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Thermal Expansion of Polyurethane FoamBradley A Lerch∗ ‡
Research EngineerRoy M. Sullivan†
Research Engineer
Closed cell foams are often used for thermal insulation. In the case of the Space Shuttle,the External Tank uses several thermal protection systems to maintain the temperature of thecryogenic fuels. A few of these systems are polyurethane, closed cell foams. In an attemptto better understand the foam behavior on the tank, we are in the process of developingand improving thermal-mechanical models for the foams. These models will start at themicrostructural level and progress to the overall structural behavior of the foams on thetank.
One of the key properties for model characterization and verification is thermal expansion.Since the foam is not a material, but a structure, the modeling of the expansion is complex.It is also exacerbated by the anisoptropy of the material. During the spraying and foamingprocess, the cells become elongated in the rise direction and this imparts different propertiesin the rise direction than in the transverse directions. Our approach is to treat the foam asa two part structure consisting of the polymeric cell structure and the gas inside the cells.The polymeric skeleton has a thermal expansion of its own which is derived from the basicpolymer chemistry. However, a major contributor to the thermal expansion is the volumechange associated with the gas inside of the closed cells. As this gas expands it exertspressure on the cell walls and changes the shape and size of the cells. The amount that thisoccurs depends on the elastic and viscoplastic properties of the polymer skeleton. The morecompliant the polymeric skelton, the more influence the gas pressure has on the expansion.An additional influence on the expansion process is that the polymeric skeleton begins tobreakdown at elevated temperatures and releases additional gas species into the cell interiors,adding to the gas pressure. The fact that this is such a complex process makes thermalexpansion ideal for testing the models.
This report focuses on the thermal expansion tests and the response of the microstructure.A novel optical method is described which is appropriate for measuring thermal expansionat high temperatures without influencing the thermal expansion measurement. Detailedmicrostructural investigations will also be described which show cell expansion as a functionof temperature. Finally, a phenomenological model on thermal expansion will be described.
∗Mechanics and Lifing Branch, NASA-GRC, 21000 Brookpark Rd, Cleveland, USA 44135†Mechanics and Lifing Branch, NASA Glenn Research Center, MS 49/7, 21000 Brookpark Rd., Cleveland,
USA 44135‡Corresponding Author; Contact Email: Bradley.a.lerch@nasa.gov
Session-PaperNumber
https://ntrs.nasa.gov/search.jsp?R=20070008201 2018-04-18T17:57:26+00:00Z
1
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Ther
mal
Exp
ansi
on o
f Pol
yure
than
e Fo
am
Brad
ley
A. L
erch
and
Roy
M. S
ulliv
anN
ASA
Gle
nn R
esea
rch
Cen
ter
pres
ente
d at
the
43rd
Ann
ual T
echn
ical
Mee
ting
of th
e So
ciet
y of
Eng
inee
ring
Scie
nce
The
Penn
sylv
ania
Sta
te U
nive
rsity
Uni
vers
ity P
ark,
PA
Aug
ust 1
4, 2
006
2
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iona
l Aer
onau
tics
and
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e Ad
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Aer
odyn
amic
Hea
ting
Tank
Wal
l
Virg
in S
OFI
Foa
m
Hea
t Aff
ecte
dC
har L
ayer
Abl
ated
Mat
eria
l
70 -
200
o F20
0 -5
00 o F
-423
o F
> 50
0 o F
-423
–70
o F
Tem
pera
ture
s
Expe
cted
Foa
m T
empe
ratu
re P
rofil
e
3
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iona
l Aer
onau
tics
and
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e Ad
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istra
tion
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Impo
rtanc
e of
CTE
•A
l-sub
stra
te h
as a
CTE
of 2
x 1
0-5 /°
C•
Pol
ymer
foam
s ha
ve a
n ap
prox
imat
e C
TE o
f 1
x 10
-4/°
C•
Ther
mal
stra
in (ε
) equ
als:
ε= Δα
ΔT
= 0.
