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Thermal Response Variability of Random Polycrystalline Microstructures

Published online by Cambridge University Press:  20 August 2015

Bin Wen
Affiliation:
Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA
Zheng Li
Affiliation:
Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China
Nicholas Zabaras
Affiliation:
Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA
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Abstract

A data-driven model reduction strategy is presented for the representation of random polycrystal microstructures. Given a set of microstructure snapshots that satisfy certain statistical constraints such as given low-order moments of the grain size distribution, using a non-linear manifold learning approach, we identify the intrinsic low-dimensionality of the microstructure manifold. In addition to grain size, a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used to reduce the texture representation. The space of viable microstructures is mapped to a low-dimensional region thus facilitating the analysis and design of polycrystal microstructures. This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture). We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation variability.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

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