Review Article Hybrid Carbon-Carbon Ablative Composites...

Review ArticleHybrid Carbon-Carbon Ablative Composites for ThermalProtection in Aerospace

P Sanoj and Balasubramanian Kandasubramanian

Department of Materials Engineering Defence Institute of Advanced Technology (DIAT) (DU) Girinagar PuneMaharashtra 411025 India

Correspondence should be addressed to Balasubramanian Kandasubramanian meetkbsgmailcom

Received 7 October 2013 Revised 19 January 2014 Accepted 19 January 2014 Published 6 March 2014

Academic Editor Hui Shen Shen

Copyright copy 2014 P Sanoj and B Kandasubramanian This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Composite materials have been steadily substituting metals and alloys due to their better thermomechanical properties Thesuccessful application of composite materials for high temperature zones in aerospace applications has resulted in extensiveexploration of cost effective ablative materials High temperature heat shielding to body be it external or internal has becomeessential in the space vehicles The heat shielding primarily protects the substrate material from external kinetic heating and theinternal insulation protects the subsystems and helps to keep coefficient of thermal expansion low The external temperature dueto kinetic heating may increase to about maximum of 500∘C for hypersonic reentry space vehicles while the combustion chambertemperatures in case of rocket andmissile engines range between 2000∘C and 3000∘CCompositematerials of which carbon-carboncomposites or the carbon allotropes are themost preferredmaterial for heat shielding applications due to their exceptional chemicaland thermal resistance

1 Introduction

Discovery of carbon-carbon composites in 1958 by BrennanChance Vought Aircraft created an opportunity to theseprinciple materials for heat shielding appliances due to theirhigh strength and thermal resistance [1] Rayon carbonfabric reinforced phenolic (CndashPh) composites are the broadlyused thermal protection systems due to the low thermalconductivity of the rayon fabric and high char yields ofthe phenolic resin In general carbon phenolic compositesshow better ablation resistance and continued enhancementof ablative property with the development of a thinnerablative composite structure for better pay load and fuelefficiency [2] The Space Shuttle Columbia disaster occurredon February 1 2003 due to the inadequate impact resistanceof the thermal insulation foam in the external tank againstair as the spacecraft reentered the earthrsquos planetary atmo-spheric domain The displaced reinforcement foam dam-aged Columbiarsquos left reinforced carbon-carbon (RCC) panelsthereby causing the unfortunate accidentThis incident pavesway for a detailed research to enhance impact tolerances

thermal resistance and fracture toughness of the RCC panels[3] Polymer nanocomposites are the three phase compositesystems invented by Toyota research group wherein nano-size particles dispersed in the two phase fiber reinforcedcomposites exhibit enhanced structural rigidity and abla-tion resistance [1] Nanocomposites have the capability towithstand the simultaneous action of thermal stresses andmechanical impact loads Addition of various nanoparticlessuch as nanosilica montmorillonite (MMT) nanoclays andpolyhedral oligomeric silsesquioxane (POSS) with surfacefunctionalization acts as thermal insulative elements forimproving char layer integrity and toughness Three phasecomposite system with heterogeneous composition (fiberreinforcement matrix and nanofillers) exhibits complexityin its ablation behaviour [4] The scientific insights intothe ablation and decomposition behaviour of the compositematerials lead us to a trustworthy analysis of the compositeperformance at high temperature working environmentThis review has focused on the recent developments in thecarbon-carbon composites and resultant thermal protectionmechanisms Microstructural changes during the transition

Hindawi Publishing CorporationJournal of CompositesVolume 2014 Article ID 825607 15 pageshttpdxdoiorg1011552014825607

2 Journal of Composites

Carbon-carbon composites

Matrices Fillers Reinforcements

Graphite Phenolic Polyimides Glass fiber Carbon fiber Polyaramid fiber

Resol phenol

Resorcinol phenol

Novolacphenol Micro filler Nano filler

Chopped fibers Continuous fiber

Graphite Glass-balloons

Flyash

Boronmodified

SiCmodified

Bariummodified

Organic Inorganic

Nano silica

Silicon carbide

Organo clay

POSS

Graphene CNTrsquoS fibersCarbon nanoCarbon

black

Functionalized Non-functionalized

Figure 1 Carbon-carbon composite system and its constituent elements [8]

from two phase composite system to three phases have beendiscussed in detailed manner

2 Structure Description of Hot Zone Assembly

Missile structures are the extremely crucial componentsin aerospace industry They should have high structuralintegrity and fire resistance against severe lateral pressure andthermal cyclic loading Nozzle the exhaust duct of the solidrocket motor gives thrust for the missile projectile motion[5] During missile flight nozzle experiences an impact ofjet flow with high temperature and pressure Since evenslight degradation in nozzle structure severely affects theengine performance structural integrity is the main concernduring nozzle operational period The nozzle liner is thelining system in the nozzle inner counter to form insulationbarrier The high temperature fluid flow in the inner contourof the nozzle system creates a soaring thermomechanicalstresses through the liner cross section This degrades thenozzle throat and widens the throat area of cross section [6]This phenomenon causes a reduction in thrust and nozzleoperational efficiency Erosion rate of the composite systemdepends on the thermal insulation capacity of the ablativecomposite char layer Minimum surface recession rate of thechar layer shows an efficient thermal shielding capacity ofthe ablator Windhorst and Blount have revealed the usageof pyrolytic graphite as thermal insulation and its brittlefailure due to the thermomechanical stresses [7] It is reported

that phenolic impregnated carbon composite is a popularablative material for rocket nozzle liners due to its shieldingagainst combustion flame and high velocity erosive fluidflow [8] These extreme working environments demand highstructural integrity for nozzle liner with minimum structuraldegradation

3 Ablative Materials

Figure 1 shows the constituent elements in the carbon-carboncomposites

31 Carbon Fibres Carbon fiber is a synthetic fiber rein-forcement with a diameter of about 5ndash10 120583m The crystallinearrangement of the carbon atoms parallel to the fiber axisenables high strength-to-volume ratio of the fiber with excel-lent applications for structural components [9] The precur-sors used for the large-scale production of carbon fibers arePAN Rayon and petroleum pitch through melt or solutionspinning PAN-based fibres show better mechanical strengthas compared to the other fibers [10] The carbon felt has beenfabricated by alternatively stacked weftless piles and short-cut-fiber webs by needle-punching techniqueThis techniqueminimizes the fiber bend and breakage with the capabilityto tailor the properties by weaving in appropriate directionsNormally nonwoven carbon composite shows highest tensilestrength over wovenmaterials [11]Weave pattern orientationof the carbon fabric affects the heat diffusion rate through

Journal of Composites 3

(a) (b)

Figure 2 TEM image of Vapour Grown Carbon Fibers (a) magnification 20 nm (b) magnification 5 nm [21]

the cross section of the composite Kuo and Keswani studiedthe changes in the weave pattern of carbon fibers in differentdirections and altered specific properties of carbon composite[5] Surface-treatment of the carbon fibres is a currentadvancement in the fiber technology in which surface treat-ment by means of physical or chemical method improvesthe adhesion between carbon fiber and polymer matrix [12]Production of carbon fiber through fiber spinning is highlyexpensive process The usage of mesophase pitches showsefficient fiber reinforcement with improved cost effective-ness Chand has described the mesophase pitches whichare of liquid crystalline nature During graphitization stepmesophase pitches form a graphitic crystalline structure withhigh modulus carbon fibers with high stiffness [11] Strengthimprovement in the fibre reinforcement is mandatory forablative composites due to dependency of the ablation rateof composite with the fiber reinforcement morphology Moreresearch needs to be focused over the enhancement in fibermorphology design of fiber laminate orientation and costeffectiveness in fiber production

