art3A10.10072Fs11148-013-9543-5

HEAT ENGINEERINGFORMATION OF THE THERMAL CONDUCTIVITY OF CARBON-CARBON COMPOSITESM.Yu.Bamborin 1and S.A.Kolesnikov 1Translated from Novye Ogneupory ,No.2,pp.22–27,February,2013.Original article submitted December 10,2012.Studies are made of the effect of structural and processing parameters on the reproducibility of the thermal conductivity of high-density carbon-carbon composites reinforced in three and four directions.The mechani-cal,physical,and thermophysical properties of the carbon semifinished products are investigated and the fac-tors that determine the average thermal conductivity of the material are ranked in importance.It is established that the property indices required for the material are reproduced when the specified manufacturing conditions are maintained.Keywords:high-temperature treatment,carbon composites,strength of a composite,thermal conductivity,electrical resistivity.Different carbon-based materials (CBMs)—including carbon-carbon composites (CCCs)and structural graphites (SGs)—which have the same levels of true and apparent density and are treated at the same temperatures also have nearly the same resistance to chemical attack,erosion,and sublimation.Carbon-carbon composites are distinguished by their mechanical strength and heat resistance.A relatively low resistance to thermal shock limits the application of CBMs in the nozzles of solid-fuel rocket engines (SFREs)[1,2]and in electrodes used in the metallurgical industry [3].Here,any criterion that is used to evaluate the heat resistance of CBMs can be represented by the factor of safety n ,which is the ratio of ultimate tensile strength [s ]to the acting ther-mal stresses s actg :n E TE Q T T ==-=-[][]()[](),s s s m a s m a d lactg 11D (1)where m is Poisson’s ratio;a T is the temperature coefficientof linear expansion (TCLE);E is Young’s modulus;D T is the temperature gradient;d is the thickness of the product;Q is heat flux.For the case in which ceramic products having the same thickness d are used under conditions whereby Q and D T are the same for each product,m is relatively low and is constant,and the values of a T and E are large,W.D.Kingery [4]con-verted this expression to a simpler form that is commonly known as the Kingery criterion R :n QR ET d m s l a 11-==[],(2)where l is the average thermal conductivity.It follows from the above that one important factor in en-suring that carbon-based materials are resistant to thermal shock is their thermal conductivity.The goal of the investiga-tion being discussed in this article was to analyze the effect of technological and structural parameters on the reproducibility of thermal conductivity in the serial produc-tion of semifinished products for spatially reinforced high-density CCCs at the Scientific Research Institute of Graphite (NIIgrafit).Questions related to the formation of thermal conductivity remain an important matter for different types of CCCs [5].In the case being discussed,the semifinished product is a thick-walled ring (Fig.1)that the manufacturer subsequently uses to make nozzle bushings for SFREs.The technology that is used to make high-density CCCs includes up to five Refractories and Industrial Ceramics Vol.54,No.1,May,2013291083-4877/13/05401-0029©2013Springer Science+Business Media New York1Scientific Research Institute of Graphite.successive operations involving isostatic carbonization(high pressure—high temperature)[6].The empirical foundation of the present investigation was the results obtained from quality-control of the material of more than200serially-pro-duced semifinished products,additional studies of the prop-erties of CBMs,and analysis of the execution of different production processes.Quality-control of the material of the mass-produced goods includes determination of the following:–apparent density;–ultimate strengths in compression and tension;–dynamic elastic modulus;–TCLE up to2800°C;–thermal conductivity in the room-temperature range.Apparent density.Density and open porosity were deter-mined by the hydrostatic method.The method is certified for values of open porosity within the range from5to35%.Ultimate compressive strength s cr was determined on specimens measuring20´20´30mm.The method is based on the determination of s cr as the quotient from the division of the breaking load for the specimen by its initial cross-sec-tional area.The principle behind the method is the applica-tion of a compressive load to the specimen with the crosshead of the testing machine moving at a constant speed. The specimen is loaded until it fracture and the load at which this takes place is recorded.Ultimate tensile strength s tsn was determined on vane-shaped specimens measuring100´25´10mm.The method is based on determination of s tsn as the quotient from the di-vision of the specimen’s breaking load by the initial cross-sectional area of its working part.The principle behind the method is the application of a tensile load to the speci-men with the crosshead of the testing machine moving at a constant speed.The specimen is loaded to fracture and the load at fracture is recorded.Elastic modulus was determined by the dynamic method on vane-shaped specimens measuring150´20´20mm. The principle behind the method is