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The existing unified theory of ultrasonic scattering can model the attenuation and phase velocity in the frequency domain by using the microstructure and mechanical properties of polycrystalline materials. However, this theory does not consider the influence of grain size distribution, thus degrading the calculation accuracy in the forward modeling. A new unified theory, which is mainly corrected by considering the grain size distribution, is developed. First, the second-order Keller approximation and the full-field Green's function are used to calculate the wave equation of inhomogeneous medium and derive the average wave in the medium, respectively. Second, the method of the truncated lognormal distribution is used to describe the grain size distribution and construct the weighted spatial correlation function. Finally, the new unified theory of ultrasonic scattering is established to reveal the influence of grain distribution on ultrasonic scattering.
Using the new unified model, the effects of the grain distribution widening on the ultrasonic scattering while the average grain size is unchanged, are analyzed for the longitudinal wave and the shear wave. The attenuation increases in the Rayleigh scattering region and the geometric scattering region, while there is less attenuation variation in the stochastic scattering region and two adjacent transition regions. The phase velocity varies strongly in the stochastic-geometric transition region, while the variation is relatively small in other scattering zones. Experiments are conducted by using a 304 stainless steel specimen. The results show that when the grain distribution characteristics are considered, the discrepancy between the longitudinal wave attenuation spectrum and experimental results, and that between the phase velocity spectrum and experimental results are reduced by 49% and 64%, respectively; for the shear wave, these discrepancies are reduced by 12% and 4%, respectively.
From all above aspects, the accuracy of the new model is higher than that of the traditional model. The new unified theory proposed in this paper can effectively correct the discrepancy of the attenuation spectrum and phase velocity spectrum caused by the grain size distribution and provide a theoretical basis for inverse problem of grain distribution. Also, the theory can be extended to materials containing elongated grains, macroscopic texture or multiple phases.[1] Li J, Rokhlin S I 2015 Wave Motion 58 145
[2] Kube C M 2017 J. Acoust. Soc. Am. 141 1804
[3] O'Donnell M, Jaynes E T, Miller J G 1978 J. Acoust. Soc. Am. 63 1935
[4] Mason W P, McSkimin H J 1947 J. Acoust. Soc. Am. 19 464
[5] Mason W P, McSkimin H J 1948 J. Appl. Phys. 19 940
[6] Huntington H B 1950 J. Acoust. Soc. Am. 22 362
[7] Papadakis E P 1965 J. Acoust. Soc. Am. 37 703
[8] Weaver R L 1990 J. Mech. Phys. Solids 38 55
[9] Calvet M, Margerin L 2012 J. Acoust. Soc. Am. 131 1843
[10] Calvet M, Margerin L 2016 Wave Motion 65 29
[11] Stanke F E, Kino G S 1984 J. Acoust. Soc. Am. 75 665
[12] Hirsekorn S 1988 J. Acoust. Soc. Am. 83 1231
[13] Ahmed S, Thompson R B 1992 Nondestr. Test. Eval. 8 525
[14] Sha G, Rokhlin S I 2018 Ultrasonics 88 84
[15] Papadakis E P 1964 J. Appl. Phys. 35 1586
[16] Papadakis E P 1961 J. Acoust. Soc. Am. 33 1616
[17] Nicoletti D, Anderson A 1997 J. Acoust. Soc. Am. 101 686
[18] Smith R L 1982 Ultrasonics 20 211
[19] Ryzy M, Grabec T, Sedlák P, Veres I A 2018 J. Acoust. Soc. Am. 143 219
[20] Arguelles A P, Turner J A 2017 J. Acoust. Soc. Am. 141 4347
[21] Bebu I, Mathew T 2009 Stat. Probabil. Lett. 79 375
[22] Zheng Q, Li J, Huang F 2011 Appl. Math. Comput. 217 9592
[23] Schwartz A J, Kumar M, Adams B L, Field D P 2009 Electron Backscatter Diffraction in Materials Science (Berlin, Heidelberg: Springer) pp53-81
[24] Treiber M, Kim J Y, Jacobs L J, Qu J 2009 J. Acoust. Soc. Am. 125 2946
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[1] Li J, Rokhlin S I 2015 Wave Motion 58 145
[2] Kube C M 2017 J. Acoust. Soc. Am. 141 1804
[3] O'Donnell M, Jaynes E T, Miller J G 1978 J. Acoust. Soc. Am. 63 1935
[4] Mason W P, McSkimin H J 1947 J. Acoust. Soc. Am. 19 464
[5] Mason W P, McSkimin H J 1948 J. Appl. Phys. 19 940
[6] Huntington H B 1950 J. Acoust. Soc. Am. 22 362
[7] Papadakis E P 1965 J. Acoust. Soc. Am. 37 703
[8] Weaver R L 1990 J. Mech. Phys. Solids 38 55
[9] Calvet M, Margerin L 2012 J. Acoust. Soc. Am. 131 1843
[10] Calvet M, Margerin L 2016 Wave Motion 65 29
[11] Stanke F E, Kino G S 1984 J. Acoust. Soc. Am. 75 665
[12] Hirsekorn S 1988 J. Acoust. Soc. Am. 83 1231
[13] Ahmed S, Thompson R B 1992 Nondestr. Test. Eval. 8 525
[14] Sha G, Rokhlin S I 2018 Ultrasonics 88 84
[15] Papadakis E P 1964 J. Appl. Phys. 35 1586
[16] Papadakis E P 1961 J. Acoust. Soc. Am. 33 1616
[17] Nicoletti D, Anderson A 1997 J. Acoust. Soc. Am. 101 686
[18] Smith R L 1982 Ultrasonics 20 211
[19] Ryzy M, Grabec T, Sedlák P, Veres I A 2018 J. Acoust. Soc. Am. 143 219
[20] Arguelles A P, Turner J A 2017 J. Acoust. Soc. Am. 141 4347
[21] Bebu I, Mathew T 2009 Stat. Probabil. Lett. 79 375
[22] Zheng Q, Li J, Huang F 2011 Appl. Math. Comput. 217 9592
[23] Schwartz A J, Kumar M, Adams B L, Field D P 2009 Electron Backscatter Diffraction in Materials Science (Berlin, Heidelberg: Springer) pp53-81
[24] Treiber M, Kim J Y, Jacobs L J, Qu J 2009 J. Acoust. Soc. Am. 125 2946
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