porous media approach for modeling closed cell … media approach for modeling closed cell foam...
TRANSCRIPT
Porous Media Approach for Modeling Closed Cell Foam
Louis J. Ghosn Ohio Aerospace Institute
Brook Park, Ohio
Roy M. Sullivan NASA Glenn Research Center
Cleveland, Ohio
Proposed Abstract for the 43rd Annual Technical Meeting Society of Engineering Science
August 13-16th, 2006
In order to minimize boil off of the liquid oxygen and liquid hydrogen and to prevent the formation of ice on its exterior surface, the Space Shuttle External Tank (ET) is insulated using various low-density, closed-cell polymeric foams. Improved analysis methods for these foam materials are needed to predict the foam structural response and to help identify the foam fracture behavior in order to help minimize foam shedding occurrences. This presentation describes a continuum based approach to modeling the foam thermo-mechanical behavior that accounts for the cellular nature of the material and explicitly addresses the effect of the internal cell gas pressure.
A porous media approach is implemented in a finite element frame work to model the mechanical behavior of the closed cell foam. The ABAQUS general purpose finite element program is used to simulate the continuum behavior of the foam. The soil mechanics element is implemented to account for the cell internal pressure and its effect on the stress and strain fields. The pressure variation inside the closed cells is calculated using the ideal gas laws. The soil mechanics element is compatible with an orthotropic materials model to capture the different behavior between the rise and in-plane directions of the foam. The porous media approach is applied to model the foam thermal strain and calculate the foam effective coefficient of thermal expansion. The calculated foam coefficients of thermal expansion were able to simulate the measured thermal strain during heat up from cryogenic temperature to room temperature in vacuum. The porous media approach was applied to an insulated substrate with one inch foam and compared to a simple elastic solution without pore pressure. The porous media approach is also applied to model the foam mechanical behavior during subscale laboratory experiments. In this test, a foam layer sprayed on a metal substrate is subjected to a temperature variation while the metal substrate is stretched to simulate the structural response of the tank during operation. The thermal expansion mismatch between the foam and the metal substrate and the thermal gradient in the foam layer causes high tensile stresses near the metal/foam interface that can lead to delamination.
https://ntrs.nasa.gov/search.jsp?R=20070008202 2018-07-07T02:31:50+00:00Z
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Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Sim
ple
Exa
mpl
e to
Det
erm
ine
the
Adv
anta
ge o
f the
P
orou
s M
edia
For
mul
atio
n
2.54
mm
Ti6
4 Su
bstra
te
25.4
mm
NC
FI
-250
C
-18
C
X
Y
Z
21
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Sim
ple
Elas
tic S
olut
ion
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
dis
tanc
e fr
om b
otto
m, Y
/t
Stress, MPa
-300
-250
-200
-150
-100
-50
0
Temperature, C
XX YY ZZ Tem
pera
ture
Foam
thro
ugh
thic
knes
s stre
ss p
rofil
es
Y
X
NC
FI S
treng
th R
ange
22
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Poro
us M
edia
Sol
utio
n
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
dis
tanc
e fr
om b
otto
m, Y
/t
Stress, MPa
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Pore Pressure, MPa
XX YY ZZ Pore
-Pre
ssur
e
Foam
thro
ugh
thic
knes
s stre
ss p
rofil
es
Y
XN
CFI
Stre
ngth
Ran
ge
1atm
23
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
dis
tanc
e fr
om b
otto
m, Y
/t
Stress, MPa
XX YY ZZ
Com
paris
on o
f the
stre
ss d
istri
butio
n be
twee
n th
e tw
o m
etho
ds
Ope
n sy
mbo
l
p
orou
s-m
edia
Clo
sed
sym
bol
s
impl
e el
astic
8% d
ecre
ase
in X
X &
ZZ
stre
sses
Incr
ease
s in
YY
stre
sses
due
to th
e re
duct
ion
of th
ece
ll po
re p
ress
ure
with
dec
reas
e te
mpe
ratu
re
Y
X
NC
FI S
treng
th R
ange
24
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Ther
mal
Gra
dien
t with
Sub
stra
te S
tress
2.54
mm
Ti6
4 Su
bstra
te
25.4
mm
NC
FI
-250
C
-18
C
150
MPa
Y
X15
0 M
Pa
25
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Foam
thro
ugh
thic
knes
s stre
ss p
rofil
esPo
rous
Med
ia S
olut
ion
with
Sub
stra
te S
tres
s (1
50 M
Pa)
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
dis
tanc
e fr
om b
otto
m, Y
/t
Stress, MPa
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Pore Pressure, MPa
XX YY ZZ Pore
-Pre
ssur
e
Y
X
NC
FI S
treng
th R
ange
1atm
26
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Foam
thro
ugh
thic
knes
s stre
ss p
rofil
es
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
dis
tanc
e fr
om b
otto
m, Y
/t
Stress, MPa
XX YY ZZ
Ope
n sy
mbo
l
T
herm
al G
radi
ent
Clo
sed
sym
bol
T
herm
al G
radi
ent +
Sub
stra
te P
ull
Loca
lized
stre
ss v
aria
tion
in th
e Y
Y d
irect
ion
7% in
crea
se in
XX
stre
ss
Y
X
1atm
NC
FI S
treng
th R
ange
27
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Al-2
195-
T8 (f
or L
o2 ta
nk)
or Ti-6
-4 fo
r (Lh
2 ta
nk)
NC
FI,
BX
-265
or
Hyb
rid B
X-P
DL
Mod
elin
g th
e C
ryof
lex
spec
imen
28
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Lh2
test
, with
Ti s
ubst
rate
Tem
pera
ture
Pro
file
for G
radi
ent T
est
5 cm
(1.9
9”)
Lo2
test
, with
Al-2
195-
T su
bstra
te
9.2
cm (3
.59”
)1.
