evaluation of micromechanical properties of carbon/carbon and carbon/carbon–silicon carbide...

Evaluation of Micromechanical Properties of Carbon/Carbon and Carbon/Carbon–Silicon Carbide Compositesat Ultralow Load

Soumya Sarkar, Arjun Dey, Probal K. Das,* and Anoop K. Mukhopadhyay

Non-Oxide Ceramic and Composite Division, Central Glass & Ceramic Research Institute (CSIR),Kolkata-700032, India

Anil Kumar

Ceramic Matrix Composite Division, ASL, DRDO, Hyderabad 500058, India

2D carbon fiber (C-fiber)-reinforced carbon/carbon (C/C) composites were prepared by vacuum infiltration with coal-tarpitch followed by carbonization and graphitization in inert atmosphere. Liquid silicon infiltration was done in controlledatmosphere at 16001C to convert the matrix carbon of the C/C composites into silicon carbide. The 2D C/C and carbon/carbon–silicon carbide (C/C—SiC) composites had density of B1.65 and B2.32 g/cm3, respectively with correspondingflexural strength of B70 and B169 MPa, respectively. The local mechanical properties like hardness, Young’s modulus,contact pressure, relative stiffness, relative spring back, and indentation energies of the two composites under different loadingconditions were measured at an ultra low load of 10 mN using a nanoindentation instrument with a Berkovich indenter. Thescatter in the data was treated in terms of the two-parameter Weibull statistical analysis. The maximum characteristic Young’smodulus (B16 GPa) and hardness (1.20 GPa) was obtained for the C/C–SiC composites in parallel direction of fabric stack-ing. The elastic rebounce was also the maximum (0.77) for the C/C–SiC composites when loaded in parallel direction of fabricstacking. The extent of structural anisotropy was higher in the C/C–SiC composite than that of the C/C composite.

Introduction

Carbon fiber (C-fiber)-reinforced carbon/carbon(C/C) and carbon/carbon–silicon carbide (C/C–SiC)composites are gaining increasing market demand for

Int. J. Appl. Ceram. Technol., 8 [2] 282–297 (2011)DOI:10.1111/j.1744-7402.2009.02451.x

Ceramic Product Development and Commercialization

This work was financially supported by DRDL, Hyderabad, India.

*[email protected]

r 2009 The American Ceramic Society

mailto:[email protected]

sophisticated and advanced applications such as in aero-space industries, medical appliances, sports accessories,high-energy brake and clutch systems, and other high-performance structural equipment due to several advan-tages over the conventional monolithic materials.1–10

However, a limitation of C/C composite is that at above4001C, the composite suffers degradation of propertiesdue to rapid oxidation of carbon.11–13 One effective wayto protect these composites from oxidation is to convertthe matrix carbon into SiC by reactive methods likechemical vapor infiltration (CVI),14–19 liquid siliconinfiltration (LSI),17–24 polycarbosilane (PCS) infiltra-tion,25,26 and polymer infiltration and pyrolysis(PIP).27–29 However, CVI and PCS require costly pre-cursors, higher processing temperatures, and take longerreaction time to obtain the desired product than LSI orPIP.20,27,29 The advantages of the C/C–SiC compositesover the C/C composites are that they offer excellentfracture toughness, better damage tolerance, higher andstable coefficient of friction, higher oxidation and abra-sion resistance, and smaller stack volume compared withthe C/C composites.14–16,19–26,29–31

Although large amount of data are available on thebulk thermo-mechanical properties of C/C3–10,24 andC/C–SiC composites,19–26 the deformation behaviorof these composites using nanoindentation is hardlyavailable in the literatures. While some dataare available on the local mechanical performanceof C/C composites,6,32–35 to the best of our knowl-edge, no published data are available on thedepth-sensitive mechanical properties of the C/C–SiCcomposites. However, for structural designing pur-poses, it is always important to have an idea aboutthe microstructural features and mechanical responseat submicrometer to nanometer scale in such hetero-geneous systems. This is mainly because all of theirconstituents like fibers, matrices, interfaces, and othersurface irregularities with different mechanical proper-ties significantly contribute to the overall performanceof the composites.

In the present work, the 2D C/C composites wereprepared by coal-tar pitch impregnation into 2D C-fiber preforms. Some of these C/C composites werethen converted into 2D C/C–SiC composites by LSI incontrolled atmosphere at 16001C with 30 min soaking.The objective of the present work was to study thedepth-sensitive deformation behavior of 2D C/C aswell as the C/C–SiC composites at an ultra low load of10 mN. The work was done by applying nanoindenta-

tion technique using a Berkovich indenter. The hard-ness, Young’s modulus, relative spring back, relativestiffness, amount of elastic, and plastic energies associ-ated with the indentation process for both C/C andC/C–SiC composites loaded in parallel as well as inperpendicular direction of C-fabric stacking were eval-uated. The scatter in the data was treated in terms of thetwo-parameter Weibull statistics to calculate the char-acteristic properties of the composites. The results werefinally correlated with the corresponding microstruc-tural aspects.

