R-curve Evaluation of 3YTZP/Graphene Composites by Indirect Compliance Method

Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 A ailable online 2 Feb ua y 2023 0955-2219/© 2023 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by- nc-nd/4.0/). R-cu e e alua ion o 3YTZP/g aphene composi es by indi ec compliance me hod C. L´ opez-Pe nía a , b , * , C. Mu˜ noz-Fe ei o a , b , c , J. P ada-Rod igo d , P. Mo eno d , H. Re e on c , J. Che alie c , A. Mo ales-Rod íguez a , R. Poya o a , b , ´ A. Galla do-L´ opez a a Uni e sidad de Se illa-ICMS (CSIC), Depa amen o de Física de la Ma e ia Condensada, Apdo. 1065, 41080 Se illa, Spain b CSIC-Uni . de Se illa, Ins i u o de Ciencia de Ma e iales de Se illa (ICMS), A da. Am´ e ico Vespucio 49, 41092 Se illa, Spain c Uni e si ´ e de Lyon, INSA Lyon, MATEIS UMR CNRS 5510, 7 A enue Jean Chapelle, F-69621 Villeu bane Cedex, F ance d G upo de In es igaci´ on en Aplicaciones del L´ ase y Fo ´ onica (ALF-USAL), Uni e sidad de Salamanca, Plaza de la Me ced s/n, 37008 Salamanca, Spain ARTICLE INFO Keywo ds: 3YTZP G aphene-based nanoma e ials (GBN) Composi es R-cu e, compliance me hod ABSTRACT This wo k add esses he c ack g ow h esis ance o 3 mol% Y ia-doped Te agonal Zi conia Polyc ys alline (3YTZP) spa k-plasma sin e ed (SPS) composi es con aining wo ypes o g aphene-based nanoma e ials (GBN): ex olia ed g aphene nanopla ele s (e-GNP) and educed g aphene oxide ( GO). The c ack g ow h esis ance o he composi es is assessed by means o hei R-Cu e beha io de e mined by h ee-poin bending es s on single edge “V” no ched beams (SEVNB), in wo di e en o ien a ions o he samples: wi h he c ack pa h pe pendicula o pa allel o he p essu e axis du ing he SPS sin e ing. The sha p edge no ches we e machined by ul asho lase pulsed abla ion (UPLA). The compliance and op ical-based me hods o e alua ing he c ack leng h a e compa ed on he basis o he expe imen al R-Cu e esul s in composi es wi h 2.5 ol% GO es ed in he pe pendicula o ien a ion. Mo eo e , he ac i a ion o ein o cemen mechanisms is e alua ed by bo h he ac u e su ace inspec ion by Scanning Elec on Mic oscopy and a compliance analysis. I is shown ha he indi ec compliance me hod is ele an and eliable o calcula ing he R-Cu e o 3YTZP/GBN composi es. The e ec o he ype and con en o GBN on he c ack g ow h esis ance o he composi es is also discussed. 1. In oduc ion Recen ly, G aphene-Based Nanoma e ials (GBN), such as G aphene Nano-Pla ele s (GNP) o Reduced G aphene Oxide ( GO), ha e a ac ed a conside able scien i ic in e es due o hei po en ial o imp o e he mechanical p ope ies o ce amic composi es. In 2011, Walke e al. epo ed o 235% enhancemen in he ac u e oughness (K IC ) o Si 3 N 4 ce amics when inco po a ing 1.5 ol% GNP [1]. Since hen, many s udies on he ac u e oughness o se e al ce amic ma ix composi es con aining g aphene-based ma e ials o ca bon nano ubes ha e been ca ied ou [1–8]. Howe e , he esul s ob ained up o da e a y s ongly wi h di e en pa ame e s such as he ype o GBN used as a ille , i s con en and i s dis ibu ion h oughou he ce amic ma ix o he me hod employed o he ac u e oughness de e mina ion. A good o e iew o he in luence o he ype and con en o he GBN inco po- a ed in ce amics is gi en by Mi anzo el al. [3], making special emphasis on hei mechanical, elas ic and wea p ope ies. Despi e he a iabili y o he esul s in he li e a u e, he ela i e enhancemen o K IC o he composi es when compa ed o he monoli hic ce amic ma ices has been epo ed o be highe o GO as ille han o GNP. Mo eo e , he ein o cemen e ec is gene ally achie ed o lowe GO con en s han o GNP. The p ocessing o ce amic/GBN composi es is a c ucial s ep in de eloping inc eased mechanical pe o mance. I no op imized, adding GBN ma e ials o he ce amic could be a he de imen al. Ano he key aspec explaining he a iabili y o he K IC alues e- po ed in he li e a u e is he me hod o de e mine K IC . The inden a ion me hod (IM) is one o he mos equen ly used due o i s simplici y[9, 10]. I consis s in he indi ec de e mina ion o K IC om he di ec measu emen o he leng h o c acks eme ging om he co ne s o Vicke s inden a ion p in s. Howe e , he alidi y o he inden a ion me hod in ce amic/GBN composi es is s ongly ques ioned since he ac u e oughness is es ima ed om a small egion o he sample which is subjec ed o e y complex s ess ields [11–14]. Mo eo e , he mic os uc u al aniso opy associa ed wi h hese ypes o composi es could lead o he absence o c acks in some di ec ions o he sample, hampe ing he co ec de e mina ion o K IC [4,15]. O he me hods like * Co esponding au ho a : Uni e sidad de Se illa-ICMS (CSIC), Depa amen o de Física de la Ma e ia Condensada, Apdo. 1065, 41080 Se illa, Spain. E-mail add ess: [email p o ec ed] (C. L´ opez-Pe nía). Con en s lis s a ailable a ScienceDi ec Jou nal o he Eu opean Ce amic Socie y jou nal homepage: www.else ie .com/loca e/jeu ce amsoc h ps://doi.o g/10.1016/j.jeu ce amsoc.2023.02.002 Recei ed 2 No embe 2022; Recei ed in e ised o m 30 Janua y 2023; Accep ed 1 Feb ua y 2023 Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3487 h ee- and ou -poin bending es s o single-edge no ched beams (SENB) allow measu ing oughness