I n d . E n g . Chem. Res. 1988,27, 702-706
702
Flash Pulse Measurement for Off-Axis Thermal Conductivity of Carbon Composite Materials Donald J. Jaklitscht and J o h n W. Walkinshaw** US.A r m y Materials, Technology Laboratory, Arsenal Street, Watertown, Massachusetts 021 72, and Chemical Engineering Department, University of Lowell, One University Avenue, Lowell, Massachusetts 01854
A variation of the flash pulse method was used to directly measure the off-axis thermal conductivity of pyrolytic graphite and Vought carbon/carbon composite. The flash pulse method, proposed by the authors, requires samples to have similar surface emissivities to that of a reference material. The samples chosen were two advanced materials, pyrolytic graphite and a Vought carbon/carbon composite; both are anisotropic, the latter being a two-dimensional laminar composite, while the reference was aluminum. To overcome the dissimilar nature of the surfaces of the aluminum to the test specimens, the carbon samples were coated with vapor deposition aluminum. This approach was verified with Armco iron samples, which yielded an error of 1.6% to the published thermal conductivity. The method was applied to specimens cut a t various angles from blocks of the two carbonous materials. The thermal conductivity of these materials is reported as a function of the angle of the specimen and as a function of the location within the original sample. The basis of the method was devised by Jenkins and Parker (1961) and Parker et al. (1961). Briefly, the experimental procedure involves exposing the front face of the sample to a short pulse of radiant energy. The time for the heat pulse to travel through a thin section of the material is measured (i.e., the temperature history of the back face is recorded), and the thermal diffusivity is determined. As long as the pulse is of short duration compared with its time of passage through the sample and as long as this passage is sufficiently short, heat losses will be negligible. The results of Parker's work can be expressed as a = 1.38-
L2
n2t,,z
(1)
where a = thermal diffusivity (m2/s),L = sample thickness (m), and tl,z = time required to reach one-half of the maximum back surface temperature (9). diNovi (1968) proposed a modification to the method which utilized Armco iron as a standard material through which the amount of energy reaching the surface of a specimen could be evaluated. Then, the thermal conductivity of the unknown specimen could be evaluated. In order to accomplish uniform surface emissivites between the iron standard and 347 stainless steel, which was evaluated as the unknown, both front faces were coated with colloidal graphite. deNovi's approach does not require any knowledge of the physical properties of the unknown, which is an advantage; however, the accuracy of predicting the thermal conductivity value of the stainless steel was estimated to be f5%. At higher temperature, the accuracy of the method decreased to +=lo%. Unlike the work of diNovi, this paper deals with the prediction of thermal conductivity of an unknown by comparison with the standard where at least one measurement of density and specific heat must be made on the unknown. With this additional information, the authors felt that the accuracy experienced by diNovi could be improved with minimal additional work. Recently, the pulse technique has been extended to carbon/carbon composites. Taylor et al. (1985) used lasers U S . Army Materials.
* University of Lowell.
0888-5885/88/2627-0702$01.50/0
for the generation of the heat pulses on fibrous carbon composites, while Jortner (1981) measured thermal diffusivities along three axis of Oo, 45', and 90'. Jortner's approach is to calculate diffusivity at various time rise fractions of 20%) 5070, and 80%, as opposed to Parker's 50% time rise to maximum back surface temperature. The lower variation of diffusivity to rise time at a 45' angle when compared to 0" and 90' axis measurements prompted Jortner to conclude that 45' measurements are more reliable indicators of bulk composite behavior. Methods The equation of Parker et al. (1961) (eq 1)can be rewritten to yield thermal conductivity ( k = apC,) as PCA2
k = 1.38-
(2) n2t1,2
Parker et al. additionally proposed that the thermal conductivity can also be expressed as a function of the amount of incident energy absorbed per unit area (Q in J/m2) on the front face of the sample and the samples maximum temperature rise (T,in K ) . This relationship is expressed as (3) The above relations will hold true, and the flash pulse method will be viable provided certain conditions are maintained: there can be no phase change in the sample; and the physical properties of thermal conductivity, density, and specific heat (and therefore thermal diffusivity) do not change over the temperature rise experienced by the sample during testing. Experimentally these conditions can be met by limiting the heat pulse, such that the back surface temperature rise is only a few degrees. Method 1 (Standard Based) Development. Method 1 is directly based on the use of eq 1 and 3. Where the thickness (L)is known, hence, the only two terms that need to be evaluated are the radiant energy pulse per unit area (Q) absorbed on the front surface of the sample and the maximum temperature (T,) rise above ambient on the back surface. The amount of energy a material absorbed from a heat pulse can be found from its mass, specific heat, and temperature rise. The mass of the sample involved 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4,1988 703 18 Laser Power source Remote Switch
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Figure 2. Diagram of the laser pulse apparatus.
