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

Mehmet Hazar Şeren; Darren C Pagan; Ismail Cevdet Noyan

doi:10.1107/S1600576723004351

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

J Appl Crystallogr. 2023 Jul 20;56(Pt 4):1144-1167. doi: 10.1107/S1600576723004351. eCollection 2023 Aug 1.

Authors

Mehmet Hazar Şeren^{1

2}, Darren C Pagan³, Ismail Cevdet Noyan¹

Affiliations

¹ Department of Applied Physics and Applied Mathematics, SEAS, Columbia University, 500W 120th Street, New York, NY 10027, USA.
² ASML (United States) LP, 77 Danbury Road, Wilton, CT 06897, USA.
³ Materials Science and Engineering and Mechanical Engineering, Pennsylvania State University, 328 Steidle Building, University Park, PA 16802, USA.

Abstract

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.

Keywords: diffraction analysis; polycrystalline solids; strain; stress.