Representative volume elements of strain/stress fields measured by diffraction techniques

• Published in: Journal of applied crystallography Vol. 56; no. 4; pp. 1144 - 1167
• Main Authors: Şeren, Mehmet Hazar, Pagan, Darren C., Noyan, Ismail Cevdet
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.08.2023; Blackwell Publishing Ltd
• Subjects: Crystallites; Crystals; Diffraction; diffraction analysis; Lattice strain; polycrystalline solids; Research Papers; Residual stress; Slabs; Strain; stress; Stress distribution; strain; stress; polycrystalline solids; diffraction analysis
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576723004351

Finite‐element modelling has been used to simulate local strains and stresses within free‐standing polycrystalline slabs of W, Cu and W–Cu, heated with free or constrained boundaries. The elastic strain values in crystallites that satisfied the diffraction condition were used to simulate the lattice strain data that would be obtained from diffraction analysis, from which the average stresses within diffracting domains were computed. Comparison of direct‐space stresses in the model with the average stresses determined from diffraction analysis shows that the representative volume elements (RVEs) required to obtain equivalent stress/strain values depend on the deformation mode suffered by the material. Further, the direct‐space and diffraction stress values agree only under strict sampling and strain/stress uniformity conditions. Consequently, in samples where measurements are conducted in volumes smaller than the RVE, or where the uniformity conditions are not satisfied, further experimental and numerical techniques might be needed for the accurate determination of applied or residual stress distributions. Representative volume elements for diffraction‐based stress/strain distributions in polycrystalline materials are compared with direct‐space values of these quantities using numerical modelling. The results indicate that these volumes and their stress states are equivalent under very specific conditions.