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Measurement of thermal conductivity for fibre-reinforced composites
Composites: Part A 35 (2004) 933–938 www.elsevier.com/locate/compositesa
Measurement of thermal conductivity for fibre-reinforced composites R.D. Sweeting*, X.L. Liu Co-operative Research Centre for Advanced Composite Structures Limited 506 Lorimer Street, Fishermen’s Bend, Vic. 3207, Australia Revised 19 December 2003; accepted 15 January 2004
Abstract A new method has been developed to determine the in-plane and through-thickness thermal conductivities of polymer matrix composites. In the method, the thermal gradient produced by an imposed one-dimensional heat flow in a given direction is measured experimentally. The recorded temperature gradient is used to calculate the thermal conductivity using an inverse numerical approach. Benchmarking was conducted using an aluminium alloy with known thermal properties, yielding excellent correlation. Testing was then performed on F593 carbon-epoxy laminates and the thermal conductivity curves for a service temperature range were determined. q 2004 Elsevier Ltd. All rights reserved. Keywords: A. Polymer-matrix composites (PMCs); B. Thermal properties; C. Numerical analysis; Thermal measurement
1. Introduction The properties of fibre-reinforced composites vary greatly, depending on their constituent materials, fibre orientation and fibre volume fractions. Knowing the accurate material properties is important if accurate and hence meaningful structural analysis or process modelling is to be performed. There are established standards and/or procedures for the measurement of various mechanical properties of fibre composites. However, the same does not apply to the measurement of a number of physical properties, including thermal conductivity, of composites. Work has been performed in measuring thermal diffusivity using the ‘flash technique’ and thermal imaging [1,2], although this requires significant set-up cost and is usually only performed at room temperature. These difficulties have meant that estimation techniques like those based on micromechanics have been the major source of available data [3,4]. The present work aims to develop a relatively simple and reliable method for measuring the thermal conductivity in the three principal directions of a composite laminate. In the method, a one-dimensional temperature gradient is generated in a laminate surrounded by an environment designed to eliminate heat flow in directions other than the one to be measured. Developing a one-dimensional thermal gradient * Corresponding author. Tel.: þ 61-3-96466544; fax: þ 61-3-96468352. E-mail address: [email protected] (R.D. Sweeting) 1359-835X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2004.01.008
simplifies the mathematical solution and reduces the number of unknown factors, which in turn simplifies the data processing and improves the accuracy of the result. Temperatures at a number of locations through the measurement direction of the laminate are recorded using embedded thermocouples. The raw data is then processed using a numerical inverse approach to determine the directional thermal conductivity of the laminate.
2. Method 2.1. Test design methodology The test set-up should be designed to produce onedimensional heat flow in the laminate, to simplify the solution and minimise the number of unknowns. To achieve this, both the thermal edge effects and environmental heat losses must be controlled. The edge effects can be reduced to negligible levels by ensuring the laminate is large enough that all edges perpendicular to the generated temperature gradient, are a sufficient distance away from the measurement zone. The three possible sources of environmental heat losses and the methods of minimising them are: Conduction—prevent thermal contact with surrounding materials.
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Fig. 1. Temperature distribution in one-dimensional models.
Convection—keep convection surfaces in a vacuum. Radiation—provide thermally identnical adjacent surfaces so the same amount of radiation is absorbed as emitted. A number of test designs were initially proposed to fulfil the above requirements. Each possible test design was then modelled using finite element thermal analysis. The results were compared to that of the ideal one-dimensional model to be used to calculate the thermal conductivity. The optimum test designs were selected based on the comparison. The predicted temperature distributions for four different in-plane test designs are compared to the ideal no-loss case in Fig. 1. The free air case (Fig. 1A) illustrates the large amount of heat being lost to the atmosphere from the laminate, assuming convection and radiation losses from its surface. Insulating the laminate (Fig. 1B) reduces the losses, although the temperature profile is still far from the ideal case. Introducing two more heated and insulated laminates outside the measurement laminate (Fig. 1C) improves the temperature profile, although the losses remain too high. Removing the insulation between the laminates and evacuating the air from the cavity (Fig. 1D), eliminates conduction and convection losses from central measurement laminate. Radiation losses are almost eliminated as the adjacent plates are at similar temperatures, leaving a temperature profile close to the ideal one-dimensional case and thus appropriate for the in-plane thermal conductivity experiments. A similar comparison was performed for the through-thickness test design. 2.2. Test set-up Due to the inherently anisotropic nature of polymer matrix composites and the preference to avoid using excessively thick laminates for the through-thickness tests, two different test set-ups were used for the in-plane and through-thickness thermal measurements, respectively.
