Thermal conductivity of textile reinforcements for composites

Thermal conductivity data for dry carbon fibre fabrics are required for modelling heat transfer during composites manufacturing processes; however, very few published data are available. This article reports in-plane and through-thickness thermal conductivities measured as a function of fibre volume fraction (Vf ) for non-crimp and twill carbon reinforcement fabrics, three-dimensional weaves and reinforcement stacks assembled with one-sided carbon stitch. Composites made from these reinforcements and glass fibre fabrics are also measured. Clear trends are observed and the effects of Vf , de-bulking and vacuum are quantified along with orthotropy ratios. Limited differences between the conductivity of dry glass and carbon fibre fabrics in the through-thickness direction are reported. An unexpected trend in the relationship between that quantity and Vf is explained summarily through simple simulations.


Introduction
Carbon fibres offer excellent tensile properties and low densities leading to extensive use as reinforcements for composite materials. Dry textiles reinforcements are available in various types and architectures; these dry reinforcements are saturated with a polymer resin upon composites manufacturing, in a separate manufacturing stage. Knowledge of the thermal conductivity of dry reinforcements is paramount in assessing and modelling heat transfer during composites manufacturing processes such as resin film infusion (RFI) or semi-preg consolidation, as heat transfer rates through the dry reinforcements will impact the evolution of resin viscosity, consolidation and cure.
Thermal conductivity values for constituent carbon fibres are found readily in the literature [1][2][3] and are often reported by manufacturers. The thermal conductivity of composites made from carbon fibres was also studied extensively. [4][5][6][7] The rule of mixture (1) is widely acknowledged for predicting the longitudinal in-plane thermal conductivity l cip of unidirectional fibre-reinforced composites where l fa is the thermal conductivity of the fibres in the axial direction and l m is the thermal conductivity of the matrix; the longitudinal in-plane thermal conductivity is a linear function of fibre volume fraction (V f ). 8, 9 Clayton's analytical model (2) is widely used for predicting the transverse thermal conductivity of unidirectional fibre-reinforced composites from the thermal conductivity of the fibres in the transverse direction l ft 8,10 yielding a mild exponential trend as a function of V f . 9 Clayton's model may also be used for predicting the through-thickness thermal conductivity l ctt of laminates manufactured from unidirectional plies as this is equal to the transverse conductivity of a single ply. 11 Conversely, little is known about the thermal conductivity of dry carbon fibre reinforcements. One source reports the through-thickness thermal conductivity l rtt of a T300 carbon fibre plain weave as 0.074 W m À1 K À1 with no stated V f ; an analytical model was proposed using an electric circuit analogy. 12 No computational models for the thermal conductivity of dry fabrics are available in the open literature. The clothing industry has studied thermal insulation for textiles such as woven cotton in a broad sense 13 but no studies were published on the effect of V f and few on the effect of fabric architecture. 14,15 This article features results from four series of tests. Test series 1 probes the effects of textile architecture, de-bulking, vacuum and V f on the in-plane and through-thickness thermal conductivity of dry reinforcements, l rip and l rtt , for two reinforcements made of the same carbon fibres. Composites were produced from the same reinforcements; l cip and l ctt were measured for comparison purposes. Test series 2 quantifies the effects of textile architecture, thickness and nature of yarns extending along the thickness for three monolithic three-dimensional (3D) woven dry reinforcements. Tests were conducted at a single V f for each reinforcement given their relative stiffness along the thickness; composites were produced and tested. Test series 3 probes the effect of stitching a stack of carbon reinforcement through its entire thickness with a structural 134 tex twisted carbon thread using a single-sided stitching head; l rip and l rtt were measured at different V f values. Finally, test series 4 probes the effects of V f on l rip and l rtt for one dry glass fibre reinforcement and glass fibre composite, enabling comparisons with results obtained in test series 1 to 3.

