Evaluation of tensile properties in in-plane auxetic carbon/epoxy and carbon-glass/epoxy composite laminates

O iginal Manusc ip
Jou nal o Composi e Ma e ials
2025, Vol. 0(0) 1–13
© The Au ho (s) 2025
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DOI: 10.1177/00219983251323881
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E alua ion o ensile p ope ies in in-plane
auxe ic ca bon/epoxy and ca bon-glass/
epoxy composi e lamina es
C is iano Veloso
1,2
, Ca los Mo a
1,2
, Fe nando Cunha
1,2
, Jose Sousa
1
, Gus a o Dias
3
,
B aian U ibe
3
and Raul Fanguei o
1,4
Abs ac
Auxe ic lamina es, i.e. wi h a nega i e Poisson’s a io (NPR), show g ea enginee ing p omise, wi h enhancemen s in shea
esis ance, ac u e oughness, ene gy abso p ion, and delamina ion and damage ex ension limi a ion. This s udy ocuses on
he ensile p ope ies o in-plane (IP) NPR fib e- ein o ced polyme (FRP) lamina es, namely ca bon/epoxy (C/E) and
ca bon-glass/epoxy (C-G/E) lamina es, wi h lay-up sequences which maximised he e ec . An analy ical s udy was con-
duc ed o achie e maximum NPR sequences. Lamina es we e manu ac u ed ia hand lay-up and ho comp ession moulding
echniques. Poisson’s a ios o 0.33 and 0.18 we e achie ed o C/E and C-G/E IP auxe ic lay-ups, espec i ely. A 72%
educ ion in longi udinal s i ness be ween he maximum IP NPR and a unidi ec ional (UD) lay-up sequence was e ified,
wi h a u he educ ion o 24% om he C/E o he C-G/E auxe ic configu a ions due o less aniso opy om G/E plies.
Rega ding longi udinal s eng h, maximum IP NPR sequences showed low ailu e s eng hs, wi h a educ ion om
1213 MPa in he UD case, o 209 MPa in he s udied C/E lamina es. An al e na i e design sequence was s udied analy ically
wi h he inco po a ion o 0° laye s in he auxe ic sequences, which imp o ed s i ness, albei a a educ ion o IP auxe ici y.
Fu he esea ch is ecommended o explo e al e na i e auxe ic lay-up sequences o s udy he influence on s i ness,
s eng h, and auxe ic enhancemen s.
Keywo ds
Auxe ici y, composi e lamina e, me ama e ial, Poisson’s a io
In oduc ion
Composi e ma e ials ha e long been a ea u e among he
highes le els o enginee ing, especially wi h he con inuous
ma u a ion o associa ed cha ac e isa ion, manu ac u ing
and ce ifica ion echnologies and sys ems. Thei excellen
specific p ope ies - namely s i ness and s eng h
1
- enable
he educ ion o weigh o a gi en s uc u e, a ac o o
pa icula impo ance in he mobili y sec o , as weigh
sa ing allows o a dec eased need o ene gy esou ces.
One o he mos commonly used ypes o composi e
ma e ials e e s o he lamina e o m, in which se e al fib e
ab ic plies a e bonded by a ma ix. Fib e- ein o ced
polyme s (FRP), such as ca bon/epoxy (C/E), glass/
epoxy (G/E) o a amid/epoxy (A/E), a e widely applied
in high-end enginee ing componen s, such as in he case o
he ae onau ic and ae ospace sec o s. Albei hei desi able
specific s eng h and s i ness, wo main issues ain FRP
lamina e pe o mance: hei low he mal esis ance, and
hei low ou -o -plane (OOP) p ope ies due o he absence
o ein o cemen in he hickness di ec ion. The la e e-
mains a p oblem o he indus y, as such lamina es o e
1
Fib enamics –Ins i u e o Inno a ion in Fibe -based Ma e ials and
Composi es, Uni e si y o Minho, Guima ães, Po ugal
2
Beyondcomposi e - Composi e Enginee ing Solu ions, Maia, Po ugal
3
IPC —Ins i u e o Polyme s and Composi es, Uni e si y o Minho,
Guima ães, Po ugal
4
Depa emen o Tex ile Enginee ing, Uni e si y o Minho, Guima ães,
Po ugal
Co esponding au ho :
C is iano Veloso, Fib enamics –Ins i u e o Inno a ion in Fibe -based
Ma e ials and Composi es, Campus de Azu ´
em, Uni e si y o Minho, 4800-
058 Guima ães, B aga, Po ugal.
Email: [email p o ec ed]
Da a A ailabili y S a emen included a he end o he a icle
sub-op imal low- eloci y impac (LVI) esis ance, leading
o inc eased suscep ibili y o he ini ia ion and p opaga ion
o ba ely isible impac damage (BVID), unde he o m o
delamina ion, i.e. he sepa a ion o wo bonded plies o
dis inc fib e o ien a ion, ha is ha d o de ec and ha can
amoun o up o 50% educ ions in he lamina e’s s eng h.
