Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications

He, Huijing

doi:10.48550/arxiv.1706.09137

Cited by 2 publications

(11 citation statements)

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“…(5) Following the standard procedure as comprehensively presented in [51], we obtain the integral representation of the perturbed field, i.e., the displacement and strain Green's functions of the polycrystalline material composed of an infinite number of randomly oriented crystallites, as follows: Green's function of the homogeneous reference medium and its derivatives. For the convenience of subsequent discussion, we rewrite Eq.…”

Section: Theoretical Fundamentalsmentioning

confidence: 99%

“…As rigorously analyzed in [51], the integral in the second term on the righthand side of Eq. ( 7) has δ singularities due to the second order derivative of the homogeneous Green's function.…”

Section: Theoretical Fundamentalsmentioning

confidence: 99%

“…( 7) has δ singularities due to the second order derivative of the homogeneous Green's function. By introducing the concept of shape-dependent principal value [51], the correct definition of the matrix D is given by: :…”

Section: Theoretical Fundamentalsmentioning

confidence: 99%

“…Similar to the elastic stiffness fluctuation δcij, the renormalized elastic variable Ξpq is also dependent on the orientation of each grain, i.e., it is a function of the Euler angles. The governing equation for the resemble average of the stochastic variable, i.e., the coherent response of the scattered field, can be obtained using the Feynman diagram technique, for which the general procedure is presented in the author's previous work [51]. If further invoking the first-order-smoothing approximation [44,51,[53][54], then we obtain Dyson's equation:…”

Section: Theoretical Fundamentalsmentioning

confidence: 99%

“…In this work, the author strives to develop a universal multiple scattering theory for polycrystalline materials with general anisotropic crystallites, regardless of whether the grains are weakly anisotropic. Following the new paradigm created in the previous work [51], the renormalized Dyson's equation for polycrystalline materials are derived in Section II, by using the Fourier transform technique, the closed form solution of the coherent wave field in spacetime is obtained. Meanwhile the dispersion equation for the longitudinal and transverse coherent waves are derived.…”

Section: Introductionmentioning

confidence: 99%

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Multiple Scattering Theory for Polycrystalline Materials with Strong Grain Anisotropy: Theoretical Fundamentals and Applications

He¹

2019

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This work is a natural extension of the author's previous work: "Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications" (arXiv:1706.09137 [physics.geo-ph]), which established the foundation for developing multiple scattering model for heterogeneous elastic continua with either weak or strong fluctuations in mass density and elastic stiffness. Polycrystalline material is another type of heterogeneous materials that widely exists in nature and extensively used in industry. In this work, the corresponding multiple scattering theory for polycrystalline materials with randomly oriented anisotropic crystallites is developed. To validate the theory, the theoretical results for a series of materials such as OFHC copper, 304 stainless steel, and Inconel 600 are compared to experimental measurements and the numerical results obtained using finite element simulations. Detailed analysis shows that the new theory is capable of predicting the dispersion and attenuation of polycrystals with satisfactory accuracy. The results also show the new model can give an estimate on the average grain size with a relative error equal to or less than ten percent. As applications in ultrasonic nondestructive evaluation, we calculated the dispersion and attenuation coefficient of one of the most important polycrystalline materials in aeronautics engineering: high-temperature titanium alloys. The effects of grain symmetry, grain size, and alloying elements on the dispersion and attenuation behaviors are examined. Key information is obtained which has significant implications for quantitatively evaluating the average grain size, monitoring the phase transition, and even estimating gradual change in chemical composition of titanium components in gas turbine engines. For applications in seismology, the velocities and Q-factors for both hexagonal and cubic polycrystalline iron models for the Earth's uppermost inner core are obtained in the whole frequency range. Using the realistic material parameters of iron under the high temperature and high-pressure conditions calculated from ab initio simulations, the numerical results show that the Q-factors range from 0.001 to 0.05, which shows good agreement with that inferred from real seismic data. The new model predicts the velocity of longitudinal waves varies between ± 1% to ± 5 % relative to the Voight average velocity, while the velocity of transverse waves varies from ± 10% to ± 20%, which gives promising explanation to the abnormally slow transverse velocity observed in practical measurements. The numerical results support the conjecture that the Earth's uppermost inner core is a solid polycrystalline medium. The comprehensive numerical examples show the new model is capable of capturing the most important scattering features of both ultrasonic and seismic waves with satisfactory accuracy. This work provides a universal, quantitative model for characterization of a large variety of polycrystalline materials. It als...

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Section: Theoretical Fundamentalsmentioning

confidence: 99%

Section: Theoretical Fundamentalsmentioning

confidence: 99%

Section: Theoretical Fundamentalsmentioning

confidence: 99%