o hese ma e ials wi h be e eliabili y [11]. Howe e , he ac u e oughness measu ed om hese me hods is s ongly limi ed by a c i ical no ch oo adius [16]. Abo e i , he calcula ed K IC could be highe han he ue ac u e oughness o he ma e ial. Thus, he oo adius o he no ch should be sha p enough o ob ain eliable K IC esul s. Simila o SENB, he Single-edge V-no ched beams (SEVNB) consis ed on he ec angula ba s whose no ch is machined wi h a saw cu . Then he no ch ip is machined in “V” by using a azo blade wi h a diamond suspension. Mo e ecen ly, i has been epo ed ha he azo blade can be eplaced by machining a shallow sha p no ch by ul a-sho pulse lase abla ion (UPLA)[17]. In mos o he s udies, he mechanical ein o cemen o GBN/ce amic composi es has been associa ed wi h ene gy dissipa ing mechanisms o igina ed by GBN ha hinde c ack p opaga ion. The mos epo ed mechanisms a e GBN pull-ou and c ack de lec ion, b anching and b idging. Despi e he undeniable in luence o hose mechanisms on he ac u e esis ance o hese composi es, de ailed s udies dedica ed o he c ack p opaga ion beha io a e e y sca ce, especially in ela ion o zi conia-based ce amic ma ix composi es [6,18,19]. In ans o ma ion oughened ce amics like y ia-s abilized e agonal zi conia poly- c ys als (YTZP), he e agonal o monoclinic phase ans o ma ion abili y (mainly a ec ed by he g ain size o he ce amic ma ix and he Y 2 O 3 con en ), also con ibu es o he a iabili y o epo ed ac u e oughness alues [20–23]. Mo eo e , in his ype o composi es, he ein o cemen e ec due o g aphene is mo e di icul o assess. Se e al ce amics show R-cu e beha io which is cha ac e ized by an inc ease in c ack g ow h esis ance (K R ) wi h inc easing c ack leng h. The s udy o he R-cu e o a gi en ma e ial allows he e alua ion o i s c ack g ow h esis ance since a ising R-cu e is indica i e o he de elopmen o oughening mechanisms. Despi e he ac ha mos s udies on GBN/ce amic composi es epo an inc ease in ac u e oughness, he e a e only a ew ha examine hei R-cu e beha io [6, 16,17]. Mo eo e , mos o hem measu e hese p ope ies only when he GBN main a-b plane is o ien ed pe pendicula o he c ack p opaga ion pa h. In mos GBN/ce amic composi es he GBN end o align pe pen- dicula ly o he comp ession o ce applied du ing sin e ing p o iding a s uc u e simila o pla ele -like o nac e-like ma e ials. In a ecen s udy, Liang e al. [24] add essed he excellen mechanical p ope ies and he ising R-Cu e o Al 2 O 3 ce amics wi h highly o ien ed g aphene nanolaye s a anged in a nac e-like laye -by-laye s uc u e. Howe e , GBN/ce amic composi es a e highly aniso opic so ques ions abou he in luence o o he o ien a ions o GBN ille wi hin he ce amic ma ix do s ill a ise. To he bes o ou knowledge only he wo k om G´ omez-G´ omez e al.[18] conside ed he R-cu e beha io o he ma e- ials o wo o ien a ions o he sample. Fo he R-cu e de e mina ion, a es specimen wi h a c ack is loaded in o de o ha e a s able o con olled c ack p opaga ion. The main di e ence be ween a ious R-cu e me hods is he p ocedu e o measu ing he c ack leng h du ing c ack ex ension. The R-cu e is o en e alua ed om load-displacemen cu es by c ack leng hs es ima ed indi ec ly by he compliance me hod which conside s he inc ease in he compliance o he ma e ial o calcula e he c ack leng h [25,26]. Al hough his me hod s ands ou o i s simplici y, i may no be p ecise o ma e ials wi h a s ong R-cu e, as he compliance could be a ec ed by b idging s esses a he c ack bo de s [27,28]. Thus, he eal c ack ex ension could be unde es ima ed. In hose cases, i becomes necessa y o check i s eliabili y by using o he me hods o a di ec (op ical) c ack leng h de e mina ion. These me hods may equi e he obse a ion o he eal c ack leng h a he su ace o he specimen wi h an op ical mic o- scope and e en, he use o a ideo- eco ding uni o a close s udy. In-si u measu emen s o he c ack leng h du ing he mechanical es di ec ly allow s ess in ensi y ac o s calcula ion bu hey a e di icul o se up, especially when conside ing nanos uc u ed ce amics. Load-unload displacemen es s could be also implemen ed o measu e he c ack leng h ex ension a di e en loads, by using op ical o scanning elec on mic oscopes. To ge a be e unde s anding o he mechanical beha io o zi conia ce amic/GBN composi es, his wo k is conduc ed wi h he ollowing objec i es: (i) o alida e he indi ec compliance me hod o he R-cu e calcula ion in zi conia/GBN composi es, by compa ing he esul s wi h he di ec op ical measu emen o c ack ex ension and (ii) o e alua e he in luence o he inco po a ion o wo di e en GBN ma e ials (ex olia ed G aphene Nano-Pla ele s (e-GNP) and educed G aphene Oxide ( GO)) and hei o ien a ion on c ack g ow h esis ance o spa k plasma sin e ed composi es. 2. Expe imen al p ocedu e 2.1. Ma e ials p epa a ion 2.1.1. Powde p ocessing and sin e ing Comme cial 3YTZP powde wi h 40 nm pa icle size (Tosoh Co po- a ion, Tokyo, Japan) was annealed in o de o emo e o ganic addi i es [29] a 850 ºC o 30 min in ai be o e p epa ing he composi e powde s. GNP ( e . N006-P, la e al dimension <5 µm and 10–20 nm hickness) and GO ( e . N002-PDE, la e al dimension ~ 7 µm and 2–3 nm hick- ness) powde s we e acqui