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Materials Science and Engineering A 527 (2010) 1835–1843

Contents lists available at ScienceDirect

Materials Science and Engineering A

journa l homepage: www.e lsev ier .com/ locate /msea

trength and fracture behavior of two-, three- and four-dimensionallyeinforced carbon/carbon composites

ourav Sarkara, Sweety Kumarib, V.G. Sekarana, R. Mitrac,∗

Advanced Systems Laboratory, Hyderabad 500058, IndiaDefence Metallurgical Research Laboratory, Hyderabad 500058, IndiaDepartment of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India

r t i c l e i n f o

rticle history:eceived 12 February 2009eceived in revised form 2 November 2009ccepted 4 November 2009

a b s t r a c t

A comparative study has been carried out on mechanical behavior of two dimensionally (2D), threedimensionally (3D) and four dimensionally (4D) reinforced carbon/carbon composites (C/Cs) having 50,48 and 37 vol.% carbon fibers, respectively. The tensile and flexural strengths of 2D- and 3D-C/Cs, foundas ∼25% higher than that of 4D-C/C, appear related to fiber volume fraction. The load–displacement plots

eywords:arbon–carbon compositesulti-dimensional

obtained from three-point bend tests on single edge notch bend specimens appear non-linear, suggestinggraceful failure. Scanning electron microscopy studies of crack paths have shown high tortuousity dueto crack deflection, branching as well as fiber debonding and breakage. The results indicate that totalfracture energy release rate (Jc) and displacement (ı0.6) at 60% of peak load are suitable parameters for

sistanı0.6 h

ensile strengthlexural strengthracture

evaluation of fracture reC/Cs. The values of Jc and

. Introduction

The carbon fiber (C-fiber) reinforced carbon composites, popu-arly known as the carbon/carbon composites (C/Cs), are of interestecause of their ability to retain strength and structural integrityill 3000 ◦C either in vacuum or in inert environment [1–6]. Notnly the mechanical properties are retained, but also the tensiletrength is found to increase with increase of temperature [7].hese composites also possess outstanding specific strength andtiffness. Hence, the C/Cs are suitable for application in jet engineomponents, as well as in thermal protection systems used in noseones and leading edges of hypersonic and re-entry type vehicles,hich are exposed to elevated temperatures [1,6]. Due to impres-

ive high temperature properties, the applications of C/Cs in theerospace industry have increased significantly in recent decades8].

A survey of literature [1–6,9–28] suggests that significantesearch has been carried out on the C/Cs with thrust on theirechanical behavior, particularly the strength, fracture toughness

nd damage tolerance. A majority of these studies have focused

rimarily on characterization of the two dimensionally reinforced2D)-C/Cs [9–11,13–20], and relatively few reports [12,21–28] inhe published literature are based on multi-dimensionally rein-orced composites. A study on the comparison of damage and

∗ Corresponding author. Tel.: +91 3222 283292; fax: +91 3222 282280.E-mail address: rahul@metal.iitkgp.ernet.in (R. Mitra).

921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2009.11.010

ce and damage tolerance, respectively of multi-directionally reinforcedave been found as maximum for 2D- and 4D-C/C, respectively.

© 2009 Elsevier B.V. All rights reserved.

fracture resistance of the 2D- and three dimensionally reinforced(3D)-C/Cs by Aly-Hassan et al. [26] has shown that the lattercomposites show lower shear strength but much higher fractureresistance, although the tensile strengths are found to be similar.However, the mechanical properties of the four dimensionally rein-forced (4D)-C/Cs are relatively less documented, and only limitedinformation is available.

It has been shown that the fiber architecture strongly influencesthe mechanical properties in 1D- and 2D-woven C/Cs [28], whilethe weave pattern has a strong effect on both fracture toughnessand failure mechanism of woven glass and carbon fiber composites[29]. In general, it is well-accepted [27–29] that elastic propertiesand fracture behavior of a given C/C is strongly dependent on thetype of fiber architecture, defects in fibers, as well as fiber–matrixinterfacial bond strength. Hence, it is intuitive that strength, energyof fracture and damage tolerance of 2D-, 3D- and 4D-C/Cs wouldvary significantly from one another, and it is important to comparethese properties, particularly to evaluate the merit of each type ofcomposite for specific structural applications.

