An eigenfunction expansion–variational method in prediction of the transverse thermal conductivity of fiber reinforced composites considering interfacial characteristics

Peng, Yan; Chen, F.L.; Jiang, Chunxiang; Song, Fan

doi:10.1016/j.compscitech.2010.06.018

Cited by 14 publications

(22 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By substituting the complex potentials into (2a, b, c), and then into , the unknown coefficients in satisfy the equations :

{\overset{A}{true}}_{2 n - 1} = η_{fm} R^{2 (2 n - 1)} [A_{0} δ_{1, n} - \sum_{j = 1}^{\infty} A_{2 j - 1} {normalC}_{2 j + 2 n - 3}^{2 n - 1} S_{2 j + 2 n - 2}], n = 1, 2, 3 . . .,

with

η_{fm} = false(k_{m} - k_{f} false) / false(k_{m} + k_{f} false)

.…”

Section: Interface Conditions and Coefficient Equationsmentioning

confidence: 99%

“…b, the heat transfer rate Φ is continuous, while the temperature is discontinuous across the interface:

{normalΦ}_{normalf} = {normalΦ}_{normalm}, q_{normalf} = q_{normalm} = - h false(T_{f} - T_{m} false), at |z| = R,

where h is the thermal contact conductance on the interface. By similar substitution, the unknown coefficients in satisfy the equations :

{\overset{A}{true}}_{2 n - 1} = \frac{η_{fm} + false(2 n - 1 false) β false(1 - η_{fm} false)}{1 + false(2 n - 1 false) β false(1 - η_{fm} false)} R^{2 (2 n - 1)} [A_{0} δ_{1, n} - \sum_{j = 1}^{\infty} A_{2 j - 1} {normalC}_{2 j + 2 n - 3}^{2 n - 1} S_{2 j + 2 n - 2}], n = 1, 2, 3 . . .,

with

β = k_{normalm} / false(2 h R false)

.…”

Section: Interface Conditions and Coefficient Equationsmentioning

confidence: 99%

“…Similarly, a series of substitutions yield the following coefficient equations :

{\overset{A}{true}}_{2 n - 1} = \frac{η_{cm} + η_{fc} {(1 + ξ)}^{2 - 4 n}}{1 + η_{cm} η_{fc} {(1 + ξ)}^{2 - 4 n}} R^{2 (2 n - 1)} [A_{0} δ_{1, n} - \sum_{j = 1}^{\infty} A_{2 j - 1} {normalC}_{2 j + 2 n - 3}^{2 n - 1} S_{2 j + 2 n - 2}], n = 1, 2, 3 . . .,

with

η_{fc} = false(k_{c} - k_{f} false) / false(k_{c} + k_{f} false), η_{cm} = false(k_{m} - k_{c} false) / false(k_{m} + k_{c} false), ξ = false(R_{1} - R false) / R .

…”

Section: Interface Conditions and Coefficient Equationsmentioning

confidence: 99%

“…By substituting the complex potentials into (2a, b, c), and then into (14), the unknown coefficients in (12) satisfy the equations [30]:…”

Section: Perfect Interfacementioning

confidence: 99%

“…where h is the thermal contact conductance on the interface. By similar substitution, the unknown coefficients in (12) satisfy the equations [30]:…”

Section: Contact Resistance Interfacementioning

confidence: 99%

See 4 more Smart Citations

Unified complex variable solution for the effective transport properties of composites with a doubly‐periodic array of fibers

Yan

Dong

Chen³

et al. 2016

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

We present a complex variable method to evaluate the transverse effective transport properties of composites with a doubly-periodic array of fibers. The obtained complex variable solution is derived in a unified form for arbitrary doublyperiodic fiber arrays, and different fiber-matrix interfaces, i.e., perfect interface, contact resistance interface and coating. The present method can be seen as an extension of the method originated by Rayleigh only for symmetric fiber arrays. The limitation of Rayleigh's method is overcome by introducing a supplementary equation. Explicit formulae of the effective transport properties approximated to finite orders are obtained, which are written in a regular form for different fiber arrays, and reveal the reciprocal relations for symmetric fiber arrays. The validity and accuracy of the solution are verified by numerical examples and comparisons with existing methods.

show abstract

“…By substituting the complex potentials into (2a, b, c), and then into , the unknown coefficients in satisfy the equations :

{\overset{A}{true}}_{2 n - 1} = η_{fm} R^{2 (2 n - 1)} [A_{0} δ_{1, n} - \sum_{j = 1}^{\infty} A_{2 j - 1} {normalC}_{2 j + 2 n - 3}^{2 n - 1} S_{2 j + 2 n - 2}], n = 1, 2, 3 . . .,

with

η_{fm} = false(k_{m} - k_{f} false) / false(k_{m} + k_{f} false)

.…”

Section: Interface Conditions and Coefficient Equationsmentioning

confidence: 99%

“…b, the heat transfer rate Φ is continuous, while the temperature is discontinuous across the interface:

{normalΦ}_{normalf} = {normalΦ}_{normalm}, q_{normalf} = q_{normalm} = - h false(T_{f} - T_{m} false), at |z| = R,

where h is the thermal contact conductance on the interface. By similar substitution, the unknown coefficients in satisfy the equations :

