Department of Mechanical Engineering, Imperial College, London SW7 2AZ, UK

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1 1 ST Intrnational Confrn on Composit Matrials Xi an, 0 5 th August 017 THE MECHANICS OF INTERFACE FRACTURE IN LAYERED COMPOSITE MATERIALS: (7) ADHESION TOUHNESS OF MULTILAYER RAPHENE MEMRANES NANOSCALE INTERFACE FRACTURES Josph D. Wood 1, Christophr M. Harvy, in Wang and Simon S. Wang, 3 1 Dpartmnt of Mhanial Enginring, Imprial Collg, London SW7 AZ, UK josph.wood@imprial.a.uk Dpartmnt of Aronautial and Automotiv Enginring, Loughborough Univrsity, Loughborough, Listrshir LE11 3TU, Unitd Kingdom s:.m.harvy@lboro.a.uk, b.wang@lboro.a.uk, s.wang@lboro.a.uk 3 Shool of Mhanial and Equipmnt Enginring, Hbi Univrsity of Enginring, Handan, China Kywords: Adhsion toughnss, raphn, Mod mixity, Silion oxid, Sliding fft ASTRACT Adhsion toughnss btwn graphn mmbrans and substrat is mod mixity dpndnt. Various xprimntal and analytial mthods ar disussd on th alulation of th sion toughnss. Th prsn of sliding in multilayr graphn mmbrans inrass th fratur mod mixity I II, lading to a dras in sion toughnss masurmnts whn using th irular blistr tst undr ithr prssur load or point load. On th mod I and II sion toughnss ar known, th sion toughnss undr gnral srvi loading onditions an b dtrmind by using mixd mod partitions basd on D lastiity and a linar failur ritrion. Th sion nrgy dfind in litraturs is gnrally diffrnt from th sion toughnss unlss th mod I sion toughnss is qual to mod II sion toughnss. 1 INTRODUCTION raphn mmbran and insulating SiO substrat omposit matrials ar th most ommonly usd ltroni dvi onfigurations. Th sion toughnss btwn th graphn mmbrans and SiO substrats has attratd attntions of many rsarhrs in rnt yars. Various xprimntal and alulation mthods hav bn rportd in litratur to dtrmin th toughnss with various outoms. It is wll known that sion toughnss or intrfa fratur toughnss is mod mixity dpndnt with smallst valu at mod I fratur and th largst valu at mod II fratur. Many prvious studis show that th toughnss varis linarly btwn ths two xtrms for intrfas of low fratur toughnss in both marosopi intrfa fraturs [1, ] and mirosopi intrfa fraturs [3, 4]. Th low sion toughnss btwn graphn mmbrans and SiO substrats is wll into this atgory of low fratur toughnss. Howvr, as far as th authors knowldg is onrnd, th work [5] is th only study so far taks th mod mixity into onsidration. In addition, th work [5] also firstly onsidrs th fft of sliding on th mod mixity btwn multilayr graphn mmbrans. Morovr, it is worth noting that sion nrgis dfind in som xisting litratur ar diffrnt from sion toughnss. Th prsnt work aims to rport svral xprimntal and analytial mthods to dtrmin th sion toughnss btwn multilayr graphn mmbrans and substrats. Som prvious onfusions ar undrstood.

