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Rathmann NM, Grinsted A, Mosegaard K, Lilien DA, Westhoff J, Hvidberg CS, Prior DJ, Lutz F, Thomas RE, Dahl-Jensen D. Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain
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-axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.
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Affiliation(s)
| | - Aslak Grinsted
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - Klaus Mosegaard
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - David A. Lilien
- Centre for Earth Observation Science, University of Manitoba, Winnipeg, Canada
| | - Julien Westhoff
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | | | - David J. Prior
- Department of Geology, University of Otago, Dunedin, New Zealand
| | - Franz Lutz
- Department of Geology, University of Otago, Dunedin, New Zealand
| | - Rilee E. Thomas
- Department of Geology, University of Otago, Dunedin, New Zealand
| | - Dorthe Dahl-Jensen
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
- Centre for Earth Observation Science, University of Manitoba, Winnipeg, Canada
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Sciegaj A, Wojtczak E, Rucka M. The effect of external load on ultrasonic wave attenuation in steel bars under bending stresses. ULTRASONICS 2022; 124:106748. [PMID: 35405600 DOI: 10.1016/j.ultras.2022.106748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Revised: 01/21/2022] [Accepted: 04/03/2022] [Indexed: 06/14/2023]
Abstract
The stress state in deformed solids has a significant impact on the attenuation of an ultrasonic wave propagating through the medium. Measuring a signal with certain attenuation characteristics can therefore provide useful diagnostic information about the stress state in the structure. In this work, basic principles behind a novel attenuation-based diagnostic framework are introduced. An experimental study on steel bars under three-point bending was carried out, and finite element analyses were used to numerically model the experiments. Obtained test results showed a strong correlation between the external load and the ultrasonic signal energy, which decreases with increasing load. A similar but positive correlation appeared between the level of attenuation of longitudinal ultrasonic wave signals and the external load, which allowed for efficient estimation of the mid-span bending moment. Upon proper calibration of testing equipment, the change in ultrasonic signal energy can therefore be used as an indicator of the external load level. As a result, this effect has potential applications in non-destructive structural health monitoring frameworks.
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Affiliation(s)
- Adam Sciegaj
- Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland.
| | - Erwin Wojtczak
- Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland.
| | - Magdalena Rucka
- Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland.
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