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aluminum composites
Accepted Manuscript Strengthening behavior of few-layered graphene/aluminum composites S.E. Shin, H.J. Choi, J.H. Shin, D.H. Bae PII: DOI: Reference:
S0008-6223(14)01006-9 http://dx.doi.org/10.1016/j.carbon.2014.10.044 CARBON 9437
To appear in:
Carbon
Received Date: Accepted Date:
26 February 2014 17 October 2014
Please cite this article as: Shin, S.E., Choi, H.J., Shin, J.H., Bae, D.H., Strengthening behavior of few-layered graphene/aluminum composites, Carbon (2014), doi: http://dx.doi.org/10.1016/j.carbon.2014.10.044
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Strengthening behavior of few-layered graphene/aluminum composites S.E. Shin1, H.J. Choi2, J.H. Shin1 and D.H. Bae1∗ 1
2
Department of Materials Science and Engineering, Yonsei University, Seoul, 120-749, Korea
School of Advanced Materials Engineering, Kookmin University, Seoul, 136-702, Korea
Abstract Strengthening behavior of composite containing discontinuous reinforcement is strongly related with load transfer at the reinforcement-matrix interface. We selected multi-walled carbon nanotube (MWCNT) and few-layer graphene (FLG) as a reinforcing agent. By varying a volume fraction of the reinforcement, aluminum (Al) matrix composites were produced by a powder metallurgy method. Uniform dispersion and uniaxial alignment of MWCNT and FLG in the Al matrix are evidenced by high-resolution transmission electron microscope analysis. Although the reinforcements have a similar molecular structure, FLG has a 12.8 times larger specific surface area per volume more than MWCNT due to geometric difference. Therefore an increment of a yield stress versus a reinforcement volume fraction for FLG shows 3.5 times higher than that of MWCNT Consequently, for both reinforcements, the composite strength proportionally increases with the specific surface area on the composite, and the composites containing 0.7 vol% FLG exhibit 440 MPa of tensile strength.
∗
Corresponding author. Tel.:+82 2-2123 5831. E-mail : [email protected] (Donghyun Bae) 1
1. Introduction Graphene has attracted interest as a reinforcing agent for metal matrix composites due to excellent mechanical properties based on the strong sp2 C–C bonds, which are similar to fullerene and carbon nanotube [1, 2]. Furthermore, it has merits over other carbon-based nano materials, which originate from its inherent two-dimensional (2-D) morphology; the planar structure is more favorable to load transfer as well as to impeding atomic diffusion at high temperatures, as compared to its 0-D and 1-D counterparts. Consequently, it provides superior strength for composites at both room temperature and high temperatures. In order to transmit the excellent properties of graphene to composites, uniform dispersion of an individually-exfoliated graphene is one key factor. Several processes have been introduced to exfoliate graphite to single-layer or few-layer graphene by mechanical and/or chemical means [3–5]. Mechanical exfoliation using a tape dispenser [2] or atomic force microscopy (AFM) [6] has exhibited inadequate productivity for large-scale industrial applications. Although large-scale synthesis of graphene by gas phase techniques (e.g., thermal chemical vapor deposition) [7–9] is actively ongoing, this process is still costly and has restrictions in terms of the selection of the substrate materials. Chemical exfoliation by a solution process has been suggested as a relatively cheap process [10–12], and yet presents difficulties for scalable synthesis due to complex synthesis steps and the requirement for a large amount of chemicals and acid. Recently, solid phase techniques, combined with ballmilling processes, have enabled production of scalable quantities of carbon-base nanomaterials by applying shear forces on pristine agglomerated particles [13–15]. Even though one has developed a scalable process to produce few-layer graphene (FLG), an additional technical hurdle is in the uniform dispersion of the graphene in the metal matrix, which has closely packed atomic structures. Hence, graphene/metal composites have 2
been seldom investigated compared to polymer matrix composites, although the great strength and light weight features of graphene/metal composites are expected to lead to applications of such composites in the automotive and aerospace industries. Aluminum (Al) matrix composites reinforced with FLG have recently been produced using different synthesis techniques with powder metallurgy (PM) routes. Table 1 summarizes the fabrication processes and resulting properties of recently developed Al/FLG composites [16 21]. Similar to other nanostructured composites, dispersion of nanoscale reinforcement is a critical issue in Al/FLG composites. Poorly dispersed FLG may act as defect sites, significantly deteriorating the performance of the final composites [16, 17]. Consolidation processes are also important for Al/FLG composites because a selection of high-processing temperatures to avoid insufficient powder consolidation leads to unfavorable reactions (e.g., transformation of FLG to carbides) [17, 18 20]. Even though some composites have been produced via cost-ineffective routes or using expensive materials (e.g., graphene oxide), they did not exhibit tensile elongation or they exhibited very limited tensile strength (<300 MPa). Furthermore, the microstructure of Al/FLG composites with an atomicscale resolution has not been well reported; atomic-scale resolution images may provide detailed information on the morphology of FLG and the interface between Al and FLG [17, 20, 21]. Reinforcement in composites may enhance the strength of the matrix by (i) carrying a great amount of load instead of the matrix and by (ii) interrupting the plastic deformation of the matrix. Hence, two important factors to determine the strengthening efficiency of reinforcement, other than its intrinsic mechanical properties and volume fraction, are (i) how much load can be effectively transmitted from the matrix to the reinforcement and (ii) how much the stress distribution can be altered by the reinforcement. Both are affected by bonding strength between the matrix and reinforcement, morphology/surface area of the reinforcement, 3
and spatial distribution of the reinforcement [22, 23]. Although experimental work on the effect of volume fraction of the reinforcement on the strength of composites [24, 25] and theoretical work on the bonding strength between metal and carbon–based nano materials [26−29] has been conducted, the role of morphology and surface area on the reinforcement has not been extensively investigated. In particular, a comparison study on the strengthening behavior of reinforcements with a variety of shapes (e.g., fullerene–sphere/0-D, carbon nanotube–tube/1-D, and graphene–planar/2-D), but with similar intrinsic mechanical properties, would be highly interesting. The primary objective of this work is to produce Al matrix composites with welldispersed FLG using a scalable powder metallurgy approach. Here, we introduce a favorable route to produce centimeter-scale Al/FLG composites with excellent performances. This work also aims to examine tensile properties of the Al/FLG composite as a function of volume fraction of FLG, so as to compare the strengthening behavior of FLG with that of multiwalled carbon nanotube (MWCNT). The present study also carefully investigates the microstructure of the composites at an atomic scale to provide detailed information on the structure of nano-carbon materials and nano-carbon/Al interface structure. Further, this work quantifies the effect of shape factor (i.e., tube versus sheet) and specific surface area of reinforcement on the composite strength.