In this study, tensile and flexural strengths as well as the fracturebehavior of 2D-, 3D- and 4D-C/Cs with identical densities have beeninvestigated with emphasis on understanding the role of C-fiberarchitecture. Relevant fracture resistance parameters have been

evaluated through a careful analysis of the load–displacement plotsfor quantitative comparison of the investigated C/Cs. Furthermore,possible relationships of the estimated fracture resistance param-eters with the mechanisms of failure in the investigated C/Cs havebeen critically examined.

1 nd Engineering A 527 (2010) 1835–1843

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836 S. Sarkar et al. / Materials Science a

. Experimental procedure

.1. Materials

The materials selected for the present study are 2D-, 3D- andD-reinforced C/Cs. The arrangement of C-fibers in the investi-ated composites is shown schematically in Fig. 1. The C-fibers inhe investigated C/C composites are knit with plain weave con-guration. In the 2D-C/Cs, the C-fibers are knit in two directionserpendicular to each other, as shown in Fig. 1(a), and account forvolume fraction of ≈50%. On the other hand, the C-fibers are ori-nted in three mutually orthogonal directions in the 3D-C/Cs, ashown in Fig. 1(b). The volume fraction of the C-fibers in the 3D-/C is ≈48% (�x = �y = �z = 16%), which is not much different fromhat in the 2D-C/C. In contrast to the fiber arrangements presentn the 2D- and 3D-C/Cs, the C-fibers in the 4D-C/Cs are laid out inhree directions (u, v, w) 120o apart, and the central carbon rodsre kept protruding in the ‘z’ direction, as shown in Fig. 1(c). Fur-hermore, the net volume fraction of the C-fibers in the 4D-C/C is37% (�u = �v = �w = 8%, and �z = 13%), which is around ≈26% and23% less than that observed in the 2D- and 3D-C/Cs, respectively.

.2. Processing

Poly acryl nitrile (PAN) type C-fibers with a tow size of 6K weresed in processing of the investigated C/Cs. The diameter of an

ndividual C-fiber was ∼7 �m, while that of each 6K bundle was0.60 mm. The specified Young’s modulus and tensile strength of

he PAN type C-fibers used in this study are 220 and 3.5 GPa, respec-ively. The investigated C/Cs were fabricated through impregnationf the C-fiber preforms by liquid mesophase pitch (with a softeningoint of 80–130 ◦C) at 250 ◦C under a pressure of 0.8 bar (680 Torr)or 3 h. Subsequently, the pitch impregnated C-fiber performs wereubjected at 800 ◦C to hot isostatic pressing at 950–1000 bar pres-ure for 36–45 h. This was followed by carbonization at 1000 ◦C for20–130 h and graphitization at 2650 ◦C for 92 h, each under 1 atmressure. The process cycle from pitch impregnation to graphitiza-ion was repeated, until a density of 1.8 g/cm3 could be obtained inhe investigated C/Cs.

.3. Characterization

.3.1. Study of microstructureThe microstructures of the investigated C/Cs were examined

sing a Carl Zeiss (Carl Zeiss NTS GmbH, Oberkochen, Germany)canning electron microscope (SEM) equipped with a field emissionun, and operated at an acceleration voltage of 20 kV. Secondarylectron (SE) images at low and high magnifications were recordedrom various locations on the specimen surface in order to studyhe nature of C-fiber distribution and defects in these fibers, respec-ively.

.3.2. Mechanical testingThe mechanical tests were carried out at ambient temperature

n air on the investigated 2D-, 3D- and 4D-C/Cs to determine tensilend flexural strength as well as fracture toughness. For each type ofest (tensile, flexural and fracture toughness), about 4–6 specimensere used.

Tension tests were carried out on the specimens having a gageength of 50 mm, width of 10 mm and thickness of 5 mm, using

crosshead velocity of 0.05 mm/min on an Instron 3369 univer-

al testing machine. The tensile strength was determined from theaximum value of load in the load–displacement plots.The flexural strength and fracture toughness were determined

hrough three point bend tests carried out using rigid silicon car-ide fixtures with a span of 40 mm on a computer controlled,

Fig. 1. Schematic illustration of the C/C composites with: (a) 2D; (b) 3D; and (c) 4Dfiber layout.

S. Sarkar et al. / Materials Science and Engineering A 527 (2010) 1835–1843 1837

Table 1Volume of a given unit cell and number of unit cells in the unbroken ligament withlength = W − a, in SENB specimen of each type of carbon–carbon composite.