311 Vapour Grown Carbon Nanofiber Vapour grown car-bon fibers (VGCFs) are the recent desirable materials inthermal shielding composites due to their superior thermalinsulation low thermal conductivity (045ndash058Wmk) andhigh thermal shock resistance [13] These nanofibers (VGC-NFs) are cylindrical nanostructures with graphene layersarranged in a stacked cones shape Synthesis of the VGCNFsis carried out through decomposing gas-phase moleculesat high temperature (deposition of carbon in the presenceof a transition metal catalyst on a substrate) [14] Tibbettset al grew a series of different diameter (7ndash30 120583m) vapourgrown carbon fibers and from these carbon fibers it wasobserved that youngrsquosmodulus and tensile strength decreasedwith increase in diameter of fibers [15] Dispersion andhomogeneity are the specialty of VGCNF in the compositesystem It leads to uniformity of properties throughout thevolume of composite Figures 2(a) and 2(b) illustrate the

fiber morphology of the vapour grown carbon fibers indifferent magnification Patton et al confirmed that 65vapour grown carbon fiber loading in VGCF composite geta good thermochemical ablation resistance for space shuttlereusable solid rocket motor [13] Recent research on theeffect of different oxidative surface treatments (nitric acidplasma air and carbon dioxide) on the fibres surface showsthe effectiveness of the nitric acid and plasma treatmentsfor improving the surface reactivity without altering themorphology of the fibres This enhances the adhesion ofVGCNFs to the phenolic matrix system [16] Fiber orienta-tion in Vapour Grown Carbon fiber is a critical factor duringthe modelling of the composite system [17 18] This can bestatistically modelled by an orientation distribution functiondescribing the probability of finding fibres with any givenorientation [19] Advani and Tucker introduced a compacttensor description for fibre orientation which allows easyintegration with conventional rheological and mechanicaltensor descriptions Due to these advantages it is now widelyused in works on short fibre composites [20]

32 Carbonaceous Matrix

321 Phenolic Resin Matrix materials in the carbon-carboncomposite have significant functional properties as it holdsthe reinforcement fiber and impart structural integrity to thecomposite system Resol type Phenolic systems have attractedgreat scientific interest as they can be effectively used as amatrix system in ablation resistant composites [21] Duringthe fire exposure phenolic resin receives heat in the initialstage and decomposes to char and forms a thermal insulationlayer Large number of aromatic rings in the Resol typephenolic resin results high carbon yield and effective charformation ability [27] High char retention of the Resol typephenolic resins makes them an effective applicant for ablativenozzle liner application Presence of hydroxyl and methyllinkages in the phenolic is prone to oxidation and demandsfurther modification in the phenolic resin compound for


(a) (b)

Figure 3 (a) 15-mm thick silica fibre-reinforced phenolic syntactic foam (b) Photograph of phenolic foam after aerothermal test [22]

practical usage as thermal ablators [28] Chemical modi-fications have been well investigated to improve oxidationresistance of phenolic resin Modification of phenolic resinwith elements such as Boron Titanium Molybdenum andPhosphorous shows better ablation resistance and char yield[29] Improvement in the tribological properties of thephenolic resin enhances the wear and aerodynamic shearresistance of the phenol based carbon composites [30] Yiand Yan studied the mechanical and tribological propertiesof phenolic composite dispersed with several inorganic fillerslike calcined petroleum coke (CPC) talcum powder (TP)and hexagonal boron nitride (h-BN) [31] The phenol basedcomposite with 10 h-BN shows excellent friction stabilityand wear resistance at various testing conditions beyond125∘C and results in formation of compact friction film on therubbing surface of compositeThere is always a constant effortfor improving the processability toughness and char yield ofthe phenolic resin by compounding with highly stable addi-tives such as SiC Boron nitride Nanosilica and zirconiumdiboride [32] This modification led to better clasping of theturbostratic carbon formed as a result of high temperaturepyrolysis of hydrocarbons consequently reducing the erosiveloss of the char layer [33] In recent years PolyhedralOligomeric Silsesquioxane finds attention due to their nano-size in organic cage like cluster morphology which producebest charred surface on burnt samples with an enhancedablation performance in carbon-carbon composite [34]

322 Phenolic Based Carbon Foam Phenolic foams arethe light weight ablators with an exceptional fire resistanceused in thermal insulation system for aerospace applicationCost effectiveness and absence of dripping molten plasticat the stage of combustion are the added advantages ofphenolic based carbon foams Generally pure phenolic resinsfoam does not have the required strength to withstandthe aerodynamic stresses and thermal fluctuations due toits friability [35] Phenolic foam reinforced with syntheticfibers is the recent potential material for thermal insulatorapplications to improve composite strength toughness andeffective fire resistance Zhou et al developed lightweightglass fiber reinforced phenolic foam with high mechanicalperformance and excellent flame resistance and noticed theimprovement in storage modulus of the foam with reductionin loss modulus [36] The current research is primarilyfocusing on the improvement in toughness and peel strength

of the carbon phenolic foams through reinforcement offlexible synthetic fibers like Glass and Kevlar Short choppedglass fibers treated with coupling agents reportedly increasedthe strength toughness and dimensional stability of pheno-lic foams However Shen et al studied the improvementsin peel strength of carbon phenolic foams with Kevlarfiber reinforcement and obtainedmultiple-fold enhancementin fracture toughness [37] Various research groups haveattempted to modify the phenolic foam through nano- andmicrosize filler dispersion like carbon black talc nanosil-ica fly ash asbestos and cork flours Exfoliated phenolicresinmontmorillonite nanocomposite shows excellent ther-mal insulation behaviour as Montmorillonite (MMT) layerswrap around the bubbles of the composite foams during hightemperature environment John et al developed medium-density foam composites based on silica fibre-filled phenolicresin which shows maximum tensile strength at silica fibreconcentration of 15 by volume with K37 glass balloons[22] The reinforcement of silica fibre phenolic foam withmicroglass balloons before and after the aerothermal test (theblack colour on the surface of the sample is an emissivitycoating) is illustrated in Figures 3(a) and 3(b) respectivelyNucleating agents are the effective materials used to reducebubble size with enhancement of strength and toughness ofphenolic foam Hollow carbon microspheres from hollowphenolic microspheres have good potential to be attractivefunctional fillers for carbon foams [38] It shows a significantimprovement in the fracture toughness of syntactic foam at20ndash30 vol microspheres [39] Activated carbon reinforcedmicrocellular phenolic foams are the incipient in heat shield-ing application as they can be effectively used for thermalshielding due to the low thermal conductivity density andreliable compressive strength [40]

33 Elastomeric Matrix Elastomeric based heat shieldingmaterials is a novel concept in the ablative compositesdue to their excellent ablation resistance char yield andhigh strain rate [41] The high strain rate performancewith excellent dimensional flexibility significantly reducesthe induced thermal stresses during thermal expansion ofcomposites The elastomers show high resistance againstrapid removal of char by mechanical shear and spallationduring aeroheating loads [42] Silicone and Nitrile rubberbased ablative materials are the initial developments in theelastomeric matrix system due to their high strain rate


5mm

(a)

5mm

(b)

200120583m

2120583m

(c)

Figure 4 ((a) and (b)) Postburning images of the EPDM based Kynol tested materials (c) SEM image of the burnt surface of EPDMKynolsamples [23]

with reduced thermal stresses Silicone based elastomericablators show better thermal insulation characteristics dueto the formation of siliceous char which is an inert charlayer having excellent thermal stability Among the otherpolymeric insulators elastomeric ablators show high densitylimited shelf life and inferior thermal resistance whichlimit their wide applications as thermal insulators Ethylenepropylene diene monomer (EPDM) rubber based matrixsystem is a novel approach in the elastomeric heat shieldingmaterials due to its high oxidation resistance with excellentlow temperature properties [43] EPDM matrix system canbe effectively strengthened through reinforcement of glasscarbon Kevlar and polysulfonamide fibers The low densityand high thermal capacity with excellent fire resistant ofthese synthetic fibers effectively improve the thermochemicalproperties of elastomeric ablative composites [44] Flameretardant additives such as ammonium polyphosphate areused as an efficient method to enhance thermal insulationproperties of the shielding composites

Recently Jia et al have studied the reinforcement effectsof polysulfonamide fibers in the EPDM matrix as a thermalinsulation fibers and also noticed the enhancement in ther-mal stability due to the presence of additional sulfone group(ndashSO2ndash) in the main chain of the sulfonamide fibers [45]

Similarly Natali et al have studied the reinforcement effectsof Kynol fibers made by acid-catalyzed cross-linking of melt-spun Novolac and noticed that Kynol fiber shows excellentthermal properties as compared to Kevlar fibers Figures 4(a)and 4(b) represent the postburning images of the EPDMbased Kynol tested materials and Figure 4(c) illustrates theSEM image of the burnt surface of EPDMKynol samples[23] Since the thermal insulation is inversely proportional tothe density of the materials low density elastomeric ablatorsneed to be designed for a better ablation performanceReinforcement of additives with a density gradient is aneffective approach for the development of a light weightablator without compromising on the ablation performanceIn the recent period hybrid ablative composites are a topical


concept in which two or more fibers reinforced in the matrixsystem for optimized balance properties in the thermal insu-lation system Regarding this Ahmed and Hoa have studiedthe effect of a chopped carbon fiber (CCF) and aramid fiberon pulp as hybrid reinforcement for ethylene propylene dienemonomer (EPDM) along with ammonium polyphosphate(AP) flame retardant agent and noticed improvement in theablation performance with an improved thermomechanicalperformance [46]

