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This is an Accep ed Manusc ip o an a icle published by Else ie in
Composi es Science and Technology, Vol. 158, on Feb ua y 2018, a ailable a :
h ps://doi.o g/10.1016/j.compsci ech.2017.12.009
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Mic oscopical obse a ions o in e - ib e ailu e unde ension
Elena Co ea, Ma ía Inmaculada Val e de, Ma ía Luisa Velasco, Fede ico Pa ís
Depa amen o de Mecánica de Medios Con inuos y Teo ía de Es uc u as, G upo de Elas icidad
y Resis encia de Ma e iales, Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa,
Camino de los Descub imien os s/n, 41092, Se illa, España
Abs ac
The nume ical s udy o he in e - ib e ailu e a mic omechanical le el p edic s he appea ance
o di e en s ages in he de elopmen o his damage mechanism; hese s udies ha e also
allowed he main ea u es o each s age (such as he in e acial debond leng h and he kinking
angle) o be iden i ied.
The de elopmen o expe imen al s udies aiming o check he ele ance o he
a o emen ioned nume ical esul s is c ucial. Based on his, his esea ch ocused on he ensile
es unde di e en loading le els o specimens manu ac u ed om ca bon-epoxy c oss-ply
symme ical lamina es. The mic oscopic obse a ion o he 90º laye s leads o he analysis o
he appea ance o he ans e se c acks as a unc ion o he load, he iden i ica ion o he
p e iously nume ically p edic ed s ages o he mechanism o damage, he measu emen o key
pa ame e s and he e alua ion o he in luence o nea by ib es. A clea connec ion be ween
he nume ical and expe imen al esul s has been ound.
Keywo ds: debonding; ans e se c acking; op ical mic oscopy; c oss-ply.
A.1. In oduc ion
Ma ix/In e - ib e ailu e a ises in plies subjec ed o ans e se loads, being cha ac e is ic,
among o he s, o 90° plies belonging o c oss-ply lamina es subjec ed o loads pa allel o hei
0° plies.
P e ious nume ical s udies allowed he iden i ica ion o h ee main s ages in he mechanism o
damage a mic omechanical le el, Figu e A.1. In pa icula , in he case o ensile loads (Pa ís e
al [1]), damage ini ia es wi h he appea ance o small debonds a he ib e-ma ix in e aces
aligned wi h he applied load (S age I); hese debonds g ow uns ably in Mixed Mode along he
in e aces un il eaching an ex ension (semi-debonding angle,

d) o 60°-70° (S age II); a his
posi ion, a change o s able g ow h in pu e Mode II akes place (caused by he appea ance o a
physically ele an con ac zone a he c ack ip), a ou ing he kinking o he c ack owa ds
he ma ix (S age III). The c ack inally p opaga es along he ma ix (uns ably and in Mode I)
ollowing he di ec ion pe pendicula o he load applied. The coalescence o his ype o
c acks coming om di e en ib es gi es ise o ans e se mac o-c acks in he ply, e en ually
leading o i s ca as ophic ailu e.
Figu e A.1. S ages o he mechanism o damage. Pa ís e al [1].
The e ec ha he p esence o a seconda y load (Pa ís e al [2], Co ea e al [3]) has on he
e olu ion o hese s ages, he conside a ion o he mal esidual cu ing s esses (Co ea e al
[4]), and he case o cyclic loading (Co ea e al [5]), ha e also been s udied nume ically. The
impo an ole ha mic omechanical s udies can play in helping i s in he unde s anding o
he mechanism o ailu e and second in e i ying and p oposing ailu e c i e ia was poin ou in
hese wo ks. In pa icula , his ou s anding ques ion was deeply analysed in Pa ís [6]. A
common pa e n o hese s udies is he usage o a single ib e (assumed isola ed) Bounda y
Elemen model. Mo e ecen wo ks, ocusing on S age II o he mechanism o damage, also
include a la ge numbe o ib es, see o ins ance Sandino e al [7] ( wo- ib es models), Tá a a
e al [8] ( en- ib es models) and Tá a a e al [9] (one hund ed- ib es models). FEA has also
been used o s udy his p oblem; see o ins ance Hojo e al [10], Kushch e al [11] y Sai o e al
[12].