Thermal conductivity of carbon fibres
Carbon fibres derived from polyacrylonitrile (PAN) precursors offer excellent tensile strength but have relatively low thermal conductivity. Typical axial thermal conductivities l fa for these fibres range from 7 W m À1 K À1 to 10 W m À1 K À1 ; however, values vary within a wide range from 4 W m À1 K À1 to 180 W m À1 K À1 as reported by Beckwith. 16 Pitch-based carbon fibres offer improved stiffness and drastically increased thermal and electrical conductivity, at the expense of reduced tensile strength compared with PANbased fibres. l fa for pitch-based fibres generally range from 10 W m À1 K À1 to 600 W m À1 K À1 7,17 : Zweben 18 reported a maximum value of 1100 W m À1 K À1 from literature; Glowania et al. 7 reported up to 800 W m À1 K À1 . Vapourgrown carbon fibres are produced in short lengths of 50 mm to 70 mm and diameters as small as 0.1 mm from the vapour of low molecular weight hydrocarbon compounds. 19 Their commercialization in the 1990s placed more emphasis on enhancing properties such as electrical and thermal conductivity, where values up to 2000 W m À1 K À1 were reported on a pilot scale. 18,20,21 Hou et al. 22 measured the thermal diffusivity of a single PAN-based fibre at 1.15 Â 10 À7 m 2 s À1 using optical heating and electrical thermal sensing techniques. Wei 23 reported l fa values for T300 and another unspecified PAN-based fibre to be 4.9 and 4.4 W m À1 K À1 , respectively, using the laser flash method, compared with 10.5 W m À1 K À1 cited by the manufacturer for T300. The effect of heat treatment temperature was probed: Katzman et al. 24 reported l fa values ranging from 2 W m À1 K À1 to 14 W m À1 K À1 for PAN-based fibres at different heat treatment temperatures, while Qiu et al. 25 measured l fa using a modified 3-o technique and obtained values ranging from 20 W m À1 K À1 to 69 W m À1 K À1 from a single PAN-based fibre heat treated at 1500 C to 2100 C.
The effect of temperature on thermal conductivity was also investigated. Yamane et al. 1 calculated l fa of a single PAN-based fibre ranging from 300 to 800 K from measured thermal diffusivities. The authors studied five MJ series high stiffness PAN-based fibres and two T series high strength PAN-based fibres from Toray. l fa values ranged from 5 W m À1 K À1 to 180 W m À1 K À1 as a function of temperature. Values for high strength fibres were within typical values for PAN-based fibres cited above, while those for the high stiffness fibres were some of the highest reported for PAN-based fibres. Correlations were often found relating thermal conductivity of carbon fibres to their stiffness, as stiffness is directly dependent on the fibre microstructure. 1 Various data sheets for PAN-based carbon fibres are available from suppliers. Values of l fa reported by Hexcel for fibres IM7, IM10 and AS4 are 5.4, 6.1 and 6.8 W m À1 K À1 , respectively. 26-28 Toho Tenax cited l fa for both HTS40 and HTS45 fibres at 10 W m À1 K À1 . 29 Toray cited 10.5 W m À1 K À1 for l fa of fibre T300 30 , while BP Amoco cited 14 and 15 W m À1 K À1 for fibres T650/35 and T650/42, respectively. 31 Published data for the transverse fibre thermal conductivity l ft are sparse. Values for PAN-based carbon fibres are often estimated through orthotropy ratios where l ft is generally 5 to 10 times lower than l fa 8 or back-calculated using various analytical models given V f and the throughthickness thermal conductivity of a composite plate l ctt made from the same fibre. 32 The only l ft values cited by suppliers are 5 W m À1 K À1 for both T650/35 and T650/42 fibres from BP Amoco. 31 Bol'shakova et al. 33 published the only paper reporting l fa as well as l ft for several carbon fibres. Measurements were done over temperatures ranging from 0 C to 600 C in either air or oil. Values of l fa and l ft are not directly comparable as the fibres used had different densities. Still, results lead to orthotropy ratios of approximately 15 for a PAN-based carbon fibre and 40 for a pitchbased fibre at room temperature. For the PAN-based fibre, l fa remained approximately constant at different temperatures while l ft increased approximately linearly as a function of temperature.