4 Nano Filler Enabled Hybrid Composite

Nanoparticles (or nanopowder or nanocluster or nanocrys-tal) are the microscopic particles which are having excep-tional high surface area to volume ratio that makes theman effective filler reinforcement for ablative compositesReinforcing effects of the nanoparticle mainly depend on thecrystalline microstructure and effective interfacial bondingwith the parent matrix [47] Nanofiller embedded ablativecomposites show enhancement in thermal degradation andability to resist high-temperature erosive aerodynamic shearforces This is mainly due to its high thermal stability lowthermal conductivity and high adhesive bonding with theparent matrix Adhesive bonding is mainly related to theimprovement in interlaminar shear strength (ILSS) in hybridcomposite structure [24] Recent research works cover thedevelopment of carbon nanofibers nanoclay and CNT inphenolic resin for better ablation resistance Dash et alstudied the mechanical characterization of a Red Mud filledhybridized composite and noticed improvement in flexuraland tensile properties [48] Generally the dispersion ofthe nanoparticle in the fiber reinforced composite systemis in the range of 1ndash4wt [49] Beyond the percolationthreshold mechanical and ablation resistance of the com-posite decreased due to the agglomeration of the nanofillersUniform dispersion of nanofillers effectively improves thestructural integrity of the char layer during ablation Inor-ganic fillers are found as more suitable materials for thermalinsulations due to the presence of thermal barrier propertiesand surface morphology [50]

41 Organic Fillers Higher aspect ratio and inherent thermo-mechanical properties are the key factors of organic fillersfor their effective usage as reinforcing agent to protect thecarbon fibers and matrix from aerodynamic forces Organicfillers include single wall carbon nanotube (SWCNT) multi-wall carbon nanotube (MWCNT) carbon nanofiber carbonblack and graphene During ablation MWCNT in the charlayer reemits the incident heat radiation in to gas phase Thisreemission decreases the heat transfer rate into the innerlayers of the composite panels and reduces the endothermicpyrolysis [51] So the presence of MWCNT leads to animprovement in the thermal insulation and reduction inmass loss Tirumali et al studied different morphologi-cal nanofibers (stacked-coin-type) and their morphologicalshape variation with respect to various mechanical andchemical treatments [47] Vapour-grown carbon nanofibershave the potential to enhance the structural properties of the

char due to its high aspect ratios and fine diameter rangingfrom 15 nm to 100 nm [46] In a review by Tirumali et alon Epoxy composites of Graphene Oxide (GO) the mor-phological characteristics of Graphene Oxide and Graphenewere studied and illustrated that platey like morphology ofGOGraphene enhanced their reinforcement effect on thepolymeric system [47] Figure 5 shows the charred surface ofthe MWCNT dispersed in carbon-carbon composite 2 wtof filler additionmakes a thermal barrier protection layer overthe carbon fiber and avoids its peel off from the bottom layer

42 Inorganic Fillers The inorganic nanofillers are theprominent filler reinforcement in the composite material forheat shielding applications These nanofillers such as mont-morillonite (MMT) nanoclay fly ash nanosilica zirconiadiboride calcium carbonate and barium sulphate are beingused for their reinforcing ability to enhance the tribologicaland thermal properties of the polymer matrix Microsizedfillers require large amount of filler loading for a uniformchar layer over the surface [47] Nonuniform dispersion andlarge void region inmicrosize fillers create a local nonuniformerosion rate with a rough surface and hence are proneto erosion Nanofillers show a significant reinforcing effectcompared to microsized fillers due to their higher specificsurface area and volume effects The in-organic fillers meltduring high temperature exposure and form a viscous meltlayer over the burned surface This layer acts as a protectiveantioxidation barrier and radiative cooling system in the hightemperature burned surface Molten fused silica reacts withchar and produces a SiC phase Silica melt layer absorbssignificant amount of heat by an endothermic process duringits phase transformation and enhances the cooling rate [52]Srikanth et al studied the effect of nanosilica in carbonphenolic composites and identified an improvement in theablation resistance along with reduced thermal conductivityand improved interlaminar shear strength [52] Xiao et alhave reported that addition of zirconium diboride to carbonphenolic composite significantly improves the ablation resis-tance during the fire exposure [53] Polyhedral oligomericsilsesquioxane is reported to be efficient filler for reducingthermal conductivity and ablation resistance in the carbonphenolic composites [53] Figure 6(a) shows the erodedcarbon fibers during plasma arc treatment while Figure 6(b)shows the protective layer of the melt nanosilica over thecarbon fibers

43 Inorganic Nanocoating on Carbon Fibers Surface coatingon the reinforcement fiber is the new development in fiberreinforced composite system The aim of coating on thereinforced fibers is to improve the oxidation resistance andadhesive bonding of the carbon fiber with surroundingmatrix Optimum coating thickness is significant constraintin order to obtain a good compressibility of the hybridcomposite system which maintains the fiber reinforcementvolume (119881fiber) in the composite system Srikanth et alstudied the effect of zirconium oxide coating (thickness 700ndash900 nm) on the carbon fabric and found the reduction inthermal conductivity and the rear face temperature Surface


(a) (b)

(c)

Figure 5 SEM images of (a) 05 wt (b) 1 wt and (c) 2 wt MWCNTs ablative nanocomposite samples [18]

(a) (b)

Figure 6 (a) Ablated surface of blank CndashPh composite (b) 20 wt nanosilica CndashPh after ablation [24]

coating causes the reduction in the effective interfacial areabetween the fiber and the matrix which leads to a decrementin flexural modulus and interlaminar shear strength [54]Thermally sprayed tungsten carbide and silicon coating arean effective method for effective thermal barrier shield-ing [55] Recently Ryu has fabricated CSiC functionally

graded coating for reducing the thermal residual stressesbetween carbon composites and SiC coating layer As perhis observation SiC rich compositional layer in the Func-tionally Graded material (FGM) shows effective release ofthe thermal stress and increment in oxidation resistance[56]


Pure SiC CSiC FGM5 layer

C-C

500120583m

Figure 7 SEM image of the linear continuous gradient microstructure of carbon-based SiCC FGM and their magnified intermediatetransition layers [25]

5 Functionally Graded Composites

Functionally graded composite material (FGM) is composedof two different phases in which volume fraction changesgradually along at least one dimension of the solid Function-ally graded nanocomposite features layer by layer variation inthe filler composition and their concentration density profilesin order to realize a designed functionality Effective designof the various layers in FGM makes minimum heat diffu-sion through thickness with maximum thermal insulation[57] Functionally graded materials are considered to havesmooth spatial variation of microstructure and homogenizedmaterial properties [26] This structural variation improvesthe compressive strength and there is enhancement in thefracture and fatigue strength Spatial variation of microstruc-ture significantly minimizes the thermal delamination whichtakes place through the difference in the thermal expansioncoefficient of the two materials [58] The distribution ofresidual thermal stresses is very important in the soundnessof FGM composite Figure 7 shows the SEM image of thelinearly continuous gradient microstructure of carbon-basedSiCC FGM It signifies that smooth gradient interface inthe FGM ensures narrow transition from one material toanother and decreases the thermal residual stresses Srikanthet al developed a composite panel in which the top layerconsists of carbon nanotube (CNT) hybrid carbon phenoliccomposite and in the bottom layer Zirconium Oxide hybridCndashPh composite Presence of the CNT in the compositeenhances the flexural and shear strength of the composite butduring charring composite loses its structural integrity due tothe improvement in thermal conductivity of the CNT [50]Powder metallurgical approach including plasma sprayingmethod has been widely used in the fabrication of thermalstress relief type of functionally graded materials [59] Liu etal reported the modelling study of thermal stress in SiCCfunctionally graded composite by finite element numericalmodels and noticed the decrement in thermal stresses withincreasing the layer number The optimum intermediategraded layer and pure SiC layer thickness was 3-4mm and

05ndash1mm [60] Bafekrpour et al studied the flexural prop-erties of the carbon nanofiberphenolic functionally gradedcomposite by varying the compositional gradient of carbonnanofiber and noticed the improvement in flexural propertiesof FGM [61]

