Modeling the scattering-induced attenuation of elastic waves in heterogeneous polycrystals has practical applications in seismology and non-destructive evaluation. However, attenuation modeling for polycrystals with preferred crystallographic orientation (statistically anisotropic or textured polycrystals) has not been well studied. The far-field approximation (FFA) model, which is applicable for arbitrary crystal (triclinic) symmetry and valid for the whole frequency range (Rayleigh region, stochastic regime, and geometric region), has been reported for texture-free polycrystalline materials. This paper extends the FFA model to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. This FFA model for textured polycrystals encompasses two advantages: a simple form of dispersion equation and high computational efficiency. Furthermore, this FFA model can predict both the attenuation and phase velocity of elastic waves in textured polycrystals. The FFA model in this study has also been validated by comparison with the full-wave second-order attenuation model on textured polycrystals of triclinic grains. This work provides a simple and efficient tool to predict the elastic wave behavior in heterogeneous polycrystalline materials.
ThompsonBR. Elastic-wave propagation in random polycrystals: fundamentals and application to nondestructive evaluation. In: FinkMKupermanWAMontagnerJPTourinA (eds) Imaging of complex media with acoustic and seismic waves. Berlin, Germany: Springer, 2002, 233–257.
2.
CalvetMMargerinL.Impact of grain shape on seismic attenuation and phase velocity in cubic polycrystalline materials. Wave Motion2016; 65: 29–43.
3.
Van PamelAShaGLoweMJS, et al. Numerical and analytic modelling of elastodynamic scattering within polycrystalline materials. J Acoust Soc Am2018; 143: 2394–2408.
4.
CalvetMMargerinL.Velocity and attenuation of scalar and elastic waves in random media: a spectral function approach. J Acoust Soc Am2012; 131: 1843.
5.
ThompsonBR.Elastic-wave propagation in random polycrystals: fundamentals and application to nondestructive evaluation. Mater Sci2002; 257: 233–257.
6.
MüllerTMShapiroSA.Seismic scattering attenuation estimates for the German KTB Area derived from well-log statistics. Geophys Res Lett2001; 28: 3761–3764.
7.
LobkisOIYangLLiJ, et al. Ultrasonic backscattering in polycrystals with elongated single phase and duplex microstructures. Ultrasonics2012; 52: 694–705.
8.
KubeCMArguellesAPTurnerJA.Ultrasonic backscatter from elongated grains using line focused ultrasound. Ultrasonics2018; 82: 79–83.
9.
LiXHanXArguellesAP, et al. Evaluating grain size in polycrystals with rough surfaces by corrected ultrasonic attenuation. Ultrasonics2017; 78: 23–29.
10.
PilchakALLiJShaG, et al. A quantitative assessment of microtexture in titanium alloys using destructive and nondestructive methods. Microsc Microanal2014; 20: 1448–1449.
11.
WeaverRL.Diffusivity of ultrasound in polycrystals. J Mech Phys Solids1990; 38: 55–86.
12.
TurnerJA.Elastic wave propagation and scattering in heterogeneous, anisotropic media: textured polycrystalline materials. J Acoust Soc Am1999; 106: 541.
13.
KubeCM.Iterative solution to bulk wave propagation in polycrystalline materials. J Acoust Soc Am2017; 141: 1804–1811.
14.
HirsekornS.The scattering of ultrasonic waves by polycrystals. J Acoust Soc Am1982; 72: 1021–1031.
15.
HirsekornS.Directional dependence of ultrasonic propagation in textured polycrystals. J Acoust Soc Am1986; 79: 1269–1279.
16.
StankeFEKinoGS.A unified theory for elastic wave propagation in polycrystalline materials. J Acoust Soc Am1984; 75: 665.
17.
YangLTurnerJA.Attenuation of ultrasonic waves in rolled metals. J Acoust Soc Am2004; 116: 3319–3327.
18.
AhmedSThompsonRB. Influence of columnar microstructure on ultrasonic backscattering. In: ThompsonDOChimentiDE (eds) Review of progress in quantitative nondestructive evaluation: volume 14. Boston, MA: Springer US, 1995, 1617–1624.
19.
YangLLiJRokhlinSI.Ultrasonic scattering in polycrystals with orientation clusters of orthorhombic crystallites. Wave Motion2013; 50: 1283–1302.
20.
ShaG.Analytical attenuation and scattering models for polycrystals with uniform equiaxed grains. J Acoust Soc Am2018; 143: EL347–353.
21.
ShaGRokhlinSI.Universal scaling of transverse wave attenuation in polycrystals. Ultrasonics2018; 88: 84–96.
22.
DuHTurnerJA.Ultrasonic attenuation in pearlitic steel. Ultrasonics2014; 54: 882–887.
23.
PilchakALLiJRokhlinSI.Quantitative comparison of microtexture in near-alpha titanium measured by ultrasonic scattering and electron backscatter diffraction. Metall Mater Trans A2014; 45: 4679–4697.
24.
RokhlinSILiJShaG.Far-field scattering model for wave propagation in random media. J Acoust Soc Am2015; 137: 2655–2669.
25.
ShaG.A simultaneous non-destructive characterisation method for grain size and single-crystal elastic constants of cubic polycrystals from ultrasonic measurements. Insight Non Destruct Test Cond Monit2018; 60: 190–193.
26.
LiJRokhlinSI.Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries. Wave Motion2015; 58: 145–164.
