Modeling and simulation of ultrasonic beam skewing in polycrystalline materials

Shivaprasad, S. M.; Krishnamurthy, C. V.; Balasubramaniam, Krishnan

doi:10.1007/s12572-018-0209-x

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…This resemblance is not coincidental; grains would form a perfect Voronoi diagram under the highly idealised cooling conditions where a molten metal starts solidifying from several points (the Voronoi generators) at exactly the same time and solidifies at exactly the same rate in every direction. Consequently, it is common to model grains as Voronoi cells 24‐27 . The typical grain size in steels is smaller than the wavelength of ultrasound, and so in this paper, we use the term grain somewhat imprecisely to mean an averaged grain cluster of a size that can be resolved by ultrasound waves.…”

Section: Derivation Of the Inverse Problemsmentioning

confidence: 99%

An inverse problem for Voronoi diagrams: A simplified model of non‐destructive testing with ultrasonic arrays

Bourne

Mulholland

Sahu

et al. 2020

Math Methods in App Sciences

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In this paper, we study the inverse problem of recovering the spatially varying material properties of a solid polycrystalline object from ultrasonic travel time measurements taken between pairs of points lying on the domain boundary. We consider a medium of constant density in which the orientation of the material's lattice structure varies in a piecewise constant manner, generating locally anisotropic regions in which the wave speed varies according to the incident wave direction and the material's known slowness curve. This particular problem is inspired by current challenges faced by the ultrasonic non‐destructive testing of polycrystalline solids. We model the geometry of the material using Voronoi tessellations and study two simplified inverse problems where we ignore wave refraction. In the first problem, the Voronoi geometry itself and the orientations associated to each region are unknowns. We solve this nonsmooth, nonconvex optimisation problem using a multistart non‐linear least squares method. Good reconstructions are achieved, but the method is shown to be sensitive to the addition of noise. The second problem considers the reconstruction of the orientations on a fixed square mesh. This is a smooth optimisation problem but with a much larger number of degrees of freedom. We prove that the orientations can be determined uniquely given enough boundary measurements and provide a numerical method that is more stable with respect to the addition of noise.

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Section: Derivation Of the Inverse Problemsmentioning

confidence: 99%

An inverse problem for Voronoi diagrams: A simplified model of non‐destructive testing with ultrasonic arrays

Bourne

Mulholland

Sahu

et al. 2020

Math Methods in App Sciences

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show abstract

“…The mechanical properties of ECF are intimately linked to its microstructural features, including grain size, grain morphology, twin, the size of grain boundaries, and the preferential orientation of crystal planes. − In polycrystalline materials, each grain exhibits a distinct crystal orientation and these orientations are randomly distributed. , However, in certain specific cases, due to the different growth rates of each crystal plane, the grains will be arranged to some extent according to certain specific orientations, exhibiting a phenomenon of preferred orientation of crystal planes at the macroscopic level, and it is called texture. , Copper possesses a face-centered cubic structure (FCC), and the prevalent textures in ECFs are (111), (100), and (110). Numerous studies reveal a connection between the mechanical properties of ECF and texture, but theoretical research regarding the intrinsic correlation between texture and mechanical properties is noticeably scarce. − …”

Section: Introductionmentioning

confidence: 99%

“…10−12 In polycrystalline materials, each grain exhibits a distinct crystal orientation and these orientations are randomly distributed. 13,14 However, in certain specific cases, due to the different growth rates of each crystal plane, the grains will be arranged to some extent according to certain specific orientations, exhibiting a phenomenon of preferred orientation of crystal planes at the macroscopic level, and it is called texture. 15,16 Copper possesses a face-centered cubic structure (FCC), and the prevalent textures in ECFs are (111), (100), and (110).…”

Section: Introductionmentioning

confidence: 99%

Relationship between the Orientation of the (100) Crystal Plane and Elongation in Ultrathin Electrolytic Copper Foils

Fan,

Hu,

et al. 2024

J. Phys. Chem. C

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Electrolytic copper foils (ECFs), owing to their excellent mechanical properties and conductivity, have become an indispensable component as an anodic current collector in lithiumion batteries. ECFs often show texture properties, but the intrinsic relationship between the texture and mechanical properties is rarely reported. The authors find a conspicuous preference for the (100) crystal plane in 6 and 8 μm ultrathin ECFs with high elongation. And certain ECFs even exhibit a positive correlation trend between elongation and the (100) relative texture coefficient. It can be inferred that enhancing the (100) texture contributes to the improvement of the elongation in ECFs. Moreover, the Schmid factor values for the ( 111), (100), and ( 110) planes are calculated. The results revealed that the number of slip systems that can be activated under different tensile directions of the (100) plane is the largest, while the number of (110) plane is the least. It implies that under equivalent conditions, ECFs with (100) plane orientation are more prone to undergo plastic deformation, thereby facilitating high elongation. In contrast, the (110) plane orientation contributes to a high tensile strength.

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“…More recently, the granular microstructure of polycrystalline materials is modeled by spatial tessellations [14][15][16][17][18][19][20][21]. Ultrasonic wave propagation is simulated in extruded 2D [22] or just 2D [23] tessellations only, even in rather recent publications. Ryzy et al [24] and Van Pamel et al [25][26][27] simulate ultrasonic wave propagation in truly 3D structures.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures

Dobrovolskij

Schladitz

2022

Acoustics

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Ultrasonic testing of polycrystalline media relies heavily on simulation of the expected signals in order to detect and correctly interpret deviations due to defects. Many effects disturb ultrasonic waves propagating in polycrystalline media. One of them is scattering due to the granular microstructure of the polycrystal. The thus arising so-called microstructural noise changes with grain size distribution and testing frequency. Here, a method for simulating this noise is introduced. We geometrically model the granular microstructure to determine its influence on the backscattered ultrasonic signal. To this end, we utilize Laguerre tessellations generated by random sphere packings dividing space into convex polytopes—the cells. The cells represent grains in a real polycrystal. Cells are characterized by their volume and act as single scatterers. We compute scattering coefficients cellwise by the Born approximation. We then combine the Generalized Point Source Superposition technique with the backscattered contributions resulting from the cell structure to compute the backscattered ultrasonic signal. Applying this new methodology, we compute the backscattered signals in a pulse-echo experiment for a coarse grain cubic crystallized Inconel-617 and a fine grain hexagonal crystallized titanium. Fitting random Laguerre tessellations to the observed grain structure allows for simulating within multiple realizations of the proposed model and thus to study the variation of the backscattered signal due to microstructural variation.

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Modeling and simulation of ultrasonic beam skewing in polycrystalline materials

Cited by 6 publications

References 27 publications

An inverse problem for Voronoi diagrams: A simplified model of non‐destructive testing with ultrasonic arrays

An inverse problem for Voronoi diagrams: A simplified model of non‐destructive testing with ultrasonic arrays

Relationship between the Orientation of the (100) Crystal Plane and Elongation in Ultrathin Electrolytic Copper Foils

Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures

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