Informing Mechanical Model Development Using Lower-Dimensional Descriptions of Lattice Distortion
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TECHNICAL ARTICLE
Informing Mechanical Model Development Using Lower‑Dimensional Descriptions of Lattice Distortion Darren C. Pagan1 · Gideon H. Schmidt2,4 · Andy D. Borum3 · Timothy J. Long4 · Armand J. Beaudoin2 Received: 12 August 2020 / Accepted: 20 November 2020 © The Minerals, Metals & Materials Society 2020
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. Keywords Unsupervised learning · Plasticity · X-ray diffraction · Constitutive modeling · Nickel
Introduction Expressing phenomenology through the evolution of internal state variables is a widely used approach to capture and predict the mechanical response of engineering alloys during plastic deformation. These state variables may rest on a physical basis, e.g., dislocation density and lattice orientation, serving to relate the current microstructure to resultant mechanical response. The standard approach to calibrate a state variable model is to optimize state variable initial values and material parameters to best fit macroscopic loading (stress–strain) data. Ideally, each state variable is isolated using a carefully chosen series of mechanical tests, but these are not always performed or are even possible. In this process, the choice of state variable may be phenomenologically * Darren C. Pagan [email protected] 1
Pennsylvania State University, University Park, PA, USA
2
Cornell High Energy Synchrotron Source, Ithaca, NY, USA
3
Department of Mathematics, Cornell University, Ithaca, NY, USA
4
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA
informed by microscopy observations, but generally, the model is never actually tested against data describing the underlying microstructural evolution that the model is trying to capture. This shortcoming leads to uncertainties regarding the capability of the model to accurately capture the physics of the mechanical response and, subsequently, future predictions from the model. New data collection techniques at synchrotron light sources (and in electron microsc
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