Fo e e ence, LVI is a e y common occu ence wi hin he
ae ospace indus y, pe aining impac s usually unde 10 m/s
which a e no domina ed by s ess wa e p opaga ion
h ough he ma e ial, bu a he by elas ic ene gy abso p-
ion.
2
Such impac s can occu du ing manu ac u ing - o
example, due o ool d ops o componen mishandling -
anspo a ion, s o age, ins alla ion, and in ope a ion -
hails one s ikes, low- eloci y bi d s ikes, unway deb is,
and belly-landing ope a ions o fixed-wing o o unmanned
ae ial ehicles (UAVs).
2–7
The a ea o me ama e ials (MMs), i.e. syn he ic com-
posi e ma e ials/s uc u es ha dispose o p ope ies a ely
ound in na u e, has g own in ecen imes, wi h he de-
elopmen o in e es ing solu ions o enginee ing p oblems
ela ing o he mal, acous ic, elec omagne ic and me-
chanical cases.
8,9
A dis up i e sec ion wi hin mechanical
me ama e ials (MMMs) ela es o auxe ic mechanical
me ama e ials (AuxMMMs). Auxe ics p esen a unique
capaci y o synch onous o hogonal comp ession o dila ion
- nega i e Poisson’s a io (NPR) - ha ansla es in p ope y
enhancemen s on shea s i ness, ac u e oughness, in-
den a ion and impac esis ance.
10
AuxMMMs can be
u he di ided in o h ee main g oups, wi h he fi s con-
ce ning la ice s uc u es wi h specific s i ma e ial pa e ns
capable o auxe ic beha iou unde loading.
11–15
The sec-
ond g oup e e s o he inclusion o an inhe en ly auxe ic
elemen - ei he ma ix, fib e o bo h - in he
me ama e ial.
16,17
The in e sec ion be ween AuxMMMs
and composi e lamina es esul s in auxe ic lamina es, he
final ca ego y wi hin AuxMMMs, ha includes auxe ic
composi e lamina es cons i u ed by con en ional, i.e. pos-
i i e Poisson’s a io, fib e(s) and ma ix.
Auxe ic beha iou is mainly a unc ion o he s uc u al
a angemen o plies in a gi en composi e lay-up. Unidi-
ec ional (UD) fib e laminae a e key o he defini ion o an
auxe ic lay-up sequence. Ne e heless, ma e ial p ope ies,
namely aniso opy - E
x
/E
y
and E
x
/G
xy
a ios, wi h Eand Gas
he Young’s and shea moduli, espec i ely, ollowing he
axis sys em se in Figu e 1 - unlocks his beha iou and
allows o he achie emen o la ge NPR. The adop ed
designa ion o local lamina (x
1
-x
2
-x
3
, o 1-2-3, wi h x
1
as
he fib e di ec ion) and global lamina e axis sys em o his
ex is depic ed in Figu e 1.
Auxe ic lamina es a e ca ego ized, in acco dance o he
NPR plane, as in-plane (IP) - o NPR on he ace plane o
he lamina e (ν
xy
) - o h ough- he- hickness (TTT) - o
NPR along he hickness plane (ν
xz
and ν
yz
). These lamina es
dispose o an in insic de o ma ion mechanism, due o hei
NPR and d i en by ex ension-shea coupling, in which,
du ing impac , a local ma e ial densifica ion occu s di ec ly
unde he impac ed a ea as he ma e ial flows owa ds i .
Due o hese mechanisms, he li e a u e in he a ea epo s
imp o ed impac , shea and a igue esis ance in hese
lamina es.
7,17–22
Rega ding IP NPR, some esea ch has ocused on he
elas ic p ope ies o C/E IP auxe ic lamina es, ei he by
analy ical o expe imen al means. Table 1 displays a sho
summa y o he analysed p ope ies, wi h Table 2 exhibi ing
IP auxe ic and e e ence alues o longi udinal s eng h,
XT
, and s ain- o- ailu e, εT
x.
In his pape , he elas ic and ailu e ensile p ope ies o
C/E and ca bon-glass/epoxy (C-G/E) IP auxe ic lay-ups
ha e been analysed. This e alua ion is an impo an s ep
o he applica ion o IP auxe ic sequences in componen s
which sus ain LVI and a e p one o delamina ion damage, as
he unde s anding o he ensile p ope ies is ele an wi h
ega ds o s i ness, s eng h and o he aspec s o mechanical
design beyond impac esis ance. The la ges NPR yielding
C/E and C-G/E - cons i u ed by T300 ca bon and E-glass
fib es, and SR8500 epoxy esin - lay-up sequences we e
selec ed om a pool o analy ically s udied bidi ec ional
ð½ðθ1=θ2ÞnSÞlay-ups
1
symme ic a chi ec u e.
