- Email: [email protected]
Toughening in ceramics containing graphene fillers
Available online at www.sciencedirect.com
CERAMICS INTERNATIONAL
Ceramics International 40 (2014) 11187–11192 www.elsevier.com/locate/ceramint
Toughening in ceramics containing graphene fillers Cristina Ramirez, Maria Isabel Osendin Institute of Ceramics and Glass (ICV), CSIC, Madrid 28049, Spain Received 19 February 2014; received in revised form 26 March 2014; accepted 26 March 2014 Available online 2 April 2014
Abstract High level of reinforcement is observed in ceramic matrix composites containing multilayer graphene, which is frequently attributed to bridging and pull-out phenomena based on microstructural observations of crack paths. Presently, we show that the toughening level observed in two ceramic matrix composites with different graphene type fillers is reasonably fitted to the well-known model for reinforcement of ceramic composites by whiskers/fibers. Furthermore, the most important toughening contribution for these composites is due to bridging by the graphene fillers. The model predicts a steady toughness increment as a function of filler volume but for filler volume concentrations close to the percolation threshold the experimentally observed reinforcement deviates from the model predictions and toughness starts to decay. Consequently, once graphene fillers are fully connected forming a three dimensional network bridging the graphene fillers stops being an effective toughening mechanism. & 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Keywords: B. Composites; D. Si3N4; Toughening; Graphene
1. Introduction Most of the works on ceramic composites with graphene fillers deal with two types of ceramics, namely Al2O3 [1–3] and Si3N4 [4–6] probably because their relevance, with fewer results reported for other ceramic systems of interest, such as SiC [7], ZrB2 [8], TaC [9], hydroxyapatite [10] or SiO2 [11]. Despite the fact that in some of these systems the intended application may not be merely structural, a higher robustness is desirable in all of them. Furthermore, a gamut of reinforcement levels ranging from 11 [12] to 130% [13] has been described for ceramic composites with graphene type fillers. Microstructural observations in these composites of indentation crack paths frequently reveal the presence of graphene sheets bridging the crack wake and also protruding graphene sheets when the fracture surfaces are examined. Nevertheless, up to now, no predictions by means of new or existing models have been done. In that sense, the reinforced model for fiber/ceramic composites [14,15] linked to elastic bridging, fiber debonding n
Corresponding author. Tel.: þ34 91 7355840; fax: þ 34 91 7355843. E-mail address: [email protected] (M.I. Osendi).
http://dx.doi.org/10.1016/j.ceramint.2014.03.150 0272-8842/& 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
and fiber pull-out phenomena seems an ideal framework for present composites. In the present work, we consider toughness data for two Si3N4 composites containing two different of graphene fillers and a range of volume fractions. In particular, one composite contains reduced graphene oxide sheets (rGO) and the other, graphene nanoplatelets (GNP), which essentially differ in the degree of exfoliation and the amount of crystalline defects of the graphene network. We consider here the basic expression developed by Campbell et al. for ceramic composites with fiber/whiskers [14], which states that the maximum toughening produced by whiskers/fibers in ceramic matrix have four essential contributions, namely: (i) the strain energy stored in the filler over the debonded length, (ii) the residual strain energy in matrix and filler within the debonded length, (iii) the energy needed to create a debond surface and (iv) the energy employed in pulling out the fiber from the debonded interface. In the present work, we apply their expression for these new composites and make a best guess over essential parameters – elastic modulus and strength of the filler, debonded length, interfacial energy – needed to test the model. These parameters are contrasted
11188
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
with experimental data when known. The relative importance of the different toughening effects is also discussed for these ceramic/graphene composites.
2. Materials and methods Two types of Si3N4 composites containing graphene nanostructures using two different graphene sources, pristine graphene nanoplatelets (GNP) and graphene oxide (GO) layers, were produced by the Spark Plasma Sintering (SPS) as described elsewhere [16]. In short, the matrix composition consisted of a homogeneous mixture of α-Si3N4 (E-10, Ube Corp.) with 2 wt% Al2O3 (Baikalox-SM8) plus 5 wt% Y2O3 (HC-Stark). Commercial GNP (N002 from Angstron Materials) and GO sheets prepared by the modified Hummers method were conveniently dispersed in ethanol and each blended with the powder matrix batches by sonication and blade mixing. These multilayer graphene sheets have similar lateral size, about 2 mm for the GNPs and 3 mm for rGO, whereas their average thickness is around 60 and 10 nm, respectively. Atomic force microscopy (AFM) images shown in Fig. 1 give a plain idea of the different thickness range of both graphene fillers.
Densification was carried out by SPS (Dr. Sinter, SPS510CE) at 1625 1C for 5 min, applying 50 MPa of uniaxial pressure and under vacuum (4–6 Pa). During the SPS cycle, thermal reduction of GO takes place along with the composite densification as described elsewhere [16]. The content of graphene in both composites ranged from 1 to 5 wt%, corresponding approximately to 0.015 to 0.072 volume fractions. Toughness values of both composites were determined on prismatic bars by the surface crack in flexure method as described in Ref. [13] and the elastic modulus (E) was measured by instrumented micro-indentation, both data are reproduced in Table 1. Fracture surfaces of the composites and crack paths produced by Vickers indentation were observed in a field emissions scanning electron microscope. 3. Reinforcement model for graphene/ceramic composites The model considers mode I crack loading and that the graphene fillers are aligned perpendicular to the crack plane. This last assumption is sustained by experimental observation of these composites that show a preferential orientation of the graphene fillers with the graphene plane perpendicular to the SPS loading axis (Fig. 2). The specimens were tested in the
Fig. 1. AFM topographic views of GNP (a) and rGO (b) sheets with corresponding height profiles along the lines shown in the images.
