Research Papers

A Descriptor-Based Design Methodology for Developing Heterogeneous Microstructural Materials System

[+] Author and Article Information
Hongyi Xu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: hongyixu2014@u.northwestern.edu

Yang Li

Department of Material Science and Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: yangli2009@u.northwestern.edu

Catherine Brinson

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: cbrinson@northwestern.edu

Wei Chen

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road, Tech A216,
Evanston, IL 60208
e-mail: weichen@northwestern.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 14, 2013; final manuscript received January 15, 2014; published online March 21, 2014. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 136(5), 051007 (Mar 21, 2014) (12 pages) Paper No: MD-13-1306; doi: 10.1115/1.4026649 History: Received July 14, 2013; Revised January 15, 2014

In designing a microstructural materials system, there are several key questions associated with design representation, design evaluation, and design synthesis: how to quantitatively represent the design space of a heterogeneous microstructure system using a small set of design variables, how to efficiently reconstruct statistically equivalent microstructures for design evaluation, and how to quickly search for the optimal microstructure design to achieve the desired material properties. This paper proposes a new descriptor-based methodology for designing microstructural materials systems. It is proposed to use a small set of microstructure descriptors to represent material morphology features quantitatively. The descriptor set should be able to cover microstructure features at different levels, including composition, dispersion status, and phase geometry. A descriptor-based multiphase microstructure reconstruction algorithm is developed accordingly that allows efficient stochastic reconstructions of microstructures in both 2D and 3D spaces for finite element analysis (FEA) of material behavior. Finally, the descriptor-based representation allows the use of parametric optimization approach to search the optimal microstructure design that meets the target material properties. To improve the search efficiency, this paper integrates state-of-the-art computational design methods such as design of experiment (DOE), metamodeling, statistical sensitivity analysis, and multi-objective optimization, into one design optimization framework to automate the microstructure design process. The proposed methodology is demonstrated using the design of a polymer nanocomposites system. The choice of descriptors for polymer nanocomposites is verified by establishing a mapping between the finite set of descriptors and the infinite dimensional correlation function.

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Fig. 1

Sample image of polymer nanocomposites

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Fig. 2

Flow chart of descriptor-based hierarchical reconstruction

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Fig. 3

Smooth profile reconstruction and free mesh of three-phase microstructure (filler, matrix, and interphase around filler)

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Fig. 4

Comparison of target microstructure and three microstructure reconstructions

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Fig. 5

Comparison of 2-point correlation functions and 2-point cluster correlation functions of target and reconstructed microstructures

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Fig. 6

3D reconstruction example: the structure is reconstructed based on the descriptors listed in the left table

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Fig. 7

Demonstration of fluctuations in 2-point correlation function and the physical meaning

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Fig. 8

Sample microstructure and comparison of the real 2-point correlation function and the analytical correlation function

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Fig. 9

Parametric microstructure optimization design framework

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Fig. 10

Three design criteria defined by three points on tan δ

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Fig. 11

(a) double layer gradient interphase model in FEM (b) viscoelastic properties of interphase

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Fig. 12

Design of experiments in four-descriptor design space

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Fig. 13

TSI of four descriptors with respect to three property responses

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Fig. 14

Pareto solutions obtained using three different metamodels: (1) Kriging model based on full descriptor set [VF¯, N¯, rd¯, el¯]; (2) Kriging model based on reduced descriptor [VF¯, N¯, rd¯] (TSI = 0.2); (3) Kriging model based on reduced descriptor [VF¯, N¯] (TSI = 0.7). The realizations of three design points (marked by circle) are also shown here.

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Fig. 15

Two baseline designs: microstructure image and descriptors

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Fig. 16

Property comparison between the baseline designs and the optimal designs




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