Type of C/C Approximate unit cell volume (mm3) Number of unit cells

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2D 0.3 3000–40003D 1.3 500–7504D 7.5 100–160

ervo-hydraulic Instron 8801 (Norwood, MA, USA) universal test-ng machine, operated using a crosshead displacement rate of.5 mm/min. The specimens used for determination of the flexu-al strength had the dimensions of 2.5 mm (thickness) × 7.5 mmwidth) × 50 mm (length). The flexural strength, �f was calculatedrom the maximum load, Pmax in the load–displacement plotsbtained from the three-point bend tests [30,31]. The fractureoughness tests were carried out on single edge notch bend (SENB)pecimens, prepared following the ASTM E-399 standard [32]. Theracture toughness specimens had dimensions of 4.8 mm (thick-ess) × 9.6 mm (width) × 50 mm (length), with a notch of depth, ‘a’long the width (W), such that 0.4 ≤ a/W ≤ 0.6. The notches of variedengths were introduced using a 0.3 mm thick diamond wafer blade,

ounted on an Isomet slow speed precision cutting machine. A jigesigned [33] especially to induce straight notches by moving the

ob across the cutting plane, was used. The depth of the notch (initialrack length, a) in each of the SENB specimens was measured alonghe width on both the faces using a graduated eye-piece mountedn an optical microscope. For the fracture toughness test results toe reliable, the number of unit cells in the unbroken ligaments ofhe SENB specimens of C/Cs should be large. The average number ofnit cells present in the unbroken ligament (W − a) in specimens ofach C/C-type has been calculated by considering their volume [27],nd is shown in Table 1. A range of values is provided for the num-er of unit cells in Table 1, because of the variations in lengths ofhe unbroken ligaments from one SENB sample to another. The unitell volumes being considered for these calculations are approxi-ate, because of the variations introduced by different amounts of

ompaction by hot isostatic pressing and densification. The resultsn Table 1 indicate that number of unit cells in the unbroken liga-

ents is significantly large, and the notch depths are appropriate,o as to lead to reproducible and acceptable results in the presenttudy.

The load–displacement curves obtained from these three-pointend tests on the SENB specimens were analyzed to determinehe fracture resistance and damage tolerance parameters using the

ethods discussed in Section 3.3. Neither the specimens for flex-ral tests, nor the SENB specimens showed complete failure, butere bent around the central supporting point of the three point

end fixture. To understand the failure mechanisms, the crack pathsn the partially fractured samples of each of the investigated C/Cs

ere observed using SEM.

. Results and discussion

.1. Microstructure

Typical microstructures depicting the nature of defects in fiberundles of the 2D-, 3D- and 4D-C/Cs are shown in Fig. 2(a)–(c),espectively. On qualitative examination of the micrographsshown in Fig. 2), it appears that the C-fiber bundles in 3D com-osites have a greater density of cracks or defects, than in 2D- and

D-C/Cs. These defects are known to be initiated by the internaltress generated during the cycles of heating and cooling duringabrication, as well as at the time of densification by hot isostaticressing [23]. It has been shown that the residual stress in the C/Cs isaused by: (i) mismatch in the coefficients of thermal expansion in

Fig. 2. SEM (SE) images showing defects present in the fiber bundles of: (a) 2D-C/C;(b) 3D-C/C; and (c) 4D-C/C.

the longitudinal and transverse directions, and (ii) shrinkage of thematrix during carbonization and graphitization [34]. The 3D-C/Cshave been found to exhibit much higher residual stress and lowerfiber–matrix interface strength than the 2D-C/Cs [34], because ofmultiple directions of fiber layout and crimps in the fibers of theformer composite. However, SEM observations have shown lowerdefect density in the 4D-C/C [Fig. 2(c)] than in the 3D-C/C [Fig. 2(b)],

probably because of much lower volume fraction of C-fibers in theformer composite. It is intuitive that infiltration of pitch during hotisostatic pressing and subsequent contraction of the matrix wouldbe less constrained in the 4D-C/C than in 3D-C/C because of thegreater free space in the former composite. As a result, much lower

1838 S. Sarkar et al. / Materials Science and Engineering A 527 (2010) 1835–1843

Table 2Tensile and flexural strengths of the 2D-, 3D- and 4D-C/Cs.