Two e e ence g oups, wi h espec o UD C/E and G/E
lamina es, we e selec ed o compa ison and o alida ion
he selec ed p ope ies o fib es and esin, based on li e -
a u e. As o he IP NPR g oups, a C/E g oup was in e ed as
a di ec compa ison o he C/E con ol g oup. The hyb id
C-G/E IP NPR g oup p esen s a di ec compa ison agains
he C/E auxe ic g oup, o e i y he e ec o he inse ion o
G/E plies in he lamina es. Mo eo e , o his poin , no
li e a u e has expe imen ally e ified he e ec o hyb id-
isa ion in auxe ici y o lamina es. Ca bon and glass hy-
b idisa ion is commonly applied and is ele an in he
enginee ing wo ld, hus i s me ge wi h he auxe ic domain
could p o e beneficial.
Tensile es s we e conduc ed acco ding o he ISO 527-
4 s anda d a a eloci y o 2 mm/min, using ideo-
ex ensome y echniques o he asse ion o s ains ε
x
and
ε
y
. An e alua ion o elas ic longi udinal and ans e se
p ope ies, and concu en ly, o longi udinal and an e se
ensile s eng hs, XT
and YT
, and o longi udinal and
ans e se s ain- o- ailu e, εT
x and εT
y, is pe o med.
This s udy in ends o p o ide, hus, an o e iew in o he
ensile beha iou o C/E and C-G/E bidi ec ional lamina es
wi h maximum IP NPR, and o analyse any possible
d awbacks inhe en o his auxe ic design s a egy.
Me hodology
The me hodology employed o his s udy can be di ided in
ma e ial selec ion, defini ion o composi e lay-up a chi ec u e,
2Jou nal o Composi e Ma e ials 0(0)
he analy ical in e ence on he maximiza ion o IP NPR,
composi e lay-up p oduc ion and disc e iza ion o ensile es
pa ame e s. Each o hese opics is desc ibed in he subsequen
subsec ions.
Ma e ial selec ion
Two dis inc fibe ypes, ca bon and glass, we e selec ed
based on hei cos -e ec i eness and enginee ing signifi-
cance. The fib e ab ics we e chosen o mee he p e-
de e mined condi ions o achie ing NPR, specifically
equi ing UD ab ics. Fo ca bon, a T300-fib e 12K UD
ab ic wi h an a eal weigh o 320 g/m
2
, supplied by Re-
belco, was selec ed. Fo glass, an E-glass UD ab ic wi h an
a eal weigh o 640 g/m
2
, p o ided by Sae ex, was used.
The espec i e fib e p ope ies a e displayed in Table 3,as
e e enced by Soden e al..
31
Wi h ega ds o he ma ix, his esea ch ocused on
he mose ing esins, namely epoxies. The esin sys em
chosen o his s udy was supplied by Sicomin -
SR8500 esin and SZ8525 ha dene . The adop ed p ope ies
o his sys em a e shown in Table 4, based on supplie
ecommenda ions and alues om Soden e al.
31
.
Defini ion o composi e lay-up a chi ec u e
Fou dis inc g oups we e defined o s udy, wi h he e -
e encing scheme p esen ed in Table 5. This scheme con-
sis ed o wo con ol g oups, one o each ab ic ype, wi h a
ull UD lay-up o ca bon ( e e ence K) and glass ( e e ence
Table 1. Elas ic p ope ies o C/E IP auxe ic lamina es ound in li e a u e.
Lead au ho Ma e ial Lay-up sequence ν
xy
E
x
(GPa) E
y
(GPa) G
xy
(GPa)
M. Miki
23
T300/5208 [(14°/62°)
n
]
s
0.380 ———
R. Zhang
24
T300/5208 [(15°/62.5°)
n
]
s
0.326 ———
M. Shok ieh
25
T300/5208 [(15°)
2
/(60°)
1
]0.354 ———
J. Donoghue
18
AS4/3501-6 [0°/15°/75°/15°]
s
0.134 63.4 27.2 6.29
C. Goncal es
26
G afil 34-700/CR83 [0°/15°/75°/15°]
s
0.120 53.4 ——
W. Lin
27
IM7/8552 [15°/65°/15°/65°/15°]
2
0.410 52.1 25.5 6.16
Table 2. Tensile ailu e p ope ies o C/E IP auxe ic lamina es, and espec i e con ol g oups, ound in li e a u e.
Lead au ho Ma e ial Lay-up sequence ν
xy
XT
(MPa) εT
x (%)
C. Goncal es
26
G afil 34-700/CR83 [0°/15°/75°/15°]
s
0.120 468 1.08
[0°]
8
0.330 1172 1.16
W. Lin
28
IM7/8552 [15°/65°/15°/65°/15°] 0.410 306 0.61
[35°/60°/ 5°/60°/35°] 0.134 567 1.04
Figu e 1. Adop ed di ec ion no a ion.
