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Proceedings ArticleDOI

Voronoi based microstructure modelling for elastic wave propagation

10 Feb 2016-Vol. 1706, Iss: 1, pp 070013
Abstract: Ultrasonic assessment of materials and defects are affected by microstructural parameters like grain size and texture. When a beam of ultrasound propagates in a polycrystalline medium, it undergoes extensive scattering by grains, grain boundaries and other microstructural features such as dislocations, voids, micro cracks etc. To understand the role of anisotropy and grain size distribution on an ultrasonic beam, a model system is proposed for carrying out ultrasonic wave propagation in a model characterized by grain size distribution and grain orientation distribution. A 2D polycrystalline medium constructed using Voronoi tessellations with a specific grain size distribution is considered and orientational averaging studies are carried out.
Topics: Grain boundary strengthening (66%), Grain boundary (64%), Grain size (57%), Crystallite (54%), Texture (crystalline) (53%)
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TL;DR: The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.
Abstract: The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.

40 citations

Journal ArticleDOI
01 Jan 2021-Materials & Design
Abstract: Describing dynamic recrystallisation is challenging with existing material characterisation tools, which are typically based on grain boundary character distribution. This is one barrier to further developments in grain boundary engineering. We consider the network of triple junctions in copper alloys as the sub-structure that governs continuous dynamic recrystallisation and propose one descriptor of this sub-structure, referred to as the structural entropy. With the limited available characterisation data we demonstrate that the proposed descriptor correlates well with the evolution of the microstructure during severe plastic deformation. Importantly, our descriptor allows for elucidating micro-localisation features in copper alloys observed in some recent experiments.

2 citations

Journal ArticleDOI
Abstract: Ultrasonic wave propagation through polycrystalline media results in scattering caused by the anisotropy of single grains and randomness in the orientation of the individual grains making up the polycrystal. Scattering leads to variation in phase velocity and beam skewing of elastic waves leading to a loss in energy of the forward propagating wave, significantly affecting the ability to perform material characterization, defect detection and sizing in structural components. The present work addresses the problem of beam skewing of ultrasonic longitudinal waves using FEM-based wave propagation studies in a simulated polycrystal. A well-established Voronoi tessellation algorithm is used to represent an equiaxed polycrystalline morphology. Numerical simulations are performed on beam skewing in both weak (Aluminum) and strong (Copper) anisotropic media as a function of beam launch angles. The effect of a small number of large grains and a large number of small grains on the beam quality is described. The effective refraction in polycrystals is quantified with respect to the corresponding reference isotropic media and the implications for various applications are discussed.

1 citations

Journal ArticleDOI
Abstract: The present article addresses the development at Centre for Non-destructive Evaluation, Indian Institute of Technology Madras, of three different numerical methods, namely finite element, ray tracing and finite-difference time-domain methods for investigating the propagation of ultrasonic waves through polycrystalline media. These methods are believed to aid in better understanding of ultrasonic wave interaction in materials exhibiting both simple and complex grain morphologies. The understanding is expected to provide an improved non-destructive assessment of material and defect characterisation.

1 citations

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01 Jan 1973-
Abstract: This work, part of a two-volume set, applies the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators). The text also covers topics such as perturbation and variational methods.

5,209 citations

Journal ArticleDOI
01 Dec 1974-Geophysics
Abstract: two methods rapidly deteriorates. This effect, known as “grid dispersion,” must be taken into account in order to avoid erroneous interpretation of seismograms obtained by finite-difference techniques. Both seconti-order accuracy and fourth-order accuracy finite-difference algorithms are considered. For the second-order scheme, a good rule of thumb is that the ratio of the upper half-power wavelength of the source to the grid interval should be of the order of ten or more. For the fourth-order scheme, it is found that the grid can be twice as coarse (five or more grid points per upper half-power wavelength) and good results are still obtained. Analytical predictions of the effect of grid dispersion are presented; these seem to be in agreement with the experimental results. ence methods to that obtained by classical analytical methods for the simple case of an infinite twodimensional wedge (quarter space) in an otherwise infinite homogeneous medium. The source field was that due to a line source distribution located parallel to the corner of the wedge (see Figure I). For analytical simplicity, the acoustic velocity of the wedge medium is taken to be zero. This is equivalent to having a perfectlj “soft” wedge medium such as a vacuum.

604 citations

01 Jan 1998-

311 citations

Journal ArticleDOI
Abstract: In this paper, a Voronoi Cell finite element method is developed to solve small deformation elastic-plasticity problems for arbitrary heterogenous materials. Dirichlet Tessellation of microstructural representative materials results in a network of arbitrary-sided polygons called Voronoi cells. Each Voronoi cell encompasses one second phase heterogeneity at most. These are natural elements for the microstructure, representing the basic structural elements of the material. In this paper, formulations are developed for directly considering Voronoi cells as elements in a finite element model without any further dissection. Furthermore, a composite Voronoi Cell finite element method is developed to account for the presence of the second phase within each polygonal element. Various numerical elastic-plastic examples are executed for validating the effectiveness of this formulation. Finally, studies are conducted to understand the effect of size, shape and distribution of second phase on the averaged and true local responses of representative material elements.

225 citations

Journal ArticleDOI
01 May 1988-Geophysics
Abstract: When finite‐difference methods are used to solve the elastic wave equation in a discontinuous medium, the error has two dominant components. Dispersive errors lead to artificial wave trains. Errors from interfaces lead to circular wavefronts emanating from each location where the interface appears “jagged” to the rectangular grid. The pseudospectral method can be viewed as the limit of finite differences with infinite order of accuracy. With this method, dispersive errors are essentially eliminated. The mappings introduced in this paper also eliminate the other dominant error source. Test calculations confirm that these mappings significantly enhance the already highly competitive pseudospectral method with only a very small additional cost. Although the mapping method is described here in connection with the pseudospectral method, it can also be used with high‐order finite‐difference approximations.

188 citations

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