Although most thermal conductivities reported for PAN-based fibres are low, some fibres returned higher values, such as the MJ series reported above and Thornel 50 with l fa of 70 W m À1 K À1 as cited by Cytec 34 ; Lee and Taylor 3 measured 59 W m À1 K À1 for the same fibre using the laser flash method. Generally, common grade commercial PAN-based carbon fibre can be expected to return l fa values in the range of 10-20 W m À1 K À1 .
Thermal conductivity of carbon fibre textile reinforcements Most data found for the thermal conductivity of textiles originate from the clothing industry for applications such as firefighter clothing or insulation for winter jackets. Matusiak 13 studied the thermal insulation of single and multilayered textile materials and concluded that porous non-woven materials offer high thermal diffusion. Uzun 35 measured the thermal conductivity of fabrics made of natural fibres. Onofrei et al. 14 conducted studies on the effect of knit structure on the thermal conductivity of fabrics made of thermoregulating yarns. Thermal conductivity was measured for nine different knitted structures; some knit structures were found to offer higher thermal conductivity than others. Matusiak and Sikorski 15 studied the effect of fabric architecture by measuring thermal conductivity of plain, twill 1/3, twill 2/2, rep 1/1, rep 2/2 and hopsack 2/2 cotton fabric weaves. The plain weave fabric yielded higher thermal conductivity which the authors attributed to its higher density, followed by the twill 1/3 and rep 2/2, while the hopsack 2/2 yielded lower thermal conductivity. The authors concluded that the effect of weave type was statistically significant.
A few articles reported on the general heat transfer behaviour of woven fabrics. Xiaogang et al. 36 investigated heat conduction in PAN-based carbon fibre fabrics based on infrared imaging. They obtained temperature-time curves for five different fabrics. Ziaei and Ghane 37 studied the thermal insulation properties of cotton and polyester spacer fabrics impregnated with ceramic powders, which effectively reduced the thermal conductivity of these fabrics. The authors stated that natural convection in porous materials with densities higher than 20 kg m À3 is negligible and that since the thermal conductivity of air is much lower than that of the fibres, air between the fibres plays an important role in determining the thermal properties of textiles.
Even fewer studies were performed by the composites or aerospace industry aiming at studying the in-plane thermal conductivity l rip or through-thickness thermal conductivity l rtt of dry carbon fibre fabrics. Yamashita et al. 38 measured the transverse thermal conductivity of T300 carbon fibres as well as that of plain woven reinforcement made from the same fibre, and fibre-epoxy composite made from the same textile. Values of l ft , l rtt and l ctt were measured as 0.095, 0.074 and 0.302 W m À1 K À1 , respectively; the authors reported no corresponding V f values for these measurements. Two models were developed for predicting the through-thickness thermal conductivity of the reinforcement and composite using an electric circuit analogy, with predictions made over V f values ranging from 20 to 50%. For the reinforcement, predicted l rtt values ranged from 0.05 W m À1 K À1 to 0.08 W m À1 K À1 , varying linearly with V f . The authors attributed the increase in content of high thermal conductivity fibres without further explanation to the linear trend. For the composite, thermal conductivity values in the through-thickness direction l ctt ranged from 0.21 W m À1 K À1 to 0.25 W m À1 K À1 and remained constant with V f , which is unexpected for carbon fibre-epoxy composites.
Bol'shakova et al. 33 measured l rip of graphite fibre textile TGN-2 M and l rtt of carbon fibre textile Ural T-22 as a function of temperature in different mediums of air, nitrogen and vacuum. The authors did not state corresponding V f values for these measurements. Thermal conductivity in air in both directions increased with temperature with l rip values ranging from 0.6 W m À1 K À1 to 1.4 W m À1 K À1 following an exponential recovery trend and l rtt values ranging from 0.22 W m À1 K À1 to 0.28 W m À1 K À1 following a linear trend. Comparing thermal conductivity in air in the in-plane and through-thickness directions yielded orthotropy ratios of approximately 3; however, the data cannot be compared directly since the measurements resulted from fabrics of different densities made from different fibres, with unspecified textile architecture. It was also observed that the through-thickness thermal conductivity of reinforcements was affected significantly when experiments were conducted in air and under vacuum. As for reinforcement data from suppliers, Cytec cited a l rtt value of 0.25 W m À1 K À1 for Thornel VCB-20 carbon fibre cloth while stating that l fa for the constituent carbon fibre was 15 W m À1 K À1 . 39 Hes and Dolezal 40 developed the LAMBDATEST device which measures thermal conductivities ranging from 1 W m À1 K À1 to 200 W m À1 K À1 , so it may be used in probing carbon fibre textile and composites.