5
- K Figure 1. Heat absorption as a function of the maximum back surface temperature rise for the aluminum standard. Temperature rise on the back surface (T,)
in energy absorption is taken as that under the area covered by the pulse. This assumption requires that the sample be relatively thin so that the time duration of the heat pulse through the sample is short. Measurements are then quite quick after the flash, thus minimizing the effeds of radial heat transport. The mass involved can then be calculated based on the area, thickness, and density of the material. Thus, the total energy absorbed (in J) is Q(absorbed) = A&pC,AT
(4)
where: A, = surface area of the sample subjected to the heat pulse (m2),L = sample thickness (m), p = density (kg/m3), C, = specific heat (kJ/(kgK)), and A T = the temperature increase in the pulse area (K). The measurement of back surface temperature uses the initial sample temperature as reference; thus, the maximum back temperature rise (T,) is the differential measurement (AT). Since there were no adjustments in the physical setup of the apparatus, A, is a constant. Minimal differences in sample thickness are maintained; thus, the heat absorbed between samples becomes a function of sample density, specific heat, and temperature rise. The model requires experimental data on the standard material; in this project, pure aluminum was chosen. By use of the same experimental setup throughout the project, the heat absorbed per unit area during the flash pulse is determined for the aluminum by (eq 1 and 3) (5) The results for the aluminum standard for the specific experimental setup are shown in Figure 1. The energy absorbed for any material can be related to aluminum by Q(unknown) = (0.177
+ 3.03Tm)(PCP)AlStd (PCp)Unk.
(6)
Thus, one measurement of density and specific heat of an unknown material will allow for the direct calculation of the thermal conductivity combining eq 3 and 6 and solving for k (in kW/(mK)):
Equation 7 can be written in terms of experimentally
determined values thru the substitution of a by eq 1 to yield
Method 2 Development. The second method of determining thermal conductivity uses the definition of thermal conductivity as expressed by k = apCp (9) and the equation of Parker et al. to yield PCA2 k = 1.38T2tl,2
where density ( p ) and specific heat (C ) were measured directly for each specimen, for each angfe of cut, and each temperature range encountered during testing.
Apparatus A schematic diagram of the experimental apparatus is displayed in Figure 2. The laser head (heat pulse source), lens, sample holder, and thermocouple assembly were all mounted on a double-rail collimating optical bench. The laser was fastened to a lab jack secured to a 1/2-in.steel block specially milled to accommodate mounting on the rail. The lab jack was used to aid in the alignment of the beam, sample, and thermocouple. Next to the laser head was a plano-convex lens that was used to adjust the laser spot size. The sample holder was located such that the sample face was 15 cm from the lens surface. The holder was fabricated from polycarbonate (Lexan). The low thermal conductivity of Lexan served to thermally isolate the sample; additionally, its high electrical resistance isolated the sample electrically. The material also provided to be easily machinable, facilitating construction of the sample holder. The thermocouplejunction was formed through the back surface of the specimen by type K junction wires located directly behind the sample holder. A spring-loaded thermocouple junction was of importance in order to ensure constant contact between the thermocouple wires and the back face of the sample. The pressure exerted by the thermocouple also served to hold the sample in place during measurements. The laser head which provided the heat source was of the ruby red type with rod dimensions of 7.3 cm in length and a diameter of 1cm, which operated at a wavelength
704 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988
mu
BEAM
LASER
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O0
30°
Zero
k Axis Degree Sample
45O
60’
9c0
Sample Cut P l a n e s
Figure 3. Orientation of the sample cut lines.
