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Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

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Abstract

Residual stress can play a significant role in the processing and performance of an engineered metallic component. The stress state within a polycrystalline part can vary significantly between its surface and its interior. To measure three-dimensional (3D) residual stress fields, a synchrotron x-ray diffraction-based experimental technique capable of non-destructively measuring a set of lattice strain pole figures (SPFs) at various surface and internal points within a component was developed. The resulting SPFs were used as input for a recently developed bi-scale optimization scheme McNelis et al. J Mech Phys Sol 61:428–1007 449 (2013) that combines crystal-scale measurements and continuum-scale constraints to determinethe 3D residual stress field in the component. To demonstrate this methodology, the 3D residual stress distribution was evaluated for an interference-fit sample fabricated from a low solvus high refractory (LSHR) polycrystalline Ni-base superalloy.

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Notes

  1. In this section, we treat the incident and diffracted beams as lines (rays) that coincide with the averages of the real distributions. This simplifies the treatment but still applies to the general case.

  2. In other words, any point on the detector is mapped through the slit to exactly one point along zL.

  3. For a detailed treatment of the \(\sin ^{2} \Psi \) analysis for the determination of residual stress at a point, readers are referred to works by Lu [16] or Hauk et al. [17].

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Acknowledgments

This research was financially supported by the U.S. Air Force Office of Scientific Research Multi-Scale Structural Mechanics Program under contract number FA9550-09-1-0642. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under contract number DE-AC02-06CH11357. Professor Jim Williams of the Ohio State University is gratefully acknowledged for motivation and guidance of this work. The LSHR material used in this work was provided by Dr. T. J. Turner at the Air Force Research Laboratory (AFRL). The DPLAB Polycrystal Library (OdfPf) at Cornell University was used extensively for this work ( http://anisotropy.mae.cornell.edu).

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Authors and Affiliations

  1. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA

    P. R. Dawson & M. P. Miller

  2. Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA

    J.-S. Park

  3. Deutsches Elektronen-Synchrotron, Hamburg, Germany

    U. Lienert

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  1. J.-S. Park
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Correspondence to M. P. Miller.

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Park, JS., Lienert, U., Dawson, P.R. et al. Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction. Exp Mech 53, 1491–1507 (2013). https://doi.org/10.1007/s11340-013-9771-0

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