Results featured herein include l rip and l rtt data measured using dedicated equipment, where the effects of reinforcement architecture and V f are documented systematically for textile reinforcements made from fibres of known conductivities l fa and l ft . Orthotropy ratios for the fabrics are quantified and compared with those of the constituent fibres. Variability induced by repeated measurements performed on different samples and by the apparatus are quantified along with the effect of dry samples being enclosed within a film as part of the measurement technique. The conductivity of samples subjected to repeated compaction cycles and to vacuum is probed as both cases are relevant to manufacturing processes for composites, along with the effect of modern preform construction techniques including carbon thread stitching and the use of monolithic, thick 3D textile reinforcements. Conductivity data obtained from composites made from the same reinforcements, and from glass fibre reinforcements, are also included for comparison purposes. Trends are identified and limitations of models developed for predicting the conductivity of composites as opposed to dry reinforcement fabrics are highlighted. Preliminary computational models are offered aiming at providing a first explanation for some of the trends derived from experimental results.

Experimental
Devices, materials and sample preparation Dedicated thermal conductivity measurement devices THISYS and THASYS manufactured by Hukseflux were used for experimental data collection, Figure 1. THISYS and THASYS measure in-plane and through-thickness thermal conductivities, respectively, requiring one or two flat samples measuring approximately 70 mm Â 110 mm. Detailed information about the configuration and operation of the devices appears in. 8 The technique used for obtaining directional in-plane conductivity values was not used here as all samples were thermally quasi-isotropic in their plane; bulk in-plane thermal conductivities were measured as envisaged by Hukseflux in regular operation.
THISYS and THASYS rely on immersing the heat source, heat sink and solid samples in glycerol to reduce contact thermal resistances and improve measurement accuracy. While the devices are typically used for measuring in-plane l cip and through-thickness l ctt thermal conductivities of solid materials, in this work, they were also used for measuring the in-plane l rip and through-thickness l rtt thermal conductivities of dry textile reinforcements in air and under vacuum. Dry fabrics, which are detailed below, were cut into 70 mm Â 110 mm plies, stacked and sealed into 50 mm thick Dahlar ® release film 125 from Airtech. Each sealed dry reinforcement sample was tested for leaks by immersion in water for 10 min, to avoid penetration of glycerol from the devices into the dry fabric samples during measurement. Most samples were sealed on three sides leaving the top side open to enable progressive compaction and increase in V f of the samples in the devices. Samples measured under vacuum were sealed on all sides and equipped with a port sealed in the release film for connection to a Gast DAA-V715A vacuum pump set to 0.02 bar absolute, Figure 1.
Dry samples in test series 1, 3 and 4 were tested at different V f to capture the evolution of l rip and l rtt in reinforcements subjected to typical consolidation profiles upon composites manufacturing. All samples mounted between spring-loaded heater plates with adjustable spacing were compacted to precise V f values using accurately milled spacers of low thermal conductivity inserted away from heat transfer pathways in the devices. Inserts with five thicknesses ranging from 4.76 mm to 3.39 mm enabled V f values ranging generally from 35% to 60%; these values correspond to reinforcements as received and subjected to compaction pressures typical of composites manufacturing processes. Samples were brought to the highest V f at 3.39 mm thickness by pre-compacting to 1.0 MPa at 4 mm min À1 using an Instron 4482 universal testing frame equipped with parallel compaction platens; all other thicknesses were reached through manual tightening in the THISYS and THASYS devices. The effect of de-bulking on conductivity was quantified in series 1 by taking thermal conductivity measurements on each sample at each V f , over three successive cycles of compaction and unloading. Dry samples in test series 2 were tested at a single V f value in each case given their relatively high stiffness in the through-thickness direction.