27.
HirsekornS.The scattering of ultrasonic waves in polycrystalline materials with texture. J Acoust Soc Am1985; 77: 832–843.
28.
BaiXTieBSchmittJ, et al. Numerical modeling of grain size effect on the ultrasonic propagation in polycrystalline materials. Ultrasonics2018; 87: 18–21.
29.
RyzyMGrabecTSedlákP, et al. Influence of grain morphology on ultrasonic wave attenuation in polycrystalline media with statistically equiaxed grains. J Acoust Soc Am2018; 143: 219–229.
30.
KocksUFToméCNWenkHR. Texture and anisotropy: preferred orientations in polycrystals and their effect on materials properties. Cambridge, UK: Cambridge University Press, 2005, 1–676.
31.
HuangM.The n-point orientation correlation function and its application. Int J Solids Struct2005; 42: 1425–1441.
RoeRJ. Description of crystallite orientation in polycrystalline materials. III. General solution to pole figure inversion. J Appl Phys1965; 36: 2024–2031.
LiJRokhlinSI.Elastic wave scattering in random anisotropic solids. Int J Solids Struct2016; 78–79: 110–124.
36.
BungeHJEslingCBechler-FerryE.Three-dimensional texture analysis after Bunge and Roe: correspondence between the respective mathematical techniques. Textures Microstruct1982; 5: 95–125.
37.
ChoJHRollettADOhKH.Determination of volume fractions of texture components with standard distributions in Euler space. Metall Mater Trans A Phys Metall Mater Sci2004; 35: 1075–1086.
38.
HuangMManCS.Explicit bounds of effective stiffness tensors for textured aggregates of cubic crystallites. Math Mech Solids2008; 13: 408–430.
39.
MatthiesS.Some remarks on theoretical developments in quantitative texture analysis and on the optimal calculation of harmonic quantities with high precision. Textures Microstruct1988; 8: 115–129.
40.
LiJYangLRokhlinSI.Effect of texture and grain shape on ultrasonic backscattering in polycrystals. Ultrasonics2014; 54: 1789–1803.
41.
YangLRokhlinSI.Ultrasonic backscattering in cubic polycrystals with ellipsoidal grains and texture. J Nondestruct Eval2013; 32: 142–155.
42.
ShaG.Explicit backscattering coefficient for ultrasonic wave propagating in hexagonal polycrystals with fiber texture. J Nondestruct Eval2018; 37: 37–51.
43.
XuPHarjoSItoT, et al. Progress in bulk texture measurement using neutron diffraction. In: Proceedings of the 2nd International Symposium on Science J-PARC — Unlocking Mysteries of Life, Matter and the Universe, 2015.
44.
AdamsBL.Orientation imaging microscopy: emerging and future applications. Ultramicroscopy1997; 67: 11–17.
45.
HanYKThompsonRB.Ultrasonic backscattering in duplex microstructures: theory and application to titanium alloys. Metall Mater Trans A1997; 28: 91–104.
46.
AhmedSThompsonRBPanettaPD.Ultrasonic attenuation as influenced by elongated grains. Rev Quant Nondestruct Eval2003; 22: 109–116.
47.
GhoshalGTurnerJAWeaverRL.Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids. J Acoust Soc Am2007; 122: 2009–2021.
48.
AhmedSThompsonRB.Attenuation of ultrasonic waves in cubic metals having elongated, oriented grains. Nondestruct Test Eval1992; 8–9: 525–531.
49.
StankeFE.Spatial autocorrelation functions for calculations of effective propagation constants in polycrystalline materials. J Acoust Soc Am1986; 80: 1479–1485.
50.
Van PamelAShaGRokhlinSI, et al. Finite-element modelling of elastic wave propagation and scattering within heterogeneous media. Proc R Soc A2017; 473: 20160738.
51.
RokhlinSIChimentiDENagyPB. Physical ultrasonics of composites. New York, USA: Oxford University Press, 2011, 1–378.
52.
YangLLobkisOIRokhlinSI.An integrated model for ultrasonic wave propagation and scattering in a polycrystalline medium with elongated hexagonal grains. Wave Motion2012; 49: 544–560.
53.
KaralFCKellerJB.Elastic, electromagnetic, and other waves in a random medium. J Math Phys1964; 5: 537.
54.
WangCYAchenbachJD.Three-dimensional time-harmonic elastodynamic Green’s functions for anisotropic solids. Proc R Soc London Ser A Math Phys Sci1995; 449: 441–458.
55.
WangCYAchenbachJD.A new method to obtain 3-D Green’s functions for anisotropic solids. Wave Motion1993; 18: 273–289.
56.
TingTCTLeeVG.The three-dimensional elastostatic Green’s function for general anisotropic linear elastic solids. Q J Mech Appl Math1997; 50: 407–426.
57.
LiJ.Ultrasonic characterization of polycrystals with texture and microtexture: theory and experiment. Columbus, Ohio: Ohio State University, 2014.
58.
YangLRokhlinSI.On comparison of experiment and theory for ultrasonic attenuation in polycrystalline niobium. J Nondestruct Eval2012; 31: 77–79.
59.
RyzyMGrabecTÖsterreicherJA, et al. Measurement of coherent surface acoustic wave attenuation in polycrystalline aluminum attenuation in polycrystalline aluminum. AIP Adv2018; 8: 125019.