2 Josph D. Wood, Christophr M. Harvy, in Wang and Simon S. Wang EXPERIMENTAL AND ANALYTICAL METHODS.1 Doubl antilvr bam tst (DC) Fig. 1 shows a shmati of th DC spimn for th masurmnt of th sion toughnss btwn a monolayr graphn and oppr by DC fratur mhanis tsting [6]. Th layups and loading onditions ar also shown. For th tst, both Si bams ar loadd and unloadd at a onstant displamnt rat whil th applid load is monitord as a funtion of th displamnt. Multipl loading/rak growth/unloading yls wr prformd to masur th rak lngths and th sion toughnss of th as-grown graphn on oppr. Th masurd rak lngth a and load P ar also shown for ah yl. Figur 1: Masurmnt of th sion toughnss btwn a monolayr graphn and Coppr by DC fratur mhanis tsting (Copy from rf. [6]). It is sn from Fig.1 that th DC an b rgardd as a symmtri DC on pur mod I loading sin th thiknss of Si is muh largr than th thiknss of othr matrials. Morovr, sin th thiknss of Si, i.. h 55 μm is of marosopi siz. Th intrfa fratur toughnss is givn by th lassial partition thory [1, ] and asily alulatd by 1P a I (1) 3 Eb h whr E is th Young s modulus of Si, a is th rak lngth shown in Fig. 1 and b is th width of th DC. Th authors ar unabl to find th valus of both E and b usd in th work [6]. Th study [6] usd th following quation to alulat th sion toughnss. 1P a h () Eb h a Masurmnts [6] of sion toughnss ar shown in Tabl 1 by using th data in Fig. 1 and Eq (1) and () whr is dfind as

3 1 ST Intrnational Confrn on Composit Matrials Xi an, 0 5 th August Eb h (3) 1 It is sn that both Eq (1) and () giv los prditions. Th avragd ar N mm and N mm from Eqs. (1) and (), rsptivly. Th study [6] stats that has th valu of J m. Thrfor, Eq. (1) givs I 0.68J m whih is th ritial mod I ERR or mod I fratur toughnss. Th prsnt authors hav no knowldg of th valu of II whih is usually muh largr than I. Whn both I and II ar known th fratur toughnss undr gnral loading onditions an b obtaind by using ERR partition thoris and failur ritria. Th work [6] alld th sion toughnss as sion nrgy. a mm N P N mm, Eq. (1) N mm, Eq. () Avrag valus Tabl 1: Masurmnts of sion toughnss btwn monolayr graphn and oppr using DC [6]. Th study [7] also usd th nam of sion nrgy onpt and dvlopd a vry diffrnt mthod to alulat it. In th study [7] th sion nrgy is dfind as U U U total (4) whr th van dr Waals intration nrgy U is alulatd by using Lnnard-Jons potntial and U is th rsidual in-plan strain nrgy in th monolayr graphn du to intrfa mismath and surfa fft. Th study givs U 0.16 J m, U 0.58 J m and U total 0.74 J m. It is intrsting to not that U total is vry los to ithr I 0.68 J m from Eq. (1) or J m from Eq. (). ut th physial maning of Eq. (4) is ompltly diffrnt from that of Eqs. (1) and (). Mor disussions on Eq. (4) will b givn latr. Again, th study [8] also usd th nam of sion nrgy and usd atomi for mirosopy (AFM) to masur it. y using th Maugis-Dugdal quation W F 1.77R (5) tip Th sion nrgy and tip W is dtrmind to b 0.11J m whr F is th pull-off sion for R is th radius of th mirosphr tip. Obviously, this valu is far from ithr I 0.68J m from Eq. (1) or J m from Eq. (). To improv th masurmnt th study [8] usd th modifid Rumpf modl whih taks th roughnss of th mirosphr tip into onsidration and gav W 0.75J m. Obviously, this is vry los to ithr I 0.68J m from Eq. (1) or J m from Eq. (). Again, th mthod in [8] is

