Three-dimensional off-lattice model for the interface growth of polycrystalline materials

1999 ◽  
Vol 59 (11) ◽  
pp. 7354-7357 ◽  
Author(s):  
E. V. Albano ◽  
R. C. Salvarezza ◽  
L. Vázquez ◽  
A. J. Arvia
Keyword(s):  
Lattice Model ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Interface Growth

scholarly journals Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

2013 ◽  
Vol 05 (01) ◽  
pp. 1350002 ◽  
Author(s):  
I. Benedetti ◽  
F. Barbe
Keyword(s):  
Three Dimensional ◽  
Constitutive Modelling ◽  
Polycrystalline Materials ◽  
High Fidelity ◽  
Computational Capability ◽  
Mechanical Models ◽  
Three Dimensional Models ◽  
The Individual ◽  
Individual Grains ◽  
Micro Structures

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material micro-structures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to two-dimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.

Combining Serial Sectioning, EBSD Analysis, and Image-Based Finite Element Modeling

MRS Bulletin ◽  
2008 ◽  
Vol 33 (6) ◽  
pp. 597-602 ◽  
Author(s):  
G. Spanos ◽  
D.J. Rowenhorst ◽  
A.C. Lewis ◽  
A.B. Geltmacher
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Electron Backscatter Diffraction ◽  
Three Dimensional ◽  
Research Area ◽  
Polycrystalline Materials ◽  
Serial Sectioning ◽  
3D Fem ◽  
Element Modeling ◽  
The Status

AbstractThis article first provides a brief review of the status of the subfield of three-dimensional (3D) materials analyses that combine serial sectioning, electron backscatter diffraction (EBSD), and finite element modeling (FEM) of materials microstructures, with emphasis on initial investigations and how they led to the current state of this research area. The discussions focus on studies of the mechanical properties of polycrystalline materials where 3D reconstructions of the microstructure—including crystallographic orientation information—are used as input into image-based 3D FEM simulations. The authors' recent work on a β-stabilized Ti alloy is utilized for specific examples to illustrate the capabilities of these experimental and modeling techniques, the challenges and the solutions associated with these methods, and the types of results and analyses that can be obtained by the close integration of experiments and simulations.

Three-dimensional reciprocal lattice model

1976 ◽  
Vol 9 (6) ◽  
pp. 510-510
Author(s):  
L. Bretherton ◽  
C. H. L. Kennard
Keyword(s):  
Lattice Model ◽  
Reciprocal Lattice ◽  
Three Dimensional

scholarly journals Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations

2012 ◽  
Author(s):  
Kaliappan Jayabal ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Three Dimensional ◽  
Specific Property ◽  
Voronoi Cell ◽  
Polycrystalline Materials ◽  
Element Formulation ◽  
Hybrid Finite Element ◽  
Grain Structures ◽  
Polygonal Elements

Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples.

scholarly journals Reconstructing intragranular strain fields in polycrystalline materials from scanning 3DXRD data

2020 ◽  
Vol 53 (2) ◽  
pp. 314-325 ◽  
Author(s):  
N. Axel Henningsson ◽  
Stephen A. Hall ◽  
Jonathan P. Wright ◽  
Johan Hektor
Keyword(s):  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Reconstruction Method ◽  
X Ray Diffraction ◽  
Reconstruction Accuracy ◽  
Strain Fields ◽  
Spatial Properties ◽  
Reconstruction Methods ◽  
Reconstruction Quality ◽  
Made In

Two methods for reconstructing intragranular strain fields are developed for scanning three-dimensional X-ray diffraction (3DXRD). The methods are compared with a third approach where voxels are reconstructed independently of their neighbours [Hayashi, Setoyama & Seno (2017). Mater. Sci. Forum, 905, 157–164]. The 3D strain field of a tin grain, located within a sample of approximately 70 grains, is analysed and compared across reconstruction methods. Implicit assumptions of sub-problem independence, made in the independent voxel reconstruction method, are demonstrated to introduce bias and reduce reconstruction accuracy. It is verified that the two proposed methods remedy these problems by taking the spatial properties of the inverse problem into account. Improvements in reconstruction quality achieved by the two proposed methods are further supported by reconstructions using synthetic diffraction data.

COMPUTATIONAL HOMOGENIZATION OF POLYCRYSTALLINE MATERIALS WITH PORES: A THREE-DIMENSIONAL GRAIN BOUNDARY FORMULATION

2012 ◽  
Vol 04 (03) ◽  
pp. 1250012 ◽  
Author(s):  
F. TRENTACOSTE ◽  
I. BENEDETTI ◽  
M. H. ALIABADI
Keyword(s):  
Grain Boundary ◽  
Mechanical Model ◽  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Elastic Problem ◽  
Polycrystalline Materials ◽  
Effective Material Properties ◽  
Boundary Integral Representation

In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a 3D grain boundary micro mechanical model. The volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The formulation is built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi Tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are obtained through material homogenization, computing the volume averages of micro-strains and stresses and taking the ensemble average over a certain number of microstructural samples. The obtained results show the capability of the model to assess the macroscopic effects of porosity.

High Resolution Synchrotron X-Ray Diffraction Tomography Of Large-Grained Samples

1996 ◽  
Vol 437 ◽  
Author(s):  
D.P. Piotrowski ◽  
S.R. Stock ◽  
A. Guvenilir ◽  
J.D. Haase ◽  
Z.U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Dimensional Distribution

AbstractIn order to understand the macroscopic response of polycrystalline structural materials to loading, it is frequently essential to know the spatial distribution of strain as well as the variation of micro-texture on the scale of 100 μm. The methods must be nondestructive, however, if the three-dimensional evolution of strain is to be studied. This paper describes an approach to high resolution synchrotron x-ray diffraction tomography of polycrystalline materials. Results from model samples of randomly-packed, millimeter-sized pieces of Si wafers and of similarly sized single-crystal Al blocks have been obtained which indicate that polychromatic beams collimated to 30 μm diameter can be used to determine the depth of diffracting volume elements within ± 70 μm. The variation in the two-dimensional distribution of diffracted intensity with changing sample to detector separation is recorded on image storage plates and used to infer the depth of diffracting volume elements.

scholarly journals Maximum a posteriori estimation of crystallographic phases in X-ray diffraction tomography

2015 ◽  
Vol 373 (2043) ◽  
pp. 20140392 ◽  
Author(s):  
Doĝa Gürsoy ◽  
Tekin Biçer ◽  
Jonathan D. Almer ◽  
Raj Kettimuthu ◽  
Stuart R. Stock ◽  
...  
Keyword(s):  
National Laboratory ◽  
Spinous Process ◽  
Argonne National Laboratory ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Reconstruction Method ◽  
Diffraction Tomography ◽  
A Posteriori ◽  
X Ray Diffraction ◽  
X Ray

A maximum a posteriori approach is proposed for X-ray diffraction tomography for reconstructing three-dimensional spatial distribution of crystallographic phases and orientations of polycrystalline materials. The approach maximizes the a posteriori density which includes a Poisson log-likelihood and an a priori term that reinforces expected solution properties such as smoothness or local continuity. The reconstruction method is validated with experimental data acquired from a section of the spinous process of a porcine vertebra collected at the 1-ID-C beamline of the Advanced Photon Source, at Argonne National Laboratory. The reconstruction results show significant improvement in the reduction of aliasing and streaking artefacts, and improved robustness to noise and undersampling compared to conventional analytical inversion approaches. The approach has the potential to reduce data acquisition times, and significantly improve beamtime efficiency.

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