A his poin , i u ns ou c ucial o check, by means o expe imen al s udies, he alidi y o he
esul s de i ed om he nume ical models, speci ically, by means o mic oscopic obse a ion
o es ed samples.
P e ious wo ks om di e en au ho s ocusing on he expe imen al mic omechanical
obse a ion o he ma ix ailu e can be ound in he li e a u e; among hem i can be s ood
ou he al eady classical wo ks by Zhang e al [13] (single ib e es s unde ension) and
Gams ed and Sjög en [14] (based on Zhang bu s udying he e ec o cyclic load), and also
hose om Sai o e al [15] (analysing he e ec o he 90º ply hickness in c oss ply lamina es),
Ba al e al [16] (s udying he e ec o he ib e ype), Hobbieb unken e al [17] (compa ing he
beha iou be ween high and low cu ing empe a u e esins in h ee poin s bending es s) o
STAGE I
a
≈10º

d=60-70º
STAGE II STAGE III
Genz e al [18] (e alua ing he p esence o he mal esidual s esses).
In he p esen wo k, an op ical mic oscope is used o obse e he 90 plies o c oss-ply
specimens es ed unde longi udinal ensile load (which will be hus ans e se o he 90
plies), in o de o check i he nume ically p edic ed mic omechanical s ages o he
ma ix/in e - ib e ailu e a e in ac p esen and can be dis inguished. The iden i ica ion o he
di e ences ha hese s ages show in eal lamina es wi h a high ib e olume con en e sus
he nume ical single (and isola ed) ib e models, is also pu sued. In addi ion, he measu emen
o he inal ex ension o he c ack a he in e ace ha gi es ise o he kinking owa ds he
ma ix (

d= 60-70, om he nume ical models), as well as he s udy o he di e en damage
ypologies, he analysis o he in luence o he applied loading le el and he e ec o he
p esence o neighbou ing ib es, a e also objec i es o he s udy.
A.2. Coupons manu ac u ing and es ing
[03,903]s ensile coupons we e manu ac u ed om ca bon-epoxy (AS4-8552) p e-p eg,
ein o cing hei ends wi h glass-epoxy abs. Thei dimensions a e de ailed in Figu e B.2.
Figu e A.2. Coupons dimensions.
A i s se o 5 coupons was selec ed o es ing unde ension. The esul s p o ided by he
ensile s eng h (X) show a mean alue o 942.47 MPa, a s anda d de ia ion o 41.25 MPa and
a a ia ion coe icien o 4.38%, he e o e implying an excellen esul in e ms o dispe sion.
Subsequen es ing campaigns we e pe o med unde maximum loads lowe han he
p e iously measu ed X, in o de o gene a e damage in he 90 plies wi hou eaching he
ca as ophic ailu e o he whole lamina e.
In pa icula , he loads applied can be g ouped in 5 le els: 80%X, 60%X, 40%X, 30%X and
20%X. The numbe and denomina ion o he coupons es ed as well as he exac loading le el
applied a e included in Table A.1.
Table A.1. Denomina ion o he coupons and co esponding es ing load.
Coupons denomina ion
Tes ing load (%X)
80-1
84.2
80-2
82
60-1
62.4
60-2
59.5
60-3
60.5
40-1
42.6
40-2
40.3
40-3
39.2
30-1
31.5
30-2
29
30-3
27.6
20-1
21
A.3. P epa a ion o samples
The cen al pa o he specimens was cu in wo hal es o app oxima ely 28 mm leng h; each
pai was encapsula ed in esin (using he Ve soCi -2 ki ). A e ha , he samples we e polished
using Saphi 20 polishe (au oma ic head and p og ammable) om NEURTEK Ins umen s,
LaboDose liquide dispense and LaboPol-5 as pe iphe al polishe om S ue s.
The esul o he polishing p ocess mus allow he ib es co esponding o he 90 plies o be
clea ly obse ed in an op ical mic oscope a 1000x magni ica ion. A sui able polishing p ocess
should also a oid he appea ance o ma ks ha could in e e e in he la e mic oscopical
inspec ion. To his pa icula end, a speci ic polishing p ocess was designed and es ed,
consis ing o ou s eps. 40N p essu e and 50 pm speed a e selec ed o all s eps, he disc
ype, e ige a o liquid and ime used a e de ailed nex :
S ep 1: Disc: SiC #320. Liquide: Wa e . Time: 5’.
