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X-ray Diffraction for the Determination of Residual Stress of Crystalline Material: An Overview

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Abstract

Though there are a variety of experimental techniques available for residual stress measurements, diffraction-based measurements have the unique advantage of estimating the individual components of the residual strain matrix in a crystalline material. This is then converted to residual stresses with appropriate continuum elasticity model(s) and X-ray elastic constants. In particular, measurements based on electron or neutron diffractions have their complexities or availability issues. The laboratory X-ray diffraction, on the other hand, may provide an easy resource and an effective tool. Such measurements range from two tilt methods to more extended d-sin2ψ measurements and multiple {hkil} grazing incident X-ray diffraction. Measurements can even be conducted on single crystals with micro-Laue diffraction and extended to stress ODF (orientation distribution function) calculations. These techniques are unquestionably extremely specialized, where measurement uncertainty plays an important role in the effectiveness plus reproducibility of the data. Unfortunately, standard textbooks or review articles typically describe some, but not all, of the techniques. In this overview, different techniques of X-ray diffraction for the determination of residual stresses in crystalline material have been summarized. It is hoped that potential users may benefit from the deliberations.

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Authors and Affiliations

  1. School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK

    Arijit Lodh

  2. Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology-Bombay, Mumbai, India

    Khushahal Thool & Indradev Samajdar

Authors
  1. Arijit Lodh
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  2. Khushahal Thool
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  3. Indradev Samajdar
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Correspondence to Indradev Samajdar.

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Appendix

Appendix

1.1 Residual Stress and Ewald Sphere Construction

Let’s consider (see Fig. 11) the diffracting crystal at the center of Ewald sphere of 1/λ with incident beam entering from point A satisfying Bragg’s law. B defines the origin of reciprocal lattice. At no stress state condition, diffracted beam exits from point D. Therefore, length of vector DB is equal to \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {d_{hkl} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${d_{hkl} }$}}\). According to state of residual stress, diffraction peak will shift. Assuming compressive state here for the same crystal, diffracted beam now exits from point C and length of vector CB is equal to \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {d_{{hkl, {\text{RS}}}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${d_{{hkl, {\text{RS}}}} }$}}\). The length difference between vector DB and CB arises from residual stress.

Fig. 11
figure 11

Ewald sphere reconstruction due to residual stress development

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Lodh, A., Thool, K. & Samajdar, I. X-ray Diffraction for the Determination of Residual Stress of Crystalline Material: An Overview. Trans Indian Inst Met 75, 983–995 (2022). https://doi.org/10.1007/s12666-022-02540-6

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