The Importance of Nanoindentation Technique

The C-fibers used in this work were about 5–6 mmin diameter. Further, the interface regions of C/C andC/C–SiC composites were about o1 mm. Now theproblem with the conventional hardness test, such as aVickers hardness test is that it can not probe down tosuch small length scales and hence, ultra small volumesof the present materials. Also, such a conventional hard-ness test is practically inapplicable in the C/C and/orC/C–SiC composites due to the additional problem ofsurface undulations. In fact, the only way such smalldimensions can be probed for a feedback in terms oflocal micromechanical properties such as hardness andYoung’s modulus, etc. of C/C and/or C/C–SiC com-posites is the nanoindentation technique. Here theunique advantage is that it can easily evaluate the me-chanical response at ultra small length scales and hence,also within a very small volume of material. In addition,the nanoindentation technique has the ability to probedown from a single constituent for example C-fiberto multiple microstructural components for examplegraphitized matrix, C-matrix, and so on, even in suchheterogeneous systems as the present C/C and C/C–SiCcomposites. Thus, in case of the C/C and C/C–SiCcomposites, nanoindentation technique can be suitablyutilized to evaluate their local micromechanical proper-ties and also to get an idea about the contribution ofdifferent phases present in such composites on theirbulk mechanical response.

Further, due to the large spring-back associatedwith the indentation in such brittle materials, clearimaging of the indents even by using atomic force mi-croscopy (AFM) has not been as successful as one wouldlike it to be.24,32–35 Thus, most of the available papersrarely bear any (AFM) images of the indented regions in

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such composite materials. The nanoindentation test, onthe other hand, utilizes depth-sensing method instead ofoptical imaging and thus one can measure the hardnessand other depth-sensitive mechanical properties of thesebrittle composites in spite of their rough surface. In ad-dition, only small specimens of square cross-section(6 mm� 6 mm� 2.5 mm) were available for propertyevaluation and testing with conventional UTMs werealso not possible for evaluation of Young’s modulus, etc.However, with the nanoindentation technique evensuch small samples were easily viable. Recently, therehas been a couple of excellent reviews on nanoindenta-tion technique and it’s applications.36,37 These excellentreviews have indeed provided unique milestones interms of knowledge and information bases in this evolv-ing exciting research area of nanoindentation of ductile,brittle, and quasi-crystalline solids. Therefore, in thefollowing only the basic theory of nanoindentation tech-nique has been briefly described.

Basic Theory of Nanoindentation

It is mentioned in the previous section that theprimary objective of this work was to evaluate the mi-cromechanical properties of C/C and C/C–SiC com-posites using nanoindentation technique. However,before going into the details of the results obtained inthis study for the composites, it is important to have abrief description on the nanoindentation process that ishow it works, the fundamental principles and the math-ematical relations required to evaluate the requiredproperties. Therefore, in this section, the fundamentalsof nanoindentation process those were ultimately uti-lized for evaluating the micromechanical properties ofthe C/C and C/C–SiC composites have been brieflydescribed.

During the indentation process, a high-resolutioninstrument continuously monitors the load (P) and thedepth of penetration (h) of an indenter. In the presentinvestigation, the indenter was a Berkovich tip. Theserecorded data are then utilized to get the load versusdepth of penetration (P–h) data plot, schematicallyshown in Fig. 1. The important physical quantities ob-tained from this P–h plot are the peak load (Pmax),maximum depth (hmax), final depth (hf), and contactstiffness (S).

According to the Oliver and Pharr (O–P) model,38

which is the most commonly used method to evaluate

the hardness (H) and Young’s modulus (E) of a materialby the instrumented nanoindentation, the hardness isexpressed as

H ¼ Pmax=Acr ð1Þ

where Acr is the real contact area between the indenterand the material.

The polynomial form of Acr can be expressed as39:

Acr ¼ 24:56h2c þ C1hc þ C2h1=2

c þ C3h1=4c þ . . .

þ C8h1=128c ð2Þ

where C1–C8 are constants and can be determined bystandard calibration method and hc is the contact depth,determined from the following expression39:

hc ¼ hmax � eðPmax=SÞ ð3Þ

where e � 0.75 for a Berkovich indenter.40

The contact stiffness that is the slope of the firstB1/3 linear part recorded during the unloading cycle ofthe P–h data plot (Fig. 1) can be expressed as41:

S ¼ ðdP=dhÞh¼hmax ¼ bCAE�p

Acr ð4Þ

where b5 1.034 and CA 5 2/Op for a Berkovich ind-enter41 and E�is the effective Young’s modulus.

Following the O–P model, E� can be given as38:

1=E� ¼ ð1� n2i Þ=Ei þ ð1� n2

s Þ=Es ð5Þ

Fig. 1. Typical P–h data plot showing various parameters.