S ep 2: Disc: MD-La go. Liquide: DiaP o Alleg o/La go 9 μm (2). Time: 6’.
S ep 3: Disc: MD-Dac. Liquide: DiaP o Dac 3 μm (1). Time: 5’.
S ep 4: Disc: MD-Dac. Liquide: DiaP o Nap B1 1 μm (3). Time: 4’.
A.4. Mic oscopic obse a ion
Once he samples ha e been polished he mic oscopic inspec ion is unde aken. The e is a
double objec i e he e: i s , using low magni ica ion (25x), he analysis o he appea ance o
ans e se c acks in he 90 plies as a unc ion o he load applied. Second, he s ages o he
mechanism o damage p e iously iden i ied by he nume ical models wan o be de ec ed,
along wi h he expe imen al alues o hei main pa ame e s; o his end, obse a ion a high
magni ica ion (500x and 1000x) is equi ed.
A.4.1. Inspec ion a low magni ica ion
A i s inspec ion is made a 25x in o de o coun he numbe o ans e se mac o-c acks ha
appea s in each specimen, and hus i s loading le el dependence.
In Table A.2 he numbe o c acks obse ed pe cm in each coupon is de ailed. The mos
ele an conclusion is ha o loads lowe han 30%X no ans e se mac o-c acks a e obse ed
in he samples. A la e inspec ion a g ea e magni ica ion will also show, Sec ion A.4.2, ha no
damage o any ype is de ec ed below his loading le el. I is also obse ed ha he numbe o
c acks encoun e ed inc eases as he loading le el does. No ice in any case he educed numbe
o samples chosen o he lowes loading le els.
Table A.2. Numbe o mac o-c acks as a unc ion o he loading le el.

%X
Numbe o mac o-c acks/cm
84.2
9
82
9.2
62.4
6.4
59.5
4
60.5
3.6
42.6
3.5
40.3
1.2
39.2
0.8
31.5
2.3
29
0
27.6
0
21
0
Al hough no being di ec ly he objec i e o his pape , making use o he Classical Lamina e
Theo y (CLT) and selec ing a sui able ailu e c i e ion i is possible o p edic he s ess
associa ed wi h i s -ply ailu e (XFPF). Then, i is in e es ing a his poin o check i he lowes
s ess alue o which damage has been de ec ed in he ma e ial (31.5%X in his case, see
Table A.2) is accu a ely p edic ed by he Lamina e Theo y in combina ion wi h ailu e c i e ia.
To his end, a selec ion o ailu e c i e ia (Maximum S ess, Tsai-Hill (Azzi and Tsai [19]), Tsai-
Wu [20], Maximum S ain, Hashin [21], Hashin and Ro em [22] and Puck [23]) has been
pe o med, and hei XFPF p edic ions calcula ed, see Table A.3.
Table 3. Fi s -ply and ul ima e ailu e p edic ions o a selec ion o ailu e c i e ia.
Failu e C i e ion
XFPF (MPa)
XUF (MPa)
XFPF/XUF (%)
Maximum S ess
374.4
1112.9
33.6
Tsai-Hill
374.1
1109.5
33.7
Tsai-Wu
368.1
1149.1
32.0
Maximum S ain
367.2
1124.6
32.7
Hashin
374.4
1112.9
33.6
Hashin-Ro em
374.4
1112.9
33.6
Puck
374.4
1113.8
33.6
Fi s o all, i can be obse ed ha all ailu e c i e ia show simila p edic ions wi h a mean
alue o 372 MPa. This alue can be compa ed wi h he lowes expe imen al load o which
ans e se c acks a e obse ed, 31.5%X in his case, which co esponds o a s ess alue o 297
MPa. Taking in o accoun ha he numbe o coupons included in he 30%-40%X g oup is small
(see Table A.2) and also ha all o hem show a e y educed numbe o ans e se c acks, a
good ag eemen be ween he analy ical p edic ion and he expe imen al esul is ound.