2.2.1. In-plane Test The in-plane conductivity test set-up selected (Fig. 2) consists of three ‘identical’ parallel composite laminates heated on the left-hand edge by fast warm-up electrical foil heaters (Thermofoil heater HK5167R264L12A). The laminate in the middle has thermocouples embedded in the midplane at given intervals to measure the transient temperature gradient. The two outer laminates are used to minimise the radiation losses from the measurement plate. They provide structural support for a vacuum cavity, minimising both conduction and convection losses from the measurement laminate. The similarity in the heat up rates of the adjacent surfaces of the laminates ensures that the radiation absorbed by a laminate is similar to that emitted. The three laminates are surrounded by insulation to reduce heat convection to the atmosphere, provide a vacuum path and protect the vacuum bag from being cut by sharp corners of the laminates.
Fig. 2. Schematic of in-plane conductivity test set-up.
2.2.2. Through-thickness test Ideally the through-thickness conductivity test (Fig. 3) should be designed using similar principles to the in-plane test. Two plates, one with thermocouples embedded at different points through the thickness, separated by a vacuum cavity with their external surfaces heated would be the ideal test set-up. However, the test developed was limited by the requirement to use an available electrical hotplate as the heat source. The through-thickness test set-up used (Fig. 4) consists of a conductivity test assembly that can be raised and lowered above the hot plate. The test assembly is the measurement laminate with a cork picture frame (spacer), aluminium plate and insulation attached to the top.
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equilibrium was achieved and the process repeated for the new temperature. 2.4. Data analysis
Fig. 3. Schematic of ideal through-thickness conductivity test set-up.
The aluminium plate makes the vacuum cavity used to minimise convection and also reflects some of the radiated energy back to the measurement laminate. Due to the small temperature differences between the top of the measurement laminate and the aluminium plate radiation losses will be minimal. Heat losses at the edges of the laminate are negligible since the distances from the measurement zone to the edges are more than 10 times the thickness. The test assembly needs to be raised and lowered due to the slow heat-up rate of the hot plate. The laminate is raised to prevent contact with the plate until the latter has reached the test temperature. Vacuum is then applied to pull the laminate back onto the hotplate, generating the desired thermal gradient in the laminate.
Thermal conductivity of the composite laminates can be identified from the temperature measurements using an inverse approach. For this purpose, an error function can be defined as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX un j j ð1Þ ðkÞ 2 Texp 2 d ¼ t ½Tnum j¼1
where T is temperature, k is the directional conductivity to be identified and subscripts ‘num’ and ‘exp’ stand for numerical and experimental, respectively. The task of data analysis is to determine k, which minimises the above error function. In the present method, the temperature for the onedimensional transient heat transfer model is solved using the finite difference method. The error function is minimised using the golden section search algorithm [5]. A FORTRAN program has been written to perform the analysis.
3. Results and discussion 3.1. Validation
Fig. 4. Schematic of actual through-thickness conductivity test set-up.