Table 1. Experimental tensile strength and hardness of FLG-reinforced composites. Graphene content
Fabrication techniques
Mechanical properties
4
Research group
0.1 wt%
Ball-milling Hot isostatic pressing: 550 oC, 4 h Hot extrusion: 550 oC, 4:1 ratio
Tensile strength: 262 MPa
Bartolucci et al. [16]
0.3 wt%
Ball-milling Sintering: 580 oC, 2 h Hot extrusion: 440 oC, 20:1 ratio
Tensile strength: 250 MPa
Wang et al. [17]
0.3 wt%
Ball-milling Sintering: 600 oC, 6 h Hot extrusion: 470 oC, 2:1 ratio
Vickers hardness: 85 Hv Tensile strength: 280 MPa
Rashad et al. [18]
0.3 wt%
Ball-milling Sintering: 500 oC, 5 h
Vickers micro-hardness: 90 μHv
Perez et al. [19]
5 wt.%
Ball-milling Sintering: 600 oC, 5 h
Vickers hardness: 70 Hv Compressive strength: 180 MPa
Latief et al. [20]
2. Experimental 2.1. Sample preparation Aluminum (Al)–based composites containing FLG were fabricated by hot-rolling of ballmilled powder. At first, graphite flakes (6−8 nm thickness and 120−150 m2/g typical specific surface area) were mechanically exfoliated by planetary ball milling in the presence of isopropyl alcohol ((CH3)2CHOH). A stainless steel bowl (500 mL) was charged with graphite flakes (2 g) and stainless steel balls (~5 mm diameter, 30 g) at a ball-to-powder weight ratio of 15:1, together with 50 ml of isopropyl alcohol. Planetary milling was performed at a rotation speed of 200 RPM for 1 h; it was paused for 75 min after every 15-min milling to maintain ambient processing temperature without any process control agent. Afterwards, the isopropyl alcohol was evaporated and dried at 150 oC for 3 h. Graphite flakes are supposed to be exfoliated by shear forces on contact between powder and balls during milling. Due to the 5
weak van der Waals-like coupling between graphite layers, the graphene sheets in graphite can slide easily with respect to one another. To address this, additional milling was conducted for further exfoliation of graphite nanosheets into FLG and for dispersion of the FLG in Al powder. The exfoliated graphite flakes were exfoliated further into FLG and were also mixed with Al powder (99.5 % purity and <150 μm diameter) using a planetary mill at a rotation speed of 100 RPM for 3 h, with a process control agent of 1 wt. % stearic acid (CH3(CH2)16CO2H). Milling was paused for 15 min after every 15 min of milling. Finally, for further dispersion of FLG in Al powder, the planetary-milled mixture was high energy ballmilled in an attritor at 500 RPM for 6 h in a purified argon atmosphere. FLG, attached on the Al powder surface, is gradually embedded and is dispersed inside Al powder. A variety of ball-milled powders were fabricated by varying the volume fraction of FLG (i.e. 0.3, 0.5 and 0.7 vol%). The ball-milled powder was containerized in a copper tube (60 mm in diameter, 150 mm in height, and 1.5 mm in thickness), compacted, and was then hotrolled. The sample was heated to a pre-determined temperature of 500 oC at a heating rate of 15 oC /min, and rolling was conducted with a 12% reduction per pass; the final thickness of samples was 1 mm. After rolling, the copper container was mechanically removed. Since FLG was embedded inside the Al powder, it did not significantly interrupt consolidation of Al powder during hot rolling, providing a fully dense composite sheet.
2.2. Characterization Morphology of the ball-milled powder varied according to milling condition, as was observed using scanning electron microscopy (SEM). Microstructure of the Al/FLG composite was observed using a high resolution transmission electron microscope (HRTEM, 6
JEOL 2000). Thin foil specimens from the sheets were carefully prepared by an ion beam 6 milling method (Gatan, Model 600, Oxford, UK). The structure of FLG was also investigated by Raman spectroscopy using a Jobin-Yvon microspectrometer (LabRam HR, Jobin-Yvon Co. Ltd., France). Spectra were collected under ambient conditions using the 532-nm line of an argon-ion laser. Uniaxial tension tests were conducted for the annealed specimens under the constant cross-head speed condition of an initial strain rate of 1×10–4s–1. The apparent yield properties were determined using the 0.2% offset method. Tensile specimens (thickness: 1 mm, gauge length: 12.5 mm, gauge width: 6mm, and grip length: 25 mm for both upper and lower) were prepared from the hot-rolled Al composite sheet according to the standard ASTM B-209 and loaded in the rolling direction. The tests were repeated five times, and each test was conducted from different samples that were processed in a different batch using the same route.
3. Results and discussion 3.1. Microstructures Morphologies of ball-milled Al/FLG composite powders are shown in Fig. 1. Exfoliated FLG sheets with sizes below 10 μm are observed on the surface of the Al powder, where FLG is marked by an arrow in Fig. 1a. Fig. 1b displays magnified images of rectangles in Fig. 1a, where FLG is thin enough to transmit the electron beam so the Al powder underneath the FLG can be seen. Fig. 1c exhibits the powder morphology after attrition milling. FLG is not observed on the powder surface even in the magnified images of Fig. 1d. Hence, the FLG is supposed to be embedded and dispersed inside the Al powder.
7
Figg. 1. 1 SEM S M im maggess off (aa) FLG F G atttacched d too Al A pow p wderr ussingg a planeetarry mill m l att 1000 RPM R M (FL LG is maarkeed by ann arrrow w). (c)) F FLG G em mbedddedd annd dispperrsedd inn Al A pow p wder usin u ng an a attrritioon miill at 5000 RPM R M. (bb) aandd (d d) dispplay the t magn m nifiied im mages of (aa) and a d (cc), respecctiv velyy.
F 2 pro Fig. p oviddes Ramaan sppecctraa off thee innitiaal ggrapphitte pow p wderr, exxfooliatted graaphhite pow wder andd Al/F A FLG G coomppossitess with w varriouus vvolum me frac fr tionns of o FLG F G. T Typpicaal D-ba D andd (fr from m defe d ect andd am mo orphhous carb c bon)), G-b G bandd (ffrom m grap g phiite),, annd 2D baand (shhappe of o the t secconnd-oorder Ram maan band b ds) off graphhiticc caarbbonss arre dete d ecteed at a 135 1 59, 16003, annd 2272 27 ccm-1 reespectiively [300, 331],, foor the t iniitiall grrapphitee pow p wderr. The T ese banndss shhift to lowerr valu v ues (reed-sshifft) as a exffoliatio on prooceeedss, pres p sum mablly beccause thee suurfaace off grraphhitee pow wderr migh m ht stro s ongly 8
interact with isopropyl alcohol, and the functionalized surface may generate a certain amount of in-plane internal stresses and weaker C-C bonds [32]. The peaks shift back toward their expected position after attrition and planetary milling with Al powder. As FLG is dispersed inside Al, it may not interact with other material any longer, and hence the residual stresses could be released. The ratio between the intensities of the D and G bands, ID/IG, is considered to be the ratio of structural defects and domain size in graphitic materials [33]. The ID/IG ratio increases significantly after planetary milling with isopropyl alcohol and remains largely the same after attrition milling and hot-rolling processes. Therefore, FLG is thought to be damaged most during milling with isopropyl alcohol. The down-shifted 2D band, which is related to the crystalline graphitic structure, from 2727 cm-1 to 2678 cm-1, arises from a reduction of the number of graphite layers during the ball milling processes [34]. For Al/FLG composites, the 2D band can be fitted with a sharp and symmetric peak, while that of graphite can be fitted with two peaks. It can be seen in Fig. 2 that the 2D band becomes sharper and shifted when the graphene thickness decreases [35].
532 nm
G band
2D band
Intensity (a.u.)
D band
Al/0.7 vol.% FLG Al/0.5 vol.% FLG Al/0.3 vol.% FLG Exfoliated graphite powder Initial graphite powder 1400
1600
1800
2000
2200
2400
2600
2800
Raman shift (cm-1)
Fig. 2. Raman spectrum of initial graphite powder, exfoliated graphite powder and hot-rolled 9
Al/FLG composites.