4 Josph D. Wood, Christophr M. Harvy, in Wang and Simon S. Wang ompltly diffrnt from Eqs. (1), () and (4). It is intrsting to not that Eq. (5) givs W 0.11J m los to U 0.16 J m in Eq. (4). Th study [8] indiats that th roughnss givs xtra 0.64 J m sion nrgy whil th study [7] stats that this is du to th rsidual inplan strain nrgy U 0.58 J m. Sin AFM masurmnt givs approximatly th mod I sion toughnss, th W 0.75J m is onsidrd to b ritial mod I ERR.. Cirular blistr tst undr prssur load In gnral, th mod I ERR I and mod II ERR matrial systms an b writtn as [1-5] II for graphn mmbrans and thik substrat I I M M R N N D R P 3 D (6) N N R II II M M (7) R D Sin th thiknss of graphn mmbrans is in nanosal Eqs. (6) and (7) ar basd on D lastiity partitions as indiatd by th subsript D. Th rak tip bnding momnt pr unit width M and in-plan axial for pr unit width N ar th xtrnally applid parts whil th M R and N R ar th rsidual parts du to rsidual strsss. P is th rak tip through thiknss shar for pr unit width. In th as of zro rsidual bnding momnt and axial for, th work [5, 9, 10] givs th mod mixity ratio I as II Th total ERR is givn as (8) (9) J S J Jnsn s J omponnt an b alulatd as [9, 10] J ( ) p (10) Th ratio S J (11) p and in Eq. (10) rprsnt th prssur load and th ntr dfltion of th blistr, rsptivly. Th paramtr in Eqs. (8) and (11) rprsnts th fft of sliding in multilayr graphn mmbrans and ( ) is a Poison s ratio -dpndnt paramtr, dtails of whih an b found in th work [5]. Th study [11] rportd sion toughnss btwn multilayr graphn mmbrans and SiO substrats using irular blistr tsts undr prssur load. Th sion toughnss was alulatd using Eq. (10) [11]. For monolayr graphn mmbran th toughnss was found to b J m whil for multilayr graphn mmbrans it was J m.

5 1 ST Intrnational Confrn on Composit Matrials Xi an, 0 5 th August 017 y using Eqs. (8) to (11) in th prsnt work, it is found that th prsn of sliding in multilayr graphn mmbrans inrass th fratur mod ratio I II, lading to a dras in sion toughnss masurmnts whn using th irular blistr tst. Th mod mixity jumps up from 43% for th monolayr graphn mmbrans to about 77% for multilayr graphn mmbrans. This inras in th mod mixity has th fft of lowring th sion toughnss from 0.44 J m to J m. Th ritial mod I and mod II sion toughnss ar dtrmind to b I 0.30J m and II J m, rsptivly. Using Eq. (4) th study [7] givs U 0.66J m, U 0.00J m and U total J m for monolayr. It is intrsting to not that U total is vry los to ithr 0.45 J m in th work [11] or 0.44J m in th prsnt work. For multilayr graphn mmbrans, Eq. (4) in th study [7] givs U 0.7 J m, U 0.15J m and U total 97 J m. Again, it is intrsting to not that U total is vry los to J m in th work [11]. Howvr, both th work [11] and th prsnt work do not onsidr th rsidual strain nrgy. Whn th rsidual strain nrgy is onsidrd, th rsidual axial for N R in Eqs. (6) and (7) nds to b inludd. ut both th work [11] and th prsnt work do not onsidr this rsidual for. Morovr, whn th sion nrgy dfind in Eq. (4) [7] is takn to b th sion toughnss dfind in Eq. (9) in prsnt work and th study [11], th sion toughnss is no longr dpndnt on mod mixity. That is, any ombination of rak tip bnding momnt M, in-plan axial for N, through thiknss shar for P, rsidual bnding momnt M R and rsidual axial for N R in Eqs. (6) and (7) will produ th sam fratur toughnss givn by Eq. (4) [7]. This is only possibl whn th mod I sion toughnss is qual to mod II sion toughnss, i.. I II. Howvr, this is gnrally not th as and II is muh largr than I. y using AFM and Maugis-Dugdal quation W F 1.66R (1) tip Th study [8] givs W 0.18J m for monolayr. y using th modifid Rumpf modl whih taks th roughnss of th mirosphr tip into onsidration, th study [8] givs W 0.46 J m whih is vry los to 0.45 J m in th work [11] or 0.44J m in th prsnt work. Sin AFM masurmnt givs approximatly th mod I sion toughnss, W 0.46 J m is onsidrd to b mod I toughnss. Howvr, it is muh largr than th I 0.30J m in th prsnt study. It is intrsting to not that W 0.18J m [8] from Maugis-Dugdal quation is los to I 0.30J m. To xamin if I 0.30J m and II J m ar th aurat valus, th sion toughnss of 5-layr graphn mmbran blistrs undr point load is onsidrd nxt..3 Cirular blistr tst undr point load Th ERR partitions for irular blistr undr point load ar vry similar to Eqs. (6-11) [5]. y using I 0.30J m, II J m and a linar failur ritrion, th sion toughnss btwn 5- layr graphn mmbrans and SiO substrats is found to b 0.438J m. Th xprimntal rsult [1] is 0.437J m. Th agrmnt is xllnt.