284 International Journal of Applied Ceramic Technology—Sarkar, et al. Vol. 8, No. 2, 2011

where E and n are the Young’s modulus and Poisson’sratio, respectively and subscripts i and s denote indenterand sample, respectively. For a Berkovich indenter,Ei 5 1140 GPa and ni 5 0.07.41 The Poisson’s ratio val-ues for the C/C and C/C–SiC samples of the presentwork were assumed as 0.22 following the work reportedin Sarkar et al.24

However, according to the O–P model, the un-loading curve simply obeys the following power law39:

P ¼ Bðh� hfÞn ð6Þ

where B and n are empirical constants those can bedetermined by fitting the experimentally measured dataon the P–h data plot to Eq. (6). Thus, S can also bedetermined using the following expression39:

S ¼ ðdP=dhÞh¼hmax ¼ Bnðh� hfÞn�1 ð7Þ

Therefore, placing the values of S, b, CA, and Acr inEq. (4), one can calculate the value of E�. The Young’smodulus of the sample, Es, can then easily be obtainedfrom Eq. (5).

Furthermore, during the nanoindentation study ofa 2D C/C composite, Kanari et al.33 calculated themean contact pressure, pm, as a representative parameterfor the indentation hardness. The mathematical expres-sion for pm is

pm ¼ Pmax=Aca ð8Þ

where Aca is the apparent projected area of contact andcan be expressed as33:

Aca ¼ 3p

3ðtanaÞ2ðhmaxÞ2 ð9Þwhere a is semiapical angle of indenter and is B65.31for a Berkovich tip. The concept of Aca is schematicallyshown in Fig. 2.

Thus, from Eq. (9)

Aca ¼ 24:56ðhmaxÞ2 ð10ÞHence, the expression for pm finally takes the form:

pm ¼ Pmax=Aca ¼ Pmax=24:56ðhmaxÞ2 ð11ÞAnother important parameter, termed as the rela-

tive stiffness that is (Smax/hmax) of the material can beexpressed as33:

Smax=hmax ¼ 5:52E�p

Acr=Aca ð12ÞThe ratio of Acr/Aca is always unity for a fully

plastic material. However, for elastoplastic materialslike ceramics and ceramic matrix composites the ratiobecomes less than unity. This means that in case ofelastoplastic materials Acr will be always lower than Aca.

In addition, the extent of elastoplastic deformationof any material can be visualized by calculating theamount of relative spring-back that is [(hmax�hf)/hmax]from its P–h data plot. This parameter gives an ideaabout the extent of elastic recovery undergone by thematerial during unloading. Hence, it may be under-stood that except for fully elastic material, the P–h plotwill consist of two separate parts as shown in Fig. 1. Thearea specifically under the unloading curve is theamount of reverse deformation energy released (We)when the test load is released. However, the area en-compassed by the loading-unloading curve is theamount of plastic deformation work (Wp) during theindentation test (Fig. 1). Thus, for an elastic materialWebWp. However, for a plastic material Wp should bemuch higher than the reverse deformation energy. Thesum of these two is called the total mechanical work ofindentation, Wt. Thus,

Wt ¼ We þWp ð13Þ

Experimental Procedure

Fabrication of the 2D C/C and C/C–SiC Composites

The 2D C/C composites were made by stacking 2DC-fiber fabrics, prepared with T-300 C-fiber tows

Fig. 2. Schematic of contact between an indenter and anelastoplastic material.


(Torayka, Tokyo, Japan), in layers followed byrepeated coal-tar pitch impregnation and subsequentpyrolysis at temperatures r10001C in inert atmo-sphere. The structures were then heat-treated at tem-peratures r26001C for 2 h in an inert atmosphere forgraphitization of the solid carbon matrix. Some of theC/C composites were then impregnated with moltensilicon at 16001C for 30 min in controlled atmospherein a high temperature controlled atmosphere furnace(ASTRO, Thermal Tech, Santa Rosa, CA) to obtain the2D C/C–SiC composites.

Microstructure Analysis

For microstructural evaluation, specimens of(10 mm� 10 mm� 2 mm) were cut from both thecomposites using a slow-speed diamond saw. The sur-faces of all the specimens were ground by different SiCgrits and subsequently polished by using 6, 3, and 1 mmdiamond paste (Eastern Diamond Products, Kolkata,India). Microstructures of the polished specimens werestudied using scanning electron microscope (SEM,s430i, Leo, Electron Microscopy, Cambridge, U.K.).

Nanoindentation Test

Specimens of square cross-section (6 mm� 6 mm�2.5 mm) were cut from both the C/C and C/C–SiCcomposites and surfaces of all the samples were lappedgently with diamond paste upto 1mm before the inden-tation test. The deformation behavior of the C/C and C/C–SiC composites at 10 mN load was studied with a Be-rkovich indenter using an automated depth sensing nano-indentation machine (FISCHERSCOPE, H100 XYp,Fischer, Hunenberg, Switzerland) with a force sensing

resolution of 0.2mN and a depth-sensing resolution of0.1 nm. The loads were applied in two directions that is inperpendicular and parallel directions of C-fabric stacking(Fig. 3) and referred as ‘‘PERP’’ and ‘‘PARA,’’ respectivelyin the succeeding figures. During the indentation process,the loading as well as unloading time was 30 s. On anaverage, the total number of observations for a particularsample in a particular loading condition was 30. Thehardness, Young’s modulus and other related propertieswere evaluated from the P–h data plots using the well-established O–P model.38