045
whe
re Δ
T =
580
°Cσ f
oam
~ U
TSfo
am
•Th
erm
al s
trai
ns a
re s
igni
fican
t and
can
ca
use
crac
king
4
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iona
l Aer
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and
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e Ad
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istra
tion
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Goa
l
The
purp
ose
of th
is st
udy
is to
inve
stig
ate
the
mec
hani
sms o
ffo
am th
erm
al e
xpan
sion
to g
uide
mod
el d
evel
opm
ent
5
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iona
l Aer
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tics
and
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e Ad
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istra
tion
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Mea
sure
men
t of T
herm
al E
xpan
sion
LVD
T
Forc
eLa
ser
Det
ecto
r
Hea
t Lam
psFo
am
Con
vent
iona
l CTE
Rig
Non
-Con
tact
ing
CTE
Rig
Cer
amic
Rod
Furn
ace
Foam
6
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iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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gov
Dis
torti
on o
f Foa
m D
ue to
Tem
pera
ture
Cha
nges
As-
cut
Hea
ted
to
170
C
Hea
ted
to
300
C
7
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iona
l Aer
onau
tics
and
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e Ad
min
istra
tion
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Pro
blem
s A
ssoc
iate
d W
ith T
herm
al M
easu
rem
ents
•Te
mpe
ratu
re m
easu
rem
ents
and
ther
mal
gra
dien
ts-F
oam
is a
ther
mal
insu
lato
r
•A
niso
tropy
of f
oam
mic
rost
ruct
ure
-El
onga
ted
cellu
lar s
truct
ure
-K
nit L
ines
-La
rge
cells
and
voi
ds
Twis
ting,
war
ping
, and
dis
torti
on o
f foa
m sa
mpl
es
8
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Foam
Mic
rost
ruct
ure
Figu
re 3
.5 –
Cel
l Geo
met
ry, N
CFI
24-1
24
•97%
air;
den
sity
= 0
.03
g/cc
•Pol
ymer
ic c
ell w
alls
•Due
to it
s mic
rost
ruct
ure,
mat
eria
l is a
niso
tropi
c (p
osse
ss
diff
eren
t mat
eria
l pro
perti
es in
diff
eren
t dire
ctio
ns)
Para
llel-t
o-ris
e di
rect
ion
Perp
endi
cula
r-to
-ris
e di
rect
ion
9
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iona
l Aer
onau
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and
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Kni
tline
s
10
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l Aer
onau
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and
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e Ad
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tion
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Res
ults
11
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iona
l Aer
onau
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tion
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Ther
mal
Exp
ansi
on P
erpe
ndic
ular
to R
ise
Dire
ctio
n
0
0.050.
1
0.150.
2
0.25
050
100
150
200
250
Tem
pera
ture
(C)
Strain
Blo
ck 3
Blo
ck 3
Blo
ck 2
F
KS
C-1
Perm
anen
tvo
lum
e ch
ange
α=
.000
2/°C
α=
0.00
5/°C
12
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Ther
mal
Exp
ansi
on P
aral
lel t
o R
ise
Dire
ctio
n
0
0.02
0.04
0.06
0.080.
1
020
4060
8010
012
014
016
018
020
0
Tem
pera
ture
(C)
Strain
Sam
ple
1
Sam
ple
2
Sam
ple
3
Sam
ple
4
Perm
anen
tvo
lum
e ch
ange
α=
0/°C
α=
0.00
3/°C
13
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Ther
mal
Exp
ansi
on in
Bot
h D
irect
ions
0
0.050.1
0.150.2
0.25
050
100
150
200
250
Tem
pera
ture
(C)
Strain
Per
pend
icul
ar to
Ris
e
Par
alle
l to
Ris
e
14