TEM images in the RD-TD and the ND-RD planes of the hot-rolled sheets are shown in Fig. 3; here, RD is the rolling direction, TD is the transverse direction, and ND is the normal direction. FLG and deformation bands are marked by a white arrow and circles, respectively. The mechanically exfoliated FLG, with sizes ranging from 50 to 200 nm, are observed to be dispersed piece by piece in the Al matrix, as shown in Figs. 3a and b. FLGs, aligned along the rolling direction (Fig. 3b) are slightly wrinkled and folded with 100−200 nm in the long axis. The folded part is clearly found on the edge of the graphene. Folding of graphene commonly occurs during mechanical exfoliation because intrasheet van der Waals attraction is sizable, and doubling over within a sheet sometimes provides an energetic minimum. However, from the rolling direction in the ND-RD plane, the FLG keep their typical two dimensional structures well. The average thickness and layer number of graphene in the composite are statistically measured to be ~5 nm and ~5 layers, respectively. The average thickness of the composite is ~5 nm (standard deviation ~2 nm), while the number of layers of the graphene is ~5 layers (standard deviation ~2 nm). Measurement of the average thickness is based on hundreds of FLGs from more than 50 TEM images. Figs. 3c and d show few-layered thick graphene and relatively thin graphene, respectively. As the composite is loaded, Al grains with an average size of ~200 nm [36] may experience plastic deformation via conventional manners; macroscopic yielding occurs when dislocation pile-ups within a deforming grain produce a stress concentration sufficient to activate slip in the adjacent grains that have an unfavorably oriented slip system. This process involves the accommodation of a strain gradient, which provides compatible displacements 10
bettweeen adjjaceent graainss. Whe W en F FLG G seepaarattes the t se ttwoo ad djaccentt grrainns, how h wevver, thee pllasttic flow w wou w uld be coonsttrainned d byy FLG G. The T exttentt off shhearr lo ocallizaation inn th he mat m trixx leaadss to a higghlyy lo ocallizeed def d form matiion baand. O Owing to thee hiighh sp peciific suurface of FL LG, FL LG maay restricct thhe mas m ss flow f w inn thhe Al A mat m trixx, reesulltinng inn a siggnifficaant deccreaase of plaasticc sttrain-to oA FLG G coomp possites. As A sho s ownn in Figg. 33e, hig ghlyy deeforrmeed regi r ions arre foun f nd in failluree off thhe Al/F thee Al/0..3 vvol% % ccom mpoositte afte a r 6% 6 defform mattionn. T Thaat iss, betw b weeen F FLG Gs, deevellopm mennt of o nannoscale shheaar baandds ccoulld acco a ommoodatte thhe con c nstraained sheear straain.
Figg. 3. 3 TEM T M im maggess off th he grap g phenness in n the hhot-rollled All/0.33 vol% v % com c mpositee obbseerveed on o thee (a)) RD-T R TD D plaanee annd (b) ( ND D-R RD plan p ne (graaphhenee iss mark m ked by whhitee arrrow ws).. Inn (c)) an nd (d), FLG F Gs (ma ( arkeed by red d liiness) are a giv venn. (ee) Bet B tweeen thee grap g phenness (m marrkedd by whi w ite 111
arrows), highly deformed regions (marked by circles) are observed after 6% deformation.
3.2. Mechanical properties To examine strengthening efficiency of FLG, tensile tests were carried out for the hotrolled Al/FLG composites having different contents of FLG, as plotted in Fig. 4a. Yield strength of monolithic Al is first enhanced by grain refinement; it increases ~2.6 times after grain refinement by ball-milling. It is also significantly enhanced further with an increase in volume fraction of FLG; specifically, a ~71.8% enhancement from 262 MPa to 440 MPa was observed when only 0.7 vol% FLG was added to the monolithic Al. On the other hand, a general trend of ductility reduction with strength enhancement is observed as the content of FLG is increased. The strain-to-failure of Al/FLG composites is lower by 3 to 5.5 % when compared with the milled pure Al (~13%). The results also indicate that the strain field around the FLGs significantly alters the plastic flow, inducing highly localized deformation behavior, as evidenced by the formation of the bands. Fig. 4b compares strengthening efficiency of FLG (solid squares, based on experimental data in the present study) and MWCNT (open squares, obtained from [36]) in Al-based composites. An increase in strength with volume fraction of the reinforcements, calculated as ⁄ , is closely related to load transfer from the matrix to the reinforcement. We may ignore other microstructural effects such as grain size differences between two composites because they both are produced by the same processing routes (hot-rolling at 500 oC subsequent to 6-h-ball-milling at 500 RPM). Interestingly, the linear fit of the slope, ⁄ , is ~25.7 GPa while ⁄ is ~7.5 GPa. Despite the similar molecular structure and mechanical properties, FLG is found to be ~3.5 times more effective in 12
strengthening aluminum as compared to MWCNT.
(a)
500
True stress (MPa)
Al/0.7 vol. % FLG 400
Al/0.5 vol. % FLG Al/0.3 vol. % FLG
300 Pure Al (milled) 200 Pure Al (unmilled) 100 -4 -1
strain rate - 1x10 s 0 0.00
0.05
0.10
0.15
0.20
0.25
True strain
(b)
650
Yield stress (MPa)
600 550 500
dσc/dVFLG= 26.5 GPa
dσc/dVMWCNT= 7.5 GPa
450 400 350
Experimental data (Al/FLG) Experimental data (Al/MWCNT [36]) Calculated strength
300 250 0.00
0.01
0.02
0.03
0.04
0.05
Reinforcement volume fraction
Fig. 4. (a) True stress-true strain curves for the hot-rolled Al/FLG composites for various volume fractions of FLG. (b) Variation of yield stress as a function of the volume fraction of reinforcements (FLG and MWCNT [36]) using the experimental and calculated data given in Table 2. 13
When a composite is loaded, the matrix is strained and then the strained matrix may transfer the load to reinforcement by means of shear stresses that develop along the reinforcement-matrix interface. The shear forces on the interface parallel to the load direction are balanced with the normal forces on the fiber cross-sections normal to the load direction. Hence, the interfacial area () and the fiber cross-sectional area () are key factors that control the amount shear stresses generated at the interface, and these eventually determine the load transfer efficiency of the reinforcement. Table 2 provides calculations of the interfacial and cross-sectional areas per unit volume for MWCNT and FLG, and also compares theoretical and experimental yield strength of composites with both reinforcements.
Table 2. Schematic depiction of effective volume difference for various reinforcements.
CNT
Graphene
ࡿ
Depiction
ࡿ
࢚
࣊ࢊࢌ
࢝
Length ( : 1 μm* Diameter ( ): 35 nm*
Width ( : 150 nm* Length ( : 100 nm* Thickness ( ): 5 nm*
Critical length ( , μm)
2
0.381
S / 1 ea
A / 1 ea Volume ⁄ 1 ea ( x 10 ) Number of
4
2
9.62
0.75
1.01
13.3 14
reinforcement/ Volume ( x 10 / )
Yield stress ( , MPa)
Vol.%
Experimental data
Calculated data
Vol.%
Experimental data
Calculated data
1.0
352
347
0.3
360
338
1.5
386
389 0.5
405
389
3.0
483
517
4.5
610
645
0.7
440
440
7.5
8.5
26.5
24.2
( , GPa) ೝ
* Values are based on statistical estimates for a given measurement of reinforcement using TEM images in Fig. 3.
