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Path-Integrated X-Ray Digital Image Correlation using Synthetic Reference Images

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Abstract

X-rays can provide images when an object is visibly obstructed, allowing for motion measurements via x-ray digital image correlation (DIC). However, x-ray images are path-integrated and contain data for all objects between the source and detector. If multiple objects are present in the x-ray path, conventional DIC algorithms may fail to correlate the x-ray images. A new DIC algorithm called path-integrated (PI)-DIC addresses this issue by reformulating the matching criterion for DIC to account for multiple, independently-moving objects. PI-DIC requires a set of reference x-ray images of each independent object. However, due to experimental constraints, such reference images might not be obtainable from the experiment. This work focuses on the reliability of synthetically-generated reference images, in such cases. A simplified exemplar is used for demonstration purposes, consisting of two aluminum plates with tantalum x-ray DIC patterns undergoing independent rigid translations. Synthetic reference images based on the “as-designed” DIC patterns were generated. However, PI-DIC with the synthetic images suffered some biases due to manufacturing defects of the patterns. A systematic study of seven identified defect types found that an incorrect feature diameter was the most influential defect. Synthetic images were re-generated with the corrected feature diameter, and PI-DIC errors were improved by a factor of 3-4. Final biases ranged from 0.00-0.04 px, and standard uncertainties ranged from 0.06-0.11 px. In conclusion, PI-DIC accurately measured the independent displacement of two plates from a single series of path-integrated x-ray images using synthetically-generated reference images, and the methods and conclusions derived here can be extended to more generalized cases involving stereo PI-DIC for arbitrary specimen geometry and motion. This work thus extends the application space of x-ray imaging for full-field DIC measurements of multiple surfaces or objects in extreme environments where optical DIC is not possible.

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Notes

  1. Equation (1) invokes several simplifying assumptions, including: (1) a monochromatic x-ray source (rather than the common polychromatic lab sources) is used; (2) the detector image intensity is linearly proportional to the x-ray intensity; (3) attenuation of the x-rays due to air is negligible compared to the attenuation due to the plate and feature materials; (4) the change in image intensity due to the emittance angle from a conical x-ray beam is negligible; (5) spatial variations of the x-ray and/or image intensity are corrected during image preprocessing. See [17] for more details.

  2. The displacements of the two individual plates are computed in a Lagrangian framework for a single plate at a time. For brevity, the algorithm is explained here for tracking the front plate displacement. However, by reversing references to the “front plate” and “back plate”, a similar analysis of the back plate can be performed.

  3. https://www.mathworks.com/help/optim/ug/fminunc.html

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Acknowledgements

The authors would like to acknowledge Andrew Lentfer for his work setting up and training the team on the x-ray imaging system, Dayna Obenauf for her contribution in the planning and execution of the plate translation experiments, and John Miers for internal peer-review.

Funding

This article has been authored by an employee of National Technology and Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all right, title and interest in and to the article and is solely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan at https://www.energy.gov/downloads/doe-public-access-plan. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525

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Authors and Affiliations

  1. Diagnostics for Extreme Environments and Hypersonics, Albuquerque, NM, USA

    S. S. Fayad & E.M.C. Jones

  2. Fire Science and Technology Sandia National Laboratories, Albuquerque, NM, USA

    C. Winters

Authors
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Contributions

Author contributions are recognized using the Contributor Roles Taxonomy (CRediT), https://doi.org/10.1002/leap.1210. Samuel S. Fayad: Methodology; Software; Data Curation; Investigation; Validation; Formal Analysis; Visualization; Writing—Original Draft; Writing—Review & Editing Elizabeth M. C. Jones: Methodology; Software; Data Curation; Writing—Review & Editing; Supervision; Conceptualization; Resources Caroline Winters: Writing - Review & Editing; Funding Acquisition; Project Administration; Resources

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Correspondence to E.M.C. Jones.

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Caroline Winters is a technical editor for Experimental Techniques.

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E.M.C. Jones and C. Winters are members of SEM.

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Fayad, S.S., Jones, E. & Winters, C. Path-Integrated X-Ray Digital Image Correlation using Synthetic Reference Images. Exp Tech (2024). https://doi.org/10.1007/s40799-024-00707-y

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