6 Ablative Mechanisms

The ablation mechanism of the carbon-carbon compositein nozzle inserts is a heterogeneous chemical interactionbetween the propellant combustion products and nozzlematerials [62] It is a thermal protection mechanism inwhich high temperature radiant energy from the combustionchamber acts on the material surface and dissipated througha series of endothermic reaction processes (thermochemicalthermophysical and thermomechanical) When the throatsurface temperature is less than of 2000ndash2500K ablationmechanism is dominated by chemical kinetics The temper-ature at 2000ndash2500K the reaction is significantly controlledby diffusion rate [62] The graphite or carbon-carbon mate-rials validate a superior advantage since their sublimation at1 atm was about 4000K and it increased with the increase inpressure Ablation concedes through a combined action ofheat transfer chemical reactions and fluid flow and finallythe material is consumed [63] Figure 8 shows the ablationmechanism in the carbon based polymermatrix ablatives andillustrates the combined thermomechanical decompositionphenomena during ablation process During the space craftpropulsion hypersonic flow of hot air creates an externalboundary layer of low pressure over the ablation surfaceThe circulation of the dissipated heat occurs within thisboundary and passes the heat away from thematerial surfaceThis phenomenon led to an added advantage for an efficientthermal shielding mechanism [50] Normally the thermo-chemical degradation of outer layer of the carbon-carboncomposite takes place through convectional heat transfer inwhich pyrolyzing layer diffuses towards the heated area of theshield In the nozzle design the pressure and temperature


Conduction flux

Materials decomposition

Surface recession

Melt flow Reaction productsMechanical erosion Pyrolysis gases

Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux

Free stream Reaction flux in

Boundary layer

X = 0

Figure 8 Pyrolysis mechanism carbon based polymer matrix [26]

of the combustion gases at the throat could not match thecondition for sublimation so sublimation was neglected asan ablation mechanism for the throat erosion [51] Interfaceregion of the fibermatrix and the defective regions of thecomposite aremore prone to ablationThis is due to the loweractivation energy and high reactivity of the defective region inthe composite system [64 65]The ablation always developedalong the direction of interface-to-fiber and interface-to-matrix due to the high oxidization tendency of the interfaceregion Donghwan has explained ablation mechanism by anerosive phenomenon who reported that decomposition ofthe ablative materials takes place through thermal oxidationduring fire exposure at high temperature of 2000ndash3000∘Cresulting in the formation of char and peels off from parentlayer by the combustion flame [12] These typical ablationcharacteristics suggest that super lightweight carbon ablatorsrequire high thermal degradation temperature and less densemicrostructure to perform as an efficient heat shieldingmate-rial [66] Figure 9 shows the schematic of parameters influ-encing ablation resistance of the carboncarbon composite

61 Thermal Decomposition In case of carbon-carbon poly-mer composites decomposition takes place through theviscous softening melting decomposition and volatiliza-tion [67] So a meticulous study over the decompositioncharacteristics to observe the real material degradation phe-nomenon is essentialThe endothermic pyrolysis mechanismduring the ablation process depends on the temperature heatflux time duration of the fire and type of aerodynamic stress(eg tension compression bending and torsion) [68] In theinitial stage of the heat flux heat transfer takes place throughpure conduction and hence it causes rise in temperatureAt a particular temperature the pyrolysis reaction (thermaldegradation) takes place followed by the elimination ofpendant aromatic rings and retention of all aromatic carbons

[69] This reaction causes the formation of a thermally cross-linked intermediate structure of new liquid or gas phasesIn the decomposition process resin evaporation takes placeand causes development of pressure in the composite dueto the penetration of evaporated gases through the fiberlaminates The excess pressure creates volume expansion inthe remaining matrix and intense material degradation ratecauses carbon laminates to lose their structural integrityDur-ing thermal degradation thermal conductivity (119870) specificheat (119862) and density (120588) of the composite change [70] Fiberdecomposition behaviour depends on the fiber reinforcementdensity area The fiber degrades to cone shape fiber duringablation in high fiber density area In the low fiber densityarea the fibers get weakened during ablation and peel offfrom the matrix due to aerodynamic stresses [71]

62 Pyrolysis Mechanism of Carbon Based Polymer MatrixPyrolysis of carbon based polymermatrix takes place througha three stage process First stage of the pyrolysis mechanismdemonstrates the formation of additional cross-links as aresult of two condensation reactions between functionalgroups of the cured phenolic At second stage breakage of thecross-links occurred followed by the evolution of methanehydrogen and carbon monoxide Similarly final stage causesstripping of the hydrogen atoms from the ring structureand evolution of hydrogen gas In pyrolysis reactions thephenolic matrix converts into amorphous carbon with lessstructural integrity This is due to the complete eliminationof the noncarbon species and char of coalesced carbonrings formation during pyrolysis Evolution of gas during thepyrolysis mechanism is controlled by controlling the heatingrate of the composite [72] Clarity in the physiochemicalreaction in pyrolysis mechanism leads to optimization ofthe factor of safety during the design of the composite heatshields Optimized factor of safety leads to an efficient design


Ablation resistance of carboncarbon composite

Heat flux Fire exposure

Aerodynamic shear and compressive force

Temperature gas velocity pressure and

Ablation behavioursChar formation

Polymer matrix Fiber reinforcementBase materials

ResinsFoams Nano filler

Airspace toughness and thermal expansion

Thermal stability char yield and adhesiveness

Adhesion surface morphology

Oxidation resistance thermal conductivity

Surface morphology weave pattern and fiber interface

Char residue

Surface morphology

Structural integrity

Thermo mechanical

Thermophysical

Thermochemical

O2 content

Figure 9 Parameters affecting ablation resistance of phenolic matrix ablatives

of heat shields with least material wastages and max thermalprotection

63 Char Formation Phenolic carbon composites are thecharring ablators which degrade into a carbonaceous residue(char) during ablation The char formation leads to an effec-tive thermal barrier layer against the material degradationDuring ablation the presence of highly ionized air in theheating region causes complex pyrolysis reactions at thesurface and within the boundary layer [73] Microstructuralstudy of the char layer reveals that gas-filled pores in thepolymermatrix and the fibre-matrix interface aremore proneto decomposition during pyrolysis mechanism [74] Thedecomposition gases cause pores to grow and coalesce in thehot viscous matrix under the high internal pressures Thismechanism leads to the weakening of the strength of the charlayer Florio et al calculated the rise in local pressure dueto the coalesces of the pores and noticed that local pressurerises as high as 15 times the ambient pressure for a phenolicmatrix laminateThis high pressure is strong enough to causedelamination matrix cracking and fibre-matrix deboning[75] The key factors which decide the reinforcing effectof fillers on the char layer is their high melting point andsurface adhesion Effect of graphene on the char layer hasbeen studied by many research groups Graphene nanofillersact as cementing agents and form network structure in thechar layer and improve the char layer resistance againststripping during high flow rate of hot gases [74] Char-fiberreaction is an intensive area in the thermal decompositionof composite panel where char structural integrity is highlydependent Torre et al studied the effect of nanosilica in the

thermal insulation properties of the char layer The higherconcentration of the nanosilica effectively freezes the highviscosity and forms a melt layer over the ablated surfaceof the composite [75] This causes an improvement in theprotection of the charred substrate and reduces the erosionrate of composite surface during the jet of hot gases Nataliet al have showed that the presence of silica on the surfaceensured higher reradiation efficiency since the adhesion ofthe charred layer over the virgin materials was strong enoughfor a longer period of time Presence of nanosilica leads to acarbothermal reduction between silica and carbon therebymaking them an effective heat insulator and ablative resistantduring the thermal degradation [76]

7 Thermal Analysis of theComposite Materials

Thermal analysis and failure modelling of the compositematerials play a significant role in the design of composites forheat shielding applicationMain focus in the thermal analysisis based on temperature distribution through the compositelaminates during fire exposure [77] Fiber reinforced compos-ite structures create explosion at high temperature (gt2000∘C)due to their organic content in the elemental compositionThe fire reaction behaviour of structural composite materialsand their characterization account for information suchas their time-to-ignition heat release rate limiting oxygenindex flame spread and smoke density [78] The thermalchemical and mechanical behaviour of the composite panelsduring the fire exposure are effectively analyzed throughstructural response of composite and degradation kinetics


