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Informing Mechanical Model Development Using Lower-Dimensional Descriptions of Lattice Distortion

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Abstract

This paper describes a method combining in situ X-ray diffraction data and dimensionality reduction (local linear embedding) to inform the development of state variable plasticity models. The method is applied to developing a state variable plasticity model for pure nickel deformed in uniaxial tension in the small strain regime. Prior to model development, connections between state variables representing evolution of mobile dislocations and the lower-dimensional representations of the data are established. Correlations between lower-dimensional representation of data and state variable evolution motivate the introduction of new evolution equation terms to increase alignment between experiment and model. These terms capture dislocation interactions leading to hardening transients prior to steady-state plastic flow. The discussion focuses on interpreting these new evolution terms and outstanding issues associated with linking lower-dimensional representations of data to state variable evolution modeled with ordinary differential equations.

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Acknowledgements

This work is based upon research conducted at the Center for High-Energy X-ray Sciences (CHEXS) which is supported by the National Science Foundation under award DMR-1829070. GHS and AJB received support through the Office of Naval Research (Contract N00014-16-1-3126). We would like to thank Dr. Edward Trigg for helpful discussions regarding orientation of the lower-dimensional embeddings. We would also like to thank Professor Matthew Miller for helpful discussions regarding this manuscript.

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Authors and Affiliations

  1. Pennsylvania State University, University Park, PA, USA

    Darren C. Pagan

  2. Cornell High Energy Synchrotron Source, Ithaca, NY, USA

    Gideon H. Schmidt & Armand J. Beaudoin

  3. Department of Mathematics, Cornell University, Ithaca, NY, USA

    Andy D. Borum

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

    Gideon H. Schmidt & Timothy J. Long

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  1. Darren C. Pagan
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  2. Gideon H. Schmidt
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  3. Andy D. Borum
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  4. Timothy J. Long
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  5. Armand J. Beaudoin
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Correspondence to Darren C. Pagan.

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Pagan, D.C., Schmidt, G.H., Borum, A.D. et al. Informing Mechanical Model Development Using Lower-Dimensional Descriptions of Lattice Distortion. Integr Mater Manuf Innov 9, 459–471 (2020). https://doi.org/10.1007/s40192-020-00196-y

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