Veloso e al. 3
L). Two mo e g oups we e defined o IP NPR lay-ups, one
o C/E lamina es - e e ence A - and one o hyb id C-G/E
lamina es - e e ence B. Ano he e e ence was conside ed
o glass/epoxy (G/E) IP NPR lamina es, howe e , as
discussed subsequen ly, he analy ical analysis de eloped
showed no esul s o auxe ici y in such lamina es. Con ol
g oups we e defined as UD, in his s udy, mainly in o de o
con ol he elas ic p ope ies calcula ed analy ically in he
subsequen sec ions, and o in e on he p ope ies selec ed
om Tables 3 and 4.
The fib e olume ac ion,
,wasdefined a his s age,
based on alues in cu en use in he ae ospace indus y.
Ha ka ie al.
32
poin ed an in e al o
2[65;80] %, wi h
he selec ion o his s udy alling on he lowe limi in
o de o maximize NPR.
29
Mo eo e , o G/E plies, his
ela ion was u he dec eased o 60% o he same
pu pose, o maximize NPR in he hyb id e e ence while
main aining simila p ocessing condi ions as o hose in
C/E e e ences.
The lay-up sequence was specified as bidi ec ional, in
acco dance o he a o emen ioned li e a u e on he opic
which indica ed ha his sequence yields he maximum
NPR e ec .
22
The ollowing subsec ion desc ibes he
employed analy ical me hodology o asse he mos auxe ic
sequences o C/E and C-G/E specimens wi h he e e enced
fib es and esin sys em, based on he possible domain o
bidi ec ional symme ic lay-ups - ð½ðθ1=θ2ÞnSÞ.
Addi ionally, o he case o hyb id sequences, no only he
fib e angle o each ply has o be defined, bu also he espec i e
ma e ial. The o al numbe o laminae, N
L
, was es ic ed o a
mul iple o 8 in o de o allow o a co ec ma ch be ween
angle and hyb id ma e ial lay-up sequences. The numbe o
plies o NPR e e ences was se as 16 acco dingly, and a
ma e ial configu a ion o ½ððM1Þ2=ðM2Þ2ÞNL=8swas adop ed,
wi h M
1
and M
2
e e encing each possible ma e ial o a gi en
ply, which in his case e e s o G/E and C/E plies, espec i ely.
This ma e ial configu a ion was selec ed in o de o simpli y
he combined e ec o ply angle and ma e ial o his s udy -
wo plies o G/E o each bidi ec ional angle combina ion,
ollowed by wo plies o C/E. A isual ep esen a ion o he
hyb id lay-up scheme is shown in Figu e 2.
Analy ical elas ic cons an p edic ion
A p elimina y e alua ion o auxe ic beha iou in C/E T300/
8500, G/E E-glass/8500 and C-G/E T300+E-glass/
8500 ð½ðθ1=θ2ÞnSÞlamina es was pe o med in a compu a-
ionalalgo i hmde elopedinMATLAB,basedonamic oand
mac omechanics analysis o a lamina e.
29
The mic omechanics
sec ion conce ns he defini ion o nine elas ic lamina cons an s
(E
1
,E
2
,E
3
,G
12
,G
13
,G
23
,ν
12
,ν
13
and ν
23
) and hei inse ion
on a o mula ion o e ec i e p ope ies es ima ed using
Maxwell’s me hodology.
30
Mac omechanics –a he lamina e
le el –makes use o he Classical Lamina ion Theo y (CLT)
and 3D cons i u i e equa ions, calcula ing E
x
,E
y
,G
xy
,ν
xy
and
ν
xz
, wi h ma e ial in a ian s and geome ic ac o s ele an o
he calcula ion o he ex ensional s i ness ma ix o each
lamina e.
The calcula ed lamina p ope ies o a
o 65%, in C/E
laminae, and 60%, in G/E laminae, a e displayed in Table 6.
As no ed in he In oduc ion, he e is a la ge disc epancy in
aniso opy be ween C/E and G/E plies (E
1
/E
2
), indica ing a
la ge p edisposi ion o he de elopmen o NPR in
C/E-based lamina es.
Da a in Table 6 se ed as inpu o he mac omechanics
module. The algo i hm was se o he calcula ion o all
possible bidi ec ional symme ic ð½ðθ1=θ2ÞnsÞlamina es,
wi h a θin he ange o [-90°;90°] in 0.1° in e als, ac-
coun ing o 3243601 i e a ions o each ma e ial combina-
ion. Fo C-G/E lamina es, a ma e ial (M) lay-up sequence o
½ððM1Þ2=ðM2Þ2ÞNL=8swas employed. The esul s, pe aining
he la ges auxe ic IP configu a ions, a e p esen ed in Table 7.