Our calculation begins with the aforementioned force balance between the interfacial shear stress and reinforcement tensile stress for the case of composites containing MWCNT as [37]:
! " #
$ (1)
where is the shear strength of the matrix (~ 0.5 , is the tensile yield strength of the matrix), which is supposed to be the shear stress that the matrix transmits to the MWCNT, ! is the axial distance from the tips of the MWCNT, is the average diameter of MWCNT, and is the (position specific) tensile stress of the MWCNT. This expression can be modified for composites containing FLG as: %2 &! "
(2)
where is the width of the FLG, is the thickness of FLG, ! is the distance from the end 15
of the FLG, and is the (position specific) tensile stress of FLG. As denoted in Table 2, the cross-section areas () for MWCNT and FLG are
and , and the interfacial areas ()
are and 2 , respectively; substituting both Eqs. (1) and (2), we obtain the following equation
! "
(3)
This formula implies that the tensile stress of the reinforcement is maximum at its mid-point and zero at its ends. When the maximum stress reaches the tensile strength of the reinforcement, the reinforcement length is a critical length ( ) of the reinforcement. If the reinforcement length exceeds the critical length ( ' ), the reinforcement carries stress equal to its tensile strength throughout a certain length ( ( ). The critical length of the reinforcements, , can be calculated as
"
(4)
where is the yield strength of the reinforcements, namely, 30 GPa for MWCNT [38] and FLG. values calculated for MWCNT and FLG are 1 μm and 0.381 μm, which are much larger than the length of MWCNT and FLG with measurements from statistically estimation from TEM images, respectively. Hence, stress that the reinforcement carries may increase proportional to the distance from the end of the reinforcement. The theoretical composite strength can be expressed as: " )*
+*
(5)
where and are the volume fraction of the reinforcements and the matrix, respectively. Applying this simplification to the reinforcements, the expression proposed for composite 16
strength can be obtained from Eq. (5):
" ) + )* +*
(6)
Consequently, the calculated data using Eq. (6), which is a good correlation containing a quantitative estimate of the reinforcements and contact area based on force balance, exhibit good agreement with the experimental values as given in Table 2 (marked by dotted lines in Fig. 4b). Stress distribution along the reinforcements occurs when the length of the reinforcements is less than some critical length. Calculations for the specific surface areacomposite strength relationship based on statistical estimates in a given measurement of reinforcements using TEM images are displayed in Table 2. The effective volume, which means equivalent quantity of reinforcements per arbitrary region, takes into consideration the length as well as quantity of the reinforcements. For MWCNT, the volume per reinforcement is 9.62 x 10-22 m3, while FLG shows a value of 0.75 x 10-22 m3. Although the ability to carry the load of MWCNT is excellent compared to FLG, nearly 12.8 times more FLG can occupy the unit volume than MWCNT, with a surface area that is 2.6 times as large. In comparison with MWCNT, a FLG containing such two dimensional sheets can provide substantial contact with the matrix due to their upper and lower surfaces. Therefore, a sheet having an efficient interface with sufficient stress transfer between the reinforcement and the matrix is very powerful and effective. To achieve such an increase in strength, the FLG contact area is estimated to be on the order of 3.5 times that of MWCNT.
17
(a)
700 Short fiber composites [37]
Yield stress (MPa)
650 600 550
Shear-lag [40]
500
Halpin-Tsai [42]
450
Present study
400 Piggott [43]
350 300 250 0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
Reinforcement volume fraction
(b)
500 [17] [18] [19] [20] Present study
Yield stress (MPa)
450 400 350 300 250 200 150 0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Reinforcement volume fraction
Fig. 5. (a) Plots of composite strengths theoretically predicted [37, 40, 42, 43] and experimentally obtained in this study. (b) Yield stresses of several Al-based composites containing graphene with varying the volume fraction of reinforcement (data taken from [17 20]) in which calculated data using Eq. (6) are marked by dotted lines.
18
Table 3 summarizes commonly used models suggested for tensile strength for MMCs, and Fig. 5a shows a comparison of the theoretical predictions and experimental results as a function of the FLG volume fraction. The short fiber and shear-lag models describe the strengthening by general discontinuous fibers. The shear-lag model [39] describes strengthening of reinforcement with a high-aspect ratio, and the modified shear-lag model [40] is complemented by considering the effect of fiber orientation. The Halpin-Tsai equation and Piggott model are specific for CNTs or platelet-reinforced composites, respectively [43]. The Halpin-Tsai model [42] gives a semi-empirical description of short-fiber reinforced composites using the rule of mixtures for discontinuous reinforcement, and the modified Halpin-Tsai equation [41] is specified for MMCs. The Piggott model modifies the discontinuous fiber model by considering two-dimensional geometric characteristics for platelet reinforcements. Experimental data and theoretically calculated values as a function of graphene content are provided in Fig. 5a. Overall, the experimental data are well-matched only with our model. Since both FLG and CNT have high volume-to-surface area ratios, the matrix/reinforcement interface plays a significant role in strengthening. However, only our model takes into account the features of matrix/reinforcement interface (e.g., effective interfacial area); the present study modifies the discontinuous fiber model with a new term (S/A), which enables the equation to be matched with the experimental data. Moreover, the model developed in the present study is adapted to compared with experimental data that have been reported in the literature, as shown in Fig. 5b [17 20]. Since the size of graphene varies reported in the article, the calculated values vary as well. The size of graphene was measured from the TEM or SEM images when information was not available. The present model shows good agreement with the experimental data except for Latief et al.’s study [20]. Insufficient consolidation, evident by a low density of composite, 19
may cause this deviation in the experimental data from the model. Overall, our calculation has a good fit for the strength of nanoscale-reinforced MMCs. As mentioned previously, an efficient interface with sufficient load transfer between the reinforcement and the matrix is very influential in the determination of the strength in nanocomposites.
Table 3. Depiction of theoretical models for prediction of composite strength. Model
Equation " #
Short-fiber [37]
$ 1 ( 2
l ,
2 1 -. " Developed Halpin-Tsai [42] 1 ( . 2/ Piggott [43] " 4 * and are the volume fraction of the fiber and platelet, / is the long axis of the "
Developed Shear-lag [40]
platelet, the value of - has to be optimized in order to take care of dispersion of the reinforcement (2/ e . ), and . depends on ( / ).
700 650
Yield stress (MPa)
600 550 500 450 400 350 FLG MWCNT
300 250
0
1
2
3
4
5 6
-1
Surface area per unit volume (10 μ m ) 20
6
Fig. 6. Variation of yield stress as a function of surface area per unit volume with various reinforcements.
Fig. 6 shows variation in yield stress as a function of surface area per composite volume, where strengthening efficiency for two reinforcements is compared. The composite strength proportionally increases with the surface area per composite volume, and the increase is very similar for both reinforcements.
4. Conclusion Al matrix composite containing FLG was successfully produced through a novel fabrication approach that combines mechanical milling and hot rolling. FLG was mechanically exfoliated using wet ball milling, and was then uniformly dispersed in the Al matrix using high energy ball milling. The strengths of the Al/FLG composites are significantly enhanced with the volume fraction of FLG. With an addition of only 0.7 vol% FLG, the composite exhibits ~440 MPa of tensile strength, about two times higher than that of monolithic Al. Furthermore, the composites produced via favorable industrial routes using inexpensive graphite will increase a potential market opportunity of Al/FLG composites. On the other hand, with respect to the yield stress of MWCNT-reinforced Al matrix composites, FLG is a much more effective reinforcement because it has a larger surface area per unit volume. Our study highlighted that the specific surface area of the reinforcement can determine the strength of the composites.
21
Acknowledgements This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A2A2A01068931). H.J. Choi acknowledges the support of the NRF funded by the Science, ICT & Future Planning (MSIP) (2013R1A1A3005759 and 2013K1A4A3055679).