Results and Discussion

Table I shows the data on the physicomechanicalproperties of the bulk 2D C/C and C/C–SiC compos-ites. It is evident that the density of the C/C compositeswas B47% lower than that of the final C/C–SiC com-posites (B2.36 g/cm3). The density of the 2D C/C–SiCcomposites, in this study, was found to be slightlyhigher than those obtained by the other research-ers.19,21,25 This was mainly due to the well-consolidatedmicrostructure formed during the conversion of theC-matrix into the SiC that resulted in the successfulremoval of the pores and voids left in the base C/Ccomposites and lead to the formation of a higher densitySiC as the major matrix phase.

Fig. 3. Schematic of C-fabric stacking and loading directions.

Table I. Physiomechanical Characteristics of theBulk 2D C/C and C/C–SiC Composites

Property C/C C/C–SiC

Density (g/cm3)� 1.55–1.77 2.20–2.41Porosity (%)� 13.21–17.30 1.92–2.70Flexural strength (MPa)w 77.5 169.4Compressive strength (MPa)z 65 (J) 165 (J)

32 (>) 150 (>)�Density and porosity were measured by standard water immersionmethod.wFlexural strengths of the composites were measured by UTM (Instron5500R, Norwood, MA) according to ASTM standard C-1341-00.zCompressive strengths of the composites were measured by UTM (In-stron 5500R) according to ASTM standard C-1424-04.J, strength along the parallel direction of C-fabric stacking; >, strengthalong the perpendicular direction of C-fabric stacking; C/C, carbonfiber (C-fiber)-reinforced carbon/carbon; C/C–SiC, carbon/carbon–silicon carbide.


The flexural strength of the C/C–SiC composites(B169 MPa) was B120% higher than that of the C/Ccomposites (B77 MPa). In both the composites, com-pressive strength values were higher in parallel directionof C-fabric stacking than that obtained in perpendiculardirection due to the inherent structural anisotropy ofsuch fiber-reinforced composites.

From the SEM images, it is clear that the C/Ccomposites had pores of various shapes and sizes (Fig.4a). Graphitic flakes were observed around the C-fibersin the base C/C composite. After siliconization, thosegraphite flakes were converted into SiC having similarstructure as both graphite and SiC have hexagonalcrystal morphology. It is evident from Fig. 4b that theC/C–SiC composites had much lower porosity thanthat of the C/C composites. This resulted in a denser

microstructure. It may also be visualized from the mi-crographs that in the siliconized C/C–SiC samples, theC-fibers remained unaffected from the action of moltensilicon (Fig. 4b). Thus, it could be expected that all themechanical properties of the C-fibers were maintainedin the C/C–SiC composites.

As mentioned before that due to the large spring-back associated with the indentation process, it is verydifficult to get clear image of the indented regionin such brittle composites. However, in the presentstudy, typical AFM image of the indented region inthe 2D C/C–SiC composite loaded at 10 mN is shownin Fig. 5. The indented spot is pointed out usingan arrow.

Although, the O–P model was utilized to evaluatethe micromechanical properties of the composites, it isimportant to mention at this stage that the results ob-tained from this model would be erroneous if the areafunction used to calculate the Acr (Eq. (2)) in this modelwas modified.41 The reason behind this modification isthe pile-up of the displaced materials around the inden-tation, particularly in case of ductile materials. Thus, toverify the applicability of this model, it is essential tocalculate the ratio of hf and hmax from the P–h plot be-cause the value of this parameter gives an indicationabout the tendency of a given material towards pilling-up around the nanoindent. To obtain reliable results

Fig. 4. Scanning electron microscopic micrographs of (a) carbonfiber (C-fiber)-reinforced carbon/carbon (C/C) composite (scale bar:5mm); (b) carbon/carbon–silicon carbide (C/C—SiC) composite(scale bar: 10mm).

Fig. 5. The typical Berkovich Indent made at 10 mN in the 2DC/C—SiC composite. C/C—SiC, carbon/carbon–silicon carbide.


from the O–P model, the value of (hf/hmax) should liebelow 0.7.41,42 In the present study, the average valuesof this ratio for the C/C and C/C–SiC compositeswere found to lie well below 0.7 (Table II). Moreover,the (hf/hmax) values also indicated that the chancesof pilling-up of the displaced materials around thenanoindents would be the least in these compositesand the effect of sink-in would be much pronounced(Fig. 2).

Typical P–h data plots tracing the response behav-ior of the bulk 2D C/C and C/C–SiC composites under

different loading conditions are shown in Figs. 6a–d. Itcan be seen that the P–h plots for the C/C compositesunder the two loading conditions showed elastoplasticdeformation with higher hf compared with those of theC/C–SiC composites. In the C/C composites, the aver-age value of hf was B95 nm in perpendicular directionof C-fabric stacking and that was B40% higher thanthat of the value measured in parallel direction (averagehfB57 nm) of loading. However, the C/C–SiC com-posites, when loaded in parallel direction of C-fabricstacking, showed the highest elastic recovery (B75–97%) and the least permanent deformation (hf 5

5–11 nm) at the test load. Details about this elasticrecovery aspect will be discussed in the later part of thisreport.