ed om Angs om Ma e ials (Day on, Ohio, USA) and used o p epa e 3YTPZ-based composi es. Composi e powde s con aining 2.5, 5 and 10 ol% o ex olia ed GNP (e-GNP) we e p epa ed using a plane a y ball mill (Pul e ise e 7, F i sch, Ge many) in d y condi ions as desc ibed in [30]. App oxima ely 4 g o he GNP and 3YTZP powde s we e placed in a 45 mL zi conia ja oge he wi h se en 15 mm-diame e Z O 2 balls. The powde s we e milled o 4 h a 350 pm. Finally, composi e powde s we e homoge- nized in an aga e mo a . Composi e powde s con aining 2.5 ol% GO we e p epa ed using a p ocedu e ha in ol es he combina ion o ul asonic dispe sion and high ene gy plane a y ball-milling as desc ibed in [31]. Fi s , he GO was dispe sed in e hanol using a KT-600 ul asonic p obe (Kon es Inc., Vineland, NJ) a 20 kHz and 95% ampli ude o 15 min, in ime in e als o 5 min o a oid he hea ing o he suspension. Then, he 3YTZP powde was added o he GO suspension and sonica ed o an addi ional 5 min. Then, he suspension was milled in he plane a y ball mill in we con- di ions du ing a sho ime (15 min) and a slow speed (250 pm) o a oid damage o he GO laye s. Finally, he powde s we e d ied in a o a y e apo a o and homogenized in an aga e mo a . Pu e 3YTZP e e ence ce amics we e p epa ed om he 3YTZP powde a e he annealing ea men . All composi e and pu e 3YTZP powde s we e consolida ed by Spa k Plasma Sin e ing (SPS Model HP D25, FCT Sys em GmbH, Ge many) in acuum a mosphe e a 1250 ºC o 5 min wi h an applied uniaxial p essu e o 75 MPa. Disc samples (30 o 40 mm diame e and ~4 mm hick) we e ob ained. The GO educ ion du ing SPS di ec ly p oduces GO-like ille s. 2.1.2. SEVNB specimen p epa a ion The R-cu e beha io o he composi es and he 3YTZP benchma k was assessed on single-edge V no ched beams (SEVNB). F om each sin e ed disc, ec angula ba s o size 25 ×4 x 3 mm 3 (L x W x B wi h L=leng h, W=wid h and B= hickness) we e cu and machined in acco dance wi h he ASTM C1421–10 s anda d es me hod. A p e-no ch o 2 mm dep h was pe o med mechanically on he 25 ×3 mm 2 ace wi h a diamond coa ed saw o 0.3 mm hick. In o de o use a sha p no ch ha will ensu e s a ing a lowe K I and hus, ob ain a mo e p ecise R-Cu e[32,33], ul asho pulsed lase abla ion (UPLA) was used o p oduce an addi ional sha p no ch o ~ 100 µm dep h a he ip o he p e-no ch wi h almos negligible he mal load on he subs a e ou o he abla ed zone [17,18,34]. The lase no ch was p oduced by a Ti: Sapphi e sys em (Tsunami, Spec a Physics, USA) deli e ing pulses o du a ion 120 s a λ =795 nm wi h pulse ene gy 34 µJ and a epe i ion a e o 1 kHz. The ull no ch leng h (a 0 ) was es ima ed as he addi ion o C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3488 he p e-no ch and he lase no ch. A a io a 0 /W ~ 0.5 was achie ed o all he specimens. An example o he sha p no ch ip is shown in Fig. 1a. In o de o e alua e he e ec o a possible GBN main plane p e e - en ial o ien a ion wi h espec o he SPS p essing z-axis ha would a ec he c ack esis ance beha io o hese ma e ials, he es s we e pe o med on samples in which he no ch was pe o med on he su ace pe pendicula (┴) o pa allel ( || ) o he SPS p essu e z-axis. The es con igu a ion is schema ically shown in Fig. 1b and c, aking as an example he composi e con aining 2.5 ol% GO. In he pe pendicula con igu a ion he main a-b plane o he GO shee s is pe pendicula o he c ack plane. In he pa allel con igu a ion he c ack pa h aces he edges o he GO shee s. Six SEVNB specimens o each ype o composi e we e p epa ed. Th ee o hem we e p epa ed in o de o be es ed in he pe pendicula (┴) con igu a ion and he o he h ee in he pa allel ( || ) one. He eina e composi e samples a e labeled acco ding o he ype o GBN, i s con en and he es ed con igu a ion as xGBN⊥o xGBN‖(being “x” he GBN con en ). Finally, h ee SEVNB specimens o 3YTZP we e es ed in pa - allel ( || ) con igu a ion and labeled 3YTZP. 2.2. Ma e ials cha ac e iza ion The densi ies o he sin e ed composi es we e measu ed using he A chimedes’ me hod, wi h dis illed wa e as he imme sion medium. The heo e ical densi ies we e calcula ed based on he ule o mix u es conside ing densi ies o 6.05 g/cm 3 o 3YTZP and 2.2 g/cm 3 o GNP and GO. The semi-quan i a i e analysis o he c ys allog aphic phases p esen in he sin e ed composi es and he e e ence monoli hic 3YTZP sample was ca ied ou by X-Ray Di ac ion (D8 Ad anced A25 X-Ray di ac- ome e , (B uke Co Massachuse s, USA). The GBN dis ibu ion in he 3YTZP ma ix as well as he mo phology o he ce amic g ains we e cha ac e ized by Scanning Elec on Mic o- scopy (SEM) pe o med on ac u ed and polished c oss-sec ion su aces (FEI Teneo, FEI, USA). Back-sca e ed elec ons (BSE) mode was used o imaging GBN dis ibu ion h oughou he ce amic ma ix. To cha ac- e ize zi conia g ain sizes, polished su aces we e he mally e ched in ai a 1150 ºC o 15 min in o de o e eal he g ain bounda ies. The g ain size was calcula ed as he equi alen plana diame e d =2(a ea/ π )1/2 and he g ain shape ac o as F=4 π a ea/(pe ime e )2. Mo e han 500 g ains measu emen s we e aking in o accoun o each sample. Raman spec oscopy was used o assess he p esence and s uc u al in eg i y o he GBN in he composi es a e he