S. Sei l e alii, F a u a ed In eg i à S u u ale, 42 (2017) 119-127; DOI: 10.3221/IGF-ESIS.42.13
119
Focused on Mechanical Fa igue o Me als
E alua ion o mixed mode I/II ac u e oughness o
C 50/60 om B azilian disc es
S anisla Sei l, Pe Mia ka
B no Uni e si y o Technology, Facul y o Ci il Enginee ing, Ins i u e o S uc u al Mechanics, Ve eří 331/95, 602 00 B no,
Czech Republic
[email p o ec ed], h p://o cid.o g/0000-0002-4953-4324
[email p o ec ed]
ABSTRACT. Du abili y and sus ainabili y o s uc u es made om conc e e
like ma e ials is ge ing mo e in o an in e es o ci il enginee s. S uc u es a e
subjec ed no only o uniaxial load, his means i he e is a c ack inside he
load could be di ided in o mode I and shea mode II, bu also o a mixed
mode I/II. The e o e, i is necessa y o pe o m es , which co e s mixed
mode loads and could be used o specimen made om conc e e co e-d ill.
Recommended es specimens used o e alua ion o ac u e mechanical
pa ame e s has usually a p isma ic o ec angula shape. The cos o eshaping
cylinde in o ec angula is expensi e and no e y e icien , he e o e i is
e y e ec i e o use B azilian disc es specimen wi h cen al no ch o ob ain
mixed mode ac u e pa ame e s. The con ibu ion deals wi h nume ical
suppo o B azilian disc es o ob ain calib a ion cu es o mode I and
mode II, e alua ion o expe imen al esul s and compa e hem wi h da a
adap ed om li e a u e.
KEYWORDS. F ac u e Mechanics; F ac u e Toughness; Cen ally C acked
B azilian disc; Mixed Mode I/II; Conc e e.
Ci a ion: Sei l, S., Mia ka, P., E alua ion o
mixed mode I/II ac u e oughness o C
50/60 om B azilian disc es , F a u a ed
In eg i à S u u ale, 42 (2017) 119-127.
Recei ed: 12.06.2017
Accep ed: 16.06.2017
Published: 01.10.2017
Copy igh : © 2017 This is an open access
a icle unde he e ms o he CC-BY 4.0,
which pe mi s un es ic ed use, dis ibu ion,
and ep oduc ion in any medium, p o ided
he o iginal au ho and sou ce a e c edi ed.
INTRODUCTION
oday’s ends in ci il enginee ing pushes in es o s and owne s o conc e e s uc u es mo e o en in o eno a ion,
han in o demoli ion o s uc u es. This ac leads in o need o knowledge o ma e ial cha ac e is ics such as bulk
densi y, Young’s modulus o elas ici y [1], comp essi e s eng h [2], lexu al s eng h [3], e c. Some ypes o ci il
enginee ing s uc u es a e subjec ed o mixed mode loading I and II, he e o e he knowledge o ac u e mechanical
pa ame e s is necessa y o p edic li e- ime o conc e e s uc u es (b idges, cooling owe s). To ob ain ma e ial sample
om conside ed s uc u e, a co e-d ill is used, which d ills ou a cylind ical sample om a s uc u e. This specimen is
es ed o ob ain mechanical p ope ies, bu no o ac u e mechanical pa ame e s.
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120
F ac u e mechanical pa ame e s o cemen i ious ma e ials a e usually ob ained om ecommended es s such as:
h ee-poin (3PBT) and ou -poin (4PBT) bending es wi h no ch in es ed specimen [4], o mixed mode load [5], wedge
spli ing es (WST) [6-9], o a combina ion o WST/3PBT [10] and modi ied compac ension es (MCT) [11, 12]. All
es s ha e a p ede ined p isma ic geome y and using hem on specimens made om he co e-d ill is expensi e and no
e y e icien , he e o e i is e y app op ia e o use a B azilian disc es specimen wi h cen al no ch (ci cle cu om he
co e-d ill cylinde ) [13-16] o de e mina e ac u e pa ame e s o building ma e ials see Fig. 1.
Figu e 1: Geome y o a ypical B azilian disc specimen wi h load posi ion alongside c ack.
The main ad an age o B azilian disc is, ha i could be used o in es iga ion o ac u e oughness o mode I, mode II
and mixed mode by o a ing he c acked agains he load posi ions. This a icle compa es he measu ed expe imen al da a
wi h da a p esen ed in [17].
THEORETICAL BACKGROUND
Mechanical p ope ies
he unno ched B azilian disc is e y o en used as an indi ec es o de e mina e ensile s eng h o ock ma e ials,
he e o e i is e y aluable o use i o ob ain ensile s eng h o conc e e [18]. The ensile s eng h can be
e alua ed om ollowing equa ion:
2
P
DB