Type of C/C Tensile strength (MPa) Flexural strength (MPa)

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Fig. 3. Load–displacement plots for the fracture toughness tests carried out on theSENB specimens of the C/C composites with 2D, 3D and 4D orientations. Each plot

damage tolerant behavior of the multi-dimensionally reinforcedC/Cs. Furthermore, it is clear that the value of ı0.6 is the greatest forthe 4D-C/C and the least in case of the 2D-C/C. In other words, thedecrease in the load bearing ability with increase in displacement is

Table 3Dimensions and initial crack lengths of single edge notch bend specimens of thethree types of C/C composites, as well as maximum load and displacement at 60%of maximum load, determined from the load–displacement plots.

Sl. no. W (mm) B (mm) a (mm) a/W Pmax (N) ı0.6 (mm)

2D-C/C1 9.47 4.8 4.31 0.45 476 0.322 9.20 4.68 4.70 0.51 318 0.393 9.06 4.30 4.80 0.52 283 0.36

3D-C/C1 9.44 4.38 4.10 0.43 343 0.472 9.59 4.44 4.40 0.46 269 0.463 9.58 4.36 4.65 0.49 256 0.474 9.55 4.38 5.17 0.54 182 0.47

2D 155 ± 8.5 122 ± 8.93D 152.8 ± 10.8 125 ± 16.34D 90.7 ± 7.8 104 ± 9.4

nternal stress is expected to be developed in the 4D-C/C than inhe 3D-C/C during fabrication.

.2. Tensile and flexural strength

The tensile and flexural strengths of the investigated 2D-, 3D-nd 4D-C/Cs along with standard deviations are shown in Table 2.he results in Table 2 indicate that: (i) the values of tensile and flex-ral strengths of 2D- and 3D-C/Cs are somewhat close to each other;ii) the average tensile strengths of the 2D- and 3D-C/Cs are about41% greater than that of the 4D-C/C; (iii) the flexural strengthsf the 2D- and 3D-C/Cs are greater than that of the 4D-C/C by ∼14nd ∼16.7%, respectively, and (iv) the standard deviations of bothensile and flexural strengths are found to be greater for the 3D-C/Chan for the other two types of composites. Higher tensile and flexu-al strengths of 2D- and 3D-C/Cs than those of 4D-C/C are attributedo the strong influence of C-fiber volume fraction on these mechan-cal properties. Larger scatter in the values of tensile and flexuraltrengths observed for the 3D-C/C than for the other compositesppears to be rooted in the larger size and greater concentrationf flaws in C-fiber bundles [as shown in Fig. 2(b)] of the formeromposite.

The average values of flexural strength found for the 2D-C/Csn this study (Table 2), resemble those reported for similar typef composites prepared by impregnation of either pitch [18] orhenolic resin [19], and are lower than the values reported forhe C/Cs processed by chemical vapor infiltration (in the range of200–600 MPa) [10,20]. Hence, it may be inferred that the processsed for fabrication, has a strong influence on densification andaw distribution of the C/Cs, which in turn affects their flexuraltrengths [23].

.3. Fracture behavior

.3.1. Load–displacement plotsTypical load–displacement plots obtained by three point bend

esting of the SENB specimens of 2D-, 3D- and 4D-C/Cs with dif-erent notch depths (initial crack lengths) are shown in Fig. 3, withrrows indicating the type of composite and the value of a/W (ini-ial crack length/specimen width) for each plot. Table 3 shows theimensions, the value of a/W, and the peak load (Pmax) obtainedrom the load–displacement plot for each specimen of the inves-igated C/Cs. Comparison of the results shown in both Table 3 andig. 3 indicates that (i) the value of Pmax for a given SENB speci-en is a function of a/W; and (ii) for almost similar values of a/W,

he highest and lowest values of Pmax are observed for 2D-C/C andD-C/C, respectively. Examination of the plots in Fig. 3 beyond theisplacement corresponding to the Pmax indicates: (i) the occur-ence of irregular rise and drop in the values of load, and (ii) arogressive deterioration of load bearing capability with increase

n displacement. The non-linear nature of load–displacement plotsFig. 3) is suggestive of a graceful or non-catastrophic failure mech-nism in the investigated C/Cs, and this phenomenon has been

eported in the literature as “pseudo-plastic behavior” [8,26]. Inther words, unstable fracture is not observed in these composites,n spite of the presence of flaws in the fiber bundles as shown inig. 2. Hence, analysis of the fracture resistance on the basis of lin-ar elastic fracture mechanics by considering the value of Pmax in

has been labeled using an arrow indicating the type of composite and the a/W ratioused in the corresponding specimen.