sin e ing p ocess. In he composi e con aining 2.5 ol% GO, he spec a we e also acqui ed on he as-p ocessed composi e powde s and compa ed o he ones ob ained on sin e ed ce amics o accoun o he in-si u educ ion o GO du ing he sin e ing p ocess [31,35]. In o de o cha ac e ize he ans- o mabili y on 3YTZ and he composi es, ac u ed su aces a e usually analyzed by XRD o Raman spec oscopy. In he p esen wo k, Raman spec oscopy was used o assess whe he he -m ans o ma ion ook place on he SEVNB es ed specimens [36]. Six o eigh spec a om each specimen we e acqui ed on ac u ed su aces using a dispe si e mi- c oscope (Ho iba Jobin LabRam HR800, Kyo o, Japan) equipped wi h a He-Ne g een lase (532.14 nm) a 20 mW. Since he -phase may no ans o m homogeneously on he en i e ac u e su ace [37], se e al spec a we e acqui ed in di e en and andom loca ions o he ac u e su aces. The Young’s modulus o all ma e ials was measu ed a oom em- pe a u e using a G indoSonic equipmen (MK6-A G indoSonic BVBA Belgium), ins umen based on he impulse exci a ion echnique in which 25 ×4 x 3 mm 3 samples we e subjec ed o an ini ial de o ma ion by means o a ligh mechanical impulse. Immedia ely, he objec ac as a sp ing-mass sys em and p oduce a ansien mechanical ib a ion. The equency o his ib a ion depends on he mass o he sample and i s s i ness, which was de e mined ollowing he ASTM E 1876–01 s an- da d es me hod. 2.3. R-cu e s udy SEVNB specimens we e es ed in a h ee-poin ix u e (suppo span 21 mm) using an Ins on 8500 machine (No wood, USA). The suppo and uppe cylinde s we e made o alumina and had a diame e o 8 mm. Du ing he es , he specimen de lec ion was eco ded using a Linea Va iable Displacemen T ansduce (LVDT) placed nea he sample no ch. The R-Cu es o he ma e ials we e buil om he load- displacemen (P-δ) da a ob ained om he h ee-poin bending es s acco ding o wo di e en me hods. In mos cases, R-Cu es we e ob- ained using he indi ec compliance me hod [26]. In addi ion, and in o de o alida e his indi ec me hod, he R-Cu e o he composi e wi h he highes c ack esis ance beha io (2.5 GO┴ composi e) was also es ima ed om he di ec measu emen o c ack g ow h by op ical mi- c oscopy (load-unload h ee-poin bending es ). 2.3.1. R-cu e de e mina ion by he indi ec compliance me hod The ins an aneous applied load (P i ) and loading poin displacemen (δ i ) da a we e eco ded un il he ailu e. The specimens we e loaded in ai wi h a cons an low speed o 10 µm/min. The R-cu e, showing he s ess in ensi y ac o (K IR ) as a unc ion o he c ack ex ension (Δa =a i – a 0 ), was ob ained by es ima ing he c ack leng h and he s ess in ensi y ac o . Fo his, K IR was calcula ed by using he ollowing exp ession: Fig. 1. (a) Op ical images showing an example o he p e-no ch (up) and he lase no ch (down) pe o med on he samples. Schema ics o he es con igu a ion o he GO samples. The no ch is sawn in he su ace (b) pe pendicula o (c) pa allel o he SPS p essing axis. The GO shee s a e “no mal” o “edge-on”, espec i ely, o he plana c ack on . C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3489 KIR =g⋅[PiS0 BW3/2]⋅[3(ai/W)1/2 2(1−ai/W)3/2](1) whe e P i is he applied load, S 0 is he span, B is he hickness o he sample, W is he wid h o he sample, a i is he c ack leng h and g is a unc ion depending on he geome y o he sample. The g unc ion was calcula ed acco ding o ASTM C1421–10 s anda d es me hod [38]. An i e a i e me hod was used o calcula e he ins an aneous c ack leng h (a i ) o each pai o expe imen al P i - δ i alues as desc ibed by Munz and Fe [26]. Fi s , he compliance (C i ) o each pai o da a is de ined as: Ci=δi Pi (2) Then a i was es ima ed om he measu ed change in he compliance using he ollowing equa ion: ai=a(i−1)+[W−a(i−1) 2⋅Ci−C(i−1) Ci](3) 2.3.2. Valida ion o he indi ec compliance me hod 2.3.2.1. R-cu e de e mina ion by he op ical me hod. Di ec R-cu e de e mina ion consis s on he op ical measu emen o he c ack ex en- sion du ing he SEVNB es . Loading-unloading sequences on he SEVNB specimens we e pe o med in ai wi h a cons an speed o 5 µm/min and load-displacemen cu es we e eco ded. K IR was s ill calcula ed using Eq. (1) wi h P as he load a he maximum δ o each load-de lec ion cu e. He e, he c ack-leng h (a op ) was measu ed di ec ly by op ical mic oscopy a e each load-unload cycle o cons uc he R-cu e which was compa ed wi h he one ob ained by he indi ec compliance me hod. The compliance was calcula ed om he load-displacemen poin (P- δ) acco ding o Eq. (2) and i s e olu ion as a unc ion o he c ack leng h, C(a), was i ed o a linea unc ion: C(a) = Ma +N(4) This unc ion was used o es ablish an empi ical exp ession o es i- ma e he c ack leng h as a unc ion o he measu ed changes in he compliance: a=C−N M(5) This exp ession was used o ecalcula e he R-cu e ob ained by he indi ec compliance me hod in Sec ion 2.3.1. This is, he co ec ed R- cu e was buil wi h K IR calcula ed om he load-displacemen da a o he i s expe imen acco ding o Eq. (1) bu subs i u ing he c ack leng h calcula ed om Eq. (5). 