The average hardness value of the C/C compositesin perpendicular direction of C-fabric stacking was0.45 GPa and that was found to be 0.50 GPa whenthe indentation was done along parallel direction (TableIII). Although, the H-value was the highest for the C/C–SiC composites (1.14 GPa) when loaded in parallel di-rection of fabric stacking, there was B74% decrease inthe same that is B0.3 GPa for the same composite whenmeasured along perpendicular direction (Table III).

(a) (b)

(c) (d)

Fig. 6. (a–d) Typical P–h data plots for carbon fiber (C-fiber)-reinforced carbon/carbon (C/C) and carbon/carbon–silicon carbide (C/C—SiC) composites.

Table II. (hf/hmax) for C/C and C/C–SiC Under TwoLoading Conditions

Sample (loading condition) hf/hmax

C/C (>) 0.46C/C (J) 0.60C/C–SiC (>) 0.41C/C–SiC (J) 0.30

J, loading along the parallel direction of C-fabric stacking; >, loadingalong the perpendicular direction of C-fabric stacking; C/C, carbon fi-ber (C-fiber)-reinforced carbon/carbon; C/C–SiC, carbon/carbon–sili-con carbide.


Furthermore, in the parallel direction of fabric stacking,the C/C–SiC composites showed much improved per-formance (H 5 1.14 GPa) compared with that of the C/C composites (H 5 0.5 GPa). This was due to the pres-ence of much harder and stiffer SiC-matrix and a betterconsolidated microstructure with less pores/defects inthe former (Fig. 4b). Thus, although both of the C/Cand the C/C–SiC composites showed anisotropic na-ture, the extent of anisotropy was much pronounced incase of the C/C–SiC composites.

The data on the average Young’s modulus valuesare also shown in Table III. This data further con-firmed the strong anisotropic nature of the C/C–SiCstructures with the highest E value of 14.7 GPa mea-sured in parallel direction and B5 GPa along per-pendicular direction of fabric stacking. This mightwell be due to the fact that in perpendicular directionof fabric stacking, the contribution of the SiC-matrixwould be higher than that of the C-fibers that re-sulted in poor mechanical response in that direction.However, in case of the C/C composites, the extent ofanisotropy was found to be less pronounced(Table III).

The large standard deviations of the measuredhardness and Young’s modulus values (Table III) re-flected the fact that both the composites have significantcontribution from each of its constituents like theC-fiber, C- and SiC-matrices, interfaces and pores orother defects like surface irregularities, valleys and hills,etc. Kanari et al.33 reported similar kind of large stan-dard deviations in the micromechanical properties of2D C/C composites during their study under differentindentation loads. However, to the best of our knowl-edge, there is no nanoindentation data available in lit-erature for the C/C–SiC composites and thus,comparison of the results obtained for the C/C–SiCcomposites were not possible.

Typical P–h plots corresponding to the differentconstituents of the two composites are shown in Figs.7a–f. The elastic properties obtained for the variousphases of the C/C composites were closely related to theliterature values.6,24,33–35 For direct comparison withthe present results, Table IV summarizes the indenta-tion hardness and modulus values of different constit-uents of C/C composites reported by other researchers.The H-value of the graphitized matrix evaluated in thepresent study (B0.43 GPa) was in between the resultsobtained by Ozcan and Filip6 (1.22 GPa) and Kanariet al.33 (0.04 GPa). On the other hand, Young’s mod-ulus value of the C-matrix (5.46 GPa) was closely re-lated to that of the result (8.75 GPa) obtained by Disset al.34 and Field and Swain43 (7.50 GPa). In addition,it may be also observed from Table IV, that dependingon the processing condition, indentation parametersused, the hardness and Young’s modulus values ofC-matrix were varied in between 0.04 and 3.32 and1.97 and 30.69 GPa, respectively. The data obtained forC-fibers were also quite close to the literature values.34–35

However, it was also noted that depending on the pro-cessing condition, indentation parameters and loadingdirection, the hardness, and Young’s modulus values ofC-fiber were varied in between 0.10 and 2.23 and 6.71and 30.31 GPa, respectively. Further, the nature of thesecurves was quite similar to that of the P–h data plotsreported by other researchers.33,35,40 However, in somecases variations were prominent because others havechosen different loading range for their study that ulti-mately led to these observed deviations. Some discon-tinuities were observed in the P–h plot of theconstituents (Figs. 7e and f). These were mainlybecause of the localized cracking and/or the interactionof the indenter with the subsurface defects of the com-posites. It is evident that being the most elastic compo-nent, the C-fibers showed the least permanent

Table III. Hardness and Young’s Modulus Values of the Composites

Sample (loading condition)

Hardness Young’s modulus

Average (GPa) SD (GPa) Average (GPa) SD (GPa)