determination of the nat-ural resonance frequency of longitudinal vibrations of the specimen when it positioned between two piezoelectric transducers.One of the transducers is used to induce vibra-tion of the specimen by means of an acoustic generator, while the other third converts the specimen’s mechanical vi-brations into electrical signals that are sent to a counter and a resonance meter.The TCLE up to2800°C was determined by direct mea-surement of the elongation of the specimen with a horizontal microscope.The graph of the dependence of the specimen’s relative elongation on the measurement temperature was used to calculate the average TCLE within prescribed tem-perature ranges.Test temperature was measured with an opti-cal pyrometer.The tests were performed in argon in a labora-tory electric vacuum furnace.A specimen with a specially shaped edge was used to reduce the error of the optical tem-perature measurement due to the incompleteness of the graybody radiation and radiation from the edge.The total ab-solute error of the method is within the range~0.1·10–6K–1.Thermal conductivity in the room-temperature range. Average thermal conductivity was measured by a method that makes use of the steady-state axial heat flow.The method is based on comparison of the thermal conductivity of the specimen versus the thermal conductivity of standard materials.Our tests were performed in a vacuum~240Pa in order to eliminate convection in the measurement cuvette. With allowance for the measuring instruments used and the difference in the heat resistances of the standard and the specimens,we took7–10°C to be the maximum theoretical error of the experiment.We also studied the changes in resistivity and the lattice parameters of the graphite.An x-ray phase analysis based on reflection geometry was performed on powder diffractometer D8Advance,which is made by the“Bruker”company.The diffractometer has an x-ray tube with a copper anode.The samples were grated to fractions smaller than80m m and placed in a thin layer on a flat cuvette made of amorphous quartz.Silicon powder was added to the sample to serve as the internal standard.The diffractograms were recorded with an increment of0.02°and11sec of exposure at each point. The preferred orientation of the carbon-carbon material leads to low-intensity reflections of the hk0type.Thus,we also re-corded the(110)reflection with an exposure of600sec in or-der to determine the parameter La.The resulting data was an-alyzed in the full-profile-refining program TOPAS.The in-strument function was described using the fundamental-pa-rameters method,while the cell parameters and crystallite di-mensions were refined by the Pauli expansion method.A phase with the space group P63/mmc was used as the model to describe the diffractograms.The initial parameters of the cell a=0.246nm and c=0.67.Crystallite size was200nm. The positions of all of the peaks are connected to single cell parameters and their intensities are independent in the ap-proach that was just described,which is advantageous from the standpoint of the crystallites’orientation.30M.Yu.Bamborin and S.A.Kolesnikovrge semifinished product made of a spatially reinforced CCC;rod diameter in each cell of the composite is1.22mm.Heat transfer in a CBM [7]takes place as a result of heat-induced vibrations of the crystalline lattice that occur at sonic velocities n .These excitations are known as phonons,which are comparable to quasi-particles of matter and move within the basal planes of crystallites (along the crystal-lite La ).l n =13C L V [],(3)where l is thermal conductivity;C v is heat capacity;L is the mean free path of the phonons.The size of the defect-free regions are small in materi-als having an amorphous or fine-crystalline structure (La »2.0–3.0nm).The mean free path of the phonons is also small.It is somewhat greater than the size of the crystal-lite itself and,strictly speaking,is not equal to the latter.Dur-ing heat treatment,the value of l of carbon-based materials increases more than tenfold.The increase in thermal conduc-tivity is due to consolidation of the material,an increase in the number of defect-free regions of the crystalline lattice,and a decrease in the amount of amorphous carbon located along the boundaries of the ordered regions.In connection with this,there is also a decrease in the resistance to oscilla-tions of the phonon system.Franklin’s estimate of the degree of graphitization —an estimate based on measurement of the average interplanar spacing [7]—is proportional to the de-crease in the percentage content of amorphous carbon.The stability of the production process was analyzed in accordance with the requirements of the standards GOST ISO 9001and GOST RV 15.002–2003.It was found that the average thermal conductivity of the semifinished products varied from 56to 66W/(m·K)and that more than 82%of the semifinished products were within this range.From 4.6to 12.5%of the semifinished products had an average thermal conductivity between 44and 74W/(m·K).The average value obtained for the standard deviation of the experimental deter-minations of thermal conductivity on 16specimens (eight determinations in the XY plane and eight in the XZ plane)was 4.86W/(m·K).The stability of the objectivity of