2.3.2.2. Re-no ching es and compliance analysis. In o de o simula e he p opaga ion o a c ack in an ideal ma e ial ee o b idging o ein o cemen mechanisms, a hi d s udy was pe o med. Du ing his expe imen , he no ch leng h o he specimen es ed was successi ely ex ended ( e-no ching) wi h a diamond coa ed saw. The e-no ching ope a ion was ca ied ou a e loading-unloading sequences, pe - o med in ai and a 5 µm/min. The applied load was s opped igh be o e he c ack could s a ed o p opaga e, so no c ack p opaga ion was enhanced. The machined no ch simula ed a ull c ack wi hou b idging and i s leng h was measu ed a e being sawn o each load-unload es by using op ical mic oscopy. The compliance was calcula ed as he slope o he linea pa o he P-δ cu e ob ained o each no ch leng h. Based on his e-no ching expe imen , he compliance o e-no ched sample was compa ed o he e olu ion o he compliance o he c acked spec- imen subjec ed o he es desc ibed in he p e ious sec ion. This ga e ise o an es ima ion o c ack b idging s esses [39]. 3. Resul s and discussion 3.1. Ma e ials cha ac e iza ion Well densi ied composi es ha ing ela i e densi ies ≥98.6% o he heo e ical densi y (Table 1) we e ob ained a e he SPS sin e ing p ocess. The addi ion o GBN ille s sligh ly a ec ed 3YTZP densi ica- ion. The 3YTZP e e ence ce amic showed a ela i e densi y o 99.4% while i anged om 99.4% o 97.9% (2.5% and 10 ol% e-GNP, espec i ely) and eached 98.6% in 2.5 ol% GO composi es. This sligh dec ease in densi y is in ag eemen wi h p e iously published s udies [30,31,35]. The p esence o he GBN phase in sin e ed composi es was con i med by Raman spec oscopy as he cha ac e is ic bands D, G and 2D loca ed om ~1350 o ~2700 cm -1 and ela ed o g aphi ic ma e ials we e obse ed in all he Raman spec a (no shown he e). We ound ha du ing he SPS p ocess he GO phase was in-si u educed o GO, as con i med by he a ia ion in he in ensi y and wid h o D, G and 2D bands [31]. Mo eo e , ega ding composi es wi h e-GNP, we also co obo a ed he absence o GNP de e io a ion a e he SPS p ocess [30, 35]. The c ys allog aphic phases p esen in monoli hic 3YTZP and he as- sin e ed composi es we e checked by a semi-quan i a i e XRD analysis (no shown he e). The only phase de ec ed in all samples was he educed e agonal zi conia (Z O 1.95 ). The educ ion o he e agonal phase is a consequence o he educing condi ions du ing he SPS since he powde s a e placed inside a g aphi e mold and he sin e ing p ocess akes place unde acuum [30,31]. Al hough some au ho s ha e e- po ed ha he e agonal o monoclinic zi conia phase ans o ma ion could be induced a e sin e ing in g aphene con aining composi es [29, 40], he main XRD monoclinic zi conia peaks loca ed a 2θ =28.2 y 31.4 º we e no obse ed in any o he samples p epa ed in he p esen wo k. Fig. 2 shows he dis ibu ion o he g aphene phase in he pe pen- dicula o he SPS p essing axis c oss-sec ions o he composi es. Due o he di e en a omic numbe o he wo main phases, hey can be dis inguished by BSE-SEM inspec ion since he da k phase will co e- spond o GO o e-GNP while he clea one will be 3YTZP. A ema kable di e ence in he GBN size and dis ibu ion is obse ed in composi es con aining GO compa ed o e-GNP. The GO phase appea s as la ge shee s wi h hei main a-b plane aligned pe pendicula ly o he SPS p essing axis (Fig. 2a). In con as , he e-GNP phase exhibi s a smalle size (Fig. 2b o d) and he pla ele s a e andomly dis ibu ed h oughou he ce amic ma ix, wi hou any p e e en ial o ien a ion. This dis ibu- ion ea u es a e obse ed in all e-GNP composi es, independen ly o he amoun o g aphene. Table 1 shows he es ima ed g ain sizes in sin e ed, polished and he mal-e ched su aces. No g ain e inemen was obse ed in he composi e con aining 2.5 ol% GO which exhibi ed a g ain size simila o ha o 3YTZP (0.24 and 0.23 µm, espec i ely). Howe e , o com- posi es con aining e-GNP and independen ly o he con en o g aphene phase (i.e. 2.5–10 ol%), a sligh ly lowe g ain size (~ 0.18 µm) was ob ained. Ce amic g ain g ow h inhibi ion by g aphene nanoshee s has been p e iously linked o he ac ha nanopla ele s su ounding ce amic g ains ac as di usion ba ie s hinde ing he mo emen o he g ain bounda ies du ing sin e ing [41–43]. In 3Y-TZP/e-GNP Table 1 Absolu e and ela i e densi ies, g ain size (d plana ) and elas ic modulus (E) o he monoli hic 3YTZP and he GBN/3YTZP composi es. Samples ρ exp (g/cm 3 ) ρ el (%) d plana ±s.d. (µm) E (GPa) 3YTZP 6.01 ±0.01 99.4 ±0.1 0.23 ±0.10 198 2.5 ol% GO 5.87 ±0.04 98.6 ±0.3 0.24 ±0.13 185 2.5 ol% e-GNP 5.93 ±0.02 99.4 ±0.2 0.18 ±0.08 200 5 ol% e-GNP 5.80 ±0.01 98.7 ±0.3 0.17 ±0.07 191 10 ol% e-GNP 5.58 ±0.01 97.9 ±0.2 0.18 ±0.08 155 C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3490 Fig. 2. BSE-SEM images om he c oss sec ions pe pendicula ly o he SPS p essing axis o he sin e ed composi es wi h (a) 2.5 ol% GO, (b) 2.5 ol% e-GNP, (c) 5 ol% e-GNP and (d) 10 ol% e-GNP. Fig. 3. Load-displacemen cu es unde con inuous loading a 10 µm/m o he monoli hic 3YTZP and he composi es con aining (a) 2.5 ol% GO, (b) 2.5 ol% e- GNP, (c) 5 ol% e-GNP and (d) 10 ol% e-GNP, in he pa allel ( || ) and pe pendicula o ien a ions (┴). C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3491 composi es, he highe hinde ing e ec may be associa ed wi h smalle (and he e o e mo e nume ous) g aphene pla