Less research has been performed on laminates with reactivefibres sandwich composite materials and the dynamics ofthe fire and the fire interaction with composite surface istotally ignored that is assumptions during analysis basedon constant heat flux or temperature conditions Xie andDesJardin developed a coupled fluid-structure modellingapproach for analysing the heat transfer from combustionflame into the ablative materials [79] Decomposition ofmatrix during ablation makes changes in boundary condi-tions and heat release rate These phenomena influence theablation behaviour of the composites and can be effectivelyanalysed through a coupled approach between the fire andcomposite using computational fluid mechanics (CFD) andfinite element analysis (FEA) [80] CFD is an analytical tech-nique used to quantify the flowdynamics and temperatures ofthe flame over the composite surface [81]Thermal modellingdeveloped by Henderson et al is the common model forcalculating the temperature distribution in composites Thisone-dimensional nonlinear equation accounts for the energytransfer through heat conduction pyrolysis mechanism anddiffusion of decomposition gases which is shown in thefollowing [82]

120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)

where ℎ119888and ℎ119892represent the enthalpy of solid and gas phase

ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)

The first term one the right hand side of (1) accounts forthe heat conduction through thickness of the compositelaminate The second term accounts for the changes in thethermal conductivity with increasing temperature The thirdterm accounts for the internal convection of thermal energydue to the flow of volatile gases from pyrolysis reactionSimilarly the last term accounts for the temperature changein the composite due to heat generation or consumptionresulting from endothermic reaction of the matrix materialEquation (1) presumes a one-dimensional material systemwith the heat transfer occurring only through thicknessdirection Equation (1) is expanded to analyse two- andthree-dimensional systems with large amount of empiricaldata on the thermal and decomposition properties of thecomposite Modification of the Hendersonrsquos thermal modelhas been done by many research groups In the recentperiod Gibson et al slightly modified the Henderson modelto include the decomposition reaction rate of the polymermatrix This model can be used to calculate the mass lossand extent of charring during decomposition [83] Gibsonet al recently proposed a simplified model by avoiding theuse of the Arrhenius decomposition model The new modelldquoapparent thermal diffusivity (ATD)rdquo involves expression of

the thermal diffusivity of the composite as a function oftemperature ATD takes into account the decomposition ofthe resin which is endothermic as well as consequentlychanges specific heat capacity and thermal conductivity ofthe composite The rate dependence of the decompositionbehaviour is neglected with the decomposition state at anytemperature being calculated directly from theTGAcurve forthe polymer matrix

71 ModellingThermal Properties of Decomposing CompositesThermal decomposition of the composite material dependson thermal and physical properties such as density thermalconductivity specific heat capacity and gas permeabilityof both virgin composite and its char residue [82] Tem-perature dependence of these properties is important forthe prediction of thermal response of the composite dur-ing thermal analysis During thermal decomposition andpyrolysis density of composite varies significantly Arrheniusdecomposition kinetics is the common approach for findingthe change in densitywith timeThedensity change in a singlestage decomposition reaction is given by the following

120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)

Thermal properties of the fully decomposed phase (char) aredifficult to obtain due to unavailability of the measured dataSo during thermal analysis the properties of the decomposingcomposite are assumed to be dependent on the relative massfractions of the virgin composite and its char The massfraction of virgin material in a decomposing composite canbe calculated as

119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)

By considering the density changes as a variable elementin the matrix decomposition thermal conductivity of thedecomposing composite can be defined as follows

119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)

Thermal conductivity depends on the thermal response ofcomposites in fire considered to be an important parameterfor thermal analysis of the composite structure HendersonandWiecek have reported that the specific heat capacities forthe virgin composite and char depend on the temperatureThe specific heat capacity is determined using the following

119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)

By using different parameters thermal decompositionbehaviour of the ablative composite can be well analyzedHowever fire-induced damage such as fibre-matrixdebonding intraply matrix cracking and fibre damagedegrade the thermal properties of the composites Delam-inations of the laminates affect the reduction in thermalconductivity of the virgin composite due to the formationof air gap between debonded ply layers [77] So there is arequirement for unified damage model by incorporating theinfluence of various damages in the composite structuresduring thermal decomposition


72 Mathematical Model of Phenolic Impregnated CarbonComposite Pyrolysis mechanism of the carbon-carbon com-posite is as same as other ablative materials in terms ofthermal decomposition charmorphology and delaminationIn case of phenolic resin the matrix decomposition takesplace at a particular temperature followed by the char layerablation at a little higher temperature [78] Thermal responseof carbon-carbon composite at various zones (virginmaterialzone pyrolysis zone and porous char layer zone) is differentand the thermal analysis needs to consider for this variationin thermal response

The main assumptions during the ablation models are asfollows

(1) Energy transfer through mass diffusion is neglected(2) Mass transfer takes place mainly through the move-

ment of pyrolysis gases(3) Pyrolysis gases considered ldquoideal gasesrdquo and their

properties are constant(4) The specific heat capacity of the composite is a mass

weighted average of the relative mass fractions ofpolymer char and fibre remaining in the composite

(5) Heat conductivity coefficient mainly depends on thetemperature variation

(6) Thermal decomposition is a single stage process andconsidered as first-order reaction

Heating region in the ablative composite is composed of theionized air that has dissociated Mass and energy transfer ofthe volatile products result in complex chemical reactionsat the surface and within the boundary layer The balancebetween the convective energy chemical energy and netradiation at the ablative composite surface are as follows [79]

120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908

minus 119902cond = 0

(7)

While considering the reaction inside the ablative compositethe effect of surface recession and pyrolysis gas is to betaken into account because rate of recession of the materialthickness affects the conduction and thermal capacitance andescaping of the volatile gas significantly affecting the thermaldecomposition [79] It can be represented as follows

120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)

In thermal shielding composites there is a constant require-ment of mechanistic based models for analyzing the tem-perature distribution damage softening and failure of theablative composite However surplus empirical data in themechanistic based model reduce the reliance of the thermalanalysis Extensive studies need to be performed on theablation mechanism in order to enhance the accuracy andprediction in thermal analysis

8 Conclusion

Ablative materials are efficient thermal insulators due totheir uniqueness in accommodating high heat flux andresistance against the heat diffusion Enhancement in theablation properties is achievable through matrix modifica-tion improving the surface texture of the fiber reinforcementand dispersion of various nanofillers Thermal decompo-sition resistance ablation resistance and char retention ofthe phenolic enhanced with modification of high thermalresistive elements such as Boron Titanium and Molybde-num Elastomeric matrix based heat shielding compositesshow excellent thermal insulation properties due to theirexcellent ablation resistance char yield and high strain rateReinforcing elastomeric matrix system with the syntheticfibers leads to a better ablation properties and enhancementin thermal insulation behaviour Organic fillers such ascarbon nanotubes carbon nanofiber graphite oxide andgraphene have high potentials in both thermal insulationand char structural integrity Thermal resistive behaviourof the nanofillers is based on their morphological featuresand inherent physiochemical characteristics Inorganic fillerslike nanosilica montmorillonite (MMT) nanoclay and glassballoons have higher thermal barrier property Nanofillershaving hollow sphere morphology (Fly ash Glass balloons)have the effective resistance against heat diffusion rate dueto the air space volume in the hollow sphere Oxidationand aerodynamic erosion resistance of the carbon fiber isachieved by improving the adhesive bonding of the fiber andinorganic coating over the carbon fiber The main challengelies in the thermal analysis of the composite materialsduring ablation Assessment of the composite propertiesduring the thermal degradation is quite challenging Com-bined thermal-structural analysis methodology is needed forcarbon-carbon composite materials to deal with the varyingworking environment and expected service requirementFurthermore mechanical damage during the fire exposuresuch as delamination cracking and skin-core debondingneeds more attention in the future thermal design of ablationmaterials

Abbreviations

119877 Load vector in transformed eqn120597119879 Change in temperature120597119905 Time step120597119909 Thermal expansion in the

through-thickness direction120597120588 Change in density of composite119860 Preexponential factor for decomposition

reaction of polymer matrix119888 Specific heat119862119901(119888)

Specific heat capacity of decomposed(char) composite

119862119901(V) Specific heat capacity of virgin composite

119864 Activation energy for decompositionreaction of polymer matrix

119865 Mass fraction of virgin material indecomposing composite


ℎ Convection heat transfer coefficientℎ119888 Enthalpy of the composite

ℎ119892 Enthalpy of the volatile gas

119896perp Through-thickness thermal conductivity

119896119888 Thermal conductivity of decomposed

(char) composite119896V Thermal conductivity of virgin composite119898119892 Mass flux of volatiles

119899 Order of the decomposition reaction ofthe polymer matrix

119873 Diffusion rate of oxygen119875og Pressure of oxygen119902 Heat flux per unit area119876119901 Decomposition energy of polymer matrix

119903 Molar oxidation rate119877 Universal gas constant119878 Compliance of composite119879 Temperature119905 Time119879infin Reference temperature