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S0008-6223(14)01006-9 http://dx.doi.org/10.1016/j.carbon.2014.10.044 CARBON 9437
To appear in:
Carbon
Received Date: Accepted Date:
26 February 2014 17 October 2014
Please cite this article as: Shin, S.E., Choi, H.J., Shin, J.H., Bae, D.H., Strengthening behavior of few-layered graphene/aluminum composites, Carbon (2014), doi: http://dx.doi.org/10.1016/j.carbon.2014.10.044
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Strengthening behavior of few-layered graphene/aluminum composites S.E. Shin1, H.J. Choi2, J.H. Shin1 and D.H. Bae1∗ 1
2
Department of Materials Science and Engineering, Yonsei University, Seoul, 120-749, Korea
School of Advanced Materials Engineering, Kookmin University, Seoul, 136-702, Korea
Abstract Strengthening behavior of composite containing discontinuous reinforcement is strongly related with load transfer at the reinforcement-matrix interface. We selected multi-walled carbon nanotube (MWCNT) and few-layer graphene (FLG) as a reinforcing agent. By varying a volume fraction of the reinforcement, aluminum (Al) matrix composites were produced by a powder metallurgy method. Uniform dispersion and uniaxial alignment of MWCNT and FLG in the Al matrix are evidenced by high-resolution transmission electron microscope analysis. Although the reinforcements have a similar molecular structure, FLG has a 12.8 times larger specific surface area per volume more than MWCNT due to geometric difference. Therefore an increment of a yield stress versus a reinforcement volume fraction for FLG shows 3.5 times higher than that of MWCNT Consequently, for both reinforcements, the composite strength proportionally increases with the specific surface area on the composite, and the composites containing 0.7 vol% FLG exhibit 440 MPa of tensile strength.
∗
Corresponding author. Tel.:+82 2-2123 5831. E-mail : [email protected] (Donghyun Bae) 1
1. Introduction Graphene has attracted interest as a reinforcing agent for metal matrix composites due to excellent mechanical properties based on the strong sp2 C–C bonds, which are similar to fullerene and carbon nanotube [1, 2]. Furthermore, it has merits over other carbon-based nano materials, which originate from its inherent two-dimensional (2-D) morphology; the planar structure is more favorable to load transfer as well as to impeding atomic diffusion at high temperatures, as compared to its 0-D and 1-D counterparts. Consequently, it provides superior strength for composites at both room temperature and high temperatures. In order to transmit the excellent properties of graphene to composites, uniform dispersion of an individually-exfoliated graphene is one key factor. Several processes have been introduced to exfoliate graphite to single-layer or few-layer graphene by mechanical and/or chemical means [3–5]. Mechanical exfoliation using a tape dispenser [2] or atomic force microscopy (AFM) [6] has exhibited inadequate productivity for large-scale industrial applications. Although large-scale synthesis of graphene by gas phase techniques (e.g., thermal chemical vapor deposition) [7–9] is actively ongoing, this process is still costly and has restrictions in terms of the selection of the substrate materials. Chemical exfoliation by a solution process has been suggested as a relatively cheap process [10–12], and yet presents difficulties for scalable synthesis due to complex synthesis steps and the requirement for a large amount of chemicals and acid. Recently, solid phase techniques, combined with ballmilling processes, have enabled production of scalable quantities of carbon-base nanomaterials by applying shear forces on pristine agglomerated particles [13–15]. Even though one has developed a scalable process to produce few-layer graphene (FLG), an additional technical hurdle is in the uniform dispersion of the graphene in the metal matrix, which has closely packed atomic structures. Hence, graphene/metal composites have 2
been seldom investigated compared to polymer matrix composites, although the great strength and light weight features of graphene/metal composites are expected to lead to applications of such composites in the automotive and aerospace industries. Aluminum (Al) matrix composites reinforced with FLG have recently been produced using different synthesis techniques with powder metallurgy (PM) routes. Table 1 summarizes the fabrication processes and resulting properties of recently developed Al/FLG composites [16 21]. Similar to other nanostructured composites, dispersion of nanoscale reinforcement is a critical issue in Al/FLG composites. Poorly dispersed FLG may act as defect sites, significantly deteriorating the performance of the final composites [16, 17]. Consolidation processes are also important for Al/FLG composites because a selection of high-processing temperatures to avoid insufficient powder consolidation leads to unfavorable reactions (e.g., transformation of FLG to carbides) [17, 18 20]. Even though some composites have been produced via cost-ineffective routes or using expensive materials (e.g., graphene oxide), they did not exhibit tensile elongation or they exhibited very limited tensile strength (<300 MPa). Furthermore, the microstructure of Al/FLG composites with an atomicscale resolution has not been well reported; atomic-scale resolution images may provide detailed information on the morphology of FLG and the interface between Al and FLG [17, 20, 21]. Reinforcement in composites may enhance the strength of the matrix by (i) carrying a great amount of load instead of the matrix and by (ii) interrupting the plastic deformation of the matrix. Hence, two important factors to determine the strengthening efficiency of reinforcement, other than its intrinsic mechanical properties and volume fraction, are (i) how much load can be effectively transmitted from the matrix to the reinforcement and (ii) how much the stress distribution can be altered by the reinforcement. Both are affected by bonding strength between the matrix and reinforcement, morphology/surface area of the reinforcement, 3
and spatial distribution of the reinforcement [22, 23]. Although experimental work on the effect of volume fraction of the reinforcement on the strength of composites [24, 25] and theoretical work on the bonding strength between metal and carbon–based nano materials [26−29] has been conducted, the role of morphology and surface area on the reinforcement has not been extensively investigated. In particular, a comparison study on the strengthening behavior of reinforcements with a variety of shapes (e.g., fullerene–sphere/0-D, carbon nanotube–tube/1-D, and graphene–planar/2-D), but with similar intrinsic mechanical properties, would be highly interesting. The primary objective of this work is to produce Al matrix composites with welldispersed FLG using a scalable powder metallurgy approach. Here, we introduce a favorable route to produce centimeter-scale Al/FLG composites with excellent performances. This work also aims to examine tensile properties of the Al/FLG composite as a function of volume fraction of FLG, so as to compare the strengthening behavior of FLG with that of multiwalled carbon nanotube (MWCNT). The present study also carefully investigates the microstructure of the composites at an atomic scale to provide detailed information on the structure of nano-carbon materials and nano-carbon/Al interface structure. Further, this work quantifies the effect of shape factor (i.e., tube versus sheet) and specific surface area of reinforcement on the composite strength.