of 694 nm. The duration of a single pulse was 900 FS. The output of the laser was controlled through a separate power source which allowed for an input of 840 J; the peak power was equal to 4 kW. The spot site of the beam had a diameter of 0.546 cm and a cross-sectional area of 0.234 cm2;hence, the average energy flux delivered by the beam was 17.1 kW/cm2. The data were acquired through a 5000 Series Tektronics storage oscilloscope fitted with a differential amplifier module (Model 5A22N) capable of displaying data in the range of 10 pV/division. The other modules comprised a waveform digitizer (Model 5D10) which allowed for the storage and subsequent output of the back face temperature history as represented by the oscilloscope trace. This trace was subsequently made into a permanent record by plotting the oscilloscope trace memory to a Hewlett-Packard X-Y recorder (Model 7476A). Specimen Preparation. The test specimens were cut at various angles from larger blocks of pyrolytic graphite and Vought carbon/carbon composite. The angles of cut are shown in Figure 3 in relation to either the basal planes or the laminae, while the individual sample orientation to the direction of the heat pulse is shown in Figure 4. After sample cutting, the individual specimens were smoothed with 600-grit Carborundum paper, cleaned with acetone, and washed with distilled water. At this point, the specimens were checked for parallelism with a micrometer and adjustments were made by smoothing with the 600-grit paper and cleaning. In order to ensure good electrical contact between the thermocouple and the back face of the pyrolytic graphite and C/C composite samples, an additional conductive layer was found to be desirable, especially in the case of the Oo configuration of pyrolytic graphite samples where thermal measurements must be made through the u ~ face n of the graphite structure. The fact that a thin layer could be applied to a sample face with no discernible effect on the measurement of diffusivity or conductivity values has been verified by diNovi (1968). The choice of coating material in this type of application would normally be graphite. However, in this work graphite could lead to problems because of the carbonous samples. Instead, both sides of the specimen were coated with room-temperature vapor-deposited aluminum. This provided the necessary electrical conductivity to the back side, while providing similar emissivities to the front side for the samples tested. The equipment used to coat the samples was manufactured by Mill Lane Engineering
Figure 4. Individual sample configurations representing axis of the sample and the direction of the laser beam.
Company. Experimental measurement indicated that a double coating on both sides contributed about 250 pm to the specimen thickness. A Perkin-Elmer differential scanning calorimeter (DSC) was used to determine the specific heat of the pyrolytic graphite and the Vought carbon/carbon composite. Indium was used to calibrate the equipment, and magnesium oxide was used as a standard and comparison material. Nitrogen gas was used as a purge through the calorimeter head in order to maintain a constant heat-transfer coefficient. Measurements of heat capacity were made at an average run temperature of 305 K over a scan range of 300-310 K.
Results To check the validity of methods 1 and 2, Armco iron samples were evaluated on the DSC to determine the heat capacity and the physical measurements used to calculate the density. Equation 8 and 10 were used to evaluate 30 heat pulse trials on the coated Armco iron specimens with the following results: thermal conductivity (std dev) dev to published (Wetly, 1969) value
method 2 (eq 11) method 1 (eq 8) 71.76 W/mK (4.86) 68.91 W/mK (4.42) 1.6%
5.0%
The two carbonous materials chosen for testing are as follows: (1) pyrolytic graphite produced by Pfizer Corporation from decomposing methane on a hot surface, in the form of a 10-cm square by 2.5-cm thickness; (2) Vought material produced by the pyrolysis of resin-bonded layers of satin weave graphite cloth; the resultant thickness is 1 cm. The first step was the calculation of the densities of the two materials from the weight and dimensions of the original materials as supplied by the manufacturer, resulting in bulk densities of density pyrolytic graphite = 2206 kg/m3 and density Vought carbon/carbon = 1600 kg/m3. The next step was specimen preparation consisting of cutting, smoothing, and coating operations. Following the coating operation, the specimens were evaluated for thermal diffusivity and conductivity using the equipment shown in Figure 2. The thermal diffusivity as a function of the angle of sample orientation to the original material is shown in Figure 5. It is obvious that the thermal diffusivity of the
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 705
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Figure 5. Thermal diffusivity as a function of the angle of sample orientation.