C/C (>) 0.45 0.29 8.4 5.0C/C (J) 0.50 0.30 8.9 4.6C/C–SiC (>) 0.30 0.22 5.1 2.9C/C–SiC (J) 1.14 0.84 14.7 13.3

SD, standard deviation; J, .loading along the parallel direction of C-fabric stacking; >, loading along the perpendicular direction of C-fabric stacking;C/C, carbon fiber (C-fiber)-reinforced carbon/carbon; C/C–SiC, carbon/carbon–silicon carbide.


deformation (hfB5–10 nm) after complete unloading(Fig. 7b) whereas, the porous areas or the irregular re-gions (Fig. 7f) showed the highest hf (B650 nm) oncomplete unloading. Hence, due to the presence of all thedifferent phases, wide scatter of the results took place.

To treat this scatter, the two-parameter Weibullstatistical analysis was utilized and the characteristic val-ues were evaluated to obtain suitable data for structuraldesigning. In fact, this statistical method has beenwidely used to calculate the characteristics values forvarious homogeneous and heterogeneous materials withvarious phases, flaws or defects that results in wide vari-ations in the mechanical properties like strength, frac-

ture toughness, hardness, elastic modulus,44–52and soforth.

The two-parameter Weibull model which providesthe survival probability, p, for a given parameter, x, canbe expressed as44,46,48:

p ¼ 1� exp½�ðx=xoÞm� ð14Þ

where xo is known as the scale parameter where theprobability of occurrence is 63.2% and m is the Weibullmodulus. The value of the Weibull modulus is a di-mensionless quantity and indicates the degree of distur-bance or scatter in the data within the distribution andincreases with decreasing scatter. The survival probabil-

(a) (b)

(c) (d)

(e) (f)

Fig. 7. (a–f) Typical P–h data plots of various phases of the two composites.


ity of the ith observation in the data list arranged inascending order can be expressed as44,46–48:

p ¼ ði � 0:5Þ=N ð15Þ

where N is the total number of observations. Although,in some literatures, the formula for the probability es-

timator ‘‘p’’ was found to be different,49–50 here we usedthe most commonly used expression.

Taking natural logarithm for two times of both thesides and simplifying, Eq. (14) can be expressed as

ln½lnf1=ð1� pÞg� ¼ m½lnðxÞ � lnðxoÞ� ð16Þ

The values of m and xo are obtained by fitting theexperimental data to Eq. (16) by least square regression.The slope of the straight line will give the value of m andthe Y-intercept will give the value of xo. Finally, by set-ting the value of ln[ln f1/(1�p)g] equal to zero andplacing the values of m and xo in Eq. (16), one can cal-culate the characteristic value of the related parameter, x.The characteristic value is of great engineering impor-tance as it provides the designer a unique and depend-able value of the required parameter of these multiphasebrittle composites with wide scatter in the data. In thepresent study, x will be H, E, (Smax/hmax), and[(hmax�hf)/hmax].

The characteristic hardness (Hch) values obtainedfrom the Weibull plots (Fig. 8) of the C/C and C/C–SiC composites under the two loading conditions aregiven in Table V. The Hch values were generally veryclose to those of the average H values (Table III). Thehighest Hch value was obtained for the C/C–SiCcomposite along parallel direction of C-fabric stacking(HchB1.20 GPa). However, the C/C–SiC compositesshowed 75% reduction in the Hch value(HchB0.30 GPa) when loaded in perpendicular direc-tion to fabric stacking. Thus, it is evident from thedata of Table V that the extent of anisotropy washigher in the C/C–SiC composites compared with theC/C composites because the Hch values of the C/Ccomposites was B0.55 GPa irrespective of loadingdirection.

Similarly, the characteristic Young’s modulus (Ech)values of the two composites were evaluated usingFig. 9. The highest Ech value was 15.7 GPa (Table V)for the C/C–SiC composite in parallel direction ofloading whereas there was B65% reduction in themodulus of this composite in perpendicular directionof loading. In addition, the modulus values were alwaysfound to be higher in the C/C–SiC composites com-pared with the C/C composites in parallel direction ofC-fabric stacking. It also indicated that a denser mi-crostructure was present in the C/C–SiC compositescompared with the C/C composites. Possibly, due tothis well-consolidated microstructure, better interfacialperformance in the former had successfully transferred