 (1)
whe e

is ensile s ess, P is comp essi e load, D is diame e o disc and B is specimen’s hickness.
F ac u e Mechanics
This con ibu ion is based on a linea elas ic ac u e mechanics. The linea elas ic ac u e mechanics concep uses he
s ess ield in he close icini y o he c ack ip desc ibed by Williams’s expansion [19]. This expansion is an in ini e powe
se ies o iginally de i ed o a homogenous elas ic iso opic c acked body, which can be desc ibed by a ollowing equa ion:
,() () (,)
III
III
i j ij ij ij
KK
O



 
(2)
whe e

ij ep esen s he s ess enso componen s, KI, KII is he s ess in ensi y ac o o mode I espec i ely mode II, Iij,
IIij, a e known shape unc ions o mode I and mode II, Oij ep esen s highe o de e ms and , θ a e he pola
coo dina es (wi h o igin a he c ack ip; c ack aces lie along he x-axis).
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121
The alues o he s ess in ensi y ac o (SIF) o a ini e specimen and he pola angle θ = 0° can be exp essed in he
ollowing o m [20-22]:
(/ , )
II
Pa
K aR
RB


 (3)
(/ , )
II II
Pa
K aR
RB


 (4)
whe e P is comp essi e load, a is a c ack leng h, R is adius o he disc (D/2), B is disc hickness and I(a/R, ), II(a/R, )
a e dimensionless shape unc ions (calib a ion cu es) o mode I and mode II, see Figs. 2 and 3.
NUMERICAL MODEL
Calib a ion cu es
o ob ain igh calib a ion cu es o each mode o SIF a nume ical simula ion was necessa y. The nume ical
simula ion was pe o med in ini e elemen (FE) so wa e Ansys 17.2 [23]. A wo-dimensional (2D) nume ical
model wi h plane s ain bounda y condi ion we e used o calcula e SIF (KI and KII). The nume ical model was
meshed wi h elemen ype PLANE183 aken om ANSYS’s elemen s lib a y and command KSCON was used o ake
in o accoun he c ack ip singula i y. Inpu ma e ial p ope ies o conc e e used in FE so wa e a e ollowing: Young’s
modulus and Possion’s a io, E = 40 GPa and ν = 0.2, espec i ely. The geome y o disc has adius R = 50 mm and he
ela i e c ack leng h a/R a ied om <0.1; 0.9>, no ch angle α a ied <0°; 90°> and was loaded wi h cons an o ce P =
100 N in all calcula ed cases.
In FE so wa e ANSYS, he ollowing equa ions a e used o calcula ion o he SIF KI and KII o θ = ±180.
2
21
I
G
K



 (5)
2
21
II
u
G
K



 (6)
whe e u, a e nodal displacemen s, G shea modulus,

is Koloso ’s cons an o plane s ain espec i ely plane s ess
condi ions and is coo dina e in cylind ical coo dina e sys em. F om B azilian disc geome y, men ion abo e a calib a ion
cu es o mode I and II o a ious no ch angle  and a/R a io can be de e mined as a ollowing unc ions [25, 26]:
(/ , ) 1
I
I
KRB a
aR R
Pa