No IN NPR was achie ed in G/E lamina es. Mo eo e , he e
is a no iceable dec ease in he la ges ν
xy
o C-G/E lamina es
due o he inse ion o less aniso opic G/E plies. A simila
end can be obse ed o E
x
.
Table 3. T300 and gene ic E-glass fib e (subsc ip ) elas ic
p ope ies.
31
Fib e ype T300 E-glass
Densi y, ρ(g/cm
3
) 1.76 2.54
Longi udinal modulus, E 1(GPa) 230 74
T ans e se modulus, E 2(GPa) 15 74
IP shea modulus, G 12 (GPa) 15 30.8
Majo Poisson’s a io, ν 12 0.2 0.2
OOP shea modulus, G 23 (GPa) 7 30.8
Table 4. SR8500/SZ8525 adop ed ma ix (subsc ip m)
mechanical p ope ies.
Resin/ha dene SR8500/SZ8525
Densi y, ρ(g/cm
3
) 1.12
Elas ic modulus, E
m
(GPa) 3.15
Shea modulus, G
m
(GPa) 1.17
Majo Poisson’s a io, ν
m
0.35
Table 5. Tensile specimen e e ence scheme.
Re e ence Ma e ial G oup
A C/E (ca bon/epoxy) IP NPR
B C-G/E (ca bon-glass/epoxy) IP NPR
K C/E (ca bon/epoxy) UD Con ol
L G/E (glass/epoxy) UD Con ol
4Jou nal o Composi e Ma e ials 0(0)
Fu he mo e, and compa ing IP C/E NPR lamina es wi h
he UD case p e iously p esen ed in Table 6, he e is a
dec ease in E
x
and inc ease o G
xy
due o he necessa y
o ien a ion ply angles o he maximiza ion o IP NPR.
F om hese analy ical esul s, he auxe ic e e ences, in
acco dance o Table 5, we e selec ed. The C/E IP NPR
e e ence A was defined as a ½ð14°=64°Þnslay-up, while o
he C-G/E IP NPR e e ence B, he selec ed lay-up sequence
was ½ð15°=69°Þns(Table 8).
Composi e lay-up p oduc ion
The ou indica ed e e ences shown in Table 5 we e
manu ac u ed in he o m o pla es using hand lay-up and
ho comp ession moulding echniques. The o e all p ocess
consis ed on he hand lay-up placemen and imp egna ion o
angled plies - acco ding o each lay-up sequence - using he
SR8500/SZ8525 esin/ha dene sys em a a 4:1 weigh a io.
In he case o con ol e e ences, hese we e used mainly o
p ope y con ol, and hus 8 plies we e u ilised in o de o
p omo e ailu e a lowe ensile loads, gi en maximum load
limi a ions in he used ensile es machine (de ailed in he
subsequen sec ion). Fo IP NPR g oups, 16 plies we e
applied o each lamina e.
Each o hese pla es was la e cu ed by ho comp ession
moulding a a empe a u e o 110°Cdu ing 10 min, in a
Fon jine LabManual 300 p ess. P essu e was con olled in
o de o achie e he a o emen ioned 65% fib e olume
ac ion alue o he lamina es - beside he 60% a ge o
he G/E lamina e. This a ge was no achie ed - alues we e
sligh ly lowe , see Table 8 - howe e his did no com-
p omise he emainde o he s udy, as no la ge disc ep-
ancies o he a ge and be ween e e ences we e e ified,
and as he co esponding adjus ed elas ic p ope ies we e
calcula ed om he analy ical algo i hm.
Pla es we e cu o specimen size in acco dance wi h he
ISO 527-4 s anda d (250 mm × 25 mm). Fo IP NPR
e e ences, addi ional specimens we e cu in he ans e se
di ec ion o measu emen o ans e se lamina e p ope ies.
Figu e 2. Adop ed hyb id lay-up angle and ma e ial scheme.
Table 6. Ma e ial p ope ies o T300/8500 and E-glass/8500 laminae.
Lamina ma e ial E-glass/8500 (
= 0.60) T300/8500 (
= 0.65)
E
1
(GPa) 45.7 151
E
2
(GPa) 10.5 7.98
G
12
(GPa) 4.10 4.10
ν
12
0.252 0.248
ν
21
0.0576 0.0131
ν
13
0.252 0.248
ν
23
0.442 0.331
Table 7. La ges IP NPR yielding configu a ions o T300/8500 C/E and T300+E-glass/8500 C-G/E bidi ec ional symme ic ½ðθ1=θ2Þns
lamina es.
Ma e ial νxymin ½ðθ1=θ2ÞnsE
x
(GPa) E
y
(GPa) G
xy
(GPa) ν
xz
T300/8500 0.412 ½ð14:0°=63:6°Þns46.1 22.7 5.69 0.498
T300+E-glass/8500 0.196 ½ð15:1°=68:6°Þns36.2 26.9 5.55 0.480
Table 8. Disc e iza ion o ensile es ed e e ences.