{\overset{A}{true}}_{2 n - 1} = \frac{η_{fm} + false(2 n - 1 false) β false(1 - η_{fm} false)}{1 + false(2 n - 1 false) β false(1 - η_{fm} false)} R^{2 (2 n - 1)} [A_{0} δ_{1, n} - \sum_{j = 1}^{\infty} A_{2 j - 1} {normalC}_{2 j + 2 n - 3}^{2 n - 1} S_{2 j + 2 n - 2}], n = 1, 2, 3 . . .,

with

β = k_{normalm} / false(2 h R false)

.…”

Section: Interface Conditions and Coefficient Equationsmentioning

confidence: 99%

“…Similarly, a series of substitutions yield the following coefficient equations :

{\overset{A}{true}}_{2 n - 1} = \frac{η_{cm} + η_{fc} {(1 + ξ)}^{2 - 4 n}}{1 + η_{cm} η_{fc} {(1 + ξ)}^{2 - 4 n}} R^{2 (2 n - 1)} [A_{0} δ_{1, n} - \sum_{j = 1}^{\infty} A_{2 j - 1} {normalC}_{2 j + 2 n - 3}^{2 n - 1} S_{2 j + 2 n - 2}], n = 1, 2, 3 . . .,

with

η_{fc} = false(k_{c} - k_{f} false) / false(k_{c} + k_{f} false), η_{cm} = false(k_{m} - k_{c} false) / false(k_{m} + k_{c} false), ξ = false(R_{1} - R false) / R .

…”

Section: Interface Conditions and Coefficient Equationsmentioning

confidence: 99%

“…By substituting the complex potentials into (2a, b, c), and then into (14), the unknown coefficients in (12) satisfy the equations [30]:…”

Section: Perfect Interfacementioning

confidence: 99%

“…where h is the thermal contact conductance on the interface. By similar substitution, the unknown coefficients in (12) satisfy the equations [30]:…”

Section: Contact Resistance Interfacementioning

confidence: 99%

See 3 more Smart Citations

Unified complex variable solution for the effective transport properties of composites with a doubly‐periodic array of fibers

Yan

Dong

Chen³

et al. 2016

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

show abstract

Study on the effect of carbon fiber ply angle on thermal response of CFRP laminate based on the thermal resistance network model

Bao,

Ma,

Yang

et al. 2023

Polymer Composites

View full text Add to dashboard Cite

Carbon fiber reinforced polymer (CFRP) exhibits different heat transfer phenomena along the fiber direction and the transverse direction during the heat transfer process due to its anisotropic thermo‐physical properties, which makes it difficult to quantitatively analyze the overall thermal performance of CFRP with different ply angles. A thermal resistance network model of composite material considering fiber ply angle and heat transfer direction was developed based on the series–parallel resistance computing method, and it was applied to describe the test results measured by the thermal response tests of unidirectional carbon fiber laminates. Thermal resistance Rx along the heat transfer direction and Ry transverse to the heat transfer direction calculated by the proposed model, which are related with the thermal response of the specimen, can be utilized to reflect the temperature values and temperature distribution maps. It was found that as the fiber ply angle θ increases from 0° to 45°, thermal resistance in the x‐axis direction increases from about 0.13 K/W to 2.56 K/W, while thermal resistance in the y‐axis direction decreases about 48.7%. As a result, major axis of quasi‐ellipse temperature profile changes by about +45° relative to the x‐axis.Highlights A CFRP thermal resistance network model considering ply angle was proposed. The series–parallel thermal resistance method is used to calculate Rx and Ry. The ply angle from 0° to 45°, Rx increases several times and Ry decreases by half. Major axis of elliptic temperature curve changes by +45° relative to the x‐axis.

show abstract

Effective transport properties of composites with a doubly‐periodic array of fiber pairs and with a triangular array of fibers

Yan

Zhang

Chen³

et al. 2017

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

This paper presents a complex variable solution for the effective transport properties of composites with a doubly-periodic array of fiber pairs. By using the centrosymmetry of the problem, the method of Rayleigh and Natanzon-Filshtinsky's approach can be simply extended to the problems with two fibers per unit cell. The infinite system constructed in this paper only slightly complicates Rayleigh's system for the problems with one fiber per unit cell. Approximate analytical formulae of the effective transport properties for different fiber-pair arrays are obtained. The influence of pairwise interaction in fiber pairs on the effective transport properties is discussed in the numerical examples. As a special case of a doubly-periodic array of fiber pairs, effective transport property of composites with a triangular array of fibers is obtained. The obtained approximate analytical formulae are written in a concise form with good accuracy, thus are convenient for engineering application in most cases, except for those approaching the limit case of percolation when the perfectly conducting fibers become touching. Besides the square array and hexagonal array, the triangular fiber array (similar to carbon atom arrangement in graphene) is another special symmetric fiber array which results into transversely isotropic effective property. Therefore, the present solution for the triangular array is an extension of those for the square array and hexagonal array. The comparison of the results for the three symmetric fiber arrays reveals that the triangular fiber array has the highest conductivity. In addition, accuracy of the present solution is analyzed in the numerical examples.

show abstract

An eigenfunction expansion–variational method in prediction of the transverse thermal conductivity of fiber reinforced composites considering interfacial characteristics

Cited by 14 publications

References 17 publications

Unified complex variable solution for the effective transport properties of composites with a doubly‐periodic array of fibers

Unified complex variable solution for the effective transport properties of composites with a doubly‐periodic array of fibers

Study on the effect of carbon fiber ply angle on thermal response of CFRP laminate based on the thermal resistance network model

Effective transport properties of composites with a doubly‐periodic array of fiber pairs and with a triangular array of fibers

Contact Info

Product

Resources

About