The appea ance o he i s c ack a a alue lowe han ha p edic ed by he c i e ia o he
ailu e o he ply is, on he o he hand, a e y cohe en ac , as he appea ance o one
ans e se c ack does no mean he o al ailu e o he ply. The appea ance o ans e se
c acks in a 90 ply is a con inuous (no sudden) phenomenon, and i can be checked ha (as
men ioned abo e), o he i s ply ailu e p edic ed by he c i e ia, only a e y educed
numbe o c acks appea in he specimen, his ac no implying a signi ican educ ion in he
con ibu ion o he 90 ply o he p ope ies and pe o mance o he lamina e.
Ano he in e es ing ea u e a ises when using he CLT o also p edic he s ess associa ed wi h
he ul ima e ailu e (XUF) and hen o calcula e he a io be ween XFPF and XUF (Table A.3), i.e.
using only he analy ical ool o e alua e a which pe cen age o he analy ical ul ima e s ess
he heo y p edic s he ini ia ion o damage. This calcula ion o XUF has been pe o med by
means o a p og essi e damage model, using a deg ada ion coe icien D equal o 0.1 ha ac s
on all ma e ial p ope ies bu jus sligh ly in his pa icula case due o i s small alue.
The esul s show again simila p edic ions o all c i e ia and an app oxima e alue o 33%XUF is
ob ained o XFPF. An excellen ag eemen is ound now be ween his p edic ion and he
expe imen al esul , as he i s ans e se c acks we e de ec ed a 31.5%X.
The obse a ion o he 25x mic og aphs shows some ele an di e ences be ween he
di e en loading le els, in pa icula :
1) Specimens es ed a 20%X (see Figu e A.3a as an example):
No damage is de ec ed.
2) Specimens es ed a 30%X (see Figu eA.3b as an example):
Jus a ew and e y hin ans e se c acks a e ound in one specimen. A educed
numbe o delamina ions be ween 90º and 0º plies a e p esen .
3) Specimens es ed a 40%X (see Figu e A.3c as an example):
Some ans e se c acks a e ound al hough hey appea like hin lines in he
mic oscope. Delamina ions be ween 90º and 0º plies a e p esen .
4) Specimens es ed a 60%X (see Figu e A.3d as an example):
Many and well de ined ans e se c acks a e ound. Some c acks show a pa h de ia ed
om he ans e se di ec ion. Delamina ions be ween 90 and 0 plies a e de ec ed.
5) Specimens es ed a 80%X (see Figu e A.3e as an example):
Many and well de ined ans e se c acks a e ound (mo e han in he p e ious case).
Mos o hem appea like hick lines a he mic oscope, which is associa ed wi h a
clea ly de eloped damage and p obably wi h a signi ican opening o he c ack lips.
Mo e de ia ed c acks a e obse ed. Delamina ions be ween 90 and 0 plies a e also
de ec ed.
I should be ema ked ha he h ough hickness c ack loca ion does no show a
p e e en ial pa e n, which seems o be in acco dance wi h CLT p edic ions (assuming
he 90 ply as homogeneous) and also wi h he ou comes o a ecen nume ical s udy
by he au ho s (modeling he 90º ply as he e ogeneous and dis inguishing be ween
ib es and ma ix), Pa ís e al [24].
(a)
(b)
(c)
(d)
(e)
Figu e A.3. 25x mic og aphy om (a) 20-1 specimen, (b) 30-1 specimen, (c) 40-1 specimen, (d)
60-1 specimen, (e) 80-2 specimen.
A.4.2. Inspec ion a high magni ica ion
The inspec ion o he samples using a g ea e magni ica ion is nex pe o med in o de o y
o expe imen ally iden i y he di e en phases o he mechanism o damage nume ically
p edic ed in [1] (Figu e A.1); in pa icula , he occu ence o S ages I, II and III, hei connec ion
wi h he loading le el as well as he measu emen o speci ic pa ame e s ele an o he
de elopmen o he mechanism o damage, a e pu sued.
Indeed, he obse a ion o samples a high magni ica ion exposes he appea ance o all s ages
o he ailu e mechanism (I, II and III, Figu e A.1) o loading le els highe han 30%X.
