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

Abstract

This work addresses the crack growth resistance of 3 mol% Yttria-doped Tetragonal Zirconia Polycrystalline (3YTZP) spark-plasma sintered (SPS) composites containing two types of graphene-based nanomaterials (GBN): exfoliated graphene nanoplatelets (e-GNP) and reduced graphene oxide (rGO). The crack growth resistance of the composites is assessed by means of their R-Curve behavior determined by three-point bending tests on single edge “V” notched beams (SEVNB), in two different orientations of the samples: with the crack path perpendicular or parallel to the pressure axis during the SPS sintering. The sharp edge notches were machined by ultrashort laser pulsed ablation (UPLA). The compliance and optical-based methods for evaluating the crack length are compared on the basis of the experimental R-Curve results in composites with 2.5 vol% rGO tested in the perpendicular orientation. Moreover, the activation of reinforcement mechanisms is evaluated by both the fracture surface inspection by Scanning Electron Microscopy and a compliance analysis. It is shown that the indirect compliance method is relevant and reliable for calculating the R-Curve of 3YTZP/GBN composites. The effect of the type and content of GBN on the crack growth resistance of the composites is also discussed.

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

Author: López Pernía, Cristina; Muñoz Ferreiro, Carmen; Prada Rodrigo, J.; Moreno, P.; Reveron, H.; Chevalier, J.; Morales Rodríguez, Ana; Poyato Galán, Rosalía; Gallardo López, Ángela María
Publisher: Elsevier
Year: 2023
DOI: 10.1016/j.jeurceramsoc.2023.02.002
Source: https://idus.us.es/bitstreams/c71e657c-ce80-44c7-9f64-65b31ff63606/download
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.