Various textile reinforcements were tested in the four successive steps of this work. Test series 1 probed the effects of textile architecture, V f , successive compaction and vacuum on l rip and l rtt for two reinforcements made from Toho Tenax HTS40 PAN-based carbon fibres. Reinforcement stack 1.1 consisted of six layers of 534 g m À2 non-crimp stitched +45 bidirectional reinforcement produced by Saertex from 12 K yarn. Reinforcement stack 1.2 consisted of 16 layers of 215 g m À2 2 Â 2 balanced twillwoven reinforcement produced by Texonic from 3 K yarn. Composites were produced from the same stacks with l cip and l ctt measured for comparison purposes, using resin R1 which is identified below.
Test series 2 quantified the effects of textile architecture, reinforcement thickness and yarns made of different fibres extending along the thickness on l rip and l rtt measured on 3D woven reinforcement fabrics. In all cases, composite plates were produced from the same reinforcement with l cip and l ctt measured for comparison purposes, using resin R2 as identified below. In view of the relatively high transverse stiffness of the 3D woven reinforcements, tests performed on dry reinforcements and composites were conducted at single nominal V f values for each material and case; the effect of V f was not probed. Reinforcement 2.1 was a monolithic 3D woven carbon reinforcement featuring 3 K and 12 K yarns of Toho Tenax HTS40 PAN-based carbon fibres balanced along the warp and weft, with 1% carbon z-fibre binding yarns extending from the top surface to the bottom surface hence interlocking all Test series 3 probed the effect on l rip and l rtt of onesided stitching applied to a 20-layer stack of aforementioned 215 g m À2 2 Â 2 balanced twill-woven reinforcement produced by Texonic from 3 K yarn through its entire thickness, using a structural 134 tex twisted carbon thread. Stacks were thermally isotropic in-plane. Stitching as shown in Figure 2 was done at Centre des Technologies Textiles, St-Hyacinthe, QC, Canada, using a one-sided Keilmann RS 530 stitching head with 25.4 mm stitch width and 4.0 mm stitch pitch. Reinforcement stack 3.1 was assembled with a single stitch line extending along its 110 mm length, centred in the width of samples, and tested at different Vf values. Tests were not performed on composites in this case.
Test series 4 probed the effects of V f on l rip and l rtt for one glass fibre reinforcement aiming at providing a general comparison with results obtained for the carbon fibre reinforcements tested in series 1 to 3. Reinforcement stack 4.1 consisted of eight layers of 305 g m À2 2 Â 2 balanced twill E glass woven reinforcement. Composites with an average thickness of 1.86 mm and V f of 53.5% were produced from the same stacks with l cip and l ctt measured for comparison purposes, again using resin R2.
Resin R1 was neat epoxy AKD/LEO 2376 supplied in 120 mm film by Axson. Composites made from non-crimp stitched and woven reinforcements in step 1 were manufactured by RFI in a PF120 Carbolite oven. Fabrics and resin film were intercalated, vacuum bagged and processed at 2 C min À1 to 130 C, dwell for 2 h, ramp at 2 C min À1 to 200 C and dwell for 2 h. Void fractions in the plates were well below 1%, consistently. Resin R2 was liquid epoxy West System 105/206 slow hardener with a 5:1 ratio. Composites made from 3D woven reinforcements in step 2 and woven E glass reinforcements in step 4 were manufactured using vacuum-assisted resin transfer moulding under full vacuum between cast aluminium plates, and cured at room temperature. Void fractions were similar to those reported above.

Variability of devices and data
Variability of the THISYS and THASYS devices for measurements taken at 20 C are quoted by the manufacturer as +2% and +1%, respectively. Two types of variability for both in-plane and through-thickness thermal conductivity data were quantified: variability of the THISYS and THASYS devices, and total variability of the data. Variability refers to the ratio of the standard deviation to the average of relevant data.
