Review of the measurement methods for elastic moduli and internal friction of solids

XIE Mingyu; LI Faxin

doi:10.6052/1000-0992-21-013

Volume 52 Issue 1

Mar. 2022

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Xie M Y, Li F X. Review of the measurement methods for elastic moduli and internal friction of solids . Advances in Mechanics, 2022, 52(1): 33-52 doi: 10.6052/1000-0992-21-013

Citation:

Xie M Y, Li F X. Review of the measurement methods for elastic moduli and internal friction of solids . Advances in Mechanics, 2022, 52(1): 33-52 doi: 10.6052/1000-0992-21-013

Xie M Y, Li F X. Review of the measurement methods for elastic moduli and internal friction of solids . Advances in Mechanics, 2022, 52(1): 33-52 doi: 10.6052/1000-0992-21-013

Citation:

Xie M Y, Li F X. Review of the measurement methods for elastic moduli and internal friction of solids . Advances in Mechanics, 2022, 52(1): 33-52 doi: 10.6052/1000-0992-21-013

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Review of the measurement methods for elastic moduli and internal friction of solids

doi: 10.6052/1000-0992-21-013

XIE Mingyu,
LI Faxin^,

LTCS and Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China

More Information

Corresponding author: lifaxin@pku.edu.cn
Received Date: 2021-03-15
Accepted Date: 2021-05-26

Available Online: 2021-07-06

Publish Date: 2022-03-25

Abstract

Abstract

Elastic moduli and internal frictions are fundamental properties of solid materials. The accuracy and convenience of the measurements these properties are of great significance to industrial production and scientific research. This paper reviews the measurement methods of elastic moduli and internal frictions of solid materials in the past 100 years. These methods can be divided into four categories: quasi-static method, low frequency method, resonance method, and wave propagation method. Firstly, the measurement principle of each type method is introduced and evaluated. Then the resonance methods, including free-free beam method, impulse excitation technique, resonant ultrasound spectrum and piezoelectric ultrasonic composite oscillator technique (PUCOT) are presented and discussed in detail. After that, a new method called modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT), proposed by the authors, are introduced. This new method is based on the principle of electro-mechanical impedance, and can measure the Young’s modulus/shear modulus and the related internal frictions simultaneously, accurately, and quickly. Finally, the significance and prospective of this new method are discussed.
- elastic moduli,
- internal frictions,
- measurement methods,
- electromechanical impedance,
- piezoelectric

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References(60)