Re e ence Ma e ial Configu a ion G oup
L
(mm)
A C/E ½ð14°=64°Þ4sIP NPR 0.61 4.64 ± 0.04
B C-G/E ½ð15°=69°Þ4sIP NPR 0.58 4.06 ± 0.07
K C/E [0°]
8
UD Con ol 0.61 2.24 ± 0.03
L G/E [0°]
8
UD Con ol 0.58 2.18 ± 0.03
Veloso e al. 5

[0°/90°]
3
G/E unbe eled end abs we e applied a e su ace
sanding, wi h a leng h o 75 mm, in o de o p e en slipping
du ing ensile es ing. Fo his, he ma ix/ha dene com-
bina ion SR G eenpoxy 33/SZ 8525 was applied, wi h
simila p ope ies o he SR8500 esin bu wi h a oom
empe a u e cu ing p ocess o app oxima ely 7 h.
Tensile es pa ame e s
Tensile expe imen s we e conduc ed on a MTS Exceed E45
ensile es ing machine p epa ed o ca y ou measu emen s
using ideoex ensome y echniques wi h an MTS AVX-205
came a, wi h a esolu ion o 0.25 μm and a maximum
cap u e a e o 30 Hz (Figu e 3). As a o emen ioned, he
s anda d ISO 527-4 was employed, wi h a es ing eloci y o
2 mm/min. A load cell o 100 kN was used, wi h an ac-
cu acy o ± 0.5% o applied o ce. Fo IP NPR e e ences,
wo dis inc ensile es s we e conduc ed in he axial and
ans e se di ec ions. Fo each e e ence and specimen
o ien a ion, a o al o fi e specimens we e es ed. The no-
mencla u e, fib e olume ac ion, and hickness (
L
, wi h
subsc ip L e e ing o he lamina e) o he es ed specimen
g oups is p esen ed in Table 5.
Videoex ensome y- ela ed p epa a ions included coa -
ing he specimens wi h ma e sp ay, and he ma king o wo
poin s xand ydi ec ions, each a an 8 mm dis ance o he
cen eline, o aling a 16 mm gauge leng h o he i ual
ex ensome e s.
Fo ce da a was ead e e y on a 5 Hz equency, while ε
x
and ε
y
we e measu ed wi h a 20 Hz equency. Da a was e-
sampled in o de o accommoda e his disc epancy, o he
lowes da a eading equency in he sys em ( o ce). σ
x
-ε
x
,
σ
y
-ε
y
and ν
xy
-σ
x
ela ionships, XT
and YT
ensile s eng h,
and εT
x and εT
y s ain- o- ailu e we e compu ed om he
p ocessed da a.
E
x
and E
y
we e e ie ed om a linea cu e fi in he
elas ic loading po ion o he espec i e σ
x
-ε
x
and σ
y
-ε
y
specimen g aphs.
As o ν
xy
p edic ions, he p esen ed expe imen al alues
we e calcula ed aking in o accoun he a e age wi hin a
selec ed egion o he elas ic domain, as he e was, in some
cases, a conside able a ia ion o ν
xy
wi h he inc ease o σ
x
,
as p e iously deno ed in a s udy by Zhang e al.
33
. Al hough
in his s udy a 100 MPa baseline o νmeasu emen was
defined, he a e aged me hod was p e e ed o his s udy
gi en he a ia ion o his p ope y, in o de o p o ide a
eliable alue, in acco dance wi h he ν
xy
-σ
x
beha iou .
Mo eo e , he ini ial phase o he elas ic domain was
neglec ed o he calcula ion o he a e age ν
xy
due o an
un easonable amoun o noise da a. This ini ial a ia ion can
be a ibu ed o he accommoda ion o he G/E end ab
in e ace o he machine’s g ips. Due o ope a ional limi s,
he ull specimen’s end ab leng h could no be g ipped,
leading o he non-g ipped leng h e en ually “opening up”
and sepa a ing om he specimen du ing he ials, which
caused ini ial ins abili y in he da a. Ne e heless, he e-
maining g ipped leng h emained bonded and p e en ed
slippage.
Resul s
Tables 9 and 10 display p edic ed and expe imen al alues
o he longi udinal and ans e se elas ic modulus, E
x
and E
y
espec i ely. Mo eo e , longi udinal - XT
and εT
x - ailu e
p ope ies a e exhibi ed o he es ed configu a ions, and
ans e se - YT
and εT
y - ailu e p ope ies a e shown o IP
NPR e e ences. All he p edic ed alues p esen ed he ein
we e calcula ed using he a o emen ioned MATLAB al-
go i hm, aking in o accoun adjus ed
alues o each
g oup, in acco dance o hose shown in Table 8.