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
most favorable orientation, specifically, with crack propagating mostly perpendicular to the graphene planes. Graphene fillers in these composites are essentially under residual tension, as the thermal expansion coefficient (α) of the platelets is higher than that of Si3N4 (αm ¼ 5 10 6 C 1). Actually, α for graphene fillers can be considered as that of graphite, i.e. αc ¼ 30 10 6 C 1 in the thickness direction and αa ¼ 1 10 6 C 1 for the in-plane, each corresponding to the c and a graphite crystalline axis [17], respectively. Therefore, on the platelet edge, a compressive misfit strain about 10 times smaller than the tensile misfit strain on the facets exists. A scheme of the condition for the crack propagation in present composites is depicted in Fig. 3. The occurrence of crack debonding along the graphene plane for an incidence angle of 901, instead of crack propagating into the platelet, is governed by the ratio of fracture energies of the interface and the graphene filler [14]. For the elastic misfit conditions of present composites, initial debond will occur when fracture surface of the interface is below 1/3 the fracture energy of the graphene fillers [14]. For lower crack incidence angles, the condition that assures debonding relaxes and fracture energy of the interface and the filler can be closer [14]. For the interfacial fracture energy, Γi, of present composites we assume the typical value of oxynitride glasses 3 J/m2 [18], which is the common phase existing at grain boundaries in Si3N4 ceramics, besides, this assumption is confirmed by high-resolution TEM observations performed in present composites that confirm the existence of an amorphous grain boundary layer [16]. Consequently, fracture energy of the graphene fillers should be above 9 J/
11189
m2 to have maximum debonding. Molecular dynamics simulations of crack growth in graphene and graphite sheets give fracture energy data in both cases within the range 36–46 J/m2 [19,20], hence the assumption of debonding even at perpendicular incidence is plainly sustained. Analysis of the crack opening displacement/stress (u/t) relations for elongated fillers (whiskers/fibers) normal to the crack plane with interfaces subjected to residual tension and constant debond length, d, was carried out by Campbell et al. [14] and corresponding toughness increment due to the fail of the filler in the wake zone at a given critical axial stress, t¼ S, was calculated by the expression Z t¼S 4f Γ i d ΔGc 2f tduþ ð1 f ÞR 0 f S2 R½ðλ1 þ λ2 ðd=RÞÞ2 ðE F eT =SÞ2 ðλ3 þ λ4 ðd=RÞÞ2 Ef ðλ1 þ λ2 ðd=RÞÞ 4f Γ i d ð1Þ þ ð1 f ÞR
¼
where, f is the filler volume fraction, S is the strength of the filler, R is the filler radius, Ef is the fiber elastic modulus, eT is the misfit strain and Γi is the interface fracture energy. The λi coefficients depend on the filler volume fraction and the ratio
Table 1 Fracture toughness data [15] and elastic modulus for both graphene filler containing composites. Si3N4/rGO Si3N4/GNP Si3N4/GNP Filler (vol. fraction) Si3N4/rGO E KIC E KIC (MPa m1/2) (GPa) (MPa m1/2) (GPa) 0.015 0.022 0.043 0.072
5.770.2 7.570.1 10.470.4 9.270.4
300710 290713 26478 20077
4.47 0.2 5.17 0.3 6.67 0.1 5.77 0.2
32076 31077 29074 22876
Fig. 3. Scheme of the crack propagating in the composite and intercepting perpendicularly the oriented graphene fillers.
Fig. 2. SEM images showing preferential alignment of the graphene fillers in composites with GNP (a) and rGO (b). The vertical direction in the images corresponds to SPS loading axis.
11190
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
between the fiber and matrix elastic modulus and appear tabulated in Ref. [14]. For present composites, λi parameters given for fo 0.1 and Ef 4Em were considered, in particular, values of λ1 ¼ λ2 ¼ λ3 ¼ λ4 ¼ 1 were used. The first term in Eq. (1) is the toughness enhancement associated to the bridging and the second derives from the debond surface energy, in present case, as the filler is under residual tension, contribution due to the filler pullout was not accounted for. Misfit strain, eT, is estimated considering the coefficients of thermal expansion of the Si3N4 matrix ( ffi5 10 6/1C) and graphite in the out-plane direction (3 10 5/1C) and a cooling interval of around 1000 1C, which assuming eT ffiΔα ΔT gives a value of 3 10 2 for tensile strain at the interface. The filler radius corresponds in present composites to half the size of the graphene sheets, as for the given crack orientation the graphene plane is the representative facet (Fig. 3). The rest of key parameters, S, Ef and d are discussed in next sections and obtained by best fitting to the experimental data. 4. Comparison with experimental toughness data Toughness data were transformed to critical strain energy release rate (Gc) using common fracture expression GI ¼ K2I /E0 (E0 ¼ E/1 ν2 for plane strain conditions). These data after subtracting values for the Si3N4 matrix (GIC ffi 63 J/m2) [13] are plotted in Fig. 4 and compared to lines given by Eq. (1) using fitting parameters of Table 2 for both composites and volume fraction of graphene fillers in the range 0.015–0.072. A strength value, S, of 40 GPa for rGO filler is required to get sensible fitting to experimental data, which corresponds to ffi 30% of the experimentally determined strength for the graphene monolayer, i.e. 130 GPa [21]. This reduced value is explained by the more defective structure of rGO; in fact, chemically reduced GO shows about a quarter the elastic modulus of pristine graphene, ErGO ¼ 0.25 TPa, [22] although no data has been reported for its strength. Considering that theoretical strength for a cohesive solid is E/10, the 600 500
ΔG (J/m2)
400
rGO calc rGO exp GNP calc GNP exp
300 200 100 0 -100
0.00
0.02
0.04
0.06
0.08
volume fraction
Fig. 4. Comparison of the level of toughening achieved for both composites as a function of the content of GNP and rGO fillers, points are experimental data and continuous lines are corresponding fittings of Eq. (1). Arrows indicate the percolation limit for electric conduction in each composite.