30
45
60
75
90
Angle of Sample Orientation
Angle of Sample Orientation
Figure 6. Thermal conductivity of pyrolytic graphite with respect to the angle of sample orientation.
Table I. Relation to Thermal Diffusivity of Pyrolytic Carbon to Specimen Location within the Sample no. of therm. diff., a,av values, specimen specimens angle, deg position tested cmz/s std dev 0.24 45 top 8 1.33 13 1.38 0.71 middle 9 1.55 0.25 bottom 60 top 11 1.98 0.72 bottom 19 2.37 0.74 90 top 14 2.95 0.81 bottom 16 3.03 0.67
pyrolytic graphite is about 10 times greater than that of the Vought material. Also, the standard deviation about each mean as indicated by the vertical bars is also much greater for graphite than the Vought material. To determine the sources of variation in the pyrolytic graphite results, the location of each specimen was determined relative to the bottom or base substrate from which the pyrolytic graphite was “grown”. It is common to find nucleation of the carbon to form a layered structure of growth cones with possibly different thermal transport properties. Table I shows that the thermal diffusivity of the pyrolytic graphite depends on the specimen location, with higher thermal diffusivities measured in specimens cut ne= the bottom of the sample. A similar analysis could not be performed on the Vought material as only one specimen could be cut from the thickness plane of the original sample. The final step is to compare the thermal conductivities of the two materials by the two methods of analysis. This portion of the work required the use of the bulk densities and the specific heats of the two materials. The specific heats were determined over temperature ranges corresponding to the average temperatures (T,)encountered during the heat pulse trials. No effects due to the samples angle or location on the specific heat were noted. The specific heat values used to calculate the constants in thermal conductivity equation (eq 8) were determined at 305 K to be material pyrolytic graphite Vought carbon/carbon
J/(kg-K) X lo-* 7.786 9.335
0
15
30 45 60 75 Angle of Sample Orientation
90
Figure 7. Thermal conductivity of Vought carbon/carbon composite with respect to the angle of sample orientation.
As a check on the differential scanning calorimeter, the specific heat of the standard pure aluminum was evaluated to be 0.930 kJ/(kg.K), deviating by only 3.8% from the published figure of 0.896 kJ/(kg.K) (Karlekar and Desmond 1982). The results of the experimental work are reported in Figures 6 and 7 which show the relationship that angle has on the thermal conductivity. Discussion The procedure developed for the direct measurement of thermal conductivity by the flash pulse method shows close agreement for the Armco iron specimens when compared to published thermal properties. When the procedure was applied to the Vought carbon/carbon composite (Figure 7 ) , a great deal of similarity is indicated between the shapes of the two curves, although there are differences in the numerical values. The results for the pyrolytic
706 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 Table 11. Comparisons of 4 5 O Angle Measured and Calculated Thermal Conductivity Values therm. conduct. a t 45' specimen angle, W/(m.K) material exDtl method measd a? pyrolytic graphite 1 159 114 2 245 262 1 18.1 19.4 Vought C/C 2 27.3 26.7
% devb
-28.3 6.94 7.18 -2.20
The averaged value is based on the measured values a t the 0 ' and 90° specimen angles. bDeviation is based on the measured value.