References

[1]	冯端. 1999. 金属物理学(第三卷): 金属力学性质. 北京: 科学出版社.
[2]	葛庭燧. 1994. 扭摆内耗仪的发明和内耗研究的开拓与发展. 力学进展, 24: 336-352
[3]	徐芝纶. 1979. 弹性力学(上册). 北京: 人民教育出版社.
[4]	Alers G A, Thompson D O. 1961. Dislocation contributions to the modulus and damping in copper at megacycle frequencies. Journal of Applied Physics, 32: 283-293. doi: 10.1063/1.1735992
[5]	Asano S. 1970. Theory of nonlinear damping due to dislocation hysteresis. Journal of the Physical Society of Japan, 29: 952-963. doi: 10.1143/JPSJ.29.952
[6]	ASTME494-10. 2002. Standard practice for measuring ultrasonic velocity in materials. Annual book of ASTM standards.
[7]	ASTME1875-13. 2013. Standard test method for dynamic Young’s modulus, shear modulus, and Poisson’s ratio by sonic resonance. Annual Book of ASTM Standards.
[8]	ASTME1876-15. 2015. Standard test method for dynamic young’s modulus, shear modulus, and poisson’s ratio by impulse excitation of vibration. Annual Book of ASTM Standards.
[9]	Ayres J W, Lalande F, Chaudhry Z, Rogers C A. 1998. Qualitative impedance-based health monitoring of civil infrastructures. Smart Materials and Structures, 7: 599. doi: 10.1088/0964-1726/7/5/004
[10]	Balakirev F F, Ennaceur S M, Migliori R J, Maiorov B, Migliori A. 2019. Resonant ultrasound spectroscopy: The essential toolbox. Review of Scientific Instruments, 90: 121401. doi: 10.1063/1.5123165
[11]	Bauer C L, Gordon R B. 1960. Dislocation damping effects in rock salt. Journal of Applied Physics, 31: 945-949. doi: 10.1063/1.1735780
[12]	Blanter M S, Golovin I S, Neuhauser H, Sinning H. 2010. Internal friction in metallic materials : a handbook. New York: Springer.
[13]	Brook G B, Sully A H. 1955. Some observations on the internal friction of polycrystalline aluminium during the early stages of creep. Acta Metallurgica, 3: 460-469. doi: 10.1016/0001-6160(55)90136-X
[14]	Devine S, Robinson W. 1998. Flexural composite oscillators for the measurement of anelastic and elastic properties of solids at frequencies of 1 to 10 kHz. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 45: 11-22. doi: 10.1109/58.646898
[15]	Fu J, Tan C, Li F. 2015. Quantitative electromechanical impedance method for nondestructive testing based on a piezoelectric bimorph cantilever. Smart Materials and Structures, 24: 065038. doi: 10.1088/0964-1726/24/6/065038
[16]	Golovin I, Sinning H-R, Göken J, Riehemann W. 2004. Fatigue-related damping in some cellular metallic materials. Materials Science and Engineering: A, 370: 537-541. doi: 10.1016/j.msea.2003.08.090
[17]	Granato A V, Lücke K. 1956. Theory of mechanical damping due to dislocations. Journal of Applied Physics, 27: 583-593. doi: 10.1063/1.1722436
[18]	Kê T S. 1947. Stress relaxation across grain boundaries in metals. Physical Review, 72: 41-46. doi: 10.1103/PhysRev.72.41
[19]	Kê T S. 1950. Internal friction of metals at very high temperatures. Journal of Applied Physics, 21: 414-419. doi: 10.1063/1.1699675
[20]	Kê T S, Mehl R F. 1999. Fifty-year study of grain-boundary relaxation. Metallurgical and Materials Transactions A, 30: 2267-2295. doi: 10.1007/s11661-999-0238-y
[21]	Kustov S, Golyandin S, Sapozhnikov K, Van Humbeeck J, De Batist R. 1998. Low-temperature anomalies in Young's modulus and internal friction of Cu–Al–Ni single crystals. Acta Materialia, 46: 5117-5126. doi: 10.1016/S1359-6454(98)00168-2
[22]	Kustov S, Gremaud G, Benoit W, Golyandin S, Sapozhnikov K, Nishino Y, Asano S. 1999. Strain amplitude-dependent anelasticity in Cu–Ni solid solution due to thermally activated and athermal dislocation–point obstacle interactions. Journal of Applied Physics, 85: 1444-1459. doi: 10.1063/1.369276
[23]	Lakes R S. 2004. Viscoelastic measurement techniques. Review of Scientific Instruments, 75: 797-810. doi: 10.1063/1.1651639
[24]	Lee T, Lakes R S, Lal A. 2000. Resonant ultrasound spectroscopy for measurement of mechanical damping: Comparison with broadband viscoelastic spectroscopy. Review of Scientific Instruments, 71: 2855-2861. doi: 10.1063/1.1150703
[25]	Leisure R G, Willis F A. 1997. Resonant ultrasound spectroscopy. Journal of Physics: Condensed Matter, 9: 6001-6029. doi: 10.1088/0953-8984/9/28/002
[26]	Marx J. 1951. Use of the piezoelectric gauge for internal friction measurements. Review of Scientific Instruments, 22: 503-509. doi: 10.1063/1.1745981
[27]	Marx J W, Sivertsen J M. 1953. Temperature dependence of the elastic moduli and internal friction of silica and glass. Journal of Applied Physics, 24: 81-87. doi: 10.1063/1.1721138
[28]	Mason W. 1956. Internal friction and fatigue in metals at large strain amplitudes. The Journal of the Acoustical Society of America, 28: 1207-1218. doi: 10.1121/1.1908595
[29]	Migliori A, Sarrao J L, Visscher W M, Bell T M, Lei M, Fisk Z, Leisure R G. 1993. Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids. Physica B: Condensed Matter, 183: 1-24. doi: 10.1016/0921-4526(93)90048-B
[30]	Ninomiya K, Ferry J D, Ōyanagi Y. 1963. Viscoelastic properties of polyvinyl acetates. II. Creep studies of blends1. The Journal of Physical Chemistry, 67: 2297-2308. doi: 10.1021/j100805a012
[31]	Nowick A S. 2012. Anelastic Relaxation in Crystalline Solids. Amsterdam: Elsevier.
[32]	Nowick A S, Heller W R. 1963. Anelasticity and stress-induced ordering of point defects in crystals. Advances in Physics , 12: 251-298. doi: 10.1080/00018736300101293