Table IV. Mechanical Properties of C/C andC/C–SiC Composite’s Constituents

MaterialH

(GPa)E

(GPa) Reference

C-matrixCharred resin 1.22 — Ozcan and

Filip6

Isotropic graphite 0.05 10.70 Kanariet al.32

CVI andgraphitized

0.04 1.97 Kanariet al.32

Pyrolytic graphite — 8.75 Diss et al.34

ACVD carbon 3.12 29.92 Marx andRiester.35

ICVD carbon 3.32 30.69 Marx andRiester35

Pyrolytic graphite — 7.50 Field andSwain43

Pyrolytic graphite 0.43 5.46 Presentstudy

C-fiber2D Pitch-based 2.00 — Ozcan and

Filip6

PAN-based 0.10 6.71 Kanariet al.32

PAN-based (J) — 11.99 Diss et al.34

PAN-based (>) — 24.90 Diss et al.34

PAN-based (//) — 13.36 Diss et al.34

Pitch-based (J) 2.23 30.31 Marx andRiester35

Pitch-based (>) 1.56 15.30 Marx andRiester35

PAN-based (>) 1.43 15.80 Marx andRiester35

PAN-based 2.70 39.00 Presentstudy

SiC-matrixSiC 0.55 12.60 Present

study

C/C, carbon fiber (C-fiber)-reinforced carbon/carbon; C/C–SiC,carbon/carbon–silicon carbide.


the load from the matrix to the fiber leading to highermodulus values.

However, it may be visualized from the data pre-sented in Table V, that when the indentation load wasapplied in perpendicular direction of C-fabric stacking,the C/C composites showed higher Hch (B0.55 GPa) aswell as Ech (B10 GPa) compared with the C/C–SiCcomposites (HchB0.30 GPa and EchB5.60 GPa). Thereason for this observation is not clear at this stage andneeds further studies.

As mentioned in ‘‘Basic Theory of Nanoindenta-tion,’’ the hardness can also be described in terms of themean contact pressure. Thus, following Kanari et al.,33

during Weibull analysis, Eq. (11) was also utilized tocalculate the contact pressures of the two compositesunder different loading conditions. Consequently, fromthe Weibull plots (Fig. 10) the characteristic contactpressure values were evaluated (Table V). Same aniso-tropic effects, as stated earlier, were observed in thepm values. It was seen that the characteristic contactpressure values were slightly lower than the Hch values inall the cases. While the highest Hch value was 1.20 GPafor the C/C–SiC composite in parallel direction ofloading, the characteristic pm value was 1.14 GPafor the same composite under the similar loadingcondition. This indicated that the magnitude of

(a) (b)

(c) (d)

Fig. 8. (a–d) Weibull plots for calculating H of the carbon fiber (C-fiber)-reinforced carbon/carbon (C/C) and carbon/carbon–silicon carbide(C/C—SiC) composites.

Table V. Characteristic Values of Hardness and Young’s Modulus

Sample (loading condition) Hch (GPa) m Ech (GPa) m pm (GPa) m

C/C (>) 0.55 1.24 9.5 1.77 0.53 1.20C/C (J) 0.55 1.45 10.1 2.37 0.52 1.40C/C–SiC (>) 0.30 1.24 5.6 2.14 0.30 1.15C/C–SiC (J) 1.20 1.32 15.7 1.50 1.14 1.20

J, loading along the parallel direction of C-fabric stacking; >, loading along the perpendicular direction of C-fabric stacking; C/C, carbon fiber (C-fiber)-reinforced carbon/carbon; C/C–SiC, carbon/carbon–silicon carbide.


Acr used in Eq. (1) was lesser than that of Aca, used inEq. (10). This also supports the argument statedearlier that there would be either minimum or nopilling-up of the displaced materials around the nano-indents in this type of highly elastoplastic compositematerials and the effect of sink-in would be much morepronounced.

It is evident from the data presented in Table V thatin both the composites, irrespective of loading condi-tion, the values of the Weibull modulus as obtainedfrom the slops of the Weibull plots (Figs. 8–10) weresmall (m 5 1.24–2.37). This data suggested that thestatistical variations in the H, pm, and E were high.This is expected, as it was the characteristic feature of ahighly heterogeneous microstructure present in thecomposites studied in the present work. In otherwords, this wide variation was mainly due to the char-acteristic presence of generically different constituentsin the composites. The values of m obtained in thepresent study compared favorably with the values re-ported (mB2.59) by other researchers.33 That is whythe characteristic values were calculated following theWeibull modulus approach so that they can providestatistically reliable design data. Therefore, it may

be argued that high characteristic scatter in the micro-mechanical properties data should not minimize theincreasing demand of these composites for high-perfor-mance applications.

Figure 11 shows the Weibull plots for relative stiff-ness, Smax/hmax, of the two composites under differentloading directions. For both the composites, Smax/hmax

was found to be higher in parallel direction comparedwith the values obtained in perpendicular direction offabric stacking. However, the highest value of Smax/hmax

was measured for the C/C–SiC composite in paralleldirection of loading (B70 GPa) which was B12%higher than that of the C/C composite (B60 GPa) un-der the similar loading condition (Table VI).

The Weibull plots for evaluating relative spring-back [(hmax�hf)/hmax] of the two composites underdifferent loading conditions are shown in Fig. 12. Themagnitudes of [(hmax�hf)/hmax] were always found tobe higher in the C/C–SiC composites compared withthe values obtained for the C/C composites (Table VI)indicating higher amount of elastic recovery on unload-ing of the former. Further, the permanent deformation,that is, hf was the least for the C/C–SiC compositeswhen loaded in parallel direction of fabric stacking. This

(a) (b)

(c) (d)

Fig. 9. (a–d) Weibull plots for calculating the Young’s modulus of carbon fiber (C-fiber)-reinforced carbon/carbon (C/C) and carbon/carbon–silicon carbide (C/C—SiC) composites.