119879infin Temperature of medium

119906 Flow velocity119909 Distance in through-thickness direction

below the fire exposed surface120572 Thermal diffusivityΔ119877 Surface recession120576 Emissivity of the compositeV Velocity component normal to surface

ms120588 Instantaneous density of composite120588119888 Density of decomposed (char) composite

120588V Density of virgin composite120590 Stephen-Boltzmann const

SuperscriptsSubscripts

119888 Chemical composite and conductivity119889 Diffusion119904 Surface119879 Transpose119903 Radiation reaction119902 Heat fluxsdot (dot) Time derivative

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank Dr Prahlada Vice Chan-cellor of Defence Institute of Advanced Technology (DIAT)for his support and encouragement In addition we aregrateful to Group Captain T Manoj Dr Renuka GonteB N Sahoo Premika G and Colonel Vijay Kumar DIAT(DU) for proofreading the paper and providing many usefulcomments

References

[1] T-C Chen and C-C Liu ldquoInverse estimation of heat flux andtemperature on nozzle throat-insert inner contourrdquo Interna-tional Journal of Heat and Mass Transfer vol 51 no 13-14 pp3571ndash3581 2008

[2] Y Tong S Bai H Zhang and Y Ye ldquoLaser ablation behaviorand mechanism of CSiC compositerdquo Ceramics Internationalvol 39 no 6 pp 6813ndash6820 2013

[3] A PMouritz S Feih E Kandare et al ldquoReview of fire structuralmodelling of polymer compositesrdquoComposites A vol 40 no 12pp 1800ndash1814 2009

[4] Y Chen P Chen C Hong B Zhang and D Hu ldquoImprovedablation resistance of carbon-phenolic composites by introduc-ing zirconiumdiboride particlesrdquoComposites B vol 47 pp 320ndash325 2013

[5] T K Kuo and S Keswani ldquoA comprehensive theoretical modelfor carbon-carbon composite nozzle recessionrdquo CombustionScience and Technology vol 42 no 3-4 pp 145ndash164 1985

[6] P Thakre and V Yang ldquoChemical erosion of carbon-carbongraphite nozzles in solid-propellant rocket motorsrdquo Journal ofPropulsion and Power vol 24 no 4 pp 822ndash833 2008

[7] T Windhorst and G Blount ldquoCarbon-carbon composites asummary of recent developments and applicationsrdquo Materialsand Design vol 18 no 1 pp 11ndash15 1997

[8] M H Al-Saleh and U Sundararaj ldquoReview of the mechanicalproperties of carbon nanofiberpolymer compositesrdquo Compos-ites A vol 42 no 12 pp 2126ndash2142 2011

[9] K A Trick and T E Saliba ldquoMechanisms of the pyrolysis ofphenolic resin in a carbonphenolic compositerdquoCarbon vol 33no 11 pp 1509ndash1515 1995

[10] C Hong J Han and X Zhag ldquoNovel phenolic impregnated 3-D fine-woven pierced carbon fabric composites microstructureand ablation behaviorrdquo Composites B vol 43 no 5 pp 2389ndash2394 2012

[11] S Chand ldquoReview carbon fibers for compositesrdquo Journal ofMaterials Science vol 35 no 6 pp 1303ndash1313 2000

[12] C Donghwan ldquoA microstructural study of the improvedablation resistance of carbonphenolic composites fabricatedusing H

3

PO4

-coated carbon fibresrdquo Journal of Materials ScienceLetters vol 15 no 20 pp 1786ndash1788 1996

[13] R D Patton C U Pittman Jr L Wang J R Hill and ADay ldquoAblationmechanical and thermal conductivity propertiesof vapor grown carbon fiberphenolic matrix compositesrdquoComposites A vol 33 no 2 pp 243ndash251 2002

[14] F W J van Hattum A study of the mechanical properties ofvapour grown carbon fibres and carbon fibre-thermoplasticcomposites [PhD dissertation] Universidade do Minho 1999httprepositoriumsdumuminhoptbitstream18222821van20Hattum-Tese20Doutoramentopdf

[15] G G Tibbetts M L Lake K L Strong and B P RiceldquoA review of the fabrication and properties of vapor-growncarbon nanofiberpolymer compositesrdquoComposites Science andTechnology vol 67 no 7-8 pp 1709ndash1718 2007

[16] K Lozano ldquoVapor-grown carbon-fiber composites processingand electrostatic dissipative applicationsrdquo Journal of Manage-ment vol 52 no 11 pp 34ndash36 2000

[17] S R Dhakate R B Mathur and T L Dhami ldquoDevelopment ofvapor grown carbon fibers (VGCF) reinforced carboncarboncompositesrdquo Journal of Materials Science vol 41 no 13 pp4123ndash4131 2006


[18] H Jaeger and T Behrsing ldquoThe dual nature of vapour-growncarbon fibresrdquo Composites Science and Technology vol 51 no 2pp 231ndash242 1994

[19] J S Tate S Gaikwad N Theodoropoulou E Trevino andJ H Koo ldquoCarbonphenolic nanocomposites as advancedthermal protection material in aerospace applicationsrdquo Journalof Composites vol 2013 Article ID 403656 9 pages 2013

[20] S G Advani and C L Tucker ldquoPart B constitutive equationsand flow processingmdashprocessing short-fiber systemsrdquo in Flowand Rheology in Polymer Composites Manufacturing S GAdvani Ed vol 10 of Composite Materials p 147 ElsevierScience 1st edition 1994

[21] J Zhao ldquoEffect of post production processing on dispersion ofcarbon nanofibers in waterrdquo Industrial amp Engineering ChemistryResearch vol 50 no 3 pp 1599ndash1604 2011

[22] B John B Deependran G Joseph R C P Nair and K NNinan ldquoMedium-density ablative composites processing char-acterisation and thermal response undermoderate atmosphericre-entry heating conditionsrdquo Journal of Materials Science vol46 no 15 pp 5017ndash5028 2011

[23] M Natali M Rallini D Puglia J Kenny and L TorreldquoEPDMbased heat shieldingmaterials for solid rocketmotors acomparative study of different fibrous reinforcementsrdquo PolymerDegradation and Stability vol 98 no 11 pp 2131ndash2139 2013

[24] D M Allison A J Marchand and R M Morchat ldquoFireperformance of composite materials in ships and offshorestructuresrdquoMarine Structures vol 4 no 2 pp 129ndash140 1991


[26] R Lipton ldquoDesign of functionally graded composite structuresin the presence of stress constraintsrdquo International Journal ofSolids and Structures vol 39 no 9 pp 2575ndash2586 2002

[27] A P Mouritz and A G Gibson ldquoFire properties of polymercomposite materialsrdquo in Solid Mechanics and Its ApplicationsG M L Gladwell Eds Ed pp 143ndash163 Springer AmsterdamThe Netherlands 1st edition 2006

[28] C P R Nair ldquoAdvances in addition-cure phenolic resinsrdquoProgress in Polymer Science vol 29 no 5 pp 401ndash498 2004

[29] Y Zhang S Shen and Y Liu ldquoThe effect of titanium incor-poration on the thermal stability of phenol-formaldehyde resinand its carbonizationmicrostructurerdquoPolymerDegradation andStability vol 98 no 2 pp 514ndash518 2013

[30] C LuoWXie and P E DesJardin ldquoFluid-structure simulationsof composite material response for fire environmentsrdquo FireTechnology vol 47 no 4 pp 887ndash912 2011

[31] G Yi and F Yan ldquoMechanical and tribological properties ofphenolic resin-based friction composites filled with severalinorganic fillersrdquoWear vol 262 no 1-2 pp 121ndash129 2007

[32] L K Kucner and H L McManus ldquoExperimental studies ofcomposite laminates damaged by firerdquo in Proceedings of the 26thInternational SAMPE Technical Conference vol 44 pp 341ndash353Paris France October 1994

[33] J Wang H Jiang and N Jiang ldquoStudy on the pyrolysisof phenol-formaldehyde (PF) resin and modified PF resinrdquoThermochimica Acta vol 496 no 1-2 pp 136ndash142 2009

[34] H Fan X Li Y Liu and R Yang ldquoThermal curing anddegradation mechanism of polyhedral oligomeric octa(propar-gylaminophenyl)silsesquioxanerdquo Polymer Degradation and Sta-bility vol 98 no 1 pp 281ndash287 2013

[35] D Wei D Li L Zhang Z Zhao and Y Ao ldquoStudy on phenolicresin foam modified by montmorillonite and carbon fibersrdquoProcedia Engineering vol 27 pp 374ndash383 2012

