The knowledge and expertise required in this field are often shaped by individual educational backgrounds and years of hands-on practice. Although diffraction-based residual stress measurement methods are included in some postgraduate curricula, it is well known that they are not widely taught in undergraduate university programs, with the exception of a few specialized institutions. 

As a result, most users acquire their knowledge through alternative paths such as self-education, conferences, and training provided in part by instrument manufacturers. Instruments themselves incorporate diverse technologies and software systems. A solid understanding of an instrument’s capabilities can serve as a valuable entry point for gaining deeper knowledge and advancing in the field. However, many instruments operate as “black boxes,” offering little to no insight into their underlying algorithms. This lack of transparency can mislead users or hinder their ability to build a strong technical foundation.

In an effort to reduce costs, some manufacturers have simplified instrument designs and algorithms, a practice that can ultimately harm the industry by increasing the risk of costly errors. Certain manufacturers promote simplified measurement using the two-tilt method or the single-exposure technique (SET) that may produce inaccurate data, especially when operators or purchasers lack the necessary education to recognize their limitations. For example, such approaches may fail to characterize stress triaxiality, including out of-plane shear stress, which is often ignored. In addition, the number of points with the necessary depth for reliable characterization is greatly limited.

To address these challenges in both industry and academic institutions, a number of well-documented training resources, such as books, handbooks, and journal articles, are available for consultation and use, offering a valuable means to recover and transfer the missing knowledge.

In the field of residual stress measurement using XRD, many important developments have been achieved over the decades. However, much of this progress has stalled due to a lack of continued dissemination and publication, with many works historically overlooking critical aspects of residual stress evaluation. This situation is partly attributable to some instrument manufacturers who have disregarded past advancements, favoring simplified approaches in instrument and software design.

In some cases, users rely on instrument training as an indirect means of gaining technical knowledge that is not explicitly provided elsewhere. This can be a double-edged sword: while it provides practical know-how, it may also expose gaps in foundational understanding, gaps that become evident in the quality and depth of users’ expertise.

Scientific technology reflects the mindset and depth of understanding of those who design and use it. The current state of user knowledge in the field of XRD residual stress measurement reflects this reality, and unfortunately, there is no simple way to bridge the gap without broad, sustained efforts in education, documentation, and transparency.

With the growing adoption of residual stress measurement techniques in both industry and academia, users now come from diverse educational backgrounds, ranging from materials and mechanical engineering to physics, chemistry, and beyond. This diversity poses challenges, especially for individuals with a mechanical engineering background. Relying solely on knowledge acquired through traditional elasticity theory courses can sometimes lead to misinterpretation of XRD results.

When using XRD, the standard boundary conditions assumed in classical elasticity may not always be verified, particularly when X-rays penetrate either very shallowly or relatively deeply into a material. This is especially relevant for heterogeneous materials subjected to non-uniform thermal or mechanical processes, or for those with a fully multi-phase structure. In such cases, the assumption of a stress-free surface may no longer be valid at the level of individual phases. Instead, it is the average residual stress across all phases that fulfills the stress-free boundary condition. Many perceptive users have recognized and accepted this scientifically validated concept. While critical thinking is essential, it should be exercised alongside a careful review of the published literature rather than in disregard of it.

The notion of out-of-plane shear stress within the measured phase, or the presence of type II pseudo-macrostress in the material, often seems almost fictional to users from certain backgrounds. However, these phenomena are well documented and scientifically validated. This disconnect is also reflected in the way some instruments are conceived and designed, often based on a limited understanding or partial adoption of well-established knowledge that is widely published and readily accessible to all users. This often results in inaccurate measurements, which can in turn mislead theoreticians relying on finite element analysis and modeling, potentially compromising the validity of their simulations and conclusions.

