T8 COMATCOMP 09 967
Th ee dimensional ini e elemen model o a non-c imp
ab ic lamina ed using geome ically s aigh ows
wi h c imped ma e ial p ope ies
L.M. Fe ei a
Depa amen o de Engenha ia Mecânica. Escola Supe io de Tecnologia de Ab an es do
Ins i u o Poli écnico de Toma , Po ugal
E. G aciani, F. Pa ís
G upo de Elas icidad y Resis encia de Ma e iales. Escuela Técnica Supe io de
Ingenie os de la Uni e sidad de Se illa, España
ABSTRACT
The comp essi e ailu e o a [0,90]
n
non-c imp ab ic lamina e is s udied using a 3D
ini e elemen model o he ep esen a i e uni cell a mesoscopic scale. In p e ious
analyses, ow elemen s coo dina e sys ems we e o ien ed in he ac ual di ec ion o he
ib es. The e o e, he same ans e sely iso opic mechanical beha iou was employed
o e e y ow elemen (de ined in he elemen coo dina e sys em). A new app oach is
p esen ed in his wo k, in which he geome ical c imp o he ows is neglec ed and
s aigh ows a e c ea ed. The ac ual c imp o he ib es is conside ed by in oducing
sui able aniso opic ma e ial p ope ies in each zone o he ow. Aniso opic p ope ies
ha e been ob ained by a o a ion o he ac ual ans e sely iso opic mechanical
beha iou , aking in o accoun he ac ual o ien a ion o he c imped ib es. This
app oach equi es a la ge amoun o wo k o de ine he ma e ial p ope ies bu , on he
con a y, he mesh can be easily c ea ed o any con igu a ion. Resul s ob ained wi h he
new app oach (i.e., he ‘s aigh ows’ model) ha e been success ully compa ed wi h
hose o he p e ious analyses (i.e., he ‘c imped ows’ model).
1. INTRODUCCIÓN
Non c imp ab ic (NCF) composi es ha e a complica ed in e nal s uc u e which a ec s
he pe o mance o he NCF composi es, depending on he load scena io. I is hen
app op ia e o de elop a nume ical model o a NCF composi e p io o expe imen al
cha ac e iza ion, in o de o unde s and he in luence o a signi ican numbe o
pa ame e s ( o example, esin and ib e p ope ies, in e nal geome y,…), in he elas ic
beha iou o he lamina e and in he mechanisms o ailu e.
A ull 3D ini e elemen model, wi h a new app oach in he de ini ion o he c imp, has
been de eloped o p edic he ailu e mechanism unde comp essi e loads.
2. MESOSCOPIC APPROACH OF THE NCF
The p esen s udy has been made a he mesoscopic le el. Tows ha e been modelled as a
homogenous ma e ial (wi hou conside ing hei mic oscopic cons i uen s: esin and
ib es). Di e en aniso opic p ope ies (de ined in he global coo dina e sys em) ha e
been employed in he di e en zones o he ows, ob ained by a o a ion o he
ans e sely iso opic mechanical beha iou , aking in o accoun he ac ual o ien a ion o
T8 COMATCOMP 09 968
he c imped ib es. Resin pocke s ha e been modelled as a homogeneous iso opic
ma e ial occupying he spaces be ween he ows.
The analysis has been made unde he hypo hesis o la ge displacemen s (using ANSYS
so wa e) and he load has been applied in a linea and p og essi e manne , un il
ins abili y is eached. Linea elas ic ma e ial beha iou has been conside ed.
2.1 Desc ip ion o he 3D FEM
To p esen he model analyzed in his s udy i is necessa y o de ine he concep o he
ep esen a i e olume elemen (RVE). I is a minimum epea able cell which allows us
o build any pa o he non-c imp ab ic composi e by s acking mul iple RVE. Due o
he symme y o he RVE, only one qua e RVE has been conside ed. The p ocess o
ob ain he RVE, as well as he model analysed, is ep esen ed in Figu e 1.
Comp essed
NCF lamina e
X
Y
ZX
Y
Z
Th ough hickness
subdomain
RVE o he NCF
model s udied
Fig. 1. P ocess o ob ain he RVE and he analysed model.
2.2 Mechanical p ope ies o he ows and esin
S uc u al solid elemen (SOLID185) wi h aniso opic beha iou in global coo dina e
sys em has been employed. The mechanical p ope ies conside ed co espond o a
T300/914 composi e wi h a 55% olume ic ib e ac ion, simila o he one used by
D apie and Wisnom (1999) and G aciani e al. (2005). The mechanical p ope ies o
esin and ows in a local coo dina e sys em a e p esen ed in Tables 1 and 2. In he ows,
di ec ion 1 is he ib e di ec ion, and di ec ions 2 and 3 a e he ans e se di ec ions.
P ope ies Value P ope ies Value
11
E
129 GPa
m
E
4.5 GPa
3322
EE =
9.77 GPa
m
ν
0.4
1312
νν
=
0.32
23
ν
0.45
23
G
1.5 GPa
Table 2. Resin’s ma e ial cons an s.
Table 1. Tow’s ma e ial cons an s.
A maximum c imp angle o 3º has been conside ed in he model. The p ope ies o each
ow elemen a e de ined aking in o accoun he ac ual c imp in he ib es loca ed a he
posi ion o he elemen . The c imped elemen s we e iden i ied and he co esponding
T8 COMATCOMP 09 969
angle o c imp was calcula ed o each elemen . The angle o o a ion used o simula e
he c imp in he elemen s ans o ms he mechanical p ope ies om ans e sely
iso opic o aniso opic. The s i ness p ope ies calcula ed o e e y elemen /angle, a e
de ined as dis inc aniso opic ma e ials in he ini e elemen model.