mea-surements of average thermal conductivity was determined for the period of 1992to 2009.Doubling the number of tests performed on specimens did not affect the standard devia-tion,which is an indication of the quality of the methodology that was used.There are no grounds for changing that methodology based on a loss of accuracy or quality in the determinations that have been made.This applies both to the present and the period during which the method was being developed.The effect of individual factors was examined by comparing the test results for semifinished products made in accordance with different programs due to changes in the raw materials or processing conditions.It was found that the use of differ-ent grades of coal-tar pitch from different manufacturing plants in Russia and the Ukraine does not affect thephysico-mechanical or thermophysical properties of the high-density composites that are made.For example,it fol-lows from the table that the thermal conductivity of these composites is affected considerably more by the type of car-bon filaments that is used than by the method employed to assemble the framework.The temperature used in the industrial high-temperature treatment of grade VMN-4a carbon filaments made of polyacrylonitrile (~2400°C)is considerably higher than the temperature (~1600°C)used to treat grade UKN-5000car-bon filaments,which are also made of polyacrylonitrile.The limiting processing temperature used in the production of composite material Desna T-1(~2170°C)has not compen-sated for the initial difference in the physical condition of the carbon fillers.An increase in the treatment temperature for the carbon filaments from 1600to 2400°C (by 800°C)could increase the thermal conductivity of Desna T-1by 21W/(m·K),i.e.by 2.625W/(m·K)for each 100°C increase in the temper-ature used to treat the carbon filaments.However,the factory which makes UKN-5000filaments cannot make such a change in treatment temperature because it does not have the necessary heating facilities.The actual scatter of treatment temperature for different UKN-5000carbon filaments is ±100°C (the scatter was determined by measurement of the thermo-emf)and the average per filament is ±60°C.Varying the treatment temperature for the initial carbon filament from 1500to 1700°C could change thermal conductivity by ~3.225W/(m·K).However,deviations of thermal conductiv-ity that average roughly 3W/(m·K)also take place when there are variations in the conditions under which the frame-work is assembled.An analysis of Schuchert diagrams in accordance with GOST RV 15.002–2003established that variation of the ap-parent density of the materials from 1.89to 1.98g/cm 3re-sults in a change in thermal conductivity by 1.1W/(m·K)forFormation of the Thermal Conductivity of Carbon-Carbon Composites 31TABLE 1.Approximation of Experimental Data Used to Deter-mine the Dependence of Average Thermal Conductivity on Test Temperature in the Range from 300to 3200KCarbon filamentFrameworkHeat-conduction equationUKN-5000Wovenl Z =+23849341.,T K ;l X YT ,.,=+249510056K VMN-41Rod-basedl Z =+28613920.,T K ;l X YT ,.,=+27213701KUKN-5000The samel Z =+22029272.,T K ;l Z =+2219170.,T Keach+0.01g/cm3.Within the apparent-density range from 1.90to1.98g/cm3that is normal for Desna materials,aver-age thermal conductivity can expected to increase by approx-imately9.9W/(m·K).The technique that has traditionally been used to control the thermal conductivity of CBMs is variation of the limiting temperature in the treatment.The thermal conductivity of carbon fibers and coal-tar-pitch-based matrices in CCCs can reach690W/(m·K)[8]if the density of the material is in-creased by more than2g/cm3and the maximum treatment temperature is raised to2800°C.An increase in the treatment temperature is accompanied by a several-fold increase in the size of the crystallites.Figure2shows the relationship that we found between thermal conductivity and the treatment temperature for graphites[9]and3D CCCs based on coke obtained from coal-tar pitch.The conductivity of the CCCs is somewhat higher than that of the CBMs,the difference depending on the treatment temperature.The reason for this difference is the high thermal conductivity of the filler(~120W/(m·K), which is attributable to its more developed texture(~85ver-sus~0.3–0.5[10]for isotropic CBMs).It also follows from Fig.2that an increase in the treatment temperature from 2100to2300°C can increase the conductivity of material Desna T-1by roughly10W/(m·K),i.e.by0.20W/(m·K)for each100°C increase in treatment temperature.The level of metrological accuracy attained in reproducing the limiting treatment temperature for semifinished products is substan-tially higher in electric vacuum furnaces(±15°C),so this fac-tor cannot be the reason for the instability seen in the repro-duction of thermal conductivity.A comparative analysis of the levels attained for resistivity and conductivity(see Fig.2) showed that the adherence to the Wiedemann–Franz law lr=const»1023±155which is seen for various CBMs[9]is also seen here within a wide range of temperatures.This means that mobile devices can be used to reliably check the quality of CCCs between processing stages,as is already be-ing done for a wide range of CBMs.For example,such qual-ity control could be performed based on an equation of the form l=135.09»3.8545r.In this case,the pairwise corre-lation coefficient R2=0.9068.It follows from Eq.