Table 2 Parameters used in Eq. (1) for both composites. Fit parameters
Si3N4/rGO
Si3N4/GNP
d (μm) S (GPa) eT R (mm) Γi (J/m2)
0.7 40 3.0 10 2 1.5 3
0.5 20 3.0 10 2 1.0 3
estimated S value of present rGO (40 GPa) is of the same order of magnitude as the predicted theoretical strength for chemically reduced GO ( 25 GPa). Furthermore, present rGO filler-thermally reduced during the composite densification in the spark plasma sintering (SPS) furnace shows a high level of network recovery [16], and probably a higher strength than may be expected for chemically reduced GO. The best match for strength of GNP in Eq. (1) in the case of Si3N4/GNP composites is achieved for an S value of 20 GPa, i. e. half the strength of rGO ligaments. This smaller S can be explained by the higher volume of the single GNP fillers that would favor the occurrence of a higher flaw size. It should also be noticed that the strength in Eq. (1) corresponds to the small gauge length of bridging along the crack. The debond length, d, estimated by observing the indentation crack paths in these composites (Fig. 5) presents a value around 700 nm for rGO composites, and slightly smaller, 500 nm, for GNP materials. The first term of Eq. (1) that corresponds to the stored energy in the graphene ligaments over the debonded length on both crack sides before failure [14] outnumbers by at least one order of magnitude the energy contribution of debonding. We observe a very good agreement with experimental data for GNP composites in the whole range of compositions; whereas, for rGO composites a perceptible divergence is observed for filler contents above 4 vol% (see Fig. 4). The explanation for this discrepancy may be linked to the percolation limit of the filler. In the case of rGO materials, the graphene sheets network is electrically connected for filler contents of 4 vol% [16], whereas for GNP composites this limit is 7 vol% [23]. Once graphene fillers are fully connected interfaces probably become an easy pathway for crack propagation, thus dominating fracture behavior instead of bridging. A similar turning point in reinforcement has been beckoned for Al2O3 with GNPs when approaching percolation limit [3]. It can be argued that a different toughening mechanism such as crack deflection could be acting in these composites, although often reinforcements associated with crack deflection in platelet composites are substantially lower. Chou and Green developed a crack deflection model for reinforcement in the case of oriented platelet/ceramic composite [24], which predicts toughening independent of the aspect ratio of the platelets for the perpendicular orientation of the platelet facet to the crack plane. This is the case for present composites and therefore, this model would not be able to explain the large
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
11191
Fig. 5. SEM image of an indentation crack path in 4 vol% rGO-Si3N4 composite showing oriented rGO fillers perpendicularly intercepting the crack (a). Images of rGO sheets bridging the crack (b) and a broken/extracted sheet (c) with indication of debond lengths.
toughening differences between both composites (Fig. 4). Besides, R-curve type of behavior has been reported for graphene/ceramic composites [25], which is not expected for the crack deflection toughening mechanism and what is more important, there are many experimental evidences of bridging events in ceramic with graphene fillers [3,4,6] (see Fig. 5). Consequently, in oriented graphene/ceramic composites, toughening is mainly due to the bridging effect. The present simplified analysis reasonably explains the observed toughening in ceramic composites containing graphene fillers. The most relevant contribution in present materials is due to the energy dissipating by the graphene fillers bridging the crack, which is favored by the preferential orientation of the graphene fillers. Accordingly, a superior strength of these ligaments and a high exfoliation degree are essential. Furthermore, toughening departs from predicted plot when the filler network is above the percolation limit. Above this limit the graphene layers form a three dimensional network that controls failure and the bridging model is not valid anymore. This behavior has not been perceived in whiskers/ fibers composites as the required filler concentrations should be much higher. 5. Conclusions The high level of reinforcements observed in Si3N4 composites containing increasing amount of oriented multilayer graphene fillers is explained by the bridging model for composites. The more important parameter for maximum enhancement is the strength of the graphene fillers. The steady
increase in toughness with the volume fraction of graphene reaches a limit for concentrations around the percolation threshold, which also marks the onset of toughness decline as bridging levels off.
Acknowledgements This work was funded by Mineco (Spain) project MAT2012-32944 and by CSIC (Spain) with project PIE 201360E063.