2.3. Test procedure It is well known that thermal properties of composite materials vary with temperature. To determine the thermal conductivity versus temperature curve, measurements were performed in 20 8C increments from room temperature (approximately 20 8C) to 180 8C. Increments of 20 8C were chosen as a compromise between, reducing errors resulting from thermal conductivity changes during the test and being of sufficient size to accurately record the temperature gradient. The thermal conductivity determined thus represents an average of the temperatures measured during the test. To achieve the required elevated temperature environment, testing was performed inside an oven. Before each test the oven air and test assembly were allowed to reach thermal equilibrium. A thermocouple baseline measurement was then performed to eliminate small errors associated with individual thermocouples. A 20 8C temperature increase was then applied to the laminate via the heaters and the transient temperatures in the laminate were recorded. After the test the oven temperature was increased by 20 8C (to the same temperature as the heaters), thermal
Validation of the in-plane conductivity test method was performed using 7075-O aluminium alloy for which the thermal conductivity is given as 173 W/m K [6]. The dimensions of the aluminium plates used were 250 £ 250 mm2 square and 4.2 mm thick. Four thermocouples were used to monitor the temperature distribution in the heat flow direction. Considering the high thermal conductivity of the aluminium alloy, the distance between each of two thermocouples was relatively large at 50 mm. The increased distance between thermocouples, increases the surface area of the measurement zone by 10 times, meaning controlling the losses is even more critical. In Fig. 5, the measured temperature profile is compared to the predictions of a one-dimensional finite element model assuming no losses and using the known material properties. The heating ramp applied in the model was the temperature profile measured by the first thermocouple. Very good agreement exists between the experimental and the predicted temperature profiles at all thermocouple locations, indicating that a one-dimensional heat flow was produced successfully by the developed test method. Processing the experimental data using the FORTRAN program, the thermal conductivity of the aluminium alloy was determined as 178 W/m K at 35 8C which is less than 3% higher than the one given in [6]. The slight difference
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Fig. 5. Comparison of measured and calculated temperature profiles for 7075-O aluminium alloy.
could be due to the 15 8C difference in the measurement temperatures used. 3.2. Conductivity of composite laminates Tests were conducted for Hexcel F593 carbon-epoxy plain weave pre-preg (W3T282-4200 -F593) laminates, autoclave cured for 2 h at 180 8C and 680 kPa. The fibre volume fraction of the laminates was 49%. The three laminates manufactured for the in-plane conductivity test were 260 mm long, 150 mm wide and 2.7 mm thick. They were made from 12 plies of F593 orientated in the 08 direction. The thermal conductivities for the two in-plane directions were assumed to be the same
and only the warp direction was measured. Four thermocouples were embedded along the warp direction, 5, 10, 15 and 20 mm away from the heater edge. The through-thickness test panel was made from 24 plies of F593 pre-preg all orientated in the 08 direction. The resulting panel was 200 £ 200 £ 5.5 mm 3. Thermocouples were embedded after the 1st, 6th, 12th and 18th plies. The accuracy of the thermocouples positioning in the laminate and the disturbance they cause to the heat flow are two problems with this test method. By using multiple thermocouples, errors resulting from positioning are reduced; the temperature profiles from all the thermocouples are used to calculate the conductivity, thus
Fig. 6. Thermal conductivity of F593 plain weave composites.
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Fig. 7. Comparison of measured and calculated temperature profiles for in-plane test.
averaging the errors. If a thermocouple was significantly out of position it would be immediately obvious and that thermocouple could be neglected. No sectioning has been performed to measure the thermocouple positions, however for the in plane specimen, the thermocouples were placed within 0.5 mm during the lay-up. The through-thickness laminates thermocouple positioning is very accurate as they were placed between the plies, thus the only errors could result from minor compaction differences above and below the thermocouple during cure. Any disturbance to the heat flow was reduced by manufacturing the thermocouples from fine wire (0.25 mm diameter) and offsetting their tips perpendicular to the direction of heat flow. The in-plane and through-thickness thermal conductivities determined are plotted in Fig. 6 as functions of
temperature. Both conductivities increase with temperature linearly, although the in-plane one increases at a slightly greater rate. Within the measurement temperature range, the in-plane conductivity increases from about 2 to 3 W/m K, while the through-thickness conductivity changes from approximately 0.5 to 0.7 W/m K. In other words, the in-plane conductivity is approximately four times the through-thickness conductivity throughout the temperature range. A comparison of the measured temperatures and those calculated from the generated thermal conductivity is shown in Figs. 7 and 8 for the in-plane and throughthickness tests at room temperature, respectively. Excellent agreement exists between the experimental and calculated transient temperature profiles at all
Fig. 8. Comparison of measured and calculated temperature profiles for through-thickness test.
