A spherical harmonic approach for the determination of HCP texture from ultrasound: a solution to the inverse problem
File(s)
Accepted version
Author(s)
Lan, B
Lowe, M
DUNNE, F
Type
Journal Article
Abstract
A new spherical convolution approach has been presented which couples HCP single crystal wave speed (the kernel function) with polycrystal c-axis pole distribution function to give the resultant polycrystal wave speed response. The three functions have been expressed as spherical harmonic expansions thus enabling application of the de-convolution technique to enable any one of the three to be determined from knowledge of the other two. Hence, the forward problem of determination of polycrystal wave speed from knowledge of single crystal wave speed response and the polycrystal pole distribution has been solved for a broad range of experimentally representative HCP polycrystal textures. The technique provides near-perfect representation of the sensitivity of wave speed to polycrystal texture as well as quantitative prediction of polycrystal wave speed. More importantly, a solution to the inverse problem is presented in which texture, as a c-axis distribution function, is determined from knowledge of the kernel function and the polycrystal wave speed response. It has also been explained why it has been widely reported in the literature that only texture coefficients up to 4th degree may be obtained from ultrasonic measurements. Finally, the de-convolution approach presented provides the potential for the measurement of polycrystal texture from ultrasonic wave speed measurements.
Date Issued
2015-10-01
Date Acceptance
2015-06-22
Citation
Journal of the Mechanics and Physics of Solids, 2015, 83 (1), pp.179-198
ISSN
0022-5096
Publisher
Elsevier
Start Page
179
End Page
198
Journal / Book Title
Journal of the Mechanics and Physics of Solids
Volume
83
Issue
1
Copyright Statement
© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
EPSRC
Identifier
https://www.sciencedirect.com/science/article/pii/S0022509615300016?via%3Dihub
Grant Number
EP/K034332/1
EP/K034332/1
Subjects
Science & Technology
Technology
Physical Sciences
Materials Science, Multidisciplinary
Mechanics
Physics, Condensed Matter
Materials Science
Physics
Texture
Spherical harmonics
Ultrasound
HCP polyaystals
STRAIN-MEASUREMENT INSTRUMENTS
WAVE-PROPAGATION
POLYCRYSTALLINE MATERIALS
HEXAGONAL MATERIALS
DEPTH CAPABILITIES
ORIENTATION
IRRADIANCE
VELOCITIES
TITANIUM
NEUTRON
Mechanical Engineering & Transports
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2015-07-02