References [1] K. Wang, Y.F. Wang, Z.J. Fan, J. Yan, T. Wei, Preparation of graphene nanosheet/alumina composites by spark plasma sintering, Mater. Res. Bull. 46 (2) (2011) 315–318. [2] Y.C. Fan, L.J. Wang, J.L. Li, J.Q. Li, S.K. Sun, F. Chen, et al., Preparation and electrical properties of graphene nanosheet/Al2O3 composites, Carbon 48 (6) (2010) 1743–1749. [3] H. Porwal, P. Tatarko, S. Grasso, J. Khaliq, I. Dlouhy, M.J. Reece, Graphene reinforced alumina nano-composites, Carbon 64 (2013) 359–369. [4] L.S. Walker, V.R. Marotto, M.A. Rafiee, N. Koratkar, Corral, Toughening in graphene ceramic composites, ACS Nano 5 (4) (2011) 3182–3190. [5] C. Ramirez, L. Garzon, P. Miranzo, M.I. Osendi, C. Ocal, Electrical conductivity maps in graphene nanoplatelet/silicon nitride composites using conducting scanning force microscopy, Carbon 49 (12) (2011) 3873–3880. [6] J. Dusza, J. Morgiel, A. Duszova, L. Kvetkova, M. Nosko, P. Kun, et al., Microstructure and fracture toughness of Si3N4þ graphene platelet composites, J. Eur. Ceram. Soc. 32 (12) (2012) 3389–3397.
11192
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
[7] P. Miranzo, C. Ramirez, B. Roman-Manso, L. Garzon, H.R. Gutierrez, M. Terrones, et al., In situ processing of electrically conducting graphene/ SiC nanocomposites, J. Eur. Ceram. Soc. 33 (10) (2013) 1665–1674. [8] G.B. Yadhukulakrishnan, S. Karumuri, A. Rahman, R.P. Singh, A. K. Kalkan, S.P. Harimkar, Spark plasma sintering of graphene reinforced zirconium diboride ultra-high temperature ceramic composites, Ceram. Int. 39 (6) (2013) 6637–6646. [9] A. Nieto, D. Lahiri, A. Agarwal, Graphene NanoPlatelets reinforced tantalum carbide consolidated by spark plasma sintering, Mater. Sci. Eng., A 582 (2013) 338–346. [10] L. Zhang, W. Liu, C. Yue, T. Zhang, P. Li, Z. Xing, et al., A tough graphene nanosheet/hydroxyapatite composite with improved in vitro biocompatibility, Carbon 61 (2013) 105–115. [11] S. Watcharotone, D.A. Dikin, S. Stankovich, R. Piner, I. Jung, G.H. B. Dommett, et al., Graphene-silica composite thin films as transparent conductors, Nano Lett 7 (7) (2007) 1888–1892. [12] J. Liu, H. Yan, K. Jiang, Mechanical properties of graphene plateletreinforced alumina ceramic composites, Ceram. Int. 39 (6) (2013) 6215–6221. [13] C. Ramirez, P. Miranzo, M. Belmonte, M.I. Osendi, P. Poza, S.M. VegaDiaz, et al., Extraordinary toughening enhancement and flexural strength in Si3N4 composites using graphene sheets, J. Eur. Ceram. Soc. 34 (2014) 161–169. [14] G.H. Campbell, M. Ruhle, B.J. Dalgleish, A.G. Evans, Whisker toughening—a comparison between aluminum-oxide and silicon-nitride toughened with silicon-carbide, J. Am. Ceram. Soc. 73 (3) (1990) 521–530. [15] M. Ruhle, A.G. Evans, High toughness ceramics and ceramic composites, Prog. Mater. Sci. 33 (2) (1989) 85–167.
[16] C. Ramirez, S.M. Vega-Diaz, A. Morelos-Gomez, F.M. Figueiredo, M. Terrones, M.I. Osendi, et al., Synthesis of conducting graphene/ Si3N4 composites by spark plasma sintering, Carbon 57 (2013) 425–432. [17] D.K.L. Tsang, B.J. Marsden, S.L. Fok, G. Hall, Graphite thermal expansion relationship for different temperature ranges, Carbon 43 (14) (2005) 2902–2906. [18] P.F. Becher, E.Y. Sun, C.H. Hsueh, K.B. Alexander, S.L. Hwang, S. B. Waters, et al., Debonding of interfaces between beta-silicon nitride whiskers and Si–Al–Y oxynitride glasses, Acta Mater. 44 (10) (1996) 3881–3893. [19] A. Omeltchenko, J. Yu, R.K. Kalia, P. Vashishta, Crack front propagation and fracture in a graphite sheet: a molecular-dynamics study on parallel computers, Phys. Rev. Lett. 78 (11) (1997) 2148–2151. [20] L. Minh-Quy, R.C. Batra, Single-edge crack growth in graphene sheets under tension, Comput. Mater. Sci. 69 (2013) 381–388. [21] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (5887) (2008) 385–388. [22] C. Gomez-Navarro, M. Burghard, K. Kern, Elastic properties of chemically derived single graphene sheets, Nano Lett 8 (7) (2008) 2045–2049. [23] C. Ramirez, F.M. Figueiredo, P. Miranzo, P. Poza, M.I. Osendi, Graphene nanoplatelet/silicon nitride composites with high electrical conductivity, Carbon 50 (10) (2012) 3607–3615. [24] Y.S. Chou, D.J. Green, Silicon-carbide platelet alumina composites.3. Toughening mechanisms, J. Am. Ceram. Soc. 76 (8) (1993) 1985–1992. [25] A. Centeno, V.G. Rocha, B. Alonso, A. Fernandez, C.F. GutierrezGonzalez, R. Torrecillas, et al., Graphene for tough and electroconductive alumina ceramics, J. Eur. Ceram. Soc. 33 (15–16) (2013) 3201–3210.
