Thermal transport properties of carbon-carbon fibre composites III. Mathematical modelling

Whittaker, A.; Taylor, Robert G.

doi:10.1098/rspa.1990.0088

Cited by 19 publications

(7 citation statements)

References 20 publications

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“…(A8) describes transverse heat conduction through a two-phase medium: the matrix material is treated as a continuous phase and the cylindrical fibres as a discontinuous phase. The shape factor X = 1 relates to a regular array of cylindrical fibres (Whittaker and Taylor, 1990). Rearrangement of Eq.…”

Section: Discussionmentioning

confidence: 99%

Influence of applied in-plane strain on transverse thermal conductivity of 0°/90° and plain weave ceramic matrix composites

Zhang

Hayhurst

2011

International Journal of Solids and Structures

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a b s t r a c tA computationally economic finite-element-based stress analysis model, developed previously by the authors, has been extended to predict the thermal behaviour of ceramic matrix composites with strain-induced damage. The finite element analysis utilises a solid element to represent a homogenised orthotropic medium of a heterogeneous uni-directional tow. The non-linear multi-axial strain dependent thermal behaviour has been discretised by multi-linear curves, which have been implemented by a user defined subroutine, USDFLD, in the commercial finite element package, ABAQUS. The model has been used to study the performance of two CMC composites: a SiC (Nicalon) fibre-calcium aluminosilicate (CAS) matrix, 0°/90°cross-ply laminate Nicalon-CAS; and, carbon fibre-dual carbon-SiC matrix (C/CSiC), plain weave laminate DLR-XT. The global through-thickness thermal conductivity degradation with composite uni-axial strain has been predicted. Comparisons have been made between the predictions and experimental data for both materials, and good agreement has been achieved. For the Nicalon-CAS 0°/90°cross-ply the dominant mechanism of thermal conductivity degradation is combined fibre failure and associated wake debonding; and, for the DLR-XT plain weave the same mechanisms act in combination with out-of-plane shear failure.

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Section: Discussionmentioning

confidence: 99%

Influence of applied in-plane strain on transverse thermal conductivity of 0°/90° and plain weave ceramic matrix composites

Zhang

Hayhurst

2011

International Journal of Solids and Structures

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“…This expression, which can be found as eqn (12) in Mottram & Taylor (1987), has its origins in the work of Rayleigh (1892) and subsequently that of Bruggeman (1935). This development has been reviewed by Clayton (1971) and formalized by Mottram & Taylor (1987) and Whittaker & Taylor (1990). Equation (3.3) describes transverse heat conduction through a two-phase medium: the inner matrix material is treated as the continuous phase and the cylindrical fibres as the discontinuous phase.…”

Section: (B) Transverse Thermal Response Of a Uni-directional Towmentioning

confidence: 99%

Uni-axial stress–strain response and thermal conductivity degradation of ceramic matrix composite fibre tows

Blacklock²,

2009

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A physical model, previously developed by one of the authors, has been extended to cover thermal conductivity degradation owing to the uni-axial stress-strain response of aligned groups of fibres or tows found in ceramic matrix composites. Both the stress-strain and thermal models, together with their coupling, have been shown to predict known composite behaviour qualitatively. The degradation of longitudinal thermal properties is shown to be driven by strain-controlled fibre failure; while the degradation of transverse thermal properties is because of the growth of fibre-matrix interface wake-debonded cracks, coupled with strain-driven fibre failure.

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“…Equation (10) describes transverse heat conduction through a two-phase medium: the matrix material is treated as a continuous phase and the cylindrical fibres as a discontinuous phase. The shape factor X ¼ 1 relates to a regular array of cylindrical fibres (Whittaker and Taylor, 1990). Rearrangement of equation (10) Table B2 from Tang et al (2011b) b. Degradation of tow transverse thermal conductivity with strain due to matrix cracking and wake debonding: A unidirectional tow, Figure 2(a), can be divided into many identical blocks of a length equal to the matrix crack spacing, w, as shown in Figure 2(b).…”

Section: Initialmentioning

confidence: 99%

“…is the transverse thermal conductivity for the fibre or discontinuous phase; k im is the thermal conductivity for the continuous phase or inner matrix; and the parameter X is a shape factor for the discontinuous phase. The development of equation (10) has been formalised by Whittaker and Taylor (1990). Equation (10) describes transverse heat conduction through a two-phase medium: the matrix material is treated as a continuous phase and the cylindrical fibres as a discontinuous phase.…”

Section: Initialmentioning

confidence: 99%

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Effects of in-plane extension on transverse thermal conductivity of a carbon–carbon 8-harness satin weave composite

Zhang

Hayhurst

2016

International Journal of Damage Mechanics

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A finite element-based technique for coupled thermo-mechanical analysis of woven Ceramic MatrixComposites sheets is presented for the prediction of the degradation of transverse thermal transport behaviour with in-plane extension. The thermal conductivity-strain characteristics have been determined, at the tow level, from the properties of the constituent elements, and then extended to tows and composite. The non-linear thermal conductivity-extension behaviour of the tow has been discretised by multi-linear curves, and implemented in a user-defined subroutine in ABAQUS to model the behaviour of the homogenised orthotropic unidirectional tow and its matrix. By using this approach, an 8-Harness Satin weave HITCO C/C composite unit cell has then been analysed. The variation of through-thickness thermal conductivity degradation with in-plane extension has been predicted and compared with the results of experiments. Very good agreement has been achieved. Two classes of behaviour have been experimentally observed: one that exhibits a brittle response, and another that shows a quasi-ductile behaviour. Both classes of behaviour have been predicted and shown to relate, respectively, to strain localisation and instantaneous pull-out deactivation, without localisation being invoked. These responses are reflected directly in the predicted and experimental rates of decay of transverse thermal conductivity with axial extension. It is advocated that the reduction in transverse thermal conductivity with extension and damage can be used as a Structural Integrity Monitor for CMC operational components.

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Thermal transport properties of carbon-carbon fibre composites III. Mathematical modelling

Cited by 19 publications

References 20 publications

Influence of applied in-plane strain on transverse thermal conductivity of 0°/90° and plain weave ceramic matrix composites

Influence of applied in-plane strain on transverse thermal conductivity of 0°/90° and plain weave ceramic matrix composites

Uni-axial stress–strain response and thermal conductivity degradation of ceramic matrix composite fibre tows

Effects of in-plane extension on transverse thermal conductivity of a carbon–carbon 8-harness satin weave composite

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