In test series 1, device variability was calculated based on two or three measurements: the original data value and either one or two repeated measurements performed on the same sample and at the same V f , taken successively without removing samples from the devices. Data variability was calculated based on four measurements: the original value measured using the original sample and three more values measured using different samples at the same V f ; hence data variability includes variability of the device, variability due to differences in mounting the samples and inserts, as well as variability due to differences in preparation of the four samples. In test series 1, device variability was generally lower than 1% except for variability of THASYS evaluated with the vacuumed reinforcement stack 1.1 which stood at 2.8%. Total variability on conductivity data ranged from 6.7% to 11.2% for dry reinforcement samples tested at the same V f and below 5% for composites, both in-plane and through-thickness. Results from test series 2 were very reproducible with values of the total variability mostly below 5%. Values of the total variability for composites were mostly below 1% while those of dry reinforcements were above 1%; variability was higher for the conductivity of dry reinforcements measured in the through-thickness direction l rtt with values of 4.3%, 8.3% and 6.3% for reinforcements 2.1, 2.2 and 2.3, respectively. Values of the total variability obtained in test series 3 were almost always below 1% for conductivities measured in the in-plane and through-thickness directions, for carbon stacks featuring one-sided stitching and those devoid of stitching, as well as for glass dry stacks and composites, with no notable outliers. The same was observed with test series 4 performed on glass reinforcement 4.1 though in that case, fluctuations with V f were far larger and the relation less clear.

Effect of release film
The effect of the Dahlar ® release film used for preparing dry samples on measured in-plane and through-thickness thermal conductivities was quantified. In-plane thermal resistance R mip of a material sample of thickness t m and in-plane conductivity l mip is where L is heat flux length and w is sample width. Combining with two in-plane thermal resistances R fip from both release film layers with identical L and w leads to apparent in-plane thermal resistance R aip Knowing the thickness t f and thermal conductivity of the film l fip , total thickness t a and the apparent thermal conductivity l aip measured for the material sample and films leads to l mip for the material sample Hence, l mip and l aip may be compared if l fip is known. Similarly, through-thickness thermal resistance R mtt of a material sample of thickness t m and through-thickness conductivity l mtt is: where A is the area normal to the heat flux. Adding two through-thickness thermal resistances R ftt from both release film layers with identical A leads to apparent throughthickness thermal resistance R att Knowing the thickness t f and thermal conductivity of the film l ftt , total thickness t a and the apparent thermal conductivity l att measured for the material sample and films leads to l mtt for the material sample hence l mtt and l att may also be compared. A thermal conductivity l fip ¼ l ftt of 0.2 W m À1 K À1 was obtained from more than 20 in-plane and transverse measurements performed on single sheets and stacks of Dahlar ® 50 mm thick release film; isotropic thermal behaviour was assumed henceforth for the film. The conservative estimates of l rip ¼ 1 W m À1 K À1 and l rtt ¼ 0.1 W m À1 K À1 from the literature along with t m ¼ 3.0 mm from apparatus configuration lead to underestimates of less than 1% for l rip and negligible for l rtt ; differences are more significant for l cip and l ctt as composites are more conductive, but Dahlar ® film was not used when taking measurements on solid composites with reinforcements saturated with cured epoxy resin.

Results
Series 1: Effect of textile architecture, V f , de-bulking and vacuum Results obtained from thermal conductivity measurements performed on reinforcement stacks 1.1 and 1.   show that l rip for both reinforcement stacks varies linearly as a function of V f . The non-crimp and twill reinforcements showed similar in-plane conductivities ranging from 1.303 W m À1 K À1 to 2.249 W m À1 K À1 for non-crimp stack 1.1 and from 1.367 W m À1 K À1 to 2.092 W m À1 K À1 for twill stack 1.2. The l rip values for non-crimp stack 1.1 were slightly higher than the values for twill stack 1.2 at the same V f . A mild but consistent effect of successive compaction cycles is seen for both reinforcements, with values measured at the same V f increasing slightly after each cycle. Vacuumed non-crimp stack 1.1 returned a value of 2.188 W m À1 K À1 at 52.6% V f ; 2.4% lower than that of its non-vacuumed counterpart.