CERAMICS INTERNATIONAL
Ceramics International 40 (2014) 11187–11192 www.elsevier.com/locate/ceramint
Toughening in ceramics containing graphene fillers Cristina Ramirez, Maria Isabel Osendin Institute of Ceramics and Glass (ICV), CSIC, Madrid 28049, Spain Received 19 February 2014; received in revised form 26 March 2014; accepted 26 March 2014 Available online 2 April 2014
Abstract High level of reinforcement is observed in ceramic matrix composites containing multilayer graphene, which is frequently attributed to bridging and pull-out phenomena based on microstructural observations of crack paths. Presently, we show that the toughening level observed in two ceramic matrix composites with different graphene type fillers is reasonably fitted to the well-known model for reinforcement of ceramic composites by whiskers/fibers. Furthermore, the most important toughening contribution for these composites is due to bridging by the graphene fillers. The model predicts a steady toughness increment as a function of filler volume but for filler volume concentrations close to the percolation threshold the experimentally observed reinforcement deviates from the model predictions and toughness starts to decay. Consequently, once graphene fillers are fully connected forming a three dimensional network bridging the graphene fillers stops being an effective toughening mechanism. & 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Keywords: B. Composites; D. Si3N4; Toughening; Graphene
1. Introduction Most of the works on ceramic composites with graphene fillers deal with two types of ceramics, namely Al2O3 [1–3] and Si3N4 [4–6] probably because their relevance, with fewer results reported for other ceramic systems of interest, such as SiC [7], ZrB2 [8], TaC [9], hydroxyapatite [10] or SiO2 [11]. Despite the fact that in some of these systems the intended application may not be merely structural, a higher robustness is desirable in all of them. Furthermore, a gamut of reinforcement levels ranging from 11 [12] to 130% [13] has been described for ceramic composites with graphene type fillers. Microstructural observations in these composites of indentation crack paths frequently reveal the presence of graphene sheets bridging the crack wake and also protruding graphene sheets when the fracture surfaces are examined. Nevertheless, up to now, no predictions by means of new or existing models have been done. In that sense, the reinforced model for fiber/ceramic composites [14,15] linked to elastic bridging, fiber debonding n
Corresponding author. Tel.: þ34 91 7355840; fax: þ 34 91 7355843. E-mail address: [email protected] (M.I. Osendi).
http://dx.doi.org/10.1016/j.ceramint.2014.03.150 0272-8842/& 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
and fiber pull-out phenomena seems an ideal framework for present composites. In the present work, we consider toughness data for two Si3N4 composites containing two different of graphene fillers and a range of volume fractions. In particular, one composite contains reduced graphene oxide sheets (rGO) and the other, graphene nanoplatelets (GNP), which essentially differ in the degree of exfoliation and the amount of crystalline defects of the graphene network. We consider here the basic expression developed by Campbell et al. for ceramic composites with fiber/whiskers [14], which states that the maximum toughening produced by whiskers/fibers in ceramic matrix have four essential contributions, namely: (i) the strain energy stored in the filler over the debonded length, (ii) the residual strain energy in matrix and filler within the debonded length, (iii) the energy needed to create a debond surface and (iv) the energy employed in pulling out the fiber from the debonded interface. In the present work, we apply their expression for these new composites and make a best guess over essential parameters – elastic modulus and strength of the filler, debonded length, interfacial energy – needed to test the model. These parameters are contrasted
11188
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
with experimental data when known. The relative importance of the different toughening effects is also discussed for these ceramic/graphene composites.
2. Materials and methods Two types of Si3N4 composites containing graphene nanostructures using two different graphene sources, pristine graphene nanoplatelets (GNP) and graphene oxide (GO) layers, were produced by the Spark Plasma Sintering (SPS) as described elsewhere [16]. In short, the matrix composition consisted of a homogeneous mixture of α-Si3N4 (E-10, Ube Corp.) with 2 wt% Al2O3 (Baikalox-SM8) plus 5 wt% Y2O3 (HC-Stark). Commercial GNP (N002 from Angstron Materials) and GO sheets prepared by the modified Hummers method were conveniently dispersed in ethanol and each blended with the powder matrix batches by sonication and blade mixing. These multilayer graphene sheets have similar lateral size, about 2 mm for the GNPs and 3 mm for rGO, whereas their average thickness is around 60 and 10 nm, respectively. Atomic force microscopy (AFM) images shown in Fig. 1 give a plain idea of the different thickness range of both graphene fillers.
Densification was carried out by SPS (Dr. Sinter, SPS510CE) at 1625 1C for 5 min, applying 50 MPa of uniaxial pressure and under vacuum (4–6 Pa). During the SPS cycle, thermal reduction of GO takes place along with the composite densification as described elsewhere [16]. The content of graphene in both composites ranged from 1 to 5 wt%, corresponding approximately to 0.015 to 0.072 volume fractions. Toughness values of both composites were determined on prismatic bars by the surface crack in flexure method as described in Ref. [13] and the elastic modulus (E) was measured by instrumented micro-indentation, both data are reproduced in Table 1. Fracture surfaces of the composites and crack paths produced by Vickers indentation were observed in a field emissions scanning electron microscope. 3. Reinforcement model for graphene/ceramic composites The model considers mode I crack loading and that the graphene fillers are aligned perpendicular to the crack plane. This last assumption is sustained by experimental observation of these composites that show a preferential orientation of the graphene fillers with the graphene plane perpendicular to the SPS loading axis (Fig. 2). The specimens were tested in the
Fig. 1. AFM topographic views of GNP (a) and rGO (b) sheets with corresponding height profiles along the lines shown in the images.