[33]	Ogi H, Sato K, Asada T, Hirao M. 2002. Complete mode identification for resonance ultrasound spectroscopy. The Journal of the Acoustical Society of America , 112: 2553-2557. doi: 10.1121/1.1512700
[34]	Ohno I. 1976. Free vibration of a rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystals. Journal of Physics of the Earth , 24: 355-379. doi: 10.4294/jpe1952.24.355
[35]	Periyannan S, Balasubramaniam K. 2015. Simultaneous moduli measurement of elastic materials at elevated temperatures using an ultrasonic waveguide method. Review of Scientific Instruments , 86: 114903. doi: 10.1063/1.4935556
[36]	Press W H, Flannery B P, Teukolsky S A, Vetterling W T. 1986. Numerical Recipes: The Art of Scientific Computing. Cambridge and New York: Cambridge University Press.
[37]	Quimby S L. 1925. On the experimental determination of viscosity of vibrating solids. Physical Review, 25: 558-573.
[38]	Robinson W H, Carpenter S H, Tallon J L. 1974. Piezoelectric method of determining torsional mechanical damping between 40 and 120 kHz. Journal of Applied Physics , 45: 1975-1981. doi: 10.1063/1.1663533
[39]	Robinson W H, Edgar A. 1974. The piezoelectric method of determining mechanical damping at frequencies of 30 to 200 kHz. IEEE Transactions on Sonics and Ultrasonics , 21: 98-105. doi: 10.1109/T-SU.1974.29798
[40]	Roebben G, Bollen B, Brebels A, Van Humbeeck J, Van der Biest O. 1997. Impulse excitation apparatus to measure resonant frequencies, elastic moduli, and internal friction at room and high temperature. Review of Scientific Instruments , 68: 4511-4515. doi: 10.1063/1.1148422
[41]	Rose J L. 1999. Ultrasonic waves in solid media. Cambridge: Cambridge University Press.
[42]	Salje E K, Schranz W. 2011. Low amplitude, low frequency elastic measurements using dynamic mechanical analyzer (DMA) spectroscopy. Zeitschrift für Kristallographie Crystalline Materials, 226: 1-17.
[43]	Sapozhnikov K, Golyandin S, Kustov S, Van Humbeeck J, De Batist R. 2000. Motion of dislocations and interfaces during deformation of martensitic Cu–Al–Ni crystals. Acta Materialia , 48: 1141-1151. doi: 10.1016/S1359-6454(99)00374-2
[44]	Schaller R, Fantozzi G, Gremaud G. 2001. Mechanical spectroscopy Q−1 2001, with applications to materials science. Trans Tech Publications Inc.
[45]	Sternstein S S, Ho T C. 1972. Biaxial stress relaxation in glassy polymers: polymethylmethacrylate. Journal of Applied Physics , 43: 4370-4383. doi: 10.1063/1.1660930
[46]	Sumino Y, Ohno I, Goto T, Kumazawa M. 1976. Measurement of elastic constants and internal frictions on single-crystal MgO by rectangular parallelepiped resonance. Journal of Physics of the Earth , 24: 263-273. doi: 10.4294/jpe1952.24.263
[47]	Sutton P M. 1953. The variation of the elastic constants of crystalline aluminum with temperature between 63k and 773k. Physical Review , 91: 816-821. doi: 10.1103/PhysRev.91.816
[48]	Thompson D O, Holmes D K. 1956. Effects of neutron irradiation upon the Young's modulus and internal friction of copper single crystals. Journal of Applied Physics , 27: 713-723. doi: 10.1063/1.1722471
[49]	Weertman J, Salkovitz E I. 1955. The internal friction of dilute alloys of lead. Acta Metallurgica , 3: 1-9. doi: 10.1016/0001-6160(55)90002-X
[50]	Woirgard J, Sarrazin Y, Chaumet H. 1977. Apparatus for the measurement of internal friction as a function of frequency between 10− 5 and 10 Hz. Review of Scientific Instruments , 48: 1322-1325. doi: 10.1063/1.1134874
[51]	Wolfenden A, Harmouche M R, Blessing G V, Chen Y T, Terranova P, Dayal V, Kinra V K, Lemmens J W, Phillips R R and Smith J S. 1989. Dynamic Young's modulus measurements in metallic materials: results of an interlaboratory testing program. Journal of Testing and Evaluation , 17: 2-13. doi: 10.1520/JTE11527J
[52]	Xie M, Ding G, Jiang M, Li F. 2021. High-frequency elastic moduli and internal frictions of Zr_41.2Ti_{13. 8}Cu1_2. ₅Ni₁₀Be_{22. 5} bulk metallic glass during glass transition and crystallization. Journal of Non-Crystalline Solids , 560: 120754. doi: 10.1016/j.jnoncrysol.2021.120754
[53]	Xie M, Huan Q, Li F. 2020. Quick and repeatable shear modulus measurement based on torsional resonance using a piezoelectric torsional transducer. Ultrasonics , 103: 106101. doi: 10.1016/j.ultras.2020.106101
[54]	Xie M, Li F. 2020a. A modified piezoelectric ultrasonic composite oscillator technique for simultaneous measurement of elastic moduli and internal frictions at varied temperature. Review of Scientific Instruments , 91: 015110. doi: 10.1063/1.5135360
[55]	Xie M, Li F. 2020b. Anomalous elastic moduli and internal frictions in unpoled and poled lead titanate zirconate ceramics near the Curie temperature. AIP Advances , 10: 045007. doi: 10.1063/5.0003808
[56]	Xie M and Li F. 2020c. New method enables multifunctional measurement of elastic moduli and internal frictions. Journal of Applied Physics , 128: 230902. doi: 10.1063/5.0034801
[57]	Zacharias J. 1933. The temperature dependence of Young’s modulus for nickel. Physical Review , 44: 116-122. doi: 10.1103/PhysRev.44.116
[58]	Zener C. 1943. Internal friction in an alpha-brass crystal. Trans. AIME, 152: 122-126.
[59]	Zener C. 1947. Stress induced preferential orientation of pairs of solute atoms in metallic solid solution. Physical Review , 71: 34. doi: 10.1103/PhysRev.71.34
[60]	Zener C. 1948. Elasticity and Anelasticity of Metals. Chicage: University of Chicago Press.