ele s which a e mo e ho- mogeneously dis ibu ed. Thei small size was p omo ed by he use o he plane a y ball milling unde d y condi ions [30]. Thus, he e is a highe p opo ion o e-GNP su ounding a highe numbe o zi conia g ains and hinde ing hei g ow h. A dec ease in he elas ic modulus (E) o 3YTZP-based composi es a e GBN addi ion was obse ed in 2.5 ol% GO, 5 ol% e-GNP and 10 ol% e-GNP (Table 1). Mo eo e , E dec eased as he e-GNP con en inc eased. Al hough po osi y can play a c ucial ole o dec easing he E o he composi es, a simila densi ica ion deg ee was achie ed o all he composi es so his beha io can be ela ed o he inco po a ion o mo e elas ic g aphene phases in o he igid ce amic ma ix [4,44,45]. Despi e o he high Young’s modulus expec ed in a mechanically ex olia ed monolaye o g aphene (~ 1.0 TPa [46]), he elas ic modulus o a monolaye o GO is only ~ 0.25 TPa and i dec eases abou one o de o magni ude in GO consis ing o mo e han 3 laye s [47]. The elas ic modulus o GNP is also conside ably lowe han he one o g aphene [48]. This would he e o e explain he dec ease o E when inco po a ing he GO and e-GNP in 3YTZP zi conia. 3.2. E ec o GBN addi ion on he c ack esis ance beha io o 3YTZP Fig. 3 shows he h ee-poin bending load-displacemen cu es o no ched samples o zi conia (3YTZP) and 3YTZP composi es ( GO and e-GNP) un il ac u e. Rega ding 3YTZP/2.5 ol% GO composi es, he lexu al de lec ion and maximum load achie ed be o e ac u e was highe in he pe pendicula o ien a ion (┴) compa ed o he pa allel o ien a ion ( || ) and he monoli hic 3YTZP (Fig. 3a). On he o he hand, he inco po a ion o e-GNP o he ma ix had no signi ican e ec in he load-displacemen cu es o 2.5 and 5 ol% e-GNP o he wo es ed o ien a ions (Fig. 3a and b). Mo eo e , he maximum load be o e ailu e dec eased in 3YTZP/10 ol% e-GNP composi es (bo h di ec ions, Fig. 3d). Rela ed R-cu es o composi es and monoli hic 3YTZP calcula ed by he compliance me hod a e displayed in Fig. 4. I can be no iced ha monoli hic 3YTZP p esen ed a e y weak R-cu e. The ini ial s ess in- ensi y ac o (K IR0 ) necessa y o he onse o s able c ack g ow h was o ~3.3 MPa m 1/2 and i inc eased du ing c ack ex ension up o a pla eau alue o ~ 3.6 MPa m 1/2 . This K IR0 alue is e y close o he one ob- ained by Eichle e al. [49] in 3YTZP ce amics ha ing simila g ain size. Such a weakly ising 3YTZP R-cu e can be explained by he ela i ely small g ain size which also in luences he ac u e oughness o Y-TZP ma e ials [50,51]. In gene al, ce amic c ack g ow h esis ance inc eases wi h inc easing g ain size. In he case o zi conia-based ce amics, highe g ain size means a s onge abili y o s ess-induced e agonal o monoclinic phase ans o ma ion [50,52]. Due o he singula s ess ield nea a c ack ip, e agonal zi conia g ains can unde go a s ess-induced ma ensi ic ans o ma ion c ea ing a ans o ma ion zone ahead o he c ack ip. As he olume o monoclinic cell is highe han ha o he e agonal one, a olume ic expansion s ain o abou 4–5% occu s and comp essi e s esses a e applied along he c ack leng h. The comp es- si e s esses lead o a shielding s ess in ensi y ac o which mus be o e come du ing c ack p opaga ion, in o he wo ds, he applied s ess in ensi y ac o mus be inc eased o main ain s able c ack g ow h. Clea ly, he low alues o K IR0 and o he pla eau alue a e linked o he small g ain size o he SPS-sin e ed 3YTZP. This would indica e a lowe p opensi y o phase ans o ma ion oughening han 3YTZP sin e ed a highe empe a u e, unde con en ional p ocesses, as discussed below. The inco po a ion o 2.5 ol% GO clea ly modi ies he ac u e beha io o 3YTZP ma ix (Fig. 4a). Highe c ack esis ance was ach- ie ed when he plana c ack on was pe pendicula ly o ien ed o he GO main a-b plane (Fig. 1a). Al hough his composi e showed an ini ial K IR0 alue o ~3.2 MPa m 1/2 simila o ha ob ained in 3YTZP, he Fig. 4. R-Cu es (s ess in ensi y ac o , K IR , as a unc ion o c ack ex ension, Δa) ob ained by he indi ec compliance me hod o he monoli hic 3YTZP and he composi es con aining (a) 2.5 ol% GO, (b) 2.5 ol% e-GNP, (c) 5 ol% e-GNP and (d) 10 ol% e-GNP, in he pa allel ( || ) and pe pendicula (┴) o ien a ions. C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3492 s ess in ensi y ac o inc eased up o ~ 4.3 MPa m 1/2 . In he pa allel o ien a ion, he ob ained R-cu e was qui e simila o ha o monoli hic 3YTZP ( he s ess in ensi y ac o sligh ly inc eased om 3.1 MPa m 1/2 o 3.4 MPa m 1/2 ). This aniso opic R-cu e beha io is in good ag ee- men wi h mic os uc u al ea u es obse ed by BSE-SEM in his com- posi e (Fig. 2a) since s onge ein o cemen is expec ed when he c ack on is unning pe pendicula o GO plane. The e ec o inco po a ing e-GNP on he R-cu e o he composi es is qui e di e en (Fig. 4a, b and c) and e en was nega i e wi h espec o he mechanical beha io . Fo 2.5 and 5 ol% e-GNP, K IR alues we e sligh ly lowe han hose obse ed on monoli hic zi conia. Al hough he mic os uc u al obse a ions did no e eal any p e e en ial o ien a ion o e-GNP, smalle di e ences be ween he wo es ed o ien a ions could be ela ed o some deg ee o aniso opy o p e e en ial o ien a ion o he pla ele s. Acco dingly, in 2.5e-GNP and 5e-GNP composi es K IR