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
most favorable orientation, specifically, with crack propagating mostly perpendicular to the graphene planes. Graphene fillers in these composites are essentially under residual tension, as the thermal expansion coefficient (α) of the platelets is higher than that of Si3N4 (αm ¼ 5 10 6 C 1). Actually, α for graphene fillers can be considered as that of graphite, i.e. αc ¼ 30 10 6 C 1 in the thickness direction and αa ¼ 1 10 6 C 1 for the in-plane, each corresponding to the c and a graphite crystalline axis [17], respectively. Therefore, on the platelet edge, a compressive misfit strain about 10 times smaller than the tensile misfit strain on the facets exists. A scheme of the condition for the crack propagation in present composites is depicted in Fig. 3. The occurrence of crack debonding along the graphene plane for an incidence angle of 901, instead of crack propagating into the platelet, is governed by the ratio of fracture energies of the interface and the graphene filler [14]. For the elastic misfit conditions of present composites, initial debond will occur when fracture surface of the interface is below 1/3 the fracture energy of the graphene fillers [14]. For lower crack incidence angles, the condition that assures debonding relaxes and fracture energy of the interface and the filler can be closer [14]. For the interfacial fracture energy, Γi, of present composites we assume the typical value of oxynitride glasses 3 J/m2 [18], which is the common phase existing at grain boundaries in Si3N4 ceramics, besides, this assumption is confirmed by high-resolution TEM observations performed in present composites that confirm the existence of an amorphous grain boundary layer [16]. Consequently, fracture energy of the graphene fillers should be above 9 J/
11189
m2 to have maximum debonding. Molecular dynamics simulations of crack growth in graphene and graphite sheets give fracture energy data in both cases within the range 36–46 J/m2 [19,20], hence the assumption of debonding even at perpendicular incidence is plainly sustained. Analysis of the crack opening displacement/stress (u/t) relations for elongated fillers (whiskers/fibers) normal to the crack plane with interfaces subjected to residual tension and constant debond length, d, was carried out by Campbell et al. [14] and corresponding toughness increment due to the fail of the filler in the wake zone at a given critical axial stress, t¼ S, was calculated by the expression Z t¼S 4f Γ i d ΔGc 2f tduþ ð1 f ÞR 0 f S2 R½ðλ1 þ λ2 ðd=RÞÞ2 ðE F eT =SÞ2 ðλ3 þ λ4 ðd=RÞÞ2 Ef ðλ1 þ λ2 ðd=RÞÞ 4f Γ i d ð1Þ þ ð1 f ÞR
¼
where, f is the filler volume fraction, S is the strength of the filler, R is the filler radius, Ef is the fiber elastic modulus, eT is the misfit strain and Γi is the interface fracture energy. The λi coefficients depend on the filler volume fraction and the ratio
Table 1 Fracture toughness data [15] and elastic modulus for both graphene filler containing composites. Si3N4/rGO Si3N4/GNP Si3N4/GNP Filler (vol. fraction) Si3N4/rGO E KIC E KIC (MPa m1/2) (GPa) (MPa m1/2) (GPa) 0.015 0.022 0.043 0.072
5.770.2 7.570.1 10.470.4 9.270.4
300710 290713 26478 20077
4.47 0.2 5.17 0.3 6.67 0.1 5.77 0.2
32076 31077 29074 22876
Fig. 3. Scheme of the crack propagating in the composite and intercepting perpendicularly the oriented graphene fillers.
Fig. 2. SEM images showing preferential alignment of the graphene fillers in composites with GNP (a) and rGO (b). The vertical direction in the images corresponds to SPS loading axis.
11190
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
between the fiber and matrix elastic modulus and appear tabulated in Ref. [14]. For present composites, λi parameters given for fo 0.1 and Ef 4Em were considered, in particular, values of λ1 ¼ λ2 ¼ λ3 ¼ λ4 ¼ 1 were used. The first term in Eq. (1) is the toughness enhancement associated to the bridging and the second derives from the debond surface energy, in present case, as the filler is under residual tension, contribution due to the filler pullout was not accounted for. Misfit strain, eT, is estimated considering the coefficients of thermal expansion of the Si3N4 matrix ( ffi5 10 6/1C) and graphite in the out-plane direction (3 10 5/1C) and a cooling interval of around 1000 1C, which assuming eT ffiΔα ΔT gives a value of 3 10 2 for tensile strain at the interface. The filler radius corresponds in present composites to half the size of the graphene sheets, as for the given crack orientation the graphene plane is the representative facet (Fig. 3). The rest of key parameters, S, Ef and d are discussed in next sections and obtained by best fitting to the experimental data. 4. Comparison with experimental toughness data Toughness data were transformed to critical strain energy release rate (Gc) using common fracture expression GI ¼ K2I /E0 (E0 ¼ E/1 ν2 for plane strain conditions). These data after subtracting values for the Si3N4 matrix (GIC ffi 63 J/m2) [13] are plotted in Fig. 4 and compared to lines given by Eq. (1) using fitting parameters of Table 2 for both composites and volume fraction of graphene fillers in the range 0.015–0.072. A strength value, S, of 40 GPa for rGO filler is required to get sensible fitting to experimental data, which corresponds to ffi 30% of the experimentally determined strength for the graphene monolayer, i.e. 130 GPa [21]. This reduced value is explained by the more defective structure of rGO; in fact, chemically reduced GO shows about a quarter the elastic modulus of pristine graphene, ErGO ¼ 0.25 TPa, [22] although no data has been reported for its strength. Considering that theoretical strength for a cohesive solid is E/10, the 600 500
ΔG (J/m2)
400
rGO calc rGO exp GNP calc GNP exp
300 200 100 0 -100
0.00
0.02
0.04
0.06
0.08
volume fraction
Fig. 4. Comparison of the level of toughening achieved for both composites as a function of the content of GNP and rGO fillers, points are experimental data and continuous lines are corresponding fittings of Eq. (1). Arrows indicate the percolation limit for electric conduction in each composite.