Academic publishing practices have evolved considerably, with notable implications for content reliability and peer review standards. Publishing a paper has become more accessible, but often at the cost of quality. Subject-matter experts with deep knowledge of the field are not always consulted for review. In the past, the primary motivation for publishing was to present novel findings and promote the exchange of original ideas, efforts that collectively advanced the state of knowledge for the benefit of all; today, however, journals are increasingly featuring previously published ideas or papers driven more by commercial or career incentives than by genuine scientific contribution. This trend risks misleading readers and users of XRD, particularly those who rely on published material to guide technical decisions. It is important to recognize that not all published work is accurate and complete, especially in conference proceedings or certain journals where critical peer review is minimal or entirely absent.

Although variations in XRD techniques may arise due to differences in instrument geometry and hardware configurations, the fundamental principles governing their application remain the same. Users should not be misled by newly introduced equations that merely offer alternate representations rather than reflecting fundamentally different assumptions, applications, or techniques. That said, there is no “better” or “worse” method, only differences in the assumptions adopted to accurately reach the final objective.

Residual stress measurement using XRD operates on the same fundamental metrological principles as any other scientific or engineering technique: measurement accuracy, precision, and the identification and management of associated errors.

The fundamental equation used for residual measurement using diffraction technique is: (1)

Specifically, for sin²ψ, the equation can be written as: (2)

This equation refers to any XRD technique and provides a suitable model for calculating residual stress in a material. It accounts for both normal and shear stress components and typically results in an elliptical strain distribution when plotted as a function of sin²ψ. The validity of this equation has been both mathematically and experimentally confirmed since 1973, when the presence of out-of-plane shear stress components in materials was first recognized in the context of XRD analysis.

The sin²ψ equation can help illustrate several potential sources of errors, including but not limited to:

• Incorrect d-spacing or peak position determination, due to poor peak statistics or overlapping peaks.

• Inaccurate ψ-angle setting, caused by goniometer misalignment or other instrumental effects.

• Use of inappropriate elastic constants (S₁ and ½S₂) for the material and the selected (hkl) plane.

• Improper model assumption, such as applying a linear fit when the actual strain distribution exhibits elliptical shape.

Other sources of error can originate from the instrument itself or the sample shape and its placement. Every aspect of the measurement process should be critically evaluated, as each component has the potential to contribute to the overall measurement uncertainty.

These errors can be described as the sum of the following error types:

• Random errors, or statistical errors, arising from factors such as peak definition uncertainty, signal noise, and variations in material microstructure.

• Systematic errors resulting from instrument misalignment or the use of an inappropriate peak fitting model that does not accurately represent the data collected.

• Errors related to the model: deviations from linearity due to material heterogeneity and pseudo-macrostress.

To minimize external factors and improve reproducibility and repeatability, i.e., gage R&R, in round robin studies, the best approach is to use a loaded, fine-grained pure material, heat treated for uniformity and minimal residual stress. This ensures consistency and reduces interlaboratory variability. A second sample with shear stress from rolling, directional shot peening, or machining can help validate the model and method beyond current academic and industrial practice, while identifying requirements for accurate results.

The interpretation of results can be challenging at times, especially when certain laboratories or instruments produce outliers. These outliers should be identified and excluded through appropriate statistical methods. Various statistical tools are available to reliably select valid results and, in turn, help certify both the instruments and the operators responsible for the measurements.

The goal is to achieve accurate and reproducible residual stress measurements. However, simplifying the procedure or methodology to reduce costs increases the risk of poor data quality and may mislead users. The following points should be considered:

• Seek technical training and consult the relevant literature.

• Avoid relying solely on information provided by instrument manufacturers.

• Understand the assumptions underlying the measurements.

• Document and disseminate validated knowledge.

• Encourage critical thinking and continuous learning.

Only with a commitment to rigor and education can XRD maintain its role as a powerful scientific technique for stress analysis.

1. I. C. Noyan and J.B. Cohen, Residual Stress: Measurement by Diffraction and Interpretation, Springer (New York, 1987).

2. V. Hauk, Structural and Residual Stress Analysis by Non-Destructive Methods, Elsevier (Amsterdam, 1997).

3. J. Lu, Handbook of Measurement of Residual Stresses, Fairmont Press (Lilburn, 1996).

Proto Manufacturing

LaSalle, Ontario, Canada

E-mail: mbelassel@protoxrd.com