Speci ically, damage appea s in clea ly less quan i y in he 30%X g oup, maximizing i s
appea ance in he 60%X g oup (p obably associa ed wi h he ac ha in he 80%X g oup
isola ed s ages disappea o ming a g ea e numbe o mac o-c acks). Figu e A.4 shows 1000x
images o S ages I and II (a), and S age III (b). No ice ha he nominal ib e adius is 3.56 m,
use ul as scale e e ence o Figu e A.4 and he o hcoming Figu es A.5, A.7, A.8 and A.9.
(a)
(b)
(c)
Figu e A.4. 1000x mic og aphies o : (a) S ages I and II (30%X), (b) S age III (40%X), (c) Aligned
debonds (40%X).
I is necessa y o ema k ha i is no possible o dis inguish be ween S ages I and II wi h he
a ailable ools because, among o he hings, i is no nume ically clea i a eal sepa a ion
be ween bo h s ages exis s. The uns able cha ac e o he mechanism o ailu e and he
dependence o he ini ia ion o ailu e on he p ope ies o he in e ace (in pa icula on he
ac u e oughness) a e some o he ea u es ha poin i as an open ques ion. The mo e
ecen publica ions on Fini e F ac u e Mechanics (Man ič [25], Man ič and Ga cía [26]) s udy in
dep h his p oblem.
Wi h e e ence o S age II, i is common o ind he debonds a his s age e y close o a eas
whe e mac o-c acks al eady exis , al hough a low loading le els hey a e also de ec ed as
isola ed, a om hese a eas. The S age II debonds o en appea aligned in high ib e densi y
zones, so ha he pa h ollowed by he u u e mac o-c ack can be en isaged, Figu e A.4c. No
e y equen ly, ib es wi h bi-la e al debonds a e obse ed (Figu e A.5a) al hough cu en ly
bo h debonds do no p esen he same ex ension and hus, no simul aneous g ow h is
deduced. The exis ence o hese bi-la e al debonds can be also obse ed in mac o-c acks,
Figu e A.5b; in hese cases he bi-la e al debond seems o appea when he ib e is placed in
he middle o he pa h o he mac o-c ack.
(a)
(b)
Figu e A.5. 1000x mic og aphies o bi-la e al debonds (a) a S age II (60%X), (b) in mac o-c acks
(60%X).
Re e ing o S age III, se e al kinking pa hs addi ional o he nume ical heo e ical one ha e
been iden i ied using he mic oscope. Figu e A.6 shows all ypologies ound, ha ing been
named as de ailed: A. Theo e ical, B.1. De ia ed +, B.2. De ia ed –, C. Bila e ally angen ial, D.
G adual ansi ion and E. Spli ing.
STAGE I
STAGE II
STAGE III
[20] S.W. Tsai, E.M. Wu, J. Comp. Ma . 5 (1971) 58-80.
[21] Z. Hashin, Failu e c i e ia o unidi ec ional ibe composi es, J Appl. Mech. 47 (1980) 329-
334.
[22] Z. Hashin, A. Ro em, A a igue ailu e c i e ion o ibe ein o ced ma e ials, J. Comp. Ma .
7 (1973) 448-464.
[23] A. Puck, Fes igkei analyse on Fase -Ma ix-Lamina en, Modelle ü die P axis (S eng h
analysis o ib e-ma ix/lamina es, models o design p ac ice), Ca l Hanse Ve lag, Munich,
1996.
[24] F. Pa ís, M.L. Velasco, E. Co ea, Mic omechanical s udy o he in luence o scale e ec in
he i s s age o damage in composi es, Compos. Sci. Technol. submi ed o publica ion.
[25] V. Man ič, In e ace c ack onse a a ci cula cylind ical inclusion unde a emo e
ans e se ension. Applica ion o a coupled s ess and ene gy c i e ion, In . J. Solids S uc .
46(6) (2009) 1287–1304.
[26] V. Man ič, I.G. Ga cía, C ack onse and g ow h a he ib e–ma ix in e ace unde a
emo e biaxial ans e se load. Applica ion o a coupled s ess and ene gy c i e ion, In . J.
Solids S uc . 49(17) (2012) 2273–2290.
[27] E. Co ea, F. Pa ís F, V. Man ič, E ec o ic ion on in e - ib e ailu e unde ension a
mic omechanical le el, 2nd ECCOMAS Thema ic Con e ence on he Mechanical Response o
Composi es, Impe ial College, London, 2009.