(a) (b)

(c) (d)

Fig. 10. (a–d) Weibull plots for calculating pm of the carbon fiber (C-fiber)-reinforced carbon/carbon (C/C) and carbon/carbon–siliconcarbide (C/C—SiC) composites.

(a) (b)

(c) (d)

Fig. 11. (a–d) Weibull plots for calculating the relative stiffness of the two composites.


was due to the maximum contribution of highly elasticC-fibers in that direction. Hence, the maximum value of0.77 was also obtained for the C/C–SiC composites inthe parallel direction of loading.

The values of [(hmax�hf)/hmax] and (Smax/hmax) ofthe C/C composites evaluated in the present work werequite similar to the values reported by Kanari et al.33

based on the nanoindentation study of a 2D C/C com-posite. However, as they had chosen different peak loadsranging from 50 mN to 20 mN, the scatter in their re-

sults were much higher than that observed in the presentstudy. Unlike the ‘‘m’’ values obtained in the cases ofparameters like H, pm, or E, the Weibull modulus valueswere little higher (e.g., 2–4) as far as [(hmax�hf)/hmax]and (Smax/hmax) were concerned (Figs. 11 and 12). Thispossibly indicated that the presence of flaws or othersurface irregularities had lesser contribution to these pa-rameters.

Table VII shows the values of elastic (We) and plas-tic (Wp) components of the total amount of energyspent (Wt) during the indentation process. The We:Wt

was always found to be higher than that of Wp:Wt. Thisinformation indicated that on complete removal of thetest load, the composites exhibited only small amount ofpermanent deformation. The elastic part of the totalenergy (Wt) was the highest (B95% of the total work)for the C/C–SiC composite when loaded in parallel di-rection of fabric stacking and unloaded, indicating thehighest elastic recovery of the system. Thus, the resultsobtained here agreed favorably with the results obtainedin case of relative spring-back calculation. Furthermore,when the C/C–SiC composites were loaded in paralleldirection of C-fabric stacking, the We:Wp was found tobe B5 times higher than that of the C/C–SiC loaded in

Table VI. Characteristic Values of Relative Stiffnessand Relative Spring-Back

SampleRelative

stiffness (GPa)Relative

spring-back

C/C (>) 49.6 0.64C/C (J) 61.7 0.57C/C–SiC (>) 28.3 0.66C/C–SiC (J) 69.6 0.77

J, loading along the parallel direction of C-fabric stacking; >, loadingalong the perpendicular direction of C-fabric stacking; C/C, carbonfiber (C-fiber)-reinforced carbon/carbon; C/C–SiC, carbon/carbon–silicon carbide.

(a) (b)

(c) (d)

Fig. 12. (a–d) Weibull plots for calculating the relative spring-back of the two composites.


perpendicular direction. This also indicated the stronganisotropic nature of the C/C–SiC structures.

Conclusions

The 2D C/C composites were prepared with wovenC-fabric and graphitic matrix. Some of these were con-verted to the C/C–SiC composites through LSI at16001C in controlled atmosphere. The average inden-tation hardness (H 5 1.14 GPa) as well as the charac-teristic hardness (Hch 5 1.20 GPa) values were thehighest for the C/C–SiC composites along the paralleldirection of C-fabric stacking among all the cases stud-ied in the present work. The characteristic Young’smodulus was also the highest (15.7 GPa) for the C/C–SiC composite when loaded in the parallel direction offabric stacking. In addition, this value was found to beB55% higher compared with the Young’s modulus ofthe C/C composite (EchB10 GPa) when loaded in thesimilar direction. This suggested better interfacial per-formance of the C/C–SiC composites. Furthermore,between the two composites, the values of the relativespring-back (0.77) and the elastic component of energy(94% of Wt) were also evaluated to be the highest for theC/C–SiC composites when loaded along parallel direc-tion of C-fabric stacking. These data suggested that theextent of the elastic recovery was the highest in theC/C–SiC composites along parallel direction of fabricstacking leading to the least permanent deformation af-ter complete unloading (hfB5–10 nm). The low valueof the Weibull modulus (1.24–2.37) suggested that allthe constituents of the composites had significant con-tribution to its local mechanical properties. Conse-quently, the scatter in the data was high. The extent

of anisotropy was found to be much higher in the C–C/SiC composites compared with the C/C composites.

Acknowledgments

The authors are grateful to Dr. H. S. Maiti, Director,Central Glass and Ceramic Research Institute, Kolkata-32, India, for his kind permission to publish this paper.The authors are also grateful to staff members of CGCRI,Kolkata and ASL, Hyderabad for their extensive helpduring this work. Finally, one of the authors (A. K. M.) isalso grateful to CSIR, India (Network Project TARE-MAC No.: NWP 0027) for the financial assistance.

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evaluation of micromechanical properties of carbon/carbon and carbon/carbon–silicon carbide...

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