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the measurement points. These graphs are typical of all the tests performed.
The in-plane conductivity is approximately four times the through-thickness conductivity.
4. Conclusion
Acknowledgements
A new and relatively simple method has been developed to measure the in-plane and through-thickness thermal conductivities of fibre reinforced composites. One-dimensional heat flow is generated in the laminates by applying heat along one edge or face. The use of vacuum cavities and the careful selection of the surrounding materials minimise convection, conduction and radiation heat flow in the directions other than the one being measured. The transient temperature gradient in the given direction is recorded using thermocouples and the result is processed numerically by an inverse approach to determine the directional thermal conductivity. A validation of the method has been conducted using an aluminium alloy with known thermal properties and the in-plane conductivity test. The correlation between the known and determined thermal conductivities is excellent. In-plane and through-thickness thermal conductivities of Hexcel F593 plain weave carbon – epoxy laminates have been determined using the method developed. It is shown that both conductivities increase with temperature linearly.
The authors wish to thank Mr J. Triantafillou of CRCACS for his assistance with the manufacture of the laminates.
References [1] Philippi I, Batsale JC, Maillet D, Degiovanni A. Measurement of thermal diffusivities through processing of infrared images. Rev Sci Instrum 1995;66(1):182–92. [2] Ouyang Z, Zhang F, Wang L, Favro LD, Thomas RL. In: Thompson DO, Chimenti DE, editors. Novel measurement of anisotropic thermal diffusivity. Review of Progress in Quantitative Nondestructive Evaluation, vol. 17. NY: Plenum Press; 1998. p. 453–6. [3] Chamis CC. Simplified composite micromechanics equations for hygral, thermal, and mechanical properties. SAMPE Quart 1984; 14–23. [4] Ning QG, Chou TW. Closed-form solutions of the in-plane effective thermal conductivities of woven-fabric composites. Compos Sci Technol 1995, 55, p. 41–8. [5] Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in FORTRAN . Cambridge: Cambridge University Press; 1992. p. 390– 5. [6] www.matweb.com.
Measurement of thermal conductivity for fibre-reinforced composites R.D. Sweeting*, X.L. Liu Co-operative Research Centre for Advanced Composite Structures Limited 506 Lorimer Street, Fishermen’s Bend, Vic. 3207, Australia Revised 19 December 2003; accepted 15 January 2004
Abstract A new method has been developed to determine the in-plane and through-thickness thermal conductivities of polymer matrix composites. In the method, the thermal gradient produced by an imposed one-dimensional heat flow in a given direction is measured experimentally. The recorded temperature gradient is used to calculate the thermal conductivity using an inverse numerical approach. Benchmarking was conducted using an aluminium alloy with known thermal properties, yielding excellent correlation. Testing was then performed on F593 carbon-epoxy laminates and the thermal conductivity curves for a service temperature range were determined. q 2004 Elsevier Ltd. All rights reserved. Keywords: A. Polymer-matrix composites (PMCs); B. Thermal properties; C. Numerical analysis; Thermal measurement
1. Introduction The properties of fibre-reinforced composites vary greatly, depending on their constituent materials, fibre orientation and fibre volume fractions. Knowing the accurate material properties is important if accurate and hence meaningful structural analysis or process modelling is to be performed. There are established standards and/or procedures for the measurement of various mechanical properties of fibre composites. However, the same does not apply to the measurement of a number of physical properties, including thermal conductivity, of composites. Work has been performed in measuring thermal diffusivity using the ‘flash technique’ and thermal imaging [1,2], although this requires significant set-up cost and is usually only performed at room temperature. These difficulties have meant that estimation techniques like those based on micromechanics have been the major source of available data [3,4]. The present work aims to develop a relatively simple and reliable method for measuring the thermal conductivity in the three principal directions of a composite laminate. In the method, a one-dimensional temperature gradient is generated in a laminate surrounded by an environment designed to eliminate heat flow in directions other than the one to be measured. Developing a one-dimensional thermal gradient * Corresponding author. Tel.: þ 61-3-96466544; fax: þ 61-3-96468352. E-mail address: [email protected] (R.D. Sweeting) 1359-835X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2004.01.008
simplifies the mathematical solution and reduces the number of unknown factors, which in turn simplifies the data processing and improves the accuracy of the result. Temperatures at a number of locations through the measurement direction of the laminate are recorded using embedded thermocouples. The raw data is then processed using a numerical inverse approach to determine the directional thermal conductivity of the laminate.