[36] J Zhou Z Yao Y ChenDWei andYWu ldquoThermomechanicalanalyses of phenolic foam reinforced with glass fiber matrdquoMaterials amp Design vol 51 pp 131ndash135 2013

[37] H Shen A J Lavoie and S R Nutt ldquoEnhanced peel resistanceof fiber reinforced phenolic foamsrdquo Composites A vol 34 no10 pp 941ndash948 2003

[38] L Zhang and J Ma ldquoEffect of coupling agent on mechanicalproperties of hollow carbonmicrospherephenolic resin syntac-tic foamrdquo Composites Science and Technology vol 70 no 8 pp1265ndash1271 2010

[39] S Lei Q Guo J Shi and L Liu ldquoPreparation of phenolic-based carbon foam with controllable pore structure and highcompressive strengthrdquo Carbon vol 48 no 9 pp 2644ndash26462010


[41] Z Jia G Li Y Yu G Sui H Liu and Y Li ldquoEffects ofpretreated polysulfonamide pulp on the ablation behavior ofEPDM compositesrdquo Materials Chemistry and Physics vol 112no 3 pp 823ndash830 2008

[42] C M Bhuvaneswari M S Sureshkumar S D Kakade andM Gupta ldquoEthylene-propylene diene rubber as a futuristicelastomer for insulation of solid rocket motorsrdquoDefence ScienceJournal vol 56 no 3 pp 309ndash320 2006

[43] W K Ho J H Koo and O A Ezekoye ldquoThermoplasticpolyurethane elastomer nanocompositesmorphology thermo-physical and flammability propertiesrdquo Journal of Nanomateri-als vol 2010 Article ID 583234 11 pages 2010

[44] A S Deuri and A K Bhowmick ldquoAgeing of rocket insulatorcompound based on EPDMrdquo Polymer Degradation and Stabil-ity vol 16 no 3 pp 221ndash239 1986

[45] X Jia G Li Y Yu et al ldquoAblation and thermal propertiesof ethylene-propylene-diene elastomer composites reinforcedwith polysulfonamide short fibersrdquo Journal of Applied PolymerScience vol 113 no 1 pp 283ndash289 2009

[46] A F Ahmed and S V Hoa ldquoThermal insulation by heatresistant polymers for solid rocket motor insulationrdquo Journal ofComposite Materials vol 46 no 13 pp 1549ndash1559 2012

[47] M Tirumali K Balasubramanian and A KumaraswamyldquoEpoxy composites of graphene oxide (GO) a reviewrdquo inProceedings of the IEEE International Conference on Researchand Development Prospects on Engineering and Technology(ICRDPET rsquo13) vol 1 p 94 Nagapattinam India March 2013

[48] A K Dash D N Thatoi and M K Sarangi ldquoAnalysis ofthe mechanical characteristics of a red mud filled hybridizedcompositerdquo in Proceedings of the International Conference onFrontiers in Automobile and Mechanical Engineering (FAMErsquo10) pp 8ndash11 November 2010

[49] M M Zurale and S J Bhide ldquoProperties of fillers and reinforc-ing fibersrdquoMechanics of Composite Materials vol 34 no 5 pp463ndash472 1998

[50] C Luo and P E DesJardin ldquoThermo-mechanical damagemodeling of a glass-phenolic composite materialrdquo CompositesScience and Technology vol 67 no 7-8 pp 1475ndash1488 2007

[51] H LMcManus ldquoPrediction of fire damage to composite aircraftstructuresrdquo in Proceedings of the 9th International Conferenceon Composite Materials (ICCM-9 rsquo93) vol 58 pp 929ndash936Madrid Spain 1993


[52] I Srikanth A Daniel S Kumar et al ldquoNano silica modifiedcarbon-phenolic composites for enhanced ablation resistancerdquoScripta Materialia vol 63 no 2 pp 200ndash203 2010

[53] J Xiao J Chen H Zhou and Q Zhang ldquoStudy of severalorganic resin coatings as anti-ablation coatings for supersoniccraft control actuatorrdquoMaterials Science and Engineering A vol452-453 pp 23ndash30 2007

[54] I Srikanth N Padmavathi S Kumar P Ghosal A Kumar andC Subrahmanyam ldquoMechanical thermal and ablative proper-ties of zirconia CNT modified carbonphenolic compositesrdquoComposites Science and Technology vol 80 pp 1ndash7 2013

[55] K-Z Li X-T Shen H-J Li S-Y Zhang T Feng and L-L Zhang ldquoAblation of the carboncarbon composite nozzle-throats in a small solid rocket motorrdquo Carbon vol 49 no 4pp 1208ndash1215 2011

[56] Y Xu W Zhang D Chamoret and M Domaszewski ldquoMini-mizing thermal residual stresses in CSiC functionally gradedmaterial coating of CC composites by using particle swarmoptimization algorithmrdquo Computational Materials Science vol61 pp 99ndash105 2012

[57] V A Rozenenkova N A Mironova S S Solntsev and S VGavrilov ldquoCeramic coatings for functionally graded high-tem-perature heat-shielding materialsrdquo Glass and Ceramics vol 70no 1-2 pp 26ndash28 2013

[58] C C Ma and Y T Chen ldquoTheoretical analysis of heat con-duction problems of nonhomogeneous functionally gradedmaterials for a layer sandwiched between two half-planesrdquoActaMechanica vol 221 no 3-4 pp 223ndash237 2011

[59] H Guo K A Khor Y C Boey and X Miao ldquoLaminated andfunctionally graded hydroxyapatiteyttria stabilized tetragonalzirconia composites fabricated by spark plasma sinteringrdquoBiomaterials vol 24 no 4 pp 667ndash675 2003

[60] G Zhang Q Guo K Wang et al ldquoFinite element designof SiCC functionally graded materials for ablation resistanceapplicationrdquo Materials Science and Engineering A vol 488 no1-2 pp 45ndash49 2008

[61] E Bafekrpour C Yang M Natali and B Fox ldquoFunctionallygraded carbon nanofiberphenolic nanocomposites and theirmechanical propertiesrdquoComposites A vol 54 pp 124ndash134 2013

[62] J H Koo H Stretz A Bray et al ldquoNanostructured materialsfor rocket propulsion system recent progressrdquo in Proceedingsof the 44th AIAAASMEASCEAHSASC Structures StructuralDynamics andMaterials Conference p 1769 Virginia Va USAApril 2003

[63] J S Tate S Gaikwad NTheodoropoulou E Trevino and J HKoo ldquoCarbonphenolic nanocomposites as advanced thermalprotection material in aerospace applicationsrdquo Journal of Com-posites vol 2013 Article ID 403656 9 pages 2013


[65] A J Goupee and S S Vel ldquoTransient multiscale thermoelasticanalysis of functionally gradedmaterialsrdquoComposite Structuresvol 92 no 6 pp 1372ndash1390 2010

[66] J Kim S W Lee and S K Won ldquoTime-to-failure of compres-sively loaded composite structures exposed to firerdquo Journal ofComposite Materials vol 41 no 22 pp 2715ndash2735 2007

[67] C Luo and P E Des Jardin ldquoThermo-mechanical damagemodeling of a glass-phenolic composite materialrdquo CompositesScience and Technology vol 67 no 7-8 pp 1475ndash1488 2007

[68] R Palaninathan ldquoBehavior of carbon-carbon composite underintense heatingrdquo International Journal of Aerospace Engineeringvol 2010 Article ID 257957 7 pages 2010

[69] T Lippert and J T Dickinson ldquoChemical and spectroscopicaspects of polymer ablation special features and novel direc-tionsrdquo Chemical Reviews vol 103 no 2 pp 453ndash486 2003

[70] W Xie and P E DesJardin ldquoAn embedded upward flame spreadmodel using 2D direct numerical simulationsrdquoCombustion andFlame vol 156 no 2 pp 522ndash530 2009

[71] G Pulci J Tirillo F Marra F Fossati C Bartuli and T ValenteldquoCarbon-phenolic ablativematerials for re-entry space vehiclesmanufacturing and propertiesrdquoComposites A vol 41 no 10 pp1483ndash1490 2010

[72] V Srebrenkoska G Bogoeva-Gaceva and D Dimeski ldquoCom-posite material based on an ablative phenolic resin and carbonfibersrdquo Journal of the Serbian Chemical Society vol 74 no 4 pp441ndash453 2009

[73] L Chen C Luo J Lua and J Shi ldquoA direct coupling approachfor fire and composite structure interactionrdquo in Proceedingsof the 17th International Conference on Composite Materials(ICCM-17 rsquo09) Edinburgh International Convention Centre(EICC) Edinburgh UK July 2009

