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

pocket

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

11

ACCIS

Confe

rence

30th

June 2

009

Univers

ity o

f Bristo

l

LS-D

YNA F

E m

odels

12

ACCIS

Confe

rence

30th

June 2

009

Univers

ity o

f Bristo

l

LS-D

YNA F

E m

odels

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