2
UD con ol g oups K and L p esen ed e y good
ag eemen wi h p edic ed E
x
alues. Wi h ega ds o IP NPR
g oups A and B, an o e es ima ion o longi udinal s i ness
was e idenced by he expe imen al esul s, a end epea ed
in he ans e se analysis o E
y
.
Figu e 4 po ays a ba cha o E
x
o he es ed g oups.
Figu es 5 and 6 ep esen he s ess-s ain beha iou in he
longi udinal and ans e se di ec ions, espec i ely. Com-
pa ing g oups K and A, he e is a educ ion in he longi-
udinal s i ness o auxe ic C/E IP specimens compa ing o
he UD case o 72%, om 141 GPa o 39 GPa, jus ified by
he C/E ply o ien a ions - a 14° and 64° - equi ed o
maximise he auxe ic e ec , which p omo es said educ ion.
Al hough he ans e se s i ness, E
y
, was no measu ed
expe imen ally o con ol g oups, i is expec ed o inc ease
in he C/E IP NPR g oup compa ed o he UD case (as
obse ed by he p edic ions indica ed in Tables 6 and 7).
Mo eo e , as expec ed, a educ ion in E
x
o 24% was
e ified om he C/E o he C-G/E IP NPR g oups A and B,
om 39 GPa o 30 GPa, due o he inclusion o less s i G/E
plies, when compa ed o C/E ones.
Rega ding longi udinal ensile s eng h, XT
, i is, as
expec ed, lowe in UD G/E - a 660 MPa - han in UD C/E
lamina es - a 1.21 GPa. Con e sely, he less aniso opic
na u e o glass fib es allow o la ge s ain- o- ailu e
alues, εT
x. Rega ding IP NPR g oups, an impo an end
was e ie ed om da a: hei s eng h capaci y in he
longi udinal di ec ion is much lowe han in he con ol
g oups. While in he case o he UD C/E con ol g oup his
alue si s a 1.21 GPa, i d ops o 209 MPa in he IP NPR
C/E g oup, educing o 204 MPa o he IP NPR C-G/E
g oup.
These findings co obo a e wi h hose o he limi ed
esea ch on he a ea. A ecen s udy conduc ed by Lin and
Wang, in which an IP auxe ic configu a ion was compa ed
agains a non-auxe ic a ian wi h ma ched elas ic moduli,
6Jou nal o Composi e Ma e ials 0(0)
also e ified low s eng h p ope ies in IM7/977-3 C/E IP
auxe ic lamina es.
28
The au ho s compa ed an IP auxe ic
lay-up sequence - [15°/65°/15°/65°/15°], wi h a ν
xy
o 0.410 - o a ma ched-moduli sequence wi h a posi i e
IP Poisson’s a io (see Table 2). A dec ease in he ul ima e
ensile s eng h o IP NPR specimens was confi med, om
567 MPa o 306 MPa, coupled wi h lowe s ain- o- ailu e
alues (1.04% s 0.61%, espec i ely, bo h ep esen ing a
educ ion o a 1.61% ailu e s ain in he UD case). Ano he
s udy by Goncal es e al., using G afil 34-700/CR83 C/E
lamina es, compa ed he ensile p ope ies o an IP auxe ic
configu a ion, [0°/15°/75°/15°]
s
, o an UD coun e pa
Table 9. P edic ed and expe imen al longi udinal elas ic modulus, E
x
, and expe imen al longi udinal ensile s eng h, XT
, and s ain- o-
ailu e, εT
x, o he es ed configu a ion g oups.
Specimen g oup
E
x
(GPa)
XT
(MPa) εT
x (%)P edic ed Expe imen al
A (C/E IP NPR) 43.11 39.51 ± 1.93 208.8 ± 6.1 0.8622 ± 0.1615
B (C-G/E IP NPR) 33.46 29.93 ± 1.98 204.3 ± 3.4 1.051 ± 0.137
K (C/E UD) 141.5 141.3 ± 6.0 1213 ± 138 0.8961 ± 0.0495
L (G/E UD) 44.26 44.39 ± 3.47 660.3 ± 33.6 1.589 ± 0.065
Figu e 3. MTS Exceed E45 ensile es ing machine wi h AVX-205 came a.
Veloso e al. 7
(Table 2). Bo h he ul ima e longi udinal ensile s eng h,
and he s ain- o- a io, we e lowe in he IP NPR lay-up, a
468 MPa e sus 1172 MPa, and a 1.08% e sus 1.16 %,
espec i ely. Thus, he lay-up configu a ion equi ed o he
maximisa ion o IP auxe ici y a ec s i s longi udinal ensile
s eng h capabili ies nega i ely.