Table 2 Parameters used in Eq. (1) for both composites. Fit parameters
Si3N4/rGO
Si3N4/GNP
d (μm) S (GPa) eT R (mm) Γi (J/m2)
0.7 40 3.0 10 2 1.5 3
0.5 20 3.0 10 2 1.0 3
estimated S value of present rGO (40 GPa) is of the same order of magnitude as the predicted theoretical strength for chemically reduced GO ( 25 GPa). Furthermore, present rGO filler-thermally reduced during the composite densification in the spark plasma sintering (SPS) furnace shows a high level of network recovery [16], and probably a higher strength than may be expected for chemically reduced GO. The best match for strength of GNP in Eq. (1) in the case of Si3N4/GNP composites is achieved for an S value of 20 GPa, i. e. half the strength of rGO ligaments. This smaller S can be explained by the higher volume of the single GNP fillers that would favor the occurrence of a higher flaw size. It should also be noticed that the strength in Eq. (1) corresponds to the small gauge length of bridging along the crack. The debond length, d, estimated by observing the indentation crack paths in these composites (Fig. 5) presents a value around 700 nm for rGO composites, and slightly smaller, 500 nm, for GNP materials. The first term of Eq. (1) that corresponds to the stored energy in the graphene ligaments over the debonded length on both crack sides before failure [14] outnumbers by at least one order of magnitude the energy contribution of debonding. We observe a very good agreement with experimental data for GNP composites in the whole range of compositions; whereas, for rGO composites a perceptible divergence is observed for filler contents above 4 vol% (see Fig. 4). The explanation for this discrepancy may be linked to the percolation limit of the filler. In the case of rGO materials, the graphene sheets network is electrically connected for filler contents of 4 vol% [16], whereas for GNP composites this limit is 7 vol% [23]. Once graphene fillers are fully connected interfaces probably become an easy pathway for crack propagation, thus dominating fracture behavior instead of bridging. A similar turning point in reinforcement has been beckoned for Al2O3 with GNPs when approaching percolation limit [3]. It can be argued that a different toughening mechanism such as crack deflection could be acting in these composites, although often reinforcements associated with crack deflection in platelet composites are substantially lower. Chou and Green developed a crack deflection model for reinforcement in the case of oriented platelet/ceramic composite [24], which predicts toughening independent of the aspect ratio of the platelets for the perpendicular orientation of the platelet facet to the crack plane. This is the case for present composites and therefore, this model would not be able to explain the large
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
11191
Fig. 5. SEM image of an indentation crack path in 4 vol% rGO-Si3N4 composite showing oriented rGO fillers perpendicularly intercepting the crack (a). Images of rGO sheets bridging the crack (b) and a broken/extracted sheet (c) with indication of debond lengths.
toughening differences between both composites (Fig. 4). Besides, R-curve type of behavior has been reported for graphene/ceramic composites [25], which is not expected for the crack deflection toughening mechanism and what is more important, there are many experimental evidences of bridging events in ceramic with graphene fillers [3,4,6] (see Fig. 5). Consequently, in oriented graphene/ceramic composites, toughening is mainly due to the bridging effect. The present simplified analysis reasonably explains the observed toughening in ceramic composites containing graphene fillers. The most relevant contribution in present materials is due to the energy dissipating by the graphene fillers bridging the crack, which is favored by the preferential orientation of the graphene fillers. Accordingly, a superior strength of these ligaments and a high exfoliation degree are essential. Furthermore, toughening departs from predicted plot when the filler network is above the percolation limit. Above this limit the graphene layers form a three dimensional network that controls failure and the bridging model is not valid anymore. This behavior has not been perceived in whiskers/ fibers composites as the required filler concentrations should be much higher. 5. Conclusions The high level of reinforcements observed in Si3N4 composites containing increasing amount of oriented multilayer graphene fillers is explained by the bridging model for composites. The more important parameter for maximum enhancement is the strength of the graphene fillers. The steady
increase in toughness with the volume fraction of graphene reaches a limit for concentrations around the percolation threshold, which also marks the onset of toughness decline as bridging levels off.
Acknowledgements This work was funded by Mineco (Spain) project MAT2012-32944 and by CSIC (Spain) with project PIE 201360E063.
