Finite element modeling of grain size effects on the ultrasonic microstructural noise backscattering in polycrystalline materials

Bai, Xue; Tié, Bing; Schmitt, Jean-Hubert; Aubry, Denis

doi:10.1016/j.ultras.2018.02.008

Cited by 28 publications

(14 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As the principle results considered are numerical measures of the attenuation coefficient and of the noise levels of the quasi-longitudinal waves, the finite element size is defined with respect to the shortest quasi-longitudinal wavelength, which is approximately twice the shortest quasi-transverse wavelength (Figure 16). We note that the influence of the finite element size on these numerical measures has been studied in [25,27]. Table II gives the time step used for each material and each solver, and the associated parameters CF L sDG and C tDG−damping .…”

Section: Upwind Numerical Fluxes Applied To Polycrystalline Materialsmentioning

confidence: 99%

See 1 more Smart Citation

A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media

Tié

Mouronval

Nguyen

et al. 2018

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

We present a unified multidimensional variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. Based on an elastic wave oriented formulation and using a tensorial formalism, the proposed framework allows a better understanding of the physical meaning of the terms involved in the discontinuous Galerkin method. The unified variational framework is written for first-order velocity-stress wave equations. An uncoupled upwind numerical flux and two coupled upwind numerical fluxes using respectively the Voigt and the Reuss averages of elastic moduli are defined. Two numerical fluxes that are exact solutions of the Riemann problem on physical interfaces are also developed and analyzed in the 1D case. The implemented solvers are then applied to different elastic media, especially to polycrystalline materials that present a particular case of piecewise homogeneous media. The use of the three upwind numerical fluxes, which only solve approximately the Riemann problem at element interfaces, is investigated.

show abstract

Section: Upwind Numerical Fluxes Applied To Polycrystalline Materialsmentioning

confidence: 99%

“…On the other hand, backscattered noise levels are numerically measured in the time domain for a given frequency f 0 by calculating normalized root-meansquare (rms) noise levels N rms (f 0 ; t) in the following way [25][26][27]:…”

Section: Upwind Numerical Fluxes Applied To Polycrystalline Materialsmentioning

confidence: 99%

A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media

Tié

Mouronval

Nguyen

et al. 2018

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…With respect to each elliptic grain in the polycrystalline case, it corresponds to about 13 elements in the major axis and about 10 element in the minor axis. This choice of element size is based on our previous studies on the mesh convergence of the time dG solver in terms of the attenuation and scattering (noise level) coefficients in the case of polycrystalline materials [21,22]. In particular, it has been shown that the mesh convergence depends not only on the wavelength to element size ratio but also on the grain size to element size ratio.…”

Section: • (4) Heterogeneous Polycrystalline Casementioning

confidence: 99%

Some comparisons and analyses of time or space discontinuous Galerkin methods applied to elastic wave propagation in anisotropic and heterogeneous media

Tié

2019

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

This research work presents some comparisons and analyses of the time discontinuous space-time Galerkin method and the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media. Mechanism of both methods to ensure their stability using time or space discontinuities of unknown fields is analyzed and compared. The most general case of anisotropic and heterogeneous media with physical interfaces of discontinuous material properties is considered, especially for the space discontinuous Galerkin method. A new stability result is proved. Numerical applications to different elastic media, more particularly polycrystalline materials containing a large number of physical interfaces, are also presented to confirm theoretical analyses.

show abstract

“…The scattering-induced attenuation in polycrystalline materials has an important implication of microstructure information [10,16,17] and thus has been extensively applied to the nondestructive characterization of grain microstructures [18,19]. It is worthy to mention that many studies [20][21][22][23] recently emerge on finite element modeling (FEM) of elastic wave attenuation in polycrystals. However, FEM is a numerical method and it has limited practical application to the ultrasonic characterization of grain microstructures.…”

Section: Introductionmentioning

confidence: 99%

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

Guo

2020

Acoustics

View full text Add to dashboard Cite

This study extends the second-order attenuation (SOA) model for elastic waves in texture-free inhomogeneous cubic polycrystalline materials with equiaxed grains to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. In term of this work, one can predict both the scattering-induced attenuation and phase velocity from Rayleigh region (wavelength >> scatter size) to geometric region (wavelength << scatter size) for an arbitrary incident wave mode (quasi-longitudinal, quasi-transverse fast or quasi-transverse slow mode) in a textured polycrystal and examine the impact of crystallographic texture on attenuation and phase velocity dispersion in the whole frequency range. The predicted attenuation results of this work also agree well with the literature on a textured stainless steel polycrystal. Furthermore, an analytical expression for quasi-static phase velocity at an arbitrary wave propagation direction in a textured polycrystal is derived from the SOA model, which can provide an alternative homogenization method for textured polycrystals based on scattering theory. Computational results using triclinic titanium polycrystals with Gaussian orientation distribution function (ODF) are also presented to demonstrate the texture effect on attenuation and phase velocity behaviors and evaluate the applicability and limitation of an existing analytical model based on the Born approximation for textured polycrystals. Finally, quasi-static phase velocities predicted by this work for a textured polycrystalline copper with generalized spherical harmonics form ODF are compared to available velocity bounds in the literature including Hashin–Shtrikman bounds, and a reasonable agreement is found between this work and the literature.

show abstract

Finite element modeling of grain size effects on the ultrasonic microstructural noise backscattering in polycrystalline materials

Cited by 28 publications

References 31 publications

A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media

A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media

Some comparisons and analyses of time or space discontinuous Galerkin methods applied to elastic wave propagation in anisotropic and heterogeneous media

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

Contact Info

Product

Resources

About