Figu e 7 shows he pos -mo em samples o each
g oup. Fo specimens in which ailu e occu ed, he ailu e
plane ollowed fib e di ec ion, as weak esin- ich planes a e
de eloped in be ween fib e bundles wi h he inc easing
elonga ion o he specimen, hence enabling he de elop-
men o ailu e planes in such a eas. In UD C/E and G/E
specimens o g oup K and L, 0° o ien a ion c acks a e
isible, wi h in e nal delamina ion. Fo he con ol C-G/E
g oup, se e e fib e b eakage o he op G/E plies was
e ified. Fo IP NPR specimens, a c ack is obse able along
he angle o he op ply.
I should also be no ed ha he na u e o he
T300 ca bon and E-glass ab ic fixa ion - wi h e enly
spaced we ya ns - c ea es a p elude condi ion o he
o ma ion o ailu e planes: as a ious ca bon o glass
bundles a e g ouped by such we ya ns, a small gap
be ween such bundles can become mo e e iden wi h
ab ic handling, and can be solely filled by esin du ing
imp egna ion, c ea ing a local weak poin ha a ou s he
de elopmen o ailu e planes and ha can a ec s eng h
p ope ies, especially in lamina es ha do no possess 0° -
o be e sus ain he applied load in he axial di ec ion - o
90° laye s.
Wi h ega ds o IP NPR esul s, Table 11 p esen s p e-
dic ed and expe imen al ν
xy
o he es ed configu a ions.
Figu e 8 displays he espec i e ba cha s.
Table 10. P edic ed and expe imen al ans e se elas ic modulus, E
y
, and expe imen al ans e se ensile s eng h, YT
, and s ain- o-
ailu e, εT
y, o he es ed configu a ion g oups.
Specimen g oup
E
y
(GPa)
YT
(MPa) εT
y (%)P edic ed Expe imen al
A (C/E IP NPR) 23.15 21.57 ± 1.29 125.2 ± 7.3 1.520 ± 0.078
B (C-G/E IP NPR) 27.32 23.36 ± 2.65 139.5 ± 2.2 1.174 ± 0.207
Figu e 4. Expe imen al longi udinal elas ic modulus, E
x
, ba
cha s o g oups A (C/E IP NPR), B (C-G/E IP NPR), K (C/E UD)
and L (G/E UD).
Figu e 5. Longi udinal s ess–s ain cu es o g oups A (C/E IP
NPR), B (C-G/E IP NPR), K (C/E UD) and L (G/E UD).
Figu e 6. T ans e se s ess–s ain cu es o g oups A (C/E IP
NPR) and B (C-G/E IP NPR).
8Jou nal o Composi e Ma e ials 0(0)
Da a e idences a la ge disc epancy be p edic ed and
expe imen al alues o ν
xy
, when compa ed o he p e ious
E
x
analysis. The p edic ions o UD specimens p esen a
conside able de ia ion o he expe imen ally ob ained
alues. This end was also e ified o g oup A, wi h he
closes p edic ion ela ing o he one o g oup B. Mo eo e ,
IP auxe ici y was o e es ima ed wi h he p edic ed alues.
Ne e heless, auxe ici y was expe imen ally achie ed o
bo h IP NPR g oups, as isible in Figu e 9, po aying he
s able domain o he ν
xy
-σ
x
ela ionship o g oups A and
B. A sligh inc ease in auxe ici y was e ified o IP NPR
g oups wi h inc easing σ
x
in he elas ic egion: as he
specimens we e con inuously s e ched in he longi udinal
ensile di ec ion, an inc ease in ans e se de o ma ion
ensued, enabled by he mo emen o he ab ic plies wi hin
he duc ile ma ix caused by he ex ension-shea coupling
e ec cha ac e is ic o such lamina es. Addi ionally, and as
expec ed, IP auxe ici y educes in magni ude wi h he in-
se ion o G/E plies, due o hei low aniso opy.
Figu e 9, displaying he s able domain o he ν
xy
-σ
x
ela ionship o UD g oups K and L, e idences an in-
c ease o ν
xy
wi h inc easing σ
x
in UD C/E specimens,
especially pos he 300 MPa ma k, wi h he ela ionship
emaining almos cons an in he case o UD G/E
specimens (Figu e 10).
Figu e 7. Failu e planes o es ed specimen configu a ions A (C/E IP NPR), B (C-G/E IP NPR), K (C/E UD) and L (G/E UD).
Table 11. P edic ed and expe imen al IP Poisson’s a io, ν
xy
,o
he es ed configu a ion g oups.
Specimen g oup
ν
xy
P edic ed Expe imen al
A (C/E IP NPR) 0.4150 0.3328 ± 0.0241
B (C-G/E IP NPR) 0.2013 0.1793 ± 0.0383
K (C/E UD) 0.2540 0.3408 ± 0.0760
L (G/E UD) 0.2544 0.3311 ± 0.0208
Figu e 8. Expe imen al IP Poisson’s a io, ν
xy
, ba cha s o he A
(C/E IP NPR), B (C-G/E IP NPR), K (C/E UD) and L (G/E UD)
g oups.
Veloso e al. 9