References [1] K. Wang, Y.F. Wang, Z.J. Fan, J. Yan, T. Wei, Preparation of graphene nanosheet/alumina composites by spark plasma sintering, Mater. Res. Bull. 46 (2) (2011) 315–318. [2] Y.C. Fan, L.J. Wang, J.L. Li, J.Q. Li, S.K. Sun, F. Chen, et al., Preparation and electrical properties of graphene nanosheet/Al2O3 composites, Carbon 48 (6) (2010) 1743–1749. [3] H. Porwal, P. Tatarko, S. Grasso, J. Khaliq, I. Dlouhy, M.J. Reece, Graphene reinforced alumina nano-composites, Carbon 64 (2013) 359–369. [4] L.S. Walker, V.R. Marotto, M.A. Rafiee, N. Koratkar, Corral, Toughening in graphene ceramic composites, ACS Nano 5 (4) (2011) 3182–3190. [5] C. Ramirez, L. Garzon, P. Miranzo, M.I. Osendi, C. Ocal, Electrical conductivity maps in graphene nanoplatelet/silicon nitride composites using conducting scanning force microscopy, Carbon 49 (12) (2011) 3873–3880. [6] J. Dusza, J. Morgiel, A. Duszova, L. Kvetkova, M. Nosko, P. Kun, et al., Microstructure and fracture toughness of Si3N4þ graphene platelet composites, J. Eur. Ceram. Soc. 32 (12) (2012) 3389–3397.
11192
C. Ramirez, M.I. Osendi / Ceramics International 40 (2014) 11187–11192
[7] P. Miranzo, C. Ramirez, B. Roman-Manso, L. Garzon, H.R. Gutierrez, M. Terrones, et al., In situ processing of electrically conducting graphene/ SiC nanocomposites, J. Eur. Ceram. Soc. 33 (10) (2013) 1665–1674. [8] G.B. Yadhukulakrishnan, S. Karumuri, A. Rahman, R.P. Singh, A. K. Kalkan, S.P. Harimkar, Spark plasma sintering of graphene reinforced zirconium diboride ultra-high temperature ceramic composites, Ceram. Int. 39 (6) (2013) 6637–6646. [9] A. Nieto, D. Lahiri, A. Agarwal, Graphene NanoPlatelets reinforced tantalum carbide consolidated by spark plasma sintering, Mater. Sci. Eng., A 582 (2013) 338–346. [10] L. Zhang, W. Liu, C. Yue, T. Zhang, P. Li, Z. Xing, et al., A tough graphene nanosheet/hydroxyapatite composite with improved in vitro biocompatibility, Carbon 61 (2013) 105–115. [11] S. Watcharotone, D.A. Dikin, S. Stankovich, R. Piner, I. Jung, G.H. B. Dommett, et al., Graphene-silica composite thin films as transparent conductors, Nano Lett 7 (7) (2007) 1888–1892. [12] J. Liu, H. Yan, K. Jiang, Mechanical properties of graphene plateletreinforced alumina ceramic composites, Ceram. Int. 39 (6) (2013) 6215–6221. [13] C. Ramirez, P. Miranzo, M. Belmonte, M.I. Osendi, P. Poza, S.M. VegaDiaz, et al., Extraordinary toughening enhancement and flexural strength in Si3N4 composites using graphene sheets, J. Eur. Ceram. Soc. 34 (2014) 161–169. [14] G.H. Campbell, M. Ruhle, B.J. Dalgleish, A.G. Evans, Whisker toughening—a comparison between aluminum-oxide and silicon-nitride toughened with silicon-carbide, J. Am. Ceram. Soc. 73 (3) (1990) 521–530. [15] M. Ruhle, A.G. Evans, High toughness ceramics and ceramic composites, Prog. Mater. Sci. 33 (2) (1989) 85–167.
[16] C. Ramirez, S.M. Vega-Diaz, A. Morelos-Gomez, F.M. Figueiredo, M. Terrones, M.I. Osendi, et al., Synthesis of conducting graphene/ Si3N4 composites by spark plasma sintering, Carbon 57 (2013) 425–432. [17] D.K.L. Tsang, B.J. Marsden, S.L. Fok, G. Hall, Graphite thermal expansion relationship for different temperature ranges, Carbon 43 (14) (2005) 2902–2906. [18] P.F. Becher, E.Y. Sun, C.H. Hsueh, K.B. Alexander, S.L. Hwang, S. B. Waters, et al., Debonding of interfaces between beta-silicon nitride whiskers and Si–Al–Y oxynitride glasses, Acta Mater. 44 (10) (1996) 3881–3893. [19] A. Omeltchenko, J. Yu, R.K. Kalia, P. Vashishta, Crack front propagation and fracture in a graphite sheet: a molecular-dynamics study on parallel computers, Phys. Rev. Lett. 78 (11) (1997) 2148–2151. [20] L. Minh-Quy, R.C. Batra, Single-edge crack growth in graphene sheets under tension, Comput. Mater. Sci. 69 (2013) 381–388. [21] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (5887) (2008) 385–388. [22] C. Gomez-Navarro, M. Burghard, K. Kern, Elastic properties of chemically derived single graphene sheets, Nano Lett 8 (7) (2008) 2045–2049. [23] C. Ramirez, F.M. Figueiredo, P. Miranzo, P. Poza, M.I. Osendi, Graphene nanoplatelet/silicon nitride composites with high electrical conductivity, Carbon 50 (10) (2012) 3607–3615. [24] Y.S. Chou, D.J. Green, Silicon-carbide platelet alumina composites.3. Toughening mechanisms, J. Am. Ceram. Soc. 76 (8) (1993) 1985–1992. [25] A. Centeno, V.G. Rocha, B. Alonso, A. Fernandez, C.F. GutierrezGonzalez, R. Torrecillas, et al., Graphene for tough and electroconductive alumina ceramics, J. Eur. Ceram. Soc. 33 (15–16) (2013) 3201–3210.