(3)that the thermal conductivity of a CBM depends on the speed of sound in it,the rate of trans-mission of kinetic energy in the material,and phonon excita-tion in the longitudinal direction n.The elastic modulus of Desna T-1was determined by a dynamic method based on information on the change in ultrasound velocity in a 120-mm-long specimen and data obtained from determina-tion of apparent density(E dynamic=rn2).The results obtained from monitoring thermal conductiv-ity are shown in Fig.3in the form of the dependence of this property on elastic modulus.The range of variation of elastic modulus was41–60GPa.The metrological error of the de-termination was3%,which confirms that there was a physi-cal reason for the broad variation of elastic modulus and, thus,thermal conductivity.With a10GPa increase in elastic modulus,thermal conductivity increases by nearly30W/(m·K) in the case when the limiting degree of graphitization in-creases from0.3to0.7.When the degree of graphitization of the material ranges from0.645to0.73,thermal conductivity undergoes an even greater jump—from30to73W/(m·K). The latter value is almost equal to the maximum allowed by existing specifications,since the average of16determina-tions was no greater than74W/(m·K).An analysis of the extent to which the specifications were met showed that lower values for elastic modulus are recorded in semifinished products which undergo a relatively small gain in mass during the second isostatic carbonization.32M.Yu.Bamborin and S.A.Kolesnikov Fig.2.Dependence of average thermal conductivity and electrical resistivity on the treatment temperature used for the carbon materials: 1)thermal conductivity of3D CCC;2)thermal conductivity of CBM;3)resistivity of CBM and CCC;4)resistivity of carbon fiber made of polyacrylonitrile;5)thermal conductivity of specimens of coke formed from coal-tar pitch previously obtained by isostatic carbonization.However,the first,third,and subsequent isostatic carboniza-tion operations produce almost no change in the results.In all probability,it is during the second operation—when appar-ent density increases from1.59to1.65g/cm3—that the in-crease in the mass of carbon in the material ensures mechani-cal bonding of the composite rods to one another.In this part of the process of forming the carbon matrix,increasingly large volume fractions of carbon fibers are involved in trans-mitting mechanical strain.The sizes of these fractions in-crease in proportion to the amount of carbonaceous matrix material that is added.A similar structural model of the for-mation of the thermal conductivity of three-dimensional CCCs based on coal-tar pitch was examined in[11].There,it was observed that the fact that the“lobes”of the carbon ma-trix are parallel and are located directly on the surface of car-bon filaments gives these materials a thermal conductivity greater than that of copper.The next jump in thermal conductivity,by10–12W/(m·K), is seen when the semifinished product is kept within the tem-perature range from2000to2200°C for a longer period of time.Due to certain features of the design of electric vacuum furnaces(the volume of the graphite fixture,the method used to switch the heaters),their effective heating capacity may vary several-fold.As a result,the heating and cooling regime may be lengthened or shortened by6–12h.It has been de-termined that in the treatment-temperature range1900–2200°C the average interplanar spacing and the corresponding degree of graphitization can deviate10–20%from the nominal val-ues.The amount of deviation depends on the actual length of time that the material is in the hot zone of the furnace(on the whole,Dl~12W/(m·K)after~180min):d 0.022100=3.4514t–0.0033,at R2=0.9746,d 0.022200=3.4345t–0.003,at R2=0.9558,where d0.02is the average interplanar spacing,Å(1Å=0.1nm);t is time,min.CONCLUSIONA ranking was established for the factors that determinethe average thermal conductivity of material Desna T-1.Thefactors are ranked below in decreasing order of importance:–the consolidation that the structure undergoes withinthe range in which there is mechanical contact between thecarbon-rod filler and the coke-based matrix(~30W/m·K);–the duration of the high-temperature treatment in therange from1900to2200°C(~12W/(m·K);–heat treatment of the composite at a temperature from2100to2300°C(~10W/(m·K);–density within the range from 1.89to 1.98g/cm3,which is the range suitable for parts of the nozzle channel ofSFREs(~9.9W/m·K);–heat treatment of the initial carbon fibers from1500to1700°C(~3.225W/m·K);–the method used for framework assembly—tex-tile-woven or mechanically assembled framework made ofrods(~3.0W/(m·K).It was established that the relationship between electricalconductivity r and thermal conductivity l conforms to theWiedemann–Franz law lr=const.REFERENCES1.M.I.Sokolovskii,V.V.Luk’yanov and Yu.G.Luzenin,“Car-bon-based materials from the Scientific Research Institute ofGraphite in solid-fuel rocket engines built by the OAO NPO“Iskra,”in:“Current Problems in the Manufacture and Use ofCarbon 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