the load–displacement plot does not appear to be appropriate fora fair comparison between the fracture behaviors of the investi-gated C/Cs. Since complete fracture has not been observed for anyof the investigated composites, the value of displacement (ı0.6) inthe load–displacement plots corresponding to 60% drop in the loadbearing ability (∼0.6Pmax) as shown in Table 3, has been consideredfor comparison of the damage tolerance of these materials. The dis-placement at 0.6Pmax has been particularly chosen, because the testwas discontinued beyond this point for some of the specimens, asthe value of load was found to be too low to be of any practicalsignificance. The value of ı0.6 is significant, because it quantifiesthe extent of damage tolerated by the investigated C/Cs with only apartial loss of its load bearing ability, and this information is impor-tant for structural applications of these composites. Examination ofthe results in Table 3 and Fig. 3 indicates that unlike Pmax, the valueof ı0.6 is either a weak function or almost independent of the valueof a/W for the corresponding specimen. Thus, it is possible to inferthat the initial crack length or flaw has a minor influence on the

4D-C/C1 9.58 4.79 3.86 0.40 300 1.112 9.55 4.84 4.00 0.42 237 1.333 9.61 4.81 4.49 0.47 155 1.704 9.68 4.82 5.76 0.59 143 1.86

nd Engineering A 527 (2010) 1835–1843 1839

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Fig. 4. SEM micrographs depicting the failure mechanisms in the 2D-C/C: (a) crackpath near notch at low magnification showing deflection (labeled as “DF”) by close

S. Sarkar et al. / Materials Science a

uch less in the 4D-C/C, than in the other two investigated compos-tes, indicating that damage tolerance is the highest in the former

aterial. Higher displacements and lower peak loads with greateregrees of pseudo-plasticity have been reported in the literature8,26] for 3D-C/C than for 2D- and 1D-C/Cs, and such observa-ions are in close agreement with the results of the present studyTable 3).

.3.2. Study of the crack pathsThe crack paths in the three point bend tested SENB specimens

f the investigated C/Cs have been carefully examined to explainhe nature of load–displacement plots. The SEM (SE) images ofhe crack paths observed in the tested SENB specimens of 2D-,D- and 4D-C/Cs are shown in Figs. 4–6, respectively. The loweragnification SEM (SE) images showing the origin of cracks at the

otch tips of 2D-, 3D- and 4D-C/C specimens are depicted in Figs.(a), 5(a) and 6(a), respectively. Examination of the crack paths inhese figures shows distinct evidence of a large degree of tortuos-ty. Although each of the SENB specimens was loaded for mode-Irack propagation, yet the nature of crack path orientations withespect to the corresponding loading axes suggests a mixed-modeype failure. It is intuitive that the amount of deviation from mode-crack propagation is strongly related to the local stress-field at

he crack tip, which is believed to be a function of the fiber ori-ntation with respect to the loading axis. Comparison of the crackaths shown in Figs. 4(a), 5(a) and 6(a) indicates that the devi-tion from mode I propagation at the notch tip is greater in theD-C/C, than in 2D- and 3D-C/Cs. The lowest value of Pmax foundor the 4D-C/C (Table 3), in spite of the maximum crack path tor-uousity, can be explained on the basis of: (i) the lower volumeraction of C-fibers than in the other two composites; and (ii) max-mum deviation from mode I cracking close to the notch tip. Awayrom the notch tip, the crack is often found to be deflected by angleso the order of ≈90◦, as shown in Figs. 4(a) and 6(a). Comparisonf the crack paths also shows evidence for the maximum amountf delamination in case of the 4D-C/Cs. In addition, branching ofhe crack paths has been observed for the specimens of 3D-C/Cs, ashown in Fig. 5(a).

Much of the crack path in the 2D-C/C, as shown at higheragnification in Fig. 4(b), appears roughly perpendicular to fibers

t a large number of locations both near the notch tip as wells well as away from it, which is somewhat analogous to crackrrester orientation for laminated composites. Examination of thisgure also confirms that the crack is forced to propagate insidehe 2D-C/C by either cracking of fibers or debonding between

atrix and fiber bundles. On the other hand, the crack propa-ates mainly by debonding of fiber bundles aligned along the crackaces in the 3D-C/C, as shown in Fig. 5(b). Furthermore, Fig. 6(b)howing a typical crack path in the 4D-C/C specimen, indicateshat the boundaries of C-fiber bundles with different orienta-ions are preferred for crack propagation. The above observationsuggest that crack propagation through the boundaries of fiberundles with different orientations is energetically more favor-ble for C/Cs with a larger number of fiber orientations. Thus,t is inferred that the orientation of crack with respect to thebers near the notch tip in 2D-C/C is responsible for the higheralue of Pmax than that of other composites for similar values of/W.