6 Josph D. Wood, Christophr M. Harvy, in Wang and Simon S. Wang 3 CONCLUSIONS Adhsion toughnss btwn graphn mmbrans and substrat is mod mixity-dpndnt. Th sliding fft in multilayr mmbrans inrass th mod I fratur mod nrgy rlas rat rsulting in lowr total sion toughnss. On th ritial mod I and II sion toughnss ar dtrmind th intrfa sion toughnss undr gnral srvi loading onditions an b found to guid pratial dsigns. Th xprimntal rsult from a point load blistr tst agrs xllntly with th modl prdition and thrfor validats th prsnt thortial modl. Th sion nrgy dfind in litraturs is gnrally diffrnt from th sion toughnss unlss th mod I sion toughnss is qual to mod II sion toughnss. REFERENCES [1] C.M. Harvy and S. Wang, Exprimntal assssmnt of mixd-mod partition thoris, Composit Struturs, 94, 01, pp (doi: /j.ompstrut ). [] C.M. Harvy, M.R. Epltt and S. Wang, Exprimntal assssmnt of mixd-mod partition thoris for gnrally laminatd omposit bams, Composit Struturs, 14, 015, pp (doi: /j.ompstrut ). [3] S. Wang, C.M. Harvy and. Wang, Room tmpratur spallation of α-aluminia films grown by oxidation, Enginring Fratur Mhanis, availabl onlin 14 th Marh 017 (doi: /j.ngframh ). [4] C.M. Harvy,. Wang and S. Wang, Spallation of thin films drivn by pokts of nrgy onntration, Thortial and Applid Fratur Mhanis, availabl on lin 1 st April (doi: /j.tafm ). [5] J.D. Wood, C.M. Harvy and S. Wang, Adhsion toughnss of multilayr graphn mmbrans. (undr rviw). [6] T. Yoon t al, Dirt masurmnt of sion nrgy of monolayr graphn as-grown on oppr and its appliation to rnwabl transfr pross, Nano Ltt. 1, 01, pp (doi: /nl0413h). [7] Y. H t al, Anomalous intrfa sion of graphn mmbrans, Sintifi Rport, 3, 013, pp. 1-7 (doi: /srp0660). [8] T. Jiang and Y. Zhu, Masuring graphn sion using atomi for mirosopy with a mirosphr tip, Nanosal 7, 015, pp (doi: /5nr0480). [9] H.M. Jnsn, Th blistr tst for intrfa toughnss masurmnt, Eng. Frat. Mh. 40, 1991, pp (doi: / (91)90144-P). [10] H.M. Jnsn, Analysis of mod mixity in blistr tsts, Int. J. Fratur 94, 1998, pp (doi:10.103/a: ). [11] S.P. Konig, N.. oddti, M.L.Dunn and J.S. unh, Ultra-strong sion of graphn mmbrans, Natur Nanothnology, 6, 011, pp (doi: /nnano ). [1] Z. Zong, C.L. Chn, M.R. Dokmi and K.T. Wan, Dirt masurmnt of graphn sion on silion surfa by intration of nanopartils, Journal of Applid Physis, 107, 010, pp (doi: / ).