alues inc eased so ly up o ~3.4 MPa m 1/2 when es ed in he pe pendicula con igu a ion while hey only eached 3.1 MPa m 1/2 in he pa allel con igu a ion. When inc easing he con en o e-GNP up o 10 ol%, he c ack g ow h esis ance ema kably dec eased compa ed o ha o he composi es wi h 2.5 and 5 ol% e-GNP and he monoli hic 3YTZP. Mo eo e , mic os uc u al aniso opy is p obably mino as he s eady- s a e K IR alues we e simila o he wo con igu a ions (~2.8 MPa m 1/2 ). In addi ion, unlike he beha io obse ed in mono- li hic 3YTZP and composi es wi h a lowe e-GNP con en , he R-cu e o 10e-GNP┴ ose ab up ly om he s a o c ack ex ension (Fig. 4d), ecalling he beha io al eady discussed o 2.5 GO┴ (Fig. 4a). To assess he e ec o he g aphene phase on he R-cu e beha io o he composi es, h ee ac o s should be conside ed. The i s one is he e ec o he s ess-induced e agonal o monoclinic ( -m) zi conia phase ans o ma ion a he c ack ip, he second one is he e ec o he g ain size and he las one is he in e ac ion o he GBN ille wi h he c ack p opaga ion (b idging e ec s). 3.2.1. S ess-induced -m phase ans o ma ion and zi conia g ain size e ec Fig. 5 shows he Raman spec a acqui ed on he ac u ed su aces o monoli hic 3YTZP and composi es, in he ange whe e he main e agonal and monoclinic zi conia peaks appea ed (100–800 cm -1 ). The six heo e ically p edic ed Raman peaks o e agonal zi conia [36,53] a 160, 266, 327, 470, 612 and 647 cm -1 we e clea ly de ec ed in all he ac u ed su aces while he wo monoclinic main peaks expec ed o appea a 178 and 189 cm -1 we e no obse ed. The absence o mono- clinic peaks sugges s a null o e y weak -m ans o ma ion du ing c ack p opaga ion. This lack o phase ans o ma ion is ela ed o he ine zi conia g ain size de eloped by SPS [50,54]. I is also consis en wi h he low alues o K IR0. The e o e, he c ack esis ance beha io o he SPS sin e ed composi es de eloped in his wo k is mainly expec ed o be d i en by he g aphene ille s. 3.2.2. F ac u e mechanisms in luenced by GBN ille s F ac u e su aces ea u es a e he SEVNB es s e ealed a combi- na ion o in e - and in ag anula ac u e in all he in es iga ed ma e- ials (Fig. S1 in he Supplemen a y Sec ion). Howe e , he s ongly in e g anula ac u e mode obse ed in 3YTZP/e-GNP composi es may explain he lowe K IR alues, as g ain bounda ies a e a eas mechanically weake han gains whe e c acks can easily p opaga e [55]. In addi ion, as he la e al size o he GBN in as-p epa ed composi es was no ably small, hey p obably did no p o ide signi ican ein o cemen o he 3YTZP ma ix. F ac u ed su aces o composi es con aining e-GNP a e shown in Figs. 6 and 7 and S1. The la e geome y and he smalle size o he e- GNP compa ed o GO is clea ly no iced, co obo a ing wha was p e- iously s a ed in he BSE-SEM images o he Fig. 2. The ac u e su ace oughness inc eases wi h he e-GNP con en (Fig. 6). Thus, al hough he ob ained R-cu e beha io seems o be simila o ha o 3YTZP, he sligh ly lowe K IR alues could be ela ed o e-GNP ha can ac as laws o de ec s a o ing c ack p opaga ion. When inc easing he e-GNP con en , he amoun o nanos uc u es ac ing as laws inc eases, so a dec ease o he ac u e esis ance would be expec ed, as obse ed. Howe e , he composi e wi h 2.5 ol% e-GNP p esen s a simila R-cu e o he one wi h 5 ol% e-GNP, in bo h o ien a ions (Fig. 4b and c). The examina ion o he ac u e su aces o he 5e-GNP┴ and he 5e-GNP || specimens show some ea u es ha could be ela ed o some oughening mechanisms. Se e al sphe ical-shaped oids o c a e s can be ound h oughou he whole ac u e su ace indica ing a lowe ene gy pa h o c ack de lec ion (Figs. 6b and 7a o c). These ea u es can be clea ly ound in bo h o ien a ions o he composi e and also o 10 ol% e-GNP. A close SEM examina ion sugges s ha he e-GNP a e i mly bonded o he zi conia g ains (Fig. 7d), which could induce he c ack o seek a lowe ene gy pa h and de lec . I is, in his case, along he e-GNP-zi - conia in e aces. The sphe ical shape o hese pa hs is no ela ed o po es bu o he dis ibu ion o he e-GNP h oughou he ce amic ma ix since he e-GNP seem o be su ounding some egions o zi conia (Fig. 2). These egions may be ela ed o he p esence o some zi conia agglome a es o med du ing he powde p ocessing s ep. As i can be obse ed in Fig. 7c, he in e ace be ween he e-GNP and he zi conia may be he mos a o able pa h o he c ack o p opaga e. The c ack p opaga es along he weak e-GNP-zi conia bounda ies c ea ing a o uous pa h and a oughe su ace han monoli hic 3YTZP. To he bes o ou knowledge, his is he i s ime ha he sphe ical de lec ion o he c acks is obse ed on ce amic ma ix composi es. Al hough he mic o- scopic obse a ions also e eal he occu ence o he pulling ou o he e- GNP (Fig. 7d), he size o he e-GNP is no enough o p o ide c ack b idging. In Fig. 7c he b anching o he c ack can also be obse ed, howe e he ene gy dissipa ion o hese mechanisms is compa a i ely lowe han he con ibu ion o b idging o he oughening. Thus, lowe c ack esis ance han monoli hic 3YTZP a e ob ained o hese com- posi es. These esul s a e in good ag eemen wi h p e ious wo ks [12, 56] ha epo ed ha he GNP p esen a high esis ance o be pulled ou con ibu ing o he dissipa ion o ene gy associa ed