In the through-thickness direction, Figures 5 and 6 show that l rtt for both reinforcements follows an exponential     recovery trend as a function of V f . Both reinforcements showed conductivities in comparable ranges; values ranged from 0.112 W m À1 K À1 to 0.209 W m À1 K À1 for non-crimp stack 1.1 and from 0.145 W m À1 K À1 to 0.219 W m À1 K À1 for twill stack 1.2. The l rtt values for the non-crimp reinforcement were very similar to the values for the twill reinforcement at the same V f . The effect of successive compaction cycles was seen with both reinforcements; amplitude was stronger in the through-thickness than for the in-plane case. Vacuumed non-crimp stack 1.1 returned a value of 0.182 W m À1 K À1 at 52.6% V f , 7.4% lower than that of its non-vacuumed counterpart.
Thermal conductivity data for two composites made from both reinforcement stacks were compared with those of the dry reinforcements in the in-plane and throughthickness directions, Figures 7 and 8. Composite plates made using stacks 1.1 and 1.2 showed V f values of 57.5% and 53.5%, respectively, while V f values for the dry reinforcements used for comparison were 52.6% and 56.4%, respectively. In the in-plane direction, l cip and l rip for stack 1.1 were 2.499 and 2.236 W m À1 K À1 , respectively, while values for stack 1.2 were 2.513 and 2.050 W m À1 K À1 , respectively. Similar comparisons made for the throughthickness data show more significant differences; l ctt and l rtt for stack 1.1 were 0.547 and 0.195 W m À1 K À1 , respectively, while values for stack 1.2 were 0.505 and 0.214 W m À1 K À1 , respectively. The in-plane to throughthickness thermal conductivity ratio was approximately    5 for the carbon fibre-epoxy composites compared to approximately 10 for the dry carbon fibre reinforcements, the latter approaching values typically reported for carbon fibres.

Series 2: 3D woven reinforcements
Results obtained from thermal conductivity measurements performed on reinforcements 2.1, 2.2 and 2.3 and their composites appear in Figures 9 and 10. Both in-plane and through-thickness conductivity values measured for 3D woven reinforcements and their composites compared generally with those obtained for stacks 1.1 and 1.2. In-plane values obtained for composites are somewhat larger than those measured with the dry reinforcements as reported above, while a significant difference is observed throughthickness. Here again, in-plane conductivity values are systematically larger than through-thickness values by a factor of approximately 10. Interestingly, the effect of V f was muted for 3D weaves; although structures of reinforcements 2.1, 2.2 and 2.3 were not entirely similar, reduced differences in both conductivities at different V f may result from superimposed yarns being much better aligned in 3D weaves as opposed to stacks 1.1 and 1.2 as a result of the manufacturing process.

Series 3: Through-thickness one-sided stitching using carbon thread
Results obtained from measurements performed on reinforcement stack 3.1 appear in Figures 11 and 12. In-plane conductivity was not affected by the presence of onesided stitching as values presented in Figure 12 replicate those presented in Figure 4 for reinforcement 1.2. Conversely, while the range of through-thickness conductivity values presented in Figure 12 was essentially unchanged and orthotropy ratios remained largely similar, an inversion in trend was observed for the effect of V f . In this case, zones of reinforcement stacks under stitching lines will undergo more compression while contact with THASYS platens may be reduced in zones immediately surrounding the stitching lines. One may conclude that through-thickness one-sided stitching with carbon thread does affect the local heat transfer through stacks of carbon reinforcements.

Series 4: Glass fibre reinforcements
Results obtained from measurements conducted on reinforcement stack 4.1 and its composite appear in Figure 13. Similar observations can be made. Values of in-plane conductivity for the dry reinforcement are larger for in-plane l rip than for through-thickness l rtt even as glass fibres are likely closer to thermal isotropy, as a result of the textile reinforcement structure. In-plane and through-thickness conductivity values for the composite l cip and l ctt are  closer, and conductivity values measured for the dry reinforcement and composite are also closer as a result of closer conductivities of the base materials. Still, the effect of resin on conductivity is more marked along the thickness. It is well worth noting that while in-plane conductivities of dry glass reinforcement 4.1 and its composite are clearly lower than those of dry carbon reinforcements and composites measured in this work, the same cannot be said of through-thickness conductivities. Hence, the kinetics of through-thickness heat transfer through dry preforms in processes such as RFI will not differ to the extent that may be expected if considering only the thermal conductivity of the constituent fibres along their axial direction.