[74] J Florio Jr J B Henderson F L Test and R HariharanldquoA study of the effects of the assumption of local-thermalequilibrium on the overall thermally-induced response of adecomposing glass-filled polymer compositerdquo InternationalJournal of Heat and Mass Transfer vol 34 no 1 pp 135ndash1471991

[75] L Torre J M Kenny and A M Maffezzoli ldquoDegradationbehaviour of a composite material for thermal protection sys-tems part I-experimental characterizationrdquo Journal of MaterialsScience vol 33 no 12 pp 3137ndash3143 1998

[76] Y Hu X W Zhang and H You ldquoMorphology measurementon phenolic-resinvitreous-silica-fabric ablation compositesmodified with tetraethoxysilicate and silsesquioxanesrdquo AppliedMechanics and Materials vol 333ndash335 pp 1934ndash1937 2013

[77] A R Bahramian M Kokabi M H N Famili and M HBeheshty ldquoAblation and thermal degradation behaviour of acomposite based on resol type phenolic resin Process modelingand experimentalrdquo Polymer vol 47 no 10 pp 3661ndash3673 2006

[78] A N Negovskii A V Drozdov V V Kutanyak et alldquoExperimental equipment for the evaluation of the strengthcharacteristics of carbon-carbon composite mateials within thetemperature range 20ndash2200∘Crdquo Strength ofMaterials vol 31 no3 pp 319ndash325 1999

[79] W Xie and P E DesJardin ldquoA level set embedded interfacemethod for conjugate heat transfer simulations of low speed 2DflowsrdquoComputers and Fluids vol 37 no 10 pp 1262ndash1275 2008

[80] J G Quintiere R N Walters and S Crowley ldquoFlammabil-ity properties of aircraft carbon-fiber structural compositerdquoTechnical Report DOTFAAAR-0757 2007 httpwwwfiretcfaagovpdf07-57pdf

[81] G L Vignoles Y Aspa andMQuintard ldquoModelling of carbon-carbon composite ablation in rocket nozzlesrdquo Composites Sci-ence and Technology vol 70 no 9 pp 1303ndash1311 2010

[82] J B Henderson J A Wiebelt and M R Tant ldquoModel forthe thermal response of polymer composite materials withexperimental verificationrdquo Journal of Composite Materials vol19 no 6 pp 579ndash595 1985

[83] A G Gibson Y-S Wu H W Chandler J A D Wilcox and PBettess ldquoModel for the thermal performance of thick compositelaminates in hydrocarbon firesrdquo Revue de lrsquoInstitute Francais duPetrole vol 50 no 1 pp 69ndash74 1995

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Carbon-carbon composites

Matrices Fillers Reinforcements

Graphite Phenolic Polyimides Glass fiber Carbon fiber Polyaramid fiber

Resol phenol

Resorcinol phenol

Novolacphenol Micro filler Nano filler

Chopped fibers Continuous fiber

Graphite Glass-balloons

Flyash

Boronmodified

SiCmodified

Bariummodified

Organic Inorganic

Nano silica

Silicon carbide

Organo clay

POSS

Graphene CNTrsquoS fibersCarbon nanoCarbon

black

Functionalized Non-functionalized

Figure 1 Carbon-carbon composite system and its constituent elements [8]

from two phase composite system to three phases have beendiscussed in detailed manner

2 Structure Description of Hot Zone Assembly

Missile structures are the extremely crucial componentsin aerospace industry They should have high structuralintegrity and fire resistance against severe lateral pressure andthermal cyclic loading Nozzle the exhaust duct of the solidrocket motor gives thrust for the missile projectile motion[5] During missile flight nozzle experiences an impact ofjet flow with high temperature and pressure Since evenslight degradation in nozzle structure severely affects theengine performance structural integrity is the main concernduring nozzle operational period The nozzle liner is thelining system in the nozzle inner counter to form insulationbarrier The high temperature fluid flow in the inner contourof the nozzle system creates a soaring thermomechanicalstresses through the liner cross section This degrades thenozzle throat and widens the throat area of cross section [6]This phenomenon causes a reduction in thrust and nozzleoperational efficiency Erosion rate of the composite systemdepends on the thermal insulation capacity of the ablativecomposite char layer Minimum surface recession rate of thechar layer shows an efficient thermal shielding capacity ofthe ablator Windhorst and Blount have revealed the usageof pyrolytic graphite as thermal insulation and its brittlefailure due to the thermomechanical stresses [7] It is reported

that phenolic impregnated carbon composite is a popularablative material for rocket nozzle liners due to its shieldingagainst combustion flame and high velocity erosive fluidflow [8] These extreme working environments demand highstructural integrity for nozzle liner with minimum structuraldegradation

3 Ablative Materials

Figure 1 shows the constituent elements in the carbon-carboncomposites

31 Carbon Fibres Carbon fiber is a synthetic fiber rein-forcement with a diameter of about 5ndash10 120583m The crystallinearrangement of the carbon atoms parallel to the fiber axisenables high strength-to-volume ratio of the fiber with excel-lent applications for structural components [9] The precur-sors used for the large-scale production of carbon fibers arePAN Rayon and petroleum pitch through melt or solutionspinning PAN-based fibres show better mechanical strengthas compared to the other fibers [10] The carbon felt has beenfabricated by alternatively stacked weftless piles and short-cut-fiber webs by needle-punching techniqueThis techniqueminimizes the fiber bend and breakage with the capabilityto tailor the properties by weaving in appropriate directionsNormally nonwoven carbon composite shows highest tensilestrength over wovenmaterials [11]Weave pattern orientationof the carbon fabric affects the heat diffusion rate through


(a) (b)








(a) (b)







5mm

(a)

5mm

(b)

200120583m

2120583m

(c)














(a) (b)

(c)


(a) (b)






C-C

500120583m








Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b)








(a) (b)







5mm

(a)

5mm

(b)

200120583m

2120583m

(c)














(a) (b)

(c)


(a) (b)






C-C

500120583m








Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b)







5mm

(a)

5mm

(b)

200120583m

2120583m

(c)














(a) (b)

(c)


(a) (b)






C-C

500120583m








Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




5mm

(a)

5mm

(b)

200120583m

2120583m

(c)














(a) (b)

(c)


(a) (b)






C-C

500120583m








Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials












(a) (b)

(c)


(a) (b)






C-C

500120583m








Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





C-C

500120583m








Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Conduction flux


Surface recession


Pyrolysis zone

Porous char

Virgin materials

Back up materials

Convective flux


Boundary layer

X = 0



















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials
















Char residue

Surface morphology


Thermo mechanical

Thermophysical

Thermochemical

O2 content









120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





120588119862119901

120597119879

120597119905= 119896perp

1205972

119879

1205971199092+120597119896perp

120597119909

120597119879

120597119909minus 119898119892119862119901(119892)

120597119879

120597119909

minus120597120588

120597119905(119876119901+ ℎ119888minus ℎ119892)

(1)


ℎ119888= int

119879

119879infin

119862119901119889119879

ℎ119892= int

119879

119879infin

119862119901(119892)

119889119879

(2)




120597120588

120597119905= minus (120588V minus 120588119888) [

120588 minus 120588119888

120588V minus 120588119888]

119899

119860119890(minus119864119877119879)

(3)


119865 = [120588 minus 120588119888

120588V minus 120588119888] (4)


119896 (119879) = 119865 sdot 119896V (119879) + (1 minus 119865) sdot 119896119888 (119879) (5)


119862119901(119879) = 119865 sdot 119862

119901(V) (119879) + (1 minus 119865) sdot 119862119901(119888) (119879) (6)












120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials













120588119890120583119890119862119867(119867119903minus ℎ119890119908) + 120588119890120583119890119862119872

times [sum(119885119899

119894119890

minus 119885119899

119894V) ℎ119879V119894

minus 1198611015840

ℎ119908] + 119888ℎ119888+ 119898119892ℎ119892

+ 120572119908119902rad minus 119865120590120576119908119879

4

119908


(7)


120588119888119901

120597119879

120597119905=1

119860

120597

120597119909119896119860

120597119879

120597119909 + (ℎ

119892minus ℎ)

120597119901

120597119905

+ 119904120588119888119901

120597119879

120597119909+

119860

120597ℎ119892

120597119909

(8)


8 Conclusion


Abbreviations


























Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





















Acknowledgments


References













3

PO4


















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials














































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Review Article Hybrid Carbon-Carbon Ablative Composites...

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