wi h c ack p opa- ga ion by c ea ing a mo e o uous pa h. Fo he composi e wi h 10 ol% e-GNP, he p esence o hese Fig. 5. E alua ion o he e agonal phase by Raman spec oscopy in he ac u e su ace o he composi es and he monoli hic 3YTZP. Do ed and solid lines co espond o he specimens es ed in he pa allel ( || ) and pe pendicula (┴) con igu a ion, espec i ely. C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3493 sphe ical oids is inc eased leading o a e y ough ac u e su ace (Fig. 6c). This sligh ly inc ease in he c ack o uosi y sugges s ha a ce ain small p opaga ion inhibi ion e ec was exe ed by e-GNP. Mo eo e , c ack de lec ion is also e idence in Fig. 7e, as shown by he ab up change in c ack di ec ion. Howe e , he low K IR alues ob ained o his composi e sugges ha he e ec o hese mechanisms o ene gy dissipa ion is coun e balanced by he p esence o mo e e-GNP ha a o he c ack p opaga ion [12]. As in he composi es wi h lowe con en o GNP, he c ack p opaga ion akes place along he GBN-zi conia in- e aces, which gi es a o uous pa h and a oughe su ace han monoli hic 3YTZP bu a lowe c ack esis ance o e all. This would explain also why, despi e he e y low K IR alues o his composi e, i s R-cu e ose e y s eeply a he beginning, o low c ack displacemen s (Fig. 4d). Fu he SEM examina ion o he ac u ed specimens e eals ha he GO laye s in e ac wi h he p opaga ing c acks p o iding di e en mechanisms o enhance he ac u e esis ance o he ma e ial in he pe pendicula o ien a ion. Figs. 6 and 8 shows he ac u e su ace o he 2.5 GO┴ composi e. The p e e en ial o ien a ion o he GO shee s, wi h hei a-b main plane pe pendicula o he SPS p essing axis is clea ly obse ed. Figs. 6 and 8 a e clea examples o he mul iple oughening e en s occu ing as he c ack p opaga es. The phenomena o c ack b anching as expe ienced du ing c ack p opaga ion is highligh ed in Fig. 8a. Figs. 6 and 8b e idences he de lec ion o he c ack when i encoun e s he g aphene plane. The ac ha se e al p o uded GO shee s a e no iced on he ac u e su ace sugges s he pulling ou o he GO shee s, which indica e he po en ial o c ack b idging being in ol ed. I is likely ha c ack b idging is he main sou ce o oughening o he 2.5 GO┴ composi e. The GO shee s also show an undula ion shape ha has been also p oposed as a po en ial ein o cemen mecha- nism [57]. These obse a ions would explain he s ong R-cu e and he high K IR pla eau alue ob ained o his composi e. The e ec o he GO laye s on he enhancemen o he c ack esis ance beha io is signi ican only when hei main a-b plane is pe pendicula ly o ien ed o he plana c ack on . Fig. 6e shows ha he de lec ion o he c ack signi ican ly dec eases when he c ack on is acing he GO laye edges (pa allel o ien a ion). Acco ding o G´ omez-G´ omez e al.[18], he eason o his beha io is he lowe “e ec i e” a ea o g aphene ma e ial in e sec ing he c ack on compa ed o wha happens when he c ack aces he a-b plane o GO. Fig. 6. F ac u e su aces o he monoli hic 3YTZP and he composi es. C. L´ opez-Pe nía e al. Jou nal o he Eu opean Ce amic Socie y 43 (2023) 3486–3497 3494 3.3. Valida ion o he R-cu e de e mina ion by he indi ec compliance me hod As i can be no ed in Fig. 4, he addi ion o a 2.5 ol% GO clea ly modi ies he ac u e beha io o monoli hic 3YTZP in he pe pendicula con igu a ion. I is he s onges R-cu e beha io de eloped in his wo k, wi h he highes K IR imp o emen wi h c ack ex ension and he only one wi h a highe pla eau compa ed o ha o he monoli hic 3YTZP. Fo his eason, he alida ion o he compliance me hod in ob aining he R-cu e o 2.5 GO┴ composi e was assessed. Le us ecall he e ha he compliance me hod can unde es ima e he eal c ack leng h i la ge b idging in e ac ions ope a e du ing he c ack p opaga- ion, in pa icula o la ge c ack ex ensions[58]. This beha io is ela ed o b idging e ec s because a pa ially b idged c ack wi h unb oken ligamen s leads o a highe s i ness o he c acked specimen han a c ack wi hou b idging in e ac ions. Fig. 9a shows he R-cu e ob ained by he di ec op ical measu e- men o he eal c ack leng h on a side su ace o he 2.5 GO┴ es specimen (blue/black ci cles). The R-cu e ob ained by he compliance me hod (g een ci cles) is also included o compa ison as well as he co ec ed one (emp y ci cles). The e olu ion o he compliance (C) wi h he eal c ack leng h i ed o a linea unc ion acco ding o Eq. (2) is shown in Fig. 9b. The ob ained pa ame e B (slope) in his i ing was B eal c ack =(4.0 ±0.3) x10 -4 N -1 . Based on his i ing, he c ack leng h calcula ed by he compliance me hod was co ec ed and hus, he R- cu e ob ained by he indi ec compliance me hod. The compliance calcula ed in a se o samples wi h a i icial c ack leng hs imposed by successi ely e-no ching o he 2.5 GO┴ composi e is also shown in Fig. 7. Sphe ical ea u es ound in bo h (a) pe pendicula and (b) pa allel o ien a ions o he composi e wi h 5 ol% e-GNP. (Comp ession axis du ing SPS is indica ed by yellow a ows). F ac u e su aces e ealing he oughening mechanisms ound in he composi es wi h 5 ol% e-GNP: (c) c ack de lec ion and b anching and (d) e-GNP pull-ou s. (e) Toughening mechanisms ound in he pe pendicula composi e wi h 10 ol% e-GNP. C. L´ opez-Pe nía e al.