27 c
m (0
.5”)
Sym
met
ry
-250
C
-18
C
29
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
LH2
Gra
dien
t (@
-17.
8C to
-245
C, 9
50M
Pa)
No
Slit,
No
Pore
Pre
ssur
e
-0.0
50
0.050.
1
0.150.
2
0.250.
3
010
2030
4050
60
Dis
tanc
e fr
om s
ubst
rate
, mm
Stress, MPa
XX YY ZZ XY XZ YZ
NC
FI S
treng
th R
ange
30
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
LH2
Gra
dien
t (@
-17.
8C to
-245
C, 9
50M
Pa)
No
Slit,
With
Por
e Pr
essu
re
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
010
2030
4050
60
Dis
tanc
e fr
om s
ubst
rate
, mm
Stress, MPa
XX YY ZZ XY XZ YZ
With
the σx
xw
ell i
n th
e fa
ilure
zon
eO
nly
1 ou
t 12
spec
imen
s fai
led
NC
FI S
treng
th R
ange
31
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
LH2
Imm
ersi
on (@
-185
C, 1
22M
Pa)
No
Slit,
With
Por
e Pr
essu
re
-0.2
0
-0.1
5
-0.1
0
-0.0
5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
010
2030
4050
60
Dis
tanc
e fr
om s
ubst
rate
, mm
Stress, MPa
XX YY ZZ XY XZ YZ
With
the σx
xw
ell b
elow
the
failu
re z
one
10 o
ut 1
0 sp
ecim
ens f
aile
d
NC
FI S
treng
th R
ange
32
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Tran
sver
sely
isot
ropi
c m
ater
ial,
Hyp
er-e
llipt
ic fa
ilure
func
tion
()
()
()
()
()
1)
()
2(2 23
2 1311
2 124
1
339
2211
733
2233
115
2211
42 33
32 22
2 111
=+
+−
+
++
++
+⋅
++
+
σσ
σ
σσ
σσ
σσ
σσ
σσ
σσ
aa
a
aa
aa
aa
33
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
asa.
gov
Sum
mar
y•
The
poro
us m
edia
app
roac
h w
as a
pplie
d to
thre
e E
T S
OFI
mat
eria
ls.
•Th
e A
niso
tropi
c C
TE te
nsor
s w
ere
deriv
ed to
pro
vide
with
goo
d re
sults
fo
r the
stra
in v
aria
tion
as a
func
tion
of te
mpe
ratu
re in
vac
uum
.•
A h
igh
tem
pera
ture
CTE
was
der
ived
bas
ed o
n TG
A d
ata
show
ing
an
in-p
lane
neg
ativ
e C
TE.
•Th
e im
plem
enta
tion
of th
e po
rous
med
ia in
to A
BA
QU
S w
as o
utlin
ed.
•Th
e st
ress
dis
tribu
tion
of th
e cr
yofle
xsp
ecim
ens
wer
e de
term
ined
for
the
imm
ersi
on a
nd g
radi
ent t
ests
.•
The
max
imum
stre
ss c
alcu
late
d w
as in
cons
iste
nt w
ith th
e ex
perim
enta
lly o
bser
ved
failu
res.
Futu
re W
ork
•In
vest
igat
e th
e so
undn
ess
of a
neg
ativ
e in
-pla
ne C
TE fo
r BX
-265
•D
evel
op a
failu
re c
riter
ia fo
r the
cry
ofle
xsp
ecim
en b
ased
on
the
expe
rimen
tal o
bser
vatio
n an
d FE
A re
sults