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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w.n
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gov
Mec
hani
sm o
f Foa
m E
xpan
sion
•H
ot s
tage
exp
erim
ents
con
duct
ed o
n fo
am s
ampl
es•
Indi
vidu
al fo
am c
ells
exa
min
ed in
SE
M d
urin
g he
atin
g an
d co
olin
g•
Exp
ansi
on a
nd c
ontra
ctio
n of
cel
ls o
bser
ved
as a
fu
nctio
n of
tem
pera
ture
•B
oth
who
le c
ells
and
face
s w
ere
exam
ined
15
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iona
l Aer
onau
tics
and
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e Ad
min
istra
tion
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Hot
Sta
ge E
xper
imen
ts
Afte
r hea
ting
Bef
ore
test
Tem
p=15
0 C
Cel
l exp
ansi
ondu
e to
ther
mal
expo
sure
Cel
l exp
ands
m
ostly
in th
ew
idth
dire
ctio
n(p
erpe
ndic
ular
to ri
se)
Tem
p (°
C)
bloc
kle
ngth
wid
th20
00
015
015
-25
6.6
28.8
205-
13-4
.613
.6
cell
stra
in (%
)
Rise
dire
ctio
n
16
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Cel
l Wid
th T
herm
al E
xpan
sion
-0.6
0
-0.4
0
-0.2
0
0.00
0.20
0.40
0.60
050
100
150
200
250
300
Tem
pera
ture
(C)
Strain (mm/mm)
Cel
l 1 w
idth
Cel
l 2 w
idth
Cel
l 3 w
idth
Cel
l 4 w
idth
Cel
l 5 w
idth
Face
6 w
idth
Cel
l 7 w
idth
Cel
l 8 w
idth
Face
9 w
idth
Face
10
wid
th
Cel
l 11
wid
th
Cel
l 12
wid
th
(Per
pend
icul
ar to
Ris
e)
17
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Cel
l Len
gth
Ther
mal
Exp
ansi
on
-0.8
0
-0.7
0
-0.6
0
-0.5
0
-0.4
0
-0.3
0
-0.2
0
-0.1
0
0.00
0.10
0.20
050
100
150
200
250
300
Tem
pera
ture
(C)
Strain (mm/mm)
Cel
l 1 le
ngth
Cel
l 2 le
ngth
Cel
l 3 L
engt
h
Cel
l 4 L
engt
h
Cel
l 5 L
engt
h
Face
6 L
engt
h
Cel
l 7 L
engt
h
Cel
l 8 L
engt
h
Face
9 L
engt
h
Face
10
Leng
th
Cel
l 11
Len
gth
Cel
l 12
Leng
th
(Par
alle
l to
Ris
e)
18
Nat
iona
l Aer
onau
tics
and
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e Ad
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istra
tion
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Bas
is fo
r Mod
el D
evel
opm
ent
•El
onga
ted
cell
stru
ctur
e•
Pore
pre
ssur
e in
crea
ses w
ith te
mpe
ratu
re•
Poly
mer
softe
ns w
ith te
mpe
ratu
re
19
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Ther
mal
Beh
avio
r of P
olym
er S
kele
ton
Tem
p.le
ngth
stra
inle
ngth
stra
in(°
C)
(μm
)(%
)(μ
m)
(%)
1758
064
010
762
7.7
51-0
.21
1744
-0.2
347
-0.2
8
Liga
men
t 1Li
gam
ent 9
1
9
Porti
ons o
f cel
ls w
ith
no in
fluen
ce
from
por
e pr
essu
re
20
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Ther
mal
Beh
avio
r of P
olym
er S
kele
ton
-0.5
0
-0.4
0
-0.3
0
-0.2
0
-0.1
0
0.00
0.10
0.20
050
100
150
200
Tem
pera
ture
(C)
Strain (mm/mm)
1 2 3 4 5 6 7 8 9 aver
age
Line
ar (f
it av
g)
α =
-0.0
0029
/°C
Liga
men
t No.
21
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
ww
w.n
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Con
clus
ions
•H
igh
tem
pera
ture
ther
mal
beh
avio
r of t
he fo
am is
a
com
plex
pro
cess
driv
en b
y:-C
ell a
niso
tropy
-Por
e pr
essu
re-P
olym
er d
egra
datio
n•
Mod
eled
usi
ng s
oils
por
e pr
essu
re a
ppro
ach
and
mic
rom
echa
nics
22
Nat
iona
l Aer
onau
tics
and
Spac
e Ad
min
istra
tion
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Ack
now
ledg
emen
ts
•M
SFC
, KS
C a
nd M
AF
for s
uppl
ying
foam
•
Cen
ter f
or S
urfa
ce A
naly
sis
of M
ater
ials
–C
WR
U fo
r pe
rform
ing
hot s
tage
exp
erim
ents
•C
hris
Bur
ke (Q
SS
, Inc
) for
dev
elop
ing
lase
r CTE
rig
and
cond
uctin
g th
erm
al e
xper
imen
ts•
Pat
Rog
ers,
Bria
n S
teev
ean
d S
cotty
Spa
rks
for t
heir
cont
inue
d su
ppor
t and
inte
rest
in th
e w
ork
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