Table 1. Experimental tensile strength and hardness of FLG-reinforced composites. Graphene content
Fabrication techniques
Mechanical properties
4
Research group
0.1 wt%
Ball-milling Hot isostatic pressing: 550 oC, 4 h Hot extrusion: 550 oC, 4:1 ratio
Tensile strength: 262 MPa
Bartolucci et al. [16]
0.3 wt%
Ball-milling Sintering: 580 oC, 2 h Hot extrusion: 440 oC, 20:1 ratio
Tensile strength: 250 MPa
Wang et al. [17]
0.3 wt%
Ball-milling Sintering: 600 oC, 6 h Hot extrusion: 470 oC, 2:1 ratio
Vickers hardness: 85 Hv Tensile strength: 280 MPa
Rashad et al. [18]
0.3 wt%
Ball-milling Sintering: 500 oC, 5 h
Vickers micro-hardness: 90 μHv
Perez et al. [19]
5 wt.%
Ball-milling Sintering: 600 oC, 5 h
Vickers hardness: 70 Hv Compressive strength: 180 MPa
Latief et al. [20]
2. Experimental 2.1. Sample preparation Aluminum (Al)–based composites containing FLG were fabricated by hot-rolling of ballmilled powder. At first, graphite flakes (6−8 nm thickness and 120−150 m2/g typical specific surface area) were mechanically exfoliated by planetary ball milling in the presence of isopropyl alcohol ((CH3)2CHOH). A stainless steel bowl (500 mL) was charged with graphite flakes (2 g) and stainless steel balls (~5 mm diameter, 30 g) at a ball-to-powder weight ratio of 15:1, together with 50 ml of isopropyl alcohol. Planetary milling was performed at a rotation speed of 200 RPM for 1 h; it was paused for 75 min after every 15-min milling to maintain ambient processing temperature without any process control agent. Afterwards, the isopropyl alcohol was evaporated and dried at 150 oC for 3 h. Graphite flakes are supposed to be exfoliated by shear forces on contact between powder and balls during milling. Due to the 5
weak van der Waals-like coupling between graphite layers, the graphene sheets in graphite can slide easily with respect to one another. To address this, additional milling was conducted for further exfoliation of graphite nanosheets into FLG and for dispersion of the FLG in Al powder. The exfoliated graphite flakes were exfoliated further into FLG and were also mixed with Al powder (99.5 % purity and <150 μm diameter) using a planetary mill at a rotation speed of 100 RPM for 3 h, with a process control agent of 1 wt. % stearic acid (CH3(CH2)16CO2H). Milling was paused for 15 min after every 15 min of milling. Finally, for further dispersion of FLG in Al powder, the planetary-milled mixture was high energy ballmilled in an attritor at 500 RPM for 6 h in a purified argon atmosphere. FLG, attached on the Al powder surface, is gradually embedded and is dispersed inside Al powder. A variety of ball-milled powders were fabricated by varying the volume fraction of FLG (i.e. 0.3, 0.5 and 0.7 vol%). The ball-milled powder was containerized in a copper tube (60 mm in diameter, 150 mm in height, and 1.5 mm in thickness), compacted, and was then hotrolled. The sample was heated to a pre-determined temperature of 500 oC at a heating rate of 15 oC /min, and rolling was conducted with a 12% reduction per pass; the final thickness of samples was 1 mm. After rolling, the copper container was mechanically removed. Since FLG was embedded inside the Al powder, it did not significantly interrupt consolidation of Al powder during hot rolling, providing a fully dense composite sheet.
2.2. Characterization Morphology of the ball-milled powder varied according to milling condition, as was observed using scanning electron microscopy (SEM). Microstructure of the Al/FLG composite was observed using a high resolution transmission electron microscope (HRTEM, 6
JEOL 2000). Thin foil specimens from the sheets were carefully prepared by an ion beam 6 milling method (Gatan, Model 600, Oxford, UK). The structure of FLG was also investigated by Raman spectroscopy using a Jobin-Yvon microspectrometer (LabRam HR, Jobin-Yvon Co. Ltd., France). Spectra were collected under ambient conditions using the 532-nm line of an argon-ion laser. Uniaxial tension tests were conducted for the annealed specimens under the constant cross-head speed condition of an initial strain rate of 1×10–4s–1. The apparent yield properties were determined using the 0.2% offset method. Tensile specimens (thickness: 1 mm, gauge length: 12.5 mm, gauge width: 6mm, and grip length: 25 mm for both upper and lower) were prepared from the hot-rolled Al composite sheet according to the standard ASTM B-209 and loaded in the rolling direction. The tests were repeated five times, and each test was conducted from different samples that were processed in a different batch using the same route.
3. Results and discussion 3.1. Microstructures Morphologies of ball-milled Al/FLG composite powders are shown in Fig. 1. Exfoliated FLG sheets with sizes below 10 μm are observed on the surface of the Al powder, where FLG is marked by an arrow in Fig. 1a. Fig. 1b displays magnified images of rectangles in Fig. 1a, where FLG is thin enough to transmit the electron beam so the Al powder underneath the FLG can be seen. Fig. 1c exhibits the powder morphology after attrition milling. FLG is not observed on the powder surface even in the magnified images of Fig. 1d. Hence, the FLG is supposed to be embedded and dispersed inside the Al powder.
7
Figg. 1. 1 SEM S M im maggess off (aa) FLG F G atttacched d too Al A pow p wderr ussingg a planeetarry mill m l att 1000 RPM R M (FL LG is maarkeed by ann arrrow w). (c)) F FLG G em mbedddedd annd dispperrsedd inn Al A pow p wder usin u ng an a attrritioon miill at 5000 RPM R M. (bb) aandd (d d) dispplay the t magn m nifiied im mages of (aa) and a d (cc), respecctiv velyy.
F 2 pro Fig. p oviddes Ramaan sppecctraa off thee innitiaal ggrapphitte pow p wderr, exxfooliatted graaphhite pow wder andd Al/F A FLG G coomppossitess with w varriouus vvolum me frac fr tionns of o FLG F G. T Typpicaal D-ba D andd (fr from m defe d ect andd am mo orphhous carb c bon)), G-b G bandd (ffrom m grap g phiite),, annd 2D baand (shhappe of o the t secconnd-oorder Ram maan band b ds) off graphhiticc caarbbonss arre dete d ecteed at a 135 1 59, 16003, annd 2272 27 ccm-1 reespectiively [300, 331],, foor the t iniitiall grrapphitee pow p wderr. The T ese banndss shhift to lowerr valu v ues (reed-sshifft) as a exffoliatio on prooceeedss, pres p sum mablly beccause thee suurfaace off grraphhitee pow wderr migh m ht stro s ongly 8
interact with isopropyl alcohol, and the functionalized surface may generate a certain amount of in-plane internal stresses and weaker C-C bonds [32]. The peaks shift back toward their expected position after attrition and planetary milling with Al powder. As FLG is dispersed inside Al, it may not interact with other material any longer, and hence the residual stresses could be released. The ratio between the intensities of the D and G bands, ID/IG, is considered to be the ratio of structural defects and domain size in graphitic materials [33]. The ID/IG ratio increases significantly after planetary milling with isopropyl alcohol and remains largely the same after attrition milling and hot-rolling processes. Therefore, FLG is thought to be damaged most during milling with isopropyl alcohol. The down-shifted 2D band, which is related to the crystalline graphitic structure, from 2727 cm-1 to 2678 cm-1, arises from a reduction of the number of graphite layers during the ball milling processes [34]. For Al/FLG composites, the 2D band can be fitted with a sharp and symmetric peak, while that of graphite can be fitted with two peaks. It can be seen in Fig. 2 that the 2D band becomes sharper and shifted when the graphene thickness decreases [35].
532 nm
G band
2D band
Intensity (a.u.)
D band
Al/0.7 vol.% FLG Al/0.5 vol.% FLG Al/0.3 vol.% FLG Exfoliated graphite powder Initial graphite powder 1400
1600
1800
2000
2200
2400
2600
2800
Raman shift (cm-1)
Fig. 2. Raman spectrum of initial graphite powder, exfoliated graphite powder and hot-rolled 9
Al/FLG composites.
