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ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Optimization of Tapered Laminates
with Ply Drops
Dr. Giuliano Allegri
2ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Conte
nt
1)Ply d
rop-o
ffs: a n
ecessary
evil?
2)Dam
age Initiation a
t ply d
rop-o
ffs: a fra
ctu
re m
echanics p
ers
pective
3)Optim
ization o
f ply d
rop sequences
3ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Ply d
rop-o
ffs: a n
ecessary
evil?
•Dro
pping o
ff p
lies a
llows changing lam
inate
thickness a
nd com
position
•Ply dro
ps re
pre
sent
an abru
pt
change in th
e geom
etric/m
echanical
pro
perties of
the lam
inate
, so th
ey behave as stress ra
isers
and
delam
ination initiato
rs
4ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Dam
age Initiation @
Ply D
rop-o
ffs
•A fra
ctu
re m
echanics p
ers
pective
•Delam
inations em
anate
from
th
e re
sin pocket tip;
if th
e latter
is
considere
d a
s a
void, initiation loads c
an b
e d
erived fro
m fra
ctu
re
mechanics considera
tions w
hen L1, L3 →
0
•The s
train e
nerg
y release rate
s (SERR) expre
ssions a
re c
om
pute
d
em
ploying b
eam
theory
and o
rthotropic rescaling
M
M-P(H/2+
Lz-
Rz)
P
P
5ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
SERR F
orm
ulas: lim
itations
Geometric idealization –limitations:
1.re
sin pockets
are
not
exactly right
triangles;
2.th
e
curv
atu
res
of
the
fibre
s
surrounding
the
resin
are
m
uch sm
ooth
er th
en a
ssum
ed
tH dL1
L2
L3
t-H
φP1
M1
M1-P1H/2
z
x
tH dL1
L2
L3
t-H
φP1
M1
M1-P1H/2
z
x
3. th
e thickness o
f th
e b
elt a
nd core
sub-lam
inate
s is n
ot consta
nt
All the assumptions above lead to conservative estimationsof the strain energy release
rates (SERR) for delaminations emanating from the resin pocket tips
6ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Topological Optim
ization
Actu
al
Idealized
An arbitrary laminate configuration comprising ply drop-offs is
idealized as a sequence of asymmetrically tapered units
7ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Topological Optim
ization T
ool
•Two sta
ge o
ptim
ization tool
1)
Dete
rmin
istic first sta
ge: find w
hich p
lies h
ave to b
e term
inate
d in
ord
er to
matc
h the thick section lam
inate
with the thin section o
ne
2)
Sto
chastic second sta
ge:
find th
e optim
al ply dro
p-o
ff sequence
via
the
min
imization
of
the
maxim
um
SERR
failure
index
associate
d w
ith the p
ly term
inations, e.g
.
Ste
p 2
) is b
ased o
n sim
ulate
d a
nnealing w
ith sto
chastic tunnellin
g
III
IcIIc
GG
FIG
G=
+
8ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Guidelines in the litera
ture
•Pra
ctical “rules o
f th
um
b”fo
r designing tapere
d lam
inate
s:
1)
alw
ays try to
dro
p th
e innerm
ost
block in ord
er
to m
atc
h th
e
lam
inate
thick a
nd thin sections;
2)
dro
p
0°
plies
close
to
the
thick
section,
±45°
in
the
middle
sections a
nd 9
0°plies close to the thin e
nd;
3)
in pure
bending cases sta
rt dro
pping th
e in
nerm
ost
plies of
the
innerm
ost block;
4)
in pure
axial fo
rce cases sta
rt dro
pping th
e oute
rmost
plies of
the
innerm
ost block
5) pro
mote
inte
rleaving b
y a
voiding d
ropping a
dja
cent plies
6)
if
inte
rleaving
is
not
possible,
try
to
maxim
ise
the
dista
nce
betw
een the a
dja
cent ply term
inations
These rules a
re e
mbedded in a
Fuzzy Logic
Optim
ization/A
nalysis T
ool called “ALTO”(p
oste
r)
9ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
A S
imple C
ase S
tudy
•Sim
ply sym
metrical ta
pere
d lam
inate
Thick Section Stacking Sequence:
[0°/0
°/+
45°/9
0°/9
0°/-
45°/0
°/0
°] 3
S
Thin Section Stacking Sequence:
[0°/0
°/+
45°/-
45°/ 0°/+
45°/-
45°/ 0°/+
45°/-
45°/ 0°] S
6 mm
3 mm
250 mm
x
z
25 m
m
MM
mm
NG
mm
NG
GPa
GGPa
GG
GPa
EE
GPa
E
IIc
Ic/
9.0
/36
.0
3.0
8.3
6.4
7.8
4.142
23
13
12
23
13
12
32
1
==
==
=
==
=
==
=
νν
ν
Mate
rial pro
perties:
T300/9
14C
10
ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
•Sim
ple In-O
ut
Term
inations
(A)
•Litera
ture
Guidelines
(B)
•Optim
ization
Algorith
m
(C)
00
450
-450
900
Configura
tions for a P
ure
Bending Load
13
ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Com
parisons
•Sim
ple in-o
ut dro
pping a
nd litera
ture
guidelines g
ive sim
ilar re
sults
•The optim
ization to
ol pre
sente
d here
pro
duces th
e b
est re
sults,but
resulting lam
inate
is n
ot sym
metric
•The analytical solution pro
vides a re
asonable estim
ate
of th
e fa
ilure
loads w
hen com
pare
d to h
igh fidelity
FEM tools
Configuration
LS-DYNA (N)
Analytical (N)
(A)
2500
1995 (-20.2 %
)
(B)
2560
1995 (-22.1%)
(C)
3000
3270 (+9%)
Delam
ination initiation load from the FE m
odel and the analytical solution
14
ACCIS
Confe
rence
30th
June 2
009
Univers
ity o
f Bristo
l
Sum
mary
& C
onclusions
•Analytical
expre
ssions
for
the
SERR
associate
d
with
delam
inations
em
anating from
ply dro
p-o
ffs locations have been work
ed out
and
validate
d a
gainst FE a
nalysis.
•Realistic p
ly d
rop-o
ff c
onfigura
tions h
ave b
een c
onsidere
d, with the a
im a
t obta
ining conserv
ative e
stim
ate
s for th
e S
ERR.
•Since the resin p
ockets
pre
sent at th
e term
ination location a
re c
onsidere
d
as v
oids, it is p
ossible to p
redict th
e d
elam
ination initiation u
sin
g the S
ERR
values for zero
debond
length
s.
•A tw
o ste
p optim
ization algorith
m has been developed fo
r m
atc
hing th
e
thick and th
in sections of
tapere
d lam
inate
s;
this pro
cedure
allows
identify
ing w
hich p
lies to d
rop a
nd w
here
(in a
topological sense)
•The o
ptim
ization p
rocedure
has b
een v
alidate
d b
y m
eans o
f virtu
al te
sting
Acknowledgem
ents
to R
olls-R
oyce P
lc for th
eir support o
f th
is researc
h
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