The nature of load–displacement plots can be explained onhe basis of crack paths shown in Figs. 4–6. The probable rea-ons for the load-drops observed in Fig. 3 are either breakage

f the fiber bundles [Fig. 4(b)] or cracking of the brittle matrixFig. 4(c)] in the investigated composites. The drop in load duringgiven test is arrested, because of the dissipation of elastic strain

nergy through the process of delamination, fiber–matrix debond-ng and crack branching (Figs. 4–6), all of which are responsible

to 90◦; (b) fiber–matrix debonding and breakage of fiber bundles; and (c) matrixcracking. The crack paths are shown with arrows.

for the requirement of higher energy for further crack propaga-tion. As a result, mode I crack propagation is interrupted withincrease in the crack path tortuosity, leading to rise in the energyof fracture. It is also intuitive that the magnitudes of displacementcorresponding to the 0.6Pmax (Fig. 3) scale with the crack path

tortuousity, which appears to be at its maximum for the 4D-C/C.Crack deflection and branching as well as fiber–matrix debond-ing are well-known and much documented [35–38] tougheningmechanisms for the fiber reinforced ceramic matrix composites,

1840 S. Sarkar et al. / Materials Science and Engineering A 527 (2010) 1835–1843

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gale

ig. 5. SEM micrographs depicting the failure mechanisms in the 3D-C/C: (a) entirerack path starting from notch at low magnification showing crack branchinglabeled as “BC”); and (b) fiber–matrix debonding (marked as “DB”). The crack pathsre shown with arrows.

s these events enhance the energy required for failure very signif-cantly.

.3.3. Elastic plastic fracture toughness and total fracture energyelease rate

Analysis of the load–displacement plots in Fig. 3 indicates thathe ratio Pmax/PQ exceeds 1.1, where PQ has been defined follow-ng the ASTM E-399 standard [32]. As a result, it is not possibleo apply the linear elastic fracture mechanics approach to deter-

ine the values of mode-I plane strain fracture toughness (KIC)rom the non-linear load–displacement plots (Fig. 3). It may beoted that the J-integral approach for elastic–plastic fracture haseen successfully extended to analyze the fracture resistance ofrittle matrix composites, such as concrete [39–42] and continuousber reinforced ceramic composites [33,43,44], showing non-linear

oad–displacement plots as evidence for pseudo-plasticity. A grad-al decrease in the stress ahead of the crack tip and stable crackropagation justify the application of J-integral approach in suchituations. In the present study, the elastic–plastic fracture tough-ess (JIC) and the total fracture energy release rates (Jc) have beenvaluated for each of the investigated C/Cs, based on the proceduresuggested in some of the earlier reports [33,45,46].

The fracture initiation energy, Eini for each specimen with aiven initial crack length has been obtained by measuring therea under the corresponding load–displacement plot (Fig. 3) foroads between zero and Pmax. Furthermore, the average values oflastic–plastic fracture toughness, JQ have been calculated for each

Fig. 6. SEM micrographs depicting the failure mechanisms in the 4D-C/C: (a) crackpath near notch at low magnification showing delamination (labeled as “DL”); and(b) location of crack path at the interface of differently oriented fiber bundles. Thecrack paths are shown with arrows.

of the investigated C/Cs using the following relationship:

JQ = �Eini

B(�a)(2)

where �Eini is the difference in the fracture initiation energies,and (a is the difference between the initial crack lengths (or notchdepth, a) in a given pair of specimens, while B is the specimenthickness. Eq. (2) suggests that the value of JQ depends on howstrongly the value of Eini depends on the initial crack length (notchdepth). It is known that JQ = JIC, when B, a ≥ 25 × (JQ/�y) [47]. Con-sidering the values of tensile strengths shown in Table 2, typicalvalues of 25 × (JQ/�y) for the 2D-, 3D- and 4D-C/Cs are found as0.94, 1.38 and 1.7 mm, respectively. Since these values are found tobe less than the corresponding values of both ‘B’ and ‘a’, as shownin Table 3, it is appropriate to consider JQ = JIC for each of the C/Cspecimens used in this study. The values of JIC calculated for theinvestigated composites are shown in Table 4. Comparison of theresults as shown in this table, indicates that the mean values of JICdecrease in the following order: JIC (2D-C/C) > JIC (3D-C/C) > JIC (4D-C/C). However, the values of JIC appear unsuitable for comparisonof fracture resistance of the C/Cs due to the large scatter (Table 4),which may be attributed partly to varying degrees of deviations