TEM images in the RD-TD and the ND-RD planes of the hot-rolled sheets are shown in Fig. 3; here, RD is the rolling direction, TD is the transverse direction, and ND is the normal direction. FLG and deformation bands are marked by a white arrow and circles, respectively. The mechanically exfoliated FLG, with sizes ranging from 50 to 200 nm, are observed to be dispersed piece by piece in the Al matrix, as shown in Figs. 3a and b. FLGs, aligned along the rolling direction (Fig. 3b) are slightly wrinkled and folded with 100−200 nm in the long axis. The folded part is clearly found on the edge of the graphene. Folding of graphene commonly occurs during mechanical exfoliation because intrasheet van der Waals attraction is sizable, and doubling over within a sheet sometimes provides an energetic minimum. However, from the rolling direction in the ND-RD plane, the FLG keep their typical two dimensional structures well. The average thickness and layer number of graphene in the composite are statistically measured to be ~5 nm and ~5 layers, respectively. The average thickness of the composite is ~5 nm (standard deviation ~2 nm), while the number of layers of the graphene is ~5 layers (standard deviation ~2 nm). Measurement of the average thickness is based on hundreds of FLGs from more than 50 TEM images. Figs. 3c and d show few-layered thick graphene and relatively thin graphene, respectively. As the composite is loaded, Al grains with an average size of ~200 nm [36] may experience plastic deformation via conventional manners; macroscopic yielding occurs when dislocation pile-ups within a deforming grain produce a stress concentration sufficient to activate slip in the adjacent grains that have an unfavorably oriented slip system. This process involves the accommodation of a strain gradient, which provides compatible displacements 10
bettweeen adjjaceent graainss. Whe W en F FLG G seepaarattes the t se ttwoo ad djaccentt grrainns, how h wevver, thee pllasttic flow w wou w uld be coonsttrainned d byy FLG G. The T exttentt off shhearr lo ocallizaation inn th he mat m trixx leaadss to a higghlyy lo ocallizeed def d form matiion baand. O Owing to thee hiighh sp peciific suurface of FL LG, FL LG maay restricct thhe mas m ss flow f w inn thhe Al A mat m trixx, reesulltinng inn a siggnifficaant deccreaase of plaasticc sttrain-to oA FLG G coomp possites. As A sho s ownn in Figg. 33e, hig ghlyy deeforrmeed regi r ions arre foun f nd in failluree off thhe Al/F thee Al/0..3 vvol% % ccom mpoositte afte a r 6% 6 defform mattionn. T Thaat iss, betw b weeen F FLG Gs, deevellopm mennt of o nannoscale shheaar baandds ccoulld acco a ommoodatte thhe con c nstraained sheear straain.
Figg. 3. 3 TEM T M im maggess off th he grap g phenness in n the hhot-rollled All/0.33 vol% v % com c mpositee obbseerveed on o thee (a)) RD-T R TD D plaanee annd (b) ( ND D-R RD plan p ne (graaphhenee iss mark m ked by whhitee arrrow ws).. Inn (c)) an nd (d), FLG F Gs (ma ( arkeed by red d liiness) are a giv venn. (ee) Bet B tweeen thee grap g phenness (m marrkedd by whi w ite 111
arrows), highly deformed regions (marked by circles) are observed after 6% deformation.
3.2. Mechanical properties To examine strengthening efficiency of FLG, tensile tests were carried out for the hotrolled Al/FLG composites having different contents of FLG, as plotted in Fig. 4a. Yield strength of monolithic Al is first enhanced by grain refinement; it increases ~2.6 times after grain refinement by ball-milling. It is also significantly enhanced further with an increase in volume fraction of FLG; specifically, a ~71.8% enhancement from 262 MPa to 440 MPa was observed when only 0.7 vol% FLG was added to the monolithic Al. On the other hand, a general trend of ductility reduction with strength enhancement is observed as the content of FLG is increased. The strain-to-failure of Al/FLG composites is lower by 3 to 5.5 % when compared with the milled pure Al (~13%). The results also indicate that the strain field around the FLGs significantly alters the plastic flow, inducing highly localized deformation behavior, as evidenced by the formation of the bands. Fig. 4b compares strengthening efficiency of FLG (solid squares, based on experimental data in the present study) and MWCNT (open squares, obtained from [36]) in Al-based composites. An increase in strength with volume fraction of the reinforcements, calculated as ⁄ , is closely related to load transfer from the matrix to the reinforcement. We may ignore other microstructural effects such as grain size differences between two composites because they both are produced by the same processing routes (hot-rolling at 500 oC subsequent to 6-h-ball-milling at 500 RPM). Interestingly, the linear fit of the slope, ⁄ , is ~25.7 GPa while ⁄ is ~7.5 GPa. Despite the similar molecular structure and mechanical properties, FLG is found to be ~3.5 times more effective in 12
strengthening aluminum as compared to MWCNT.
(a)
500
True stress (MPa)
Al/0.7 vol. % FLG 400
Al/0.5 vol. % FLG Al/0.3 vol. % FLG
300 Pure Al (milled) 200 Pure Al (unmilled) 100 -4 -1
strain rate - 1x10 s 0 0.00
0.05
0.10
0.15
0.20
0.25
True strain
(b)
650
Yield stress (MPa)
600 550 500
dσc/dVFLG= 26.5 GPa
dσc/dVMWCNT= 7.5 GPa
450 400 350
Experimental data (Al/FLG) Experimental data (Al/MWCNT [36]) Calculated strength
300 250 0.00
0.01
0.02
0.03
0.04
0.05
Reinforcement volume fraction
Fig. 4. (a) True stress-true strain curves for the hot-rolled Al/FLG composites for various volume fractions of FLG. (b) Variation of yield stress as a function of the volume fraction of reinforcements (FLG and MWCNT [36]) using the experimental and calculated data given in Table 2. 13
When a composite is loaded, the matrix is strained and then the strained matrix may transfer the load to reinforcement by means of shear stresses that develop along the reinforcement-matrix interface. The shear forces on the interface parallel to the load direction are balanced with the normal forces on the fiber cross-sections normal to the load direction. Hence, the interfacial area () and the fiber cross-sectional area () are key factors that control the amount shear stresses generated at the interface, and these eventually determine the load transfer efficiency of the reinforcement. Table 2 provides calculations of the interfacial and cross-sectional areas per unit volume for MWCNT and FLG, and also compares theoretical and experimental yield strength of composites with both reinforcements.
Table 2. Schematic depiction of effective volume difference for various reinforcements.
CNT
Graphene
ࡿ
Depiction
ࡿ
࢚
࣊ࢊࢌ
࢝
Length ( : 1 μm* Diameter ( ): 35 nm*
Width ( : 150 nm* Length ( : 100 nm* Thickness ( ): 5 nm*
Critical length ( , μm)
2
0.381
S / 1 ea
A / 1 ea Volume ⁄ 1 ea ( x 10 ) Number of
4
2
9.62
0.75
1.01
13.3 14
reinforcement/ Volume ( x 10 / )
Yield stress ( , MPa)
Vol.%
Experimental data
Calculated data
Vol.%
Experimental data
Calculated data
1.0
352
347
0.3
360
338
1.5
386
389 0.5
405
389
3.0
483
517
4.5
610
645
0.7
440
440
7.5
8.5
26.5
24.2
( , GPa) ೝ
* Values are based on statistical estimates for a given measurement of reinforcement using TEM images in Fig. 3.