graphite (Figure 6) show differences in both the shape of the curve and numerical values determined. Part of the differences noted that the pyrolytic graphite could be due to the nonuniformity of thermal transport properties with respect to specimen location within the original sample block. As noted in Table I, the thermal diffusivity is a function of the location ofthe specimen with respect to the thickness plane. This phenomenon could be due in part to the process by which pyrolytic graphite is formed by continuous nucleation and formation of growth cones. As the growth of the graphite continues, a more irregular pattern is developed in the growth cones due to secondary nucleation and new growth development. This may account for lower thermal diffusivities in specimens cut at locations away from the bottom of the sample. The effect of specimen location was noted after some of the testing had taken place, and thus not all of the information for the Oo and 30" specimens was available for comparison to the 45O, 60°, and 90" data reported in Table I. Further analysis for the graphite measurements comes from the work of Kelley (1969), who compared the conductivities of very perfect deposition graphite. The data of decambarieu (1968) at 333 K indicated an anisotropy ratio of 340 (anisotropy ratio equals the thermal conductivity parallel to the basal or deposition plane divided by the thermal conductivity perpendicular to the basal plane). Hooker et al. (1966) found the equivalent ratio to be 210. In this work, the equivalent anisotropy ratio would be expressed as k at 90°/k at Oo and is equal to 210 as measured by method 1 and 520 as measured by method 2. The second method gives an anisotropy ratio much larger than the decambarieu data for well-oriented pyrolytic graphite. This would indicate that method 1 yields
more consistent results as the angle of measurement was altered. Another method of comparison is possible by use of the recommendations of Jortner (1981) for the analysis of three-dimensional carbon/carbon composites by comparison of the 45O data to the averages of Oo and 90° specimens. The comparisons are listed in Table I1 for both pyrolytic graphite and Vought carbon/carbon samples. As in the previous analysis, the Vought material shows close agreement between the measured and the averaged values. The pyrolytic graphite comparisons also show close agreement for analysis by method 2. It is not clear at this point if the variation on method 1 data is due to the nonuniformity of the pyrolytic graphite or to the attempt to extend the Jortner approach to the analysis to nonthree-dimensional composite materials. Despite the problems associated with the nonuniformity of the transport properties for the pyrolytic graphite specimens, method 1used in this work has proven to be a faster and more direct means to measure the thermal conductivity of unknown materials once the standard material has been evaluated. Registry No. Al, 7429-90-5; graphite, 7782-42-5.
Literature Cited decambarieu, A. J. Phys. (Orsay, Fr.) 1968 28, 931. diNovi, R. A. J. Sci. Inst., E 1968, 1 , 379. Hooker, C. N.; Ubbelohde, A. R.; Young, D. A. Proc. R. SOC.,London, A 1966, 353, 1. Jenkins, R. H.; Parker, W. J. "Flash Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity". WADD Technical Report 61-95, June 1961; U.S.N. Rad. Det. Lab., Project No. 7360. Jortner, J. "On the Use of Off-Axis Testing to Characterize the Thermal Diffusivities of Orthagonally Reinforced Carbon-Carbon Composites". Special Report of AFOSR, 1981, AFOSR, Grant F, 49620-81-k-0011. Karlekar, V. V.; Desmond, R. M. Heat Transfer, 2nd ed.; West Publishing: New York, 1982; p, 768. Kelley, B. T. Chemistry and P h y s m of Carbon; Walker, P. L., Ed.; Marcel Dekker: New York, 1969; Vol. 5. Parker, W. J.; Jenkins, R. J.; Butler, C. P.; Abbott, G . L. J. Appl. Phys. 1961,32, 1679. Taylor, R. E.; Jortner, J.; Groot, H. Carbon 1985, 23(2), 215. Wetly, J. R.; Wicks, C. E.; Wilson, R. E. Fundamentals ofMomentum, Heat and Mass Transfer, 2nd ed.; Wiley: New York, 1969; p 730.
Received f o r review March 5, 1987 Revised manuscript received November 16, 1987 Accepted December 16, 1987
