Estimation of effective thermal conductivity tensor from composite microstructure images

Thomas, Matthieu; Boyard, Nicolas; Jarny, Y.; Delaunay, Didier

doi:10.1088/1742-6596/135/1/012097

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…For a set of zero-volume points, the conventional Delaunay triangulation is the set of connections between points such that no point lies inside the circumcircle of any other triangle (Lee & Lin, 1986). It is used extensively in a wide array of applications where spatial relationships between zero-volume points are desired, such as metallurgy (Bertram & Wendrock, 1996), thermal analysis, (Thomas et al, 2008), biology (Wen et al, 2009), and circuit design (Wu et al, 2008).…”

Section: Figmentioning

confidence: 99%

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

Carson

Levine

2016

Journal of Microscopy

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The concept of a finite body Dirichlet tessellation has been extended to that of a finite body Delaunay 'triangulation' to provide a more meaningful description of the spatial distribution of nonspherical secondary phase bodies in 2- and 3-dimensional images. A finite body triangulation (FBT) consists of a network of minimum edge-to-edge distances between adjacent objects in a microstructure. From this is also obtained the characteristic object chords formed by the intersection of the object boundary with the finite body tessellation. These two sets of distances form the basis of a parsimonious homogeneity estimation. The characteristics of the spatial distribution are then evaluated with respect to the distances between objects and the distances within them. Quantitative analysis shows that more physically representative distributions can be obtained by selecting subgraphs, such as the relative neighbourhood graph and the minimum spanning tree, from the finite body tessellation. To demonstrate their potential, we apply these methods to 3-dimensional X-ray computed tomographic images of foamed cement and their 2-dimensional cross sections. The Python computer code used to estimate the FBT is made available. Other applications for the algorithm - such as porous media transport and crack-tip propagation - are also discussed.

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Section: Figmentioning

confidence: 99%

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

Carson

Levine

2016

Journal of Microscopy

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“…Source: Thomas et al, 2008. Where E fiber is the modulus of reinforcement, E matrix is the matrix modulus, V fiber is the volume fraction of fibers, V matrix is the volume fraction of matrix.…”

Section: (A) (B)mentioning

confidence: 99%

“…However, because of the differences in the thermal expansivities of the phases (fiber and matrix), a state of micro-stress often exists between them, influencing the thermal expansion behavior of the body and giving rise to discrepancies. Thus, its thermal expansion coefficient does not follow the rule of mixtures (Thomas et al, 2008;Mukerji, 1993). Karadeniz and Kumlutas (2007) investigated the existing theories for prediction of coefficient of thermal expansion based on micromechanics and finite element analysis, considering the fiber volume fraction ranging from 10 to 90% for the studied composites (Mukerji, 1993).…”

Section: (8)mentioning

confidence: 99%

Modeling elastic and thermal properties of 2.5D carbon fiber C/SiC hybrid matrix composites by homogenization method

Pardini¹,

Gregori²

2010

JATM

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Advanced carbon fiber hybrid carbon-ceramic matrix composites are realizing their potential in many thermostructural components for aerospace vehicles. This work presents ab-initio predictions of elastic constants and thermal properties for 2.5D carbon fiber reinforced carbon-silicon carbide hybrid matrix composites, by using the homogenization technique. The homogenization technique takes properties of individual components of the composites (fiber and matrix) and characteristics of the geometrical architecture of the preform to perform calculations. Ab-initio modeling of mechanical and thermal properties is very attractive, especially during the material development stage, when larger samples may be prohibitively expensive or impossible to fabricate. Modeling is also useful when bigger samples would be prohibitively expensive or impractical. Thermostructural composites made of 2.5D preforms are easy to manufacture in relation to 3D preforms. Besides, 2.5D preforms are also resistant to thermo cycling and have high resistance to crack propagation in relation to ply stacked composites such as unidirectional (1D) and bidirectional (2D) structures. The calculations were performed by setting an overall carbon fiber volume fraction at 40, 45 and 50 for a 2D stacked composite, and volume fraction in Z-direction of 2, 4 and 6.

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“…Thomas et al . [] developed a new computational model to estimate the 2‐D effective thermal conductivity tensor and its main axes of a heterogeneous composite. In this model, the microstructure of a composite is described as a two‐phase medium composed of a matrix and elliptical or circular inclusions distributed within the matrix.…”

Section: Introductionmentioning

confidence: 99%

Effective thermal conductivity of heterogeneous rocks from laboratory experiments and numerical modeling

et al. 2013

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[1] Studying heat transfer processes in sedimentary crustal rocks requires the correct thermal conductivity of the respective rock type. Often a single value is used for a given rock type, obtained from the measurements on homogenous samples. We demonstrate how variations in rock layering and microfractures on the subcentimeter scale may influence thermal conductivity values at much larger scale. We obtain thermal conductivity images from lab measurements on two different, heterogeneous samples performed with an optical thermal conductivity scanner in two directions. We study different spatial averaging methods for parameterizing the structural heterogeneities and the associated variation of thermal conductivity within the samples. For each of these structural simplifications, we set up a numerical model for a numerical heat transfer experiment in order to determine effective thermal conductivity values in two directions. We compare these values and the mean thermal conductivities obtained from different mixing laws and find that, in heterogeneous rocks, effective and mean thermal conductivity may differ substantially. This may cause significant errors in reservoir-scale simulations of heat transfer with associated severe consequences for estimated heat flow and temperatures.Citation: Jorand, R., C. Vogt, G. Marquart, and C. Clauser (2013), Effective thermal conductivity of heterogeneous rocks from laboratory experiments and numerical modeling,

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Estimation of effective thermal conductivity tensor from composite microstructure images

Cited by 5 publications

References 16 publications

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

Modeling elastic and thermal properties of 2.5D carbon fiber C/SiC hybrid matrix composites by homogenization method

Effective thermal conductivity of heterogeneous rocks from laboratory experiments and numerical modeling

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