Discussion
The linear effect of V f on l rip was expected from the rule of mixtures. Conversely, the exponential recovery trend on l rtt was unexpected. Hind and Robitaille 8 reported broadly exponential trends from Clayton's model 10 applied to composites. No analytical or semi-empirical models of the through-thickness thermal conductivity of textiles were found in the literature, hence this was probed. Twodimensional (2D) steady-state simulations were performed using FLUENT ANSYS 13.0 in an attempt to replicate the trend on l rtt . The simulations did not account for reinforcement architecture based on the limited differences in data measured for stacks 1.1 and 1.2. Simulation results were compared with data measured for stack 1.1. Heat transfer in dry fabrics was assumed to occur primarily through conduction; air convection in the samples was assumed to be negligible. Constant temperatures were imposed on top and bottom domain walls while side walls were set as adiabatic. The through-thickness thermal conductivity l rtt was calculated using Fourier's law based on the average of the resulting heat flux measured at the top and bottom boundaries, which were always consistent within 5%.
A first group of simulations that did not model contacts between fibres were referred to as SimNC. Equally spaced and regularly aligned fibres of circular cross sections surrounded by air were represented by square unit cells, Figure  14. Eight unit cells were used in each simulation. Four cases were run with V f values ranging from 38.0% to 53.0%. Diameter of the fibres was set to 7 mm. 29 V f was  increased by reducing the height and width of each unit cell hence reducing the distance between adjacent fibres. Constant temperatures were imposed to the top and bottom walls of the domain while side walls were adiabatic. The throughthickness thermal conductivity l rtt was calculated using Fourier's law based on the average heat flux on the top and bottom boundaries which were consistent within 5%. SimNC simulation results presented in Figure 15 ranged from 0.058 W m À1 K À1 to 0.095 W m À1 K À1 and could not replicate the exponential trend observed experimentally.
It was suspected that SimNC simulations underestimated l rtt values due to the lack of fibre contacts providing paths for heat conduction. A second group of 2D steady-state simulations referred to as SimC and featuring contacts were performed in FLUENT, using otherwise identical conditions. Five cases, SimC1 to SimC5, were run with V f ranging from 33.4% to 65.8%, Figure 16. The cases offer a simplified representation of contacts between adjacent fibres developing during compaction. SimC1 represents an initial state where contacts between fibres are limited. Additional contacts develop in SimC2 and SimC3 where direct paths for conduction in the throughthickness appear, reducing the reliance of heat transfer through air. Fibres shift in SimC4 as a result of further compaction, connecting more heat paths; the network is further enhanced in SimC5. While the cases represent five possible local configurations among a wide array of alternatives, they aim at modelling incremental changes in fibre contacts with increasing V f . SimC simulation results appear in Figure 15 along with SimNC simulation results and experimental data for stack 1.1. SimC simulations featuring fibre contacts yielded reasonable predictions for l rtt of dry fabrics and replicated the exponential recovery trend seen with measured data. Plots showing temperature distributions appear in Figures 17 and 18.

Conclusion
Reproducible values of l rip and l rtt were obtained for reinforcements. Orthotropy ratios quoted in the literature were validated. The effects of de-bulking and vacuum were quantified. Limited differences were seen between the inplane conductivities for reinforcements and composites made from the reinforcements; conversely, the throughthickness conductivities for reinforcements were markedly lower than those of composites. Textile structures were found to affect properties. The in-plane conductivities of non-crimp reinforcements were marginally larger while the through-thickness conductivities of weaves were marginally higher. 3D weaving had limited impact on conductivity while one-sided through-thickness stitching affected the relationship between l rtt and V f . Differences in l rtt for glass and carbon fabrics were markedly lower than one may have expected. The above is useful for process engineering as the through-thickness heat transfer can play a major role, say for RFI or consolidation with semi-pregs or featuring heavier ancillary materials.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.