2. Method 2.1. Test design methodology The test set-up should be designed to produce onedimensional heat flow in the laminate, to simplify the solution and minimise the number of unknowns. To achieve this, both the thermal edge effects and environmental heat losses must be controlled. The edge effects can be reduced to negligible levels by ensuring the laminate is large enough that all edges perpendicular to the generated temperature gradient, are a sufficient distance away from the measurement zone. The three possible sources of environmental heat losses and the methods of minimising them are: Conduction—prevent thermal contact with surrounding materials.
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Fig. 1. Temperature distribution in one-dimensional models.
Convection—keep convection surfaces in a vacuum. Radiation—provide thermally identnical adjacent surfaces so the same amount of radiation is absorbed as emitted. A number of test designs were initially proposed to fulfil the above requirements. Each possible test design was then modelled using finite element thermal analysis. The results were compared to that of the ideal one-dimensional model to be used to calculate the thermal conductivity. The optimum test designs were selected based on the comparison. The predicted temperature distributions for four different in-plane test designs are compared to the ideal no-loss case in Fig. 1. The free air case (Fig. 1A) illustrates the large amount of heat being lost to the atmosphere from the laminate, assuming convection and radiation losses from its surface. Insulating the laminate (Fig. 1B) reduces the losses, although the temperature profile is still far from the ideal case. Introducing two more heated and insulated laminates outside the measurement laminate (Fig. 1C) improves the temperature profile, although the losses remain too high. Removing the insulation between the laminates and evacuating the air from the cavity (Fig. 1D), eliminates conduction and convection losses from central measurement laminate. Radiation losses are almost eliminated as the adjacent plates are at similar temperatures, leaving a temperature profile close to the ideal one-dimensional case and thus appropriate for the in-plane thermal conductivity experiments. A similar comparison was performed for the through-thickness test design. 2.2. Test set-up Due to the inherently anisotropic nature of polymer matrix composites and the preference to avoid using excessively thick laminates for the through-thickness tests, two different test set-ups were used for the in-plane and through-thickness thermal measurements, respectively.
2.2.1. In-plane Test The in-plane conductivity test set-up selected (Fig. 2) consists of three ‘identical’ parallel composite laminates heated on the left-hand edge by fast warm-up electrical foil heaters (Thermofoil heater HK5167R264L12A). The laminate in the middle has thermocouples embedded in the midplane at given intervals to measure the transient temperature gradient. The two outer laminates are used to minimise the radiation losses from the measurement plate. They provide structural support for a vacuum cavity, minimising both conduction and convection losses from the measurement laminate. The similarity in the heat up rates of the adjacent surfaces of the laminates ensures that the radiation absorbed by a laminate is similar to that emitted. The three laminates are surrounded by insulation to reduce heat convection to the atmosphere, provide a vacuum path and protect the vacuum bag from being cut by sharp corners of the laminates.
Fig. 2. Schematic of in-plane conductivity test set-up.
2.2.2. Through-thickness test Ideally the through-thickness conductivity test (Fig. 3) should be designed using similar principles to the in-plane test. Two plates, one with thermocouples embedded at different points through the thickness, separated by a vacuum cavity with their external surfaces heated would be the ideal test set-up. However, the test developed was limited by the requirement to use an available electrical hotplate as the heat source. The through-thickness test set-up used (Fig. 4) consists of a conductivity test assembly that can be raised and lowered above the hot plate. The test assembly is the measurement laminate with a cork picture frame (spacer), aluminium plate and insulation attached to the top.
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equilibrium was achieved and the process repeated for the new temperature. 2.4. Data analysis
Fig. 3. Schematic of ideal through-thickness conductivity test set-up.
