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Materials 2015, 8(9), 6326-6345; doi:10.3390/ma8095303

Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms

Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
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Academic Editor: Sergey Kustov
Received: 25 July 2015 / Revised: 2 September 2015 / Accepted: 14 September 2015 / Published: 17 September 2015
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Abstract

Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) to delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. View Full-Text
Keywords: property closures; Elastic properties; orientation distribution function; anisotropy; spectral methods property closures; Elastic properties; orientation distribution function; anisotropy; spectral methods
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Landry, N.W.; Knezevic, M. Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms. Materials 2015, 8, 6326-6345.

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