Our calculation begins with the aforementioned force balance between the interfacial shear stress and reinforcement tensile stress for the case of composites containing MWCNT as [37]:
! " #
$ (1)
where is the shear strength of the matrix (~ 0.5 , is the tensile yield strength of the matrix), which is supposed to be the shear stress that the matrix transmits to the MWCNT, ! is the axial distance from the tips of the MWCNT, is the average diameter of MWCNT, and is the (position specific) tensile stress of the MWCNT. This expression can be modified for composites containing FLG as: %2 &! "
(2)
where is the width of the FLG, is the thickness of FLG, ! is the distance from the end 15
of the FLG, and is the (position specific) tensile stress of FLG. As denoted in Table 2, the cross-section areas () for MWCNT and FLG are
and , and the interfacial areas ()
are and 2 , respectively; substituting both Eqs. (1) and (2), we obtain the following equation
! "
(3)
This formula implies that the tensile stress of the reinforcement is maximum at its mid-point and zero at its ends. When the maximum stress reaches the tensile strength of the reinforcement, the reinforcement length is a critical length ( ) of the reinforcement. If the reinforcement length exceeds the critical length ( ' ), the reinforcement carries stress equal to its tensile strength throughout a certain length ( ( ). The critical length of the reinforcements, , can be calculated as
"
(4)
where is the yield strength of the reinforcements, namely, 30 GPa for MWCNT [38] and FLG. values calculated for MWCNT and FLG are 1 μm and 0.381 μm, which are much larger than the length of MWCNT and FLG with measurements from statistically estimation from TEM images, respectively. Hence, stress that the reinforcement carries may increase proportional to the distance from the end of the reinforcement. The theoretical composite strength can be expressed as: " )*
+*
(5)
where and are the volume fraction of the reinforcements and the matrix, respectively. Applying this simplification to the reinforcements, the expression proposed for composite 16
strength can be obtained from Eq. (5):
" ) + )* +*
(6)
Consequently, the calculated data using Eq. (6), which is a good correlation containing a quantitative estimate of the reinforcements and contact area based on force balance, exhibit good agreement with the experimental values as given in Table 2 (marked by dotted lines in Fig. 4b). Stress distribution along the reinforcements occurs when the length of the reinforcements is less than some critical length. Calculations for the specific surface areacomposite strength relationship based on statistical estimates in a given measurement of reinforcements using TEM images are displayed in Table 2. The effective volume, which means equivalent quantity of reinforcements per arbitrary region, takes into consideration the length as well as quantity of the reinforcements. For MWCNT, the volume per reinforcement is 9.62 x 10-22 m3, while FLG shows a value of 0.75 x 10-22 m3. Although the ability to carry the load of MWCNT is excellent compared to FLG, nearly 12.8 times more FLG can occupy the unit volume than MWCNT, with a surface area that is 2.6 times as large. In comparison with MWCNT, a FLG containing such two dimensional sheets can provide substantial contact with the matrix due to their upper and lower surfaces. Therefore, a sheet having an efficient interface with sufficient stress transfer between the reinforcement and the matrix is very powerful and effective. To achieve such an increase in strength, the FLG contact area is estimated to be on the order of 3.5 times that of MWCNT.
17
(a)
700 Short fiber composites [37]
Yield stress (MPa)
650 600 550
Shear-lag [40]
500
Halpin-Tsai [42]
450
Present study
400 Piggott [43]
350 300 250 0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
Reinforcement volume fraction
(b)
500 [17] [18] [19] [20] Present study
Yield stress (MPa)
450 400 350 300 250 200 150 0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Reinforcement volume fraction
Fig. 5. (a) Plots of composite strengths theoretically predicted [37, 40, 42, 43] and experimentally obtained in this study. (b) Yield stresses of several Al-based composites containing graphene with varying the volume fraction of reinforcement (data taken from [17 20]) in which calculated data using Eq. (6) are marked by dotted lines.
18
Table 3 summarizes commonly used models suggested for tensile strength for MMCs, and Fig. 5a shows a comparison of the theoretical predictions and experimental results as a function of the FLG volume fraction. The short fiber and shear-lag models describe the strengthening by general discontinuous fibers. The shear-lag model [39] describes strengthening of reinforcement with a high-aspect ratio, and the modified shear-lag model [40] is complemented by considering the effect of fiber orientation. The Halpin-Tsai equation and Piggott model are specific for CNTs or platelet-reinforced composites, respectively [43]. The Halpin-Tsai model [42] gives a semi-empirical description of short-fiber reinforced composites using the rule of mixtures for discontinuous reinforcement, and the modified Halpin-Tsai equation [41] is specified for MMCs. The Piggott model modifies the discontinuous fiber model by considering two-dimensional geometric characteristics for platelet reinforcements. Experimental data and theoretically calculated values as a function of graphene content are provided in Fig. 5a. Overall, the experimental data are well-matched only with our model. Since both FLG and CNT have high volume-to-surface area ratios, the matrix/reinforcement interface plays a significant role in strengthening. However, only our model takes into account the features of matrix/reinforcement interface (e.g., effective interfacial area); the present study modifies the discontinuous fiber model with a new term (S/A), which enables the equation to be matched with the experimental data. Moreover, the model developed in the present study is adapted to compared with experimental data that have been reported in the literature, as shown in Fig. 5b [17 20]. Since the size of graphene varies reported in the article, the calculated values vary as well. The size of graphene was measured from the TEM or SEM images when information was not available. The present model shows good agreement with the experimental data except for Latief et al.’s study [20]. Insufficient consolidation, evident by a low density of composite, 19
may cause this deviation in the experimental data from the model. Overall, our calculation has a good fit for the strength of nanoscale-reinforced MMCs. As mentioned previously, an efficient interface with sufficient load transfer between the reinforcement and the matrix is very influential in the determination of the strength in nanocomposites.
Table 3. Depiction of theoretical models for prediction of composite strength. Model
Equation " #
Short-fiber [37]
$ 1 ( 2
l ,
2 1 -. " Developed Halpin-Tsai [42] 1 ( . 2/ Piggott [43] " 4 * and are the volume fraction of the fiber and platelet, / is the long axis of the "
Developed Shear-lag [40]
platelet, the value of - has to be optimized in order to take care of dispersion of the reinforcement (2/ e . ), and . depends on ( / ).
700 650
Yield stress (MPa)
600 550 500 450 400 350 FLG MWCNT
300 250
0
1
2
3
4
5 6
-1
Surface area per unit volume (10 μ m ) 20
6
Fig. 6. Variation of yield stress as a function of surface area per unit volume with various reinforcements.
Fig. 6 shows variation in yield stress as a function of surface area per composite volume, where strengthening efficiency for two reinforcements is compared. The composite strength proportionally increases with the surface area per composite volume, and the increase is very similar for both reinforcements.
4. Conclusion Al matrix composite containing FLG was successfully produced through a novel fabrication approach that combines mechanical milling and hot rolling. FLG was mechanically exfoliated using wet ball milling, and was then uniformly dispersed in the Al matrix using high energy ball milling. The strengths of the Al/FLG composites are significantly enhanced with the volume fraction of FLG. With an addition of only 0.7 vol% FLG, the composite exhibits ~440 MPa of tensile strength, about two times higher than that of monolithic Al. Furthermore, the composites produced via favorable industrial routes using inexpensive graphite will increase a potential market opportunity of Al/FLG composites. On the other hand, with respect to the yield stress of MWCNT-reinforced Al matrix composites, FLG is a much more effective reinforcement because it has a larger surface area per unit volume. Our study highlighted that the specific surface area of the reinforcement can determine the strength of the composites.
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Acknowledgements This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A2A2A01068931). H.J. Choi acknowledges the support of the NRF funded by the Science, ICT & Future Planning (MSIP) (2013R1A1A3005759 and 2013K1A4A3055679).
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