(7)
(/ , ) 1
II
II
KRB a
aR R
Pa



(8)
F om Fig. 2, i can be no iced, ha o some angle  and a/R, he alue o calib a ion cu e o mode I equals ze o
( I(a/R,) = 0). This means, ha he e is only mode II (pu e shea mode). The e o e, he ac u e oughness o mode II
could be e alua ed.
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122
Figu e 2: Calib a ion cu e I(a/R,) o mode I.
Figu e 3: Calib a ion cu e II(a/R, α) o mode II.
EXPERIMENT FOR MATERIAL C 50/60
Ma e ial
a e ial used in he expe imen al p og am was s anda d conc e e C 50/60, maximum agg ega e size was 8 mm.
Specimen’s geome y
B azilian disc specimens we e p epa ed om s anda dized cylind ical specimens used o e alua ion o cylind ical
comp essi e s eng h o conc e e [2]. No ches we e p epa ed by using wa e je cu e . The dimensions o specimens a e
in oduced in Tabs. 1 and 2.
Specimen nm . Diame e D
[mm]
Thickness B
[mm]
04 150 28.59
05 150 30.52
06 150 29.90
Table 1: Dimensions o B azilian disc specimens.
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123
Specimen nm . a/R [-] Diame e D
[mm]
Thickness B
[mm]
No ch
leng h a
[mm]
05_4 0.2667 150 31.83 40.06
09_4 0.2667 150 30.68 40.00
04_4 0.2667 150 31.65 40.09
09_6 0.4 150 29.93 60.17
01_6 0.4 150 31.44 60.92
04_6 0.4 150 30.97 60.15
07_6 0.4 150 31.17 59.94
Table 2: Dimensions o B azilian disc specimens wi h a cen e no ch.
Expe imen al p ocedu e
The machine o es s was Seidne D7940 wi h maximum loading capaci y 4 000 kN. The load a e was 0.01 kN/s.
B azilian disc specimens wi hou no ch we e es ed o ob ain he ensile s eng h.
B azilian disc specimens wi h he no ch we e es ed unde he selec ed angles inclined agains loading posi ions see Tab. 3.
Figu e 4: Example o specimens used o B azilian disc es wi hou and wi h no ch
Specimen nm . a/R [-] Inclina ion
angle  [°]
05_4 0.2667 0.0
09_4 0.2667 10.0
04_4 0.2667 27.2
09_6 0.4 0.0
01_6 0.4 0.0
04_6 0.4 10
07_6 0.4 25.2
Table 3: The ela i e leng h o no ch in B azilian disc specimens and angle o used angle posi ion.