2.3 Bounda y condi ions
The bounda y condi ions applied o he aces o he model se e o impose he
comp essi e s ess s a e and gua an ee he displacemen s compa ibili y in he limi s o
he model wi h he es o he s uc u e. Symme y condi ions ha e been assumed in he
aces pa allel o he XY plane and one o he aces pa allel o YZ plane. The opposi e
ace pa allel o he YZ plane has a pu e comp essi e load applied and displacemen s o
i s nodes a e coupled o ensu e ha all nodes displace he same in he load di ec ion.
The bounda y condi ions in he op and bo om aces (pa allel o he XZ plane) mus
gua an ee he compa ibili y o he RVE unde conside a ion wi h he adjacen RVEs.
Thus, displacemen s o he nodes in bo h aces a e coupled o ensu e ha he ex ension
in he hickness di ec ion is cons an h ough he whole model.
3. RESULTS
Conside ing he bounda y condi ions and he load imposed, i is expec able ha he 0º
ows su e ins abili y phenomenon, known as mesobuckling.
Longi udinal sec ion
o he 0º ow C imped
zone
C imped
zone
Resin
pocke
Resin
pocke
Longi udinal sec ion
o he 0º ow
T ans e se sec ion
o he 90º ow
T ans e se sec ion
o he 90º ow
Comp essi e load
1
MN
MX
X
Y
Z
-.053065 -.045139 -.037214 -.029288 -.021363 -.013437 -.005512 .002414 .010339 .018265
FEB 24 2009
12:11:11
ELEMENT SOLUTION
STEP=1
SUB =163
TIME=1
EPTOXY (NOAVG)
RSYS=0
DMX =.195E-04
SMN =-.053065
SMX =.018265
(a)
(b)
Fig. 2. Resul s in
0
=
z
ace. (a) Ske ch o he model (b)
xy
γ
shea s ains.
Figu e 2(b) ep esen s he
xy
γ
shea s ain h ough he on ace o he model (no mal
o Z axis). The model is ske ched in Fig. 2(a) showing he di e en zones conside ed in
he model. I is possible o app ecia e he epe i i e solu ion o s ains wi hin he ows
ha ing he same o ien a ion. I can also be obse ed ha he la ge s ain g adien s a ise
in he zone whe e he 0
º
ows a e a ec ed by he c imp (i.e, whe e packages o esin
appea be ween he 90
º
ows). Two consecu i e e ical ows o elemen s appea in he
0
º
ows, one o hem ha ing he maximum posi i e alue o
xy
γ
, and he o he ha ing
he maximum nega i e alue o
xy
γ
. The e olu ion o
xy
γ
s ains along he ideal
di ec ion o he ib es in he 0
º
ows (called di ec ion B) can be clea ly app ecia ed in
Figu e 3.
T8 COMATCOMP 09 970
Fig. 3. E olu ion o
γ
xy
shea s ains along he ep esen ed di ec ion.
The esul s lead o hink ha he ailu e o he NCF unde his ype o load is con olled
by he shea s ains ha appea in he 0º ow. The ab up jumps in he shea s ain ake
place in he zone whe e he 0
º
ow s ops o be in con ac wi h he adjacen 90
º
ow, and
s a o be in con ac wi h he esin. The di e ence be ween he s i ness o he 90º ow
and he s i ness o he esin is esponsible o his jump in he shea s ain and
consequen ly i is in he oo o he ailu e o he composi e. This ailu e mechanism is in
ag eemen wi h he esul s shown by G aciani e al. (2005), using a mo e complica ed
FEM model in which he ow elemen s we e o ien ed ollowing he ac ual c imp o he
ib es.
4. CONCLUSIONS
The beha iou o an an isymme ic [0,90]
n
NCF composi e unde in-plane comp essi e
load has been s udied using a new 3D ini e elemen model. In his model he ib e c imp
is modelled by means o an app op ia e de ini ion o he ma e ial p ope ies in he
elemen s. The esul s ob ained a e simila o hose shown in G aciani e al. (2005).
The ad an ages o his model in compa ison wi h p e ious models a e he apid
modelling and meshing and he possibili y o in oducing complex c imps wi hou
changing he geome y o he model ( o simula e, o example, he e ec o s i ching in
he NCF composi e). Howe e he geome ical simpli ica ion implies he use o ce ain
algeb aic calcula ions o de e mine he mechanical p ope ies in he c imped zones. As
an addi ional ad an age, he use o a simple geome y in he new FEM esul s in a
highe quali y mesh, which leads o be e con e gence o he non-linea analysis.
REFERENCES
DRAPIER, S., WISNOM, M.R. (1999), Fini e-elemen in es iga ion o he comp essi e
s eng h o non-c imp- ab ic-based composi es. Compos Sci Technol, 59, 1287-1297.
GRACIANI, E., GONZÁLEZ, A., PARÍS, F. (2005) Análisis del compo amien o a
comp esión de un laminado [0,90,0,90] de ejido no ondulado median e un modelo 3D
de elemen os ini os. Ma e iales Compues os 05 (Ed. Amigo, V., Payá, J.J., Sal ado ,
M.D., Monzó, J.M., Sego ia, F., Bo ache o, V.), 877-884, Edi o ial de la UPV.