The aluminium plate makes the vacuum cavity used to minimise convection and also reflects some of the radiated energy back to the measurement laminate. Due to the small temperature differences between the top of the measurement laminate and the aluminium plate radiation losses will be minimal. Heat losses at the edges of the laminate are negligible since the distances from the measurement zone to the edges are more than 10 times the thickness. The test assembly needs to be raised and lowered due to the slow heat-up rate of the hot plate. The laminate is raised to prevent contact with the plate until the latter has reached the test temperature. Vacuum is then applied to pull the laminate back onto the hotplate, generating the desired thermal gradient in the laminate.
Thermal conductivity of the composite laminates can be identified from the temperature measurements using an inverse approach. For this purpose, an error function can be defined as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX un j j ð1Þ ðkÞ 2 Texp 2 d ¼ t ½Tnum j¼1
where T is temperature, k is the directional conductivity to be identified and subscripts ‘num’ and ‘exp’ stand for numerical and experimental, respectively. The task of data analysis is to determine k, which minimises the above error function. In the present method, the temperature for the onedimensional transient heat transfer model is solved using the finite difference method. The error function is minimised using the golden section search algorithm [5]. A FORTRAN program has been written to perform the analysis.
3. Results and discussion 3.1. Validation
Fig. 4. Schematic of actual through-thickness conductivity test set-up.
2.3. Test procedure It is well known that thermal properties of composite materials vary with temperature. To determine the thermal conductivity versus temperature curve, measurements were performed in 20 8C increments from room temperature (approximately 20 8C) to 180 8C. Increments of 20 8C were chosen as a compromise between, reducing errors resulting from thermal conductivity changes during the test and being of sufficient size to accurately record the temperature gradient. The thermal conductivity determined thus represents an average of the temperatures measured during the test. To achieve the required elevated temperature environment, testing was performed inside an oven. Before each test the oven air and test assembly were allowed to reach thermal equilibrium. A thermocouple baseline measurement was then performed to eliminate small errors associated with individual thermocouples. A 20 8C temperature increase was then applied to the laminate via the heaters and the transient temperatures in the laminate were recorded. After the test the oven temperature was increased by 20 8C (to the same temperature as the heaters), thermal
Validation of the in-plane conductivity test method was performed using 7075-O aluminium alloy for which the thermal conductivity is given as 173 W/m K [6]. The dimensions of the aluminium plates used were 250 £ 250 mm2 square and 4.2 mm thick. Four thermocouples were used to monitor the temperature distribution in the heat flow direction. Considering the high thermal conductivity of the aluminium alloy, the distance between each of two thermocouples was relatively large at 50 mm. The increased distance between thermocouples, increases the surface area of the measurement zone by 10 times, meaning controlling the losses is even more critical. In Fig. 5, the measured temperature profile is compared to the predictions of a one-dimensional finite element model assuming no losses and using the known material properties. The heating ramp applied in the model was the temperature profile measured by the first thermocouple. Very good agreement exists between the experimental and the predicted temperature profiles at all thermocouple locations, indicating that a one-dimensional heat flow was produced successfully by the developed test method. Processing the experimental data using the FORTRAN program, the thermal conductivity of the aluminium alloy was determined as 178 W/m K at 35 8C which is less than 3% higher than the one given in [6]. The slight difference
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Fig. 5. Comparison of measured and calculated temperature profiles for 7075-O aluminium alloy.
could be due to the 15 8C difference in the measurement temperatures used. 3.2. Conductivity of composite laminates Tests were conducted for Hexcel F593 carbon-epoxy plain weave pre-preg (W3T282-4200 -F593) laminates, autoclave cured for 2 h at 180 8C and 680 kPa. The fibre volume fraction of the laminates was 49%. The three laminates manufactured for the in-plane conductivity test were 260 mm long, 150 mm wide and 2.7 mm thick. They were made from 12 plies of F593 orientated in the 08 direction. The thermal conductivities for the two in-plane directions were assumed to be the same
and only the warp direction was measured. Four thermocouples were embedded along the warp direction, 5, 10, 15 and 20 mm away from the heater edge. The through-thickness test panel was made from 24 plies of F593 pre-preg all orientated in the 08 direction. The resulting panel was 200 £ 200 £ 5.5 mm 3. Thermocouples were embedded after the 1st, 6th, 12th and 18th plies. The accuracy of the thermocouples positioning in the laminate and the disturbance they cause to the heat flow are two problems with this test method. By using multiple thermocouples, errors resulting from positioning are reduced; the temperature profiles from all the thermocouples are used to calculate the conductivity, thus
Fig. 6. Thermal conductivity of F593 plain weave composites.