from mode-I propagation (Figs. 4–6). Due to such a scatter in thedata, the lowest value of JIC for the 2D-C/C appears very close to thehighest value obtained for the 4D-C/C. Moreover, significant devi-ations from mode-I crack propagation, as is evident from the SEMmicrographs of crack paths (Figs. 4–6), imply that neither KIC nor JIC

S. Sarkar et al. / Materials Science and Engineering A 527 (2010) 1835–1843 1841

Table 4Elastic–plastic fracture toughness (JIC) and total fracture energy release rate (Jc)obtained from analysis of the load–displacement data.

Type of C/C Displacement(ı, mm)

ıc (mm) (Efr/(a (J/m) Jc (kJ/m2) JIC (kJ/m2)

2D

0.20

0.25

−39.0 8.5

9.9 ± 5.90.25 −61.0 13.30.30 −69.0 15.00.40 −80.0 17.40.50 −80.0 17.4

3D

0.20

0.31

−9.39 2.14

6.6 ± 5.8

0.30 −22.34 5.090.40 −36.36 8.280.50 −41.67 9.490.60 −43.33 9.870.70 −43.33 9.87

0.25 −9.07 1.89

ioiilc(itbm

ellimapduoidaFdvd[

J

wrcfTainficCdd

4D 0.48 3.0 ± 1.30.50 −26.6 5.530.75 −40.8 8.491.00 −46.0 9.56

s an appropriate parameter for quantifying the fracture resistancef the investigated C/Cs. Another reason for considering the JIC asnappropriate is the use of fracture initiation energies correspond-ng to the peak loads in the load–displacement plots, which is ofittle use for analysis of pseudo-plastic behavior of the investigatedomposites. The load–displacement plots (Fig. 3) and crack pathsFigs. 4–6), clearly indicate that the interactions of the progress-ng crack with the fiber bundles contribute significantly to bothhe total fracture energy and the damage tolerance, which have toe accounted for a rigorous evaluation of fracture behavior of theulti-dimensionally reinforced C/Cs.An alternative method involving the measurement of the total

nergy of fracture (Efr) at the values of selected displacements in theoad–displacement plots for specimens with different initial crackengths (a), has been used to assess the fracture resistance of thenvestigated C/Cs. The values of Efr at selected values of displace-

ent have been calculated by measurement of the correspondingreas under the load–displacement plots, starting from the initialosition of crack (origin of load–displacement plot) to the selectedisplacement value. This approach differs considerably from thatsed to determine JQ, as the total energy for different displacementsf crack tip and not just the energy for crack initiation (correspond-ng to Pmax) is being considered. The plots of ‘Efr’ for the selectedisplacements, ı1, ı2 and ı3 against ‘a’ are shown for the 2D-, 3D-nd 4D-C/Cs in Fig. 7(a)–(c), respectively. From the plots shown inig. 7(a) through (c), it is clear that the Efr of all the SENB specimensecreases with increasing initial crack length (a), as expected. Thealues of total fracture energy release rate (Jc) for different values ofisplacements have been obtained using the following relationship33,44]:

c = −(�Efr/�a)B

(3)

here (Efr/(a is the slope of the best fit line obtained using linearegression analysis for the plot of Efr against a. This relation indi-ates that Jc increases with increasing dependence of the energy ofracture on the initial crack lengths (notch depth) of the samples.he estimated values of (Efr/(a and Jc for all the three types of C/Csre shown in Table 4. In order to further analyze the results depictedn Fig. 7(a)–(c), the selected displacements, ı1, ı2 and ı3 have beenormalized by ıc, the average displacement at the peak loads (the

rst peak) of the three or four test specimens with different initialrack lengths. The values of ıc for the three types of investigated/Cs are shown in Table 4. The values of Jc calculated by the proce-ure mentioned above are plotted against the different normalizedisplacements (ı/ıc) in Fig. 8. On examination of the results for each