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124
RESULTS AND DISCUSSION
Selec ed ma e ial and mechanical p ope ies
nno ched B azilian disc specimens we e subjec ed o comp essi e load o e alua e ensile s eng h om Eq. 1.
The measu ed o ces and calcula ed ensile s eng h a e showed in Tab. 4.
Specimen nm . Measu ed
o ce P [kN]
Tensile
s eng h
[MPa]
04 34.9 5.18
05 38.8 5.39
06 35.7 5.06
Table 4: Measu ed o ces and calcula ed ensile s eng h om eq. (1) o unno ched B azilian disc.
The p ope ies o used conc e e a e compa ed wi h ma e ial cha ac e is ics o mo a and conc e e om Hou [17], o
de ailed in o ma ion abou composi ion o hese ma e ials see [17]. Compa ison o selec ed mechanical p ope ies is
showed in Tab. 5.
Bulk
densi y ρ
[kgm-3]
Comp essi e
s eng h c
[MPa]
Tensile
s eng h
[MPa]
Mo a om [17] 2018 25.56 3.6
Conc e e [17] 2373 34.42 3.1
Conc e e – p esen s udy 2321 55.4 5.21
Table 5: Compa ison o selec ed mechanical cha ac e is ics o used conc e e wi h da a adap ed om li e a u e [17]
F ac u e mechanical p ope ies
F ac u e mechanical p ope ies o s uc u al conc e e we e e alua ed om Eq. (2) and (3). The alues o s ess in ensi y
ac o s we e e alua ed o mode I (specimens 05_4,09_6 and 01_6), o mode II (specimens 04_4 and 07_6) and o
mixed mode I/II. The e alua ed ac u e mechanical p ope ies a e summed up in Tab. 6.
Specimen nm . Measu ed
o ce P [kN]
KI
[MPamm1/2]
KII
[MPamm1/2]
05_4 26.8 38.069 0.0006
09_4 24.3 30.513 25.906
04_4 25.2 0.0466 54.604
09_6 19.6 36.858 0.0012
01_6 20.0 35.784 0.0012
04_6 17.7 26.104 25.337
07_6 15.8 0.005 44.9745
Table 6: Measu ed expe imen al load P and calcula ed ac u e mechanical pa ame e s KI and KII o each specimen.
U
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125
Figu e 5: Compa ison o ac u e esis ance KII/KIC (y axis) agains KI/KIC (x axis) beha io wi h da a om li e a u e [17].
Compa ison o expe imen al da a
Expe imen al esul s om Hou [17] we e digi alized and measu ed o ces we e used o be compa ed wi h da a measu ed
in he p esen ed s udy. The compa ison o esul s is done in wo ways. The i s one compa es ac u e esis ance alues
o KII/KIIC (y axis) agains KI/KIC (x axis) which is aluable o see pu e mode I and pu e mode II ac u e esis ance. An
en elope cu e (a ci cle wi h adius KI/KIC = 1 and KII/KIIC = 1) is plo ed in Fig. 5. o see e ec o mixed mode I/II
ailu e o each es ed specimen (di e en inclina ion angle  o no ch).
The compa ison made in Fig. 4. is no e y o en, he e o e i is being necessa y o made compa ison which can be usually
seen in li e a u e. Fig. 5 compa es no ma i e alues o KII/KIC (y axis) agains KI/KIC (x axis) which is aluable o see mode
II e ec s ac u e esis ance. An en elope cu e (an ellipse wi h adius KII/KIC = mean alue and KI/KIC = 1) is plo ed in
Fig. 6. o see e ec o mixed mode ailu e o each es ed specimen (di e en inclina ion angle o no ch).
Figu e 6: Compa ison o ac u e esis ance KII/KIC (y axis) agains KI/KIC (x axis) beha io wi h da a om li e a u e [17].
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126
CONCLUSIONS
he p esen pape aims a analyzing he mixed mode ac u e in a conc e e C50/60 using he B azilian disc es . A
ini e elemen analysis o B azilian disc specimen, e ec s o c ack angle o a ion a e s udied based ac u e
mechanic app oach. The ollowing p incipal conclusions could be de i ed:
 The classical solu ions o Linea Elas ici y o he s ess ields in he neighbo hood o a c ack ip in pu e mode I
o II can be ob ained independen ly
 The solu ion o he s ess ield in a combined mode si ua ion is ob ained simply by o a ion o a ini ia ion c ack.
 Expe imen ally ob ain da a o C 50/60 is compa ed wi h da a om li e a u e.
The p esen ed nume ical calcula ion and expe imen al esul s (C 50/60) will be used o u u e wo-pa ame e ac u e
e alua ion on alkali ac i a ed conc e e [27, 28].
ACKNOWLEDGMENT
his pape has been wo ked ou unde he “Na ional Sus ainabili y P og amme I” p ojec “AdMaS UP – Ad anced
Ma e ials, S uc u es and Technologies” (No. LO1408) suppo ed by he Minis y o Educa ion, You h and Spo s
o he Czech Republic.
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