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Fig. 7. Comparison of measured and calculated temperature profiles for in-plane test.
averaging the errors. If a thermocouple was significantly out of position it would be immediately obvious and that thermocouple could be neglected. No sectioning has been performed to measure the thermocouple positions, however for the in plane specimen, the thermocouples were placed within 0.5 mm during the lay-up. The through-thickness laminates thermocouple positioning is very accurate as they were placed between the plies, thus the only errors could result from minor compaction differences above and below the thermocouple during cure. Any disturbance to the heat flow was reduced by manufacturing the thermocouples from fine wire (0.25 mm diameter) and offsetting their tips perpendicular to the direction of heat flow. The in-plane and through-thickness thermal conductivities determined are plotted in Fig. 6 as functions of
temperature. Both conductivities increase with temperature linearly, although the in-plane one increases at a slightly greater rate. Within the measurement temperature range, the in-plane conductivity increases from about 2 to 3 W/m K, while the through-thickness conductivity changes from approximately 0.5 to 0.7 W/m K. In other words, the in-plane conductivity is approximately four times the through-thickness conductivity throughout the temperature range. A comparison of the measured temperatures and those calculated from the generated thermal conductivity is shown in Figs. 7 and 8 for the in-plane and throughthickness tests at room temperature, respectively. Excellent agreement exists between the experimental and calculated transient temperature profiles at all
Fig. 8. Comparison of measured and calculated temperature profiles for through-thickness test.
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the measurement points. These graphs are typical of all the tests performed.
The in-plane conductivity is approximately four times the through-thickness conductivity.
4. Conclusion
Acknowledgements
A new and relatively simple method has been developed to measure the in-plane and through-thickness thermal conductivities of fibre reinforced composites. One-dimensional heat flow is generated in the laminates by applying heat along one edge or face. The use of vacuum cavities and the careful selection of the surrounding materials minimise convection, conduction and radiation heat flow in the directions other than the one being measured. The transient temperature gradient in the given direction is recorded using thermocouples and the result is processed numerically by an inverse approach to determine the directional thermal conductivity. A validation of the method has been conducted using an aluminium alloy with known thermal properties and the in-plane conductivity test. The correlation between the known and determined thermal conductivities is excellent. In-plane and through-thickness thermal conductivities of Hexcel F593 plain weave carbon – epoxy laminates have been determined using the method developed. It is shown that both conductivities increase with temperature linearly.
The authors wish to thank Mr J. Triantafillou of CRCACS for his assistance with the manufacture of the laminates.
References [1] Philippi I, Batsale JC, Maillet D, Degiovanni A. Measurement of thermal diffusivities through processing of infrared images. Rev Sci Instrum 1995;66(1):182–92. [2] Ouyang Z, Zhang F, Wang L, Favro LD, Thomas RL. In: Thompson DO, Chimenti DE, editors. Novel measurement of anisotropic thermal diffusivity. Review of Progress in Quantitative Nondestructive Evaluation, vol. 17. NY: Plenum Press; 1998. p. 453–6. [3] Chamis CC. Simplified composite micromechanics equations for hygral, thermal, and mechanical properties. SAMPE Quart 1984; 14–23. [4] Ning QG, Chou TW. Closed-form solutions of the in-plane effective thermal conductivities of woven-fabric composites. Compos Sci Technol 1995, 55, p. 41–8. [5] Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in FORTRAN . Cambridge: Cambridge University Press; 1992. p. 390– 5. [6] www.matweb.com.