Fig. 7. Plots depicting the variation of energy of fracture (Efr) with the initial cracklength (a) for three selected values of displacements, ı1, ı2 and ı3 in: (a) 2D-C/C; (b)3D-C/C; and (c) 4D-C/C. The values of ı1, ı2 and ı3 are shown in the legend.

type of C/C in this figure, it is clear that the value of Jc increaseswith normalized displacement and then becomes almost constant.The rise in the value of Jc with ı indicates that the resistance tofracture increases with increase in crack length, thus suggesting an

R-curve type behavior for each type of the investigated composites.Furthermore, the value of Jc at a chosen normalized displacementobserved for the 2D-C/C is higher than that for the 3D- and 4D-C/Cs. It is therefore proposed that orientation of the propagatingcrack perpendicular to fiber-layout, maximizes both the Pmax and

1842 S. Sarkar et al. / Materials Science and En

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ig. 8. Plots showing the variation of the total fracture energy release rate (Jc) withormalized displacement (ı/ıc) for 2D-, 3D- and 4D-C/Cs.

he energy absorbed in crack propagation by fiber–matrix decohe-ion and fiber-breakage. Again, the results shown in Fig. 8 indicatehat the values of Jc at a chosen normalized displacement for theD- and 4D-C/Cs are not too different from one another, in spitef the fact that the mean values of JIC for these composites are dif-erent (Table 4). The similarities in the values of Jc observed forD- and 4D-C/Cs can be explained on the basis of the observationhat crack propagation is preferred through interfaces between the

atrix and fiber bundles with different orientations in both theomposites. Hence, the results of this study lead to the inferencehat the value of Jc is more appropriate than JIC for quantifying theomposite’s fracture resistance, as the former parameter is morelosely related to the energy absorbed during crack propagation.oreover, damage tolerance expressed in terms of ı0.6 for a given

/C in this study is not directly related to Jc at a specific value ofisplacement.

. Conclusions

The tensile and flexural strengths as well as the fracture resis-ance of 2D-, 3D- and 4D-C/Cs, prepared by liquid impregnation ofhe preforms with 6K C-fiber bundles in plain weave configurationnd hot isostatic pressing have been comprehensively evaluated,nd the following conclusions are drawn from the present study:

a) The tensile and flexural strengths of the C/Cs are found to begreater for 2D- and 3D-C/Cs than for 4D-C/C, indicating thatthese values increase with increase in C-fiber volume fraction.

b) The load–displacement plots obtained from three point bendtests carried out on the SENB specimens of all the three C/Cs bearsignatures of non-catastrophic failure with gradual drop in loadafter the maximum is reached. This pseudo-plastic behavioris consistent with evidence of mixed mode crack propaga-tion, crack deflection and branching as well as fiber-debonding,observed using SEM. Hence, total fracture energy release ratefor a given displacement, Jc and displacement at 60% of max-imum load, ı0.6 have been found to be more suitable thanelastic–plastic fracture toughness, JIC, for the purpose of quanti-tative comparison of fracture resistance and damage tolerance,

respectively of the investigated multi-dimensional C/Cs.

c) For a given normalized displacement, the values of Jc are foundto be closer for 3D- and 4D-C/Cs, but are lower than that of2D-C/C. R-curve type behavior has been observed for all theinvestigated materials, where the Jc increases with displace-

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gineering A 527 (2010) 1835–1843

ment of the crack front, indicating its strong dependence onthe nature of crack–fiber interactions. On the other hand, theload–displacement plots of 4D-C/C exhibit much higher ı0.6 andhence greater damage tolerance than that of 2D- and 3D-C/Cs.The damage tolerance in the investigated C/Cs appears to beclosely related to the degree of tortuousity of the crack paths,caused by crack deflection, branching as well as fiber–matrixdebonding and delamination of layers.

Acknowledgements

The authors thank Mr. Manab Mallik and Mr. Ankan Paria fortechnical assistance with specimen preparation and scanning elec-tron microscopy. The authors are grateful to Dr. G. Malakondiah,Director, Defence Metallurgical Research Laboratory for permis-sion to use the Mechanical Testing Facility. The authors also expresstheir sincere gratitude to Mrs. G. Rohini Devi and Mr. G. Ramaguru,Senior Scientists at the Defence Research and Development Labora-tory for their valuable suggestions. The facilities provided by themduring the period of work are duly acknowledged.

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