graphite/polyimide composites subjected to biaxial loads ...€¦ · graphite/polyimide composites...
TRANSCRIPT
Gra
phit
e/P
olyi
mid
e C
ompo
site
s Su
bjec
ted
to B
iaxi
al L
oads
at
Elev
ated
Tem
pera
ture
s
Mac
iej
S. K
um
osa*
an
d J.
K. S
utt
er*
*
*C
ente
r fo
r A
dvan
ced
Mat
eria
ls a
nd
Stru
ctu
res
Dep
artm
ent
of E
ngi
nee
rin
g, U
niv
ersi
ty o
f D
enve
r2
39
0 S
. Yor
k St
., D
enve
r C
olor
ado
mku
mos
a@du
.edu
, tel
: (3
03
) 6
99
-32
36
**
NA
SA G
len
n R
esea
rch
Cen
ter
at L
ewis
Fie
ld2
10
00
Bro
okpa
rk R
oad,
Cle
vela
nd,
OH
44
13
5
https://ntrs.nasa.gov/search.jsp?R=20070022361 2020-05-01T08:18:32+00:00Z
Abs
trac
tFi
rst,
we
will
rev
iew
ou
r m
ost
impo
rtan
t re
sear
ch
acco
mpl
ish
men
ts f
rom
a f
ive
year
stu
dy c
once
rned
w
ith
th
e pr
edic
tion
of
mec
han
ical
pro
pert
ies
of
un
idir
ecti
onal
an
d w
oven
gra
phit
e/po
lyim
ide
com
posi
tes
base
d on
T6
50
-35
, M4
0J
and
M6
0J
fibe
rs e
mbe
dded
in e
ith
er P
MR
-15
or
PM
R-I
I-5
0
poly
imid
e re
sin
s.
Then
, an
agi
ng
mod
el r
ecen
tly
deve
lope
d fo
r th
e co
mpo
site
s ag
ed in
nit
roge
n w
ill b
e pr
opos
ed a
nd
expe
rim
enta
lly v
erif
ied
on a
n e
igh
t h
arn
ess
sati
n
(8H
S) w
oven
T6
50
-35
/PM
R-1
5 c
ompo
site
age
d in
n
itro
gen
at
31
5°C
for
up
to 1
50
0 h
ours
.
The
stu
dy w
as s
upp
orte
d jo
intl
y be
twee
n 1
99
9
and
20
05
by
the
AFO
SR, t
he
NA
SA G
len
n R
esea
rch
C
ente
r, a
nd
the
Nat
ion
al S
cien
ce F
oun
dati
on.
We
Wer
e a
Par
t of
Th
ese
Effo
rts!
!!
Roc
ket
Bas
ed C
ombi
ned
Cyc
leC
omb
ust
ion
Ch
amb
er S
upp
ort
Str
uct
ure
NA
SA G
lenn
Ann
ounc
emen
t, M
arch
200
4.
“A li
ghtw
eigh
t hig
h te
mpe
ratu
re p
olym
er m
atrix
com
posi
te (H
TPM
C)c
ombu
stor
su
ppor
t cha
mbe
r for
a R
ocke
t Bas
ed C
ombi
ned
Cyc
le e
ngin
e su
cces
sful
ly su
rviv
ed
hot-f
ire te
stin
g at
ATK
-GA
SL.
This
test
ing
conc
lude
s a th
ree
year
col
labo
ratio
n be
twee
n N
ASA
Gle
nn a
nd B
oein
g to
des
ign,
fabr
icat
e an
d te
st th
e su
ppor
t stru
ctur
e an
d fu
lfills
a G
PRA
(Gov
ernm
ent P
erfo
rman
ce R
efor
m A
ct) m
ilest
one
for t
he
UEE
T (U
ltra-
effic
ient
Eng
ine
Prog
ram
).Th
e su
ppor
t stru
ctur
e w
as p
repa
red
from
a
high
tem
pera
ture
com
posi
te m
ater
ial,
PMR
-II-
50”
Shea
r Te
stin
g of
8H
S T6
50
-35
/PM
R-1
5,
4H
S M
40
J/P
MR
-II-
50
an
d 4
HS
M6
0J/
PM
R-I
I-5
0
Mec
han
ical
beh
avio
r of
un
idir
ecti
onal
an
d w
oven
gr
aph
ite/
poly
imid
e co
mpo
site
s ba
sed
on
med
ium
(T
65
0-3
5)
and
hig
h
(M4
0J
and
M6
0J)
m
odu
lus
grap
hit
e fi
bers
w
ith
P
MR
-15
an
d P
MR
-II-
50
po
lyim
ide
resi
ns
test
ed
un
der
biax
ial
shea
r do
min
ated
st
ress
co
ndi
tion
s ov
er
a te
mpe
ratu
re
ran
ge
of
20
°C
to
31
6°C
u
nde
r dr
y an
d w
et
con
diti
ons
has
be
en
inve
stig
ated
bo
th
expe
rim
enta
lly a
nd
nu
mer
ical
ly.
M.
Ku
mos
a et
al.,
Com
pari
son
of t
he
45°
off
Axi
s an
d Io
sipe
scu
Shea
r Te
sts
for
Wov
en F
abri
c C
ompo
site
M
ater
ials
, Com
posi
tes
Tech
nolo
gy &
Res
earc
h, V
ol. 2
4 (2
002)
pp.
3-1
6.
M.
Gen
tz e
t al
., M
ech
anic
al B
ehav
ior
of a
Wov
en G
raph
ite/
PM
R-1
5 C
ompo
site
at
Roo
m a
nd E
leva
ted
Tem
pera
ture
s D
eter
min
ed f
rom
th
e ±4
5°Te
nsile
and
Ios
ipes
cu S
hea
r Te
sts,
Jou
rnal
of
Com
posi
tes
Tech
nolo
gy &
Res
earc
h, V
ol. 2
5, I
ssu
e 1
(200
3) p
p. 2
2-34
.
M. G
entz
, et
al.,
In
-Pla
ne S
hea
r Te
stin
g of
Wov
en G
raph
ite/
Pol
yim
ide
Com
posi
tes
wit
h M
ediu
m a
nd H
igh
Mod
ulu
s G
raph
ite
Fibe
rs a
t R
oom
and
31
6°C
Tem
pera
ture
s, C
ompo
site
s Sc
ienc
e an
d Te
chno
logy
, V
ol.
64
(200
4) p
p. 2
03-2
20.
Gra
phit
e/P
olyi
mid
e C
ompo
site
s
Wov
en c
ompo
site
sys
tem
s; p
lain
(le
ft)
and
eigh
t h
arn
ess
sati
n 8
HS
(rig
ht)
A
maj
or
limit
atio
n
of
wov
en
fibe
r/po
lym
er
mat
rix
com
posi
te
syst
ems
is t
he
inab
ility
of
thes
e m
ater
ials
to
resi
st i
ntr
alam
inar
an
d in
terl
amin
ar d
amag
e in
itia
tion
an
d pr
opag
atio
n u
nde
r sh
ear-
dom
inat
ed b
iaxi
al lo
adin
g co
ndi
tion
s.
Bia
xial
Sh
ear
Dom
inat
ed S
tren
gth
of
8H
S T6
50
-35
/PM
R-1
5 S
yste
m
Ther
e ar
e n
um
erou
s sh
ear
test
met
hod
s fo
r w
oven
fab
ric
com
posi
tes,
eac
h w
ith
its
ow
n
adva
nta
ges
and
disa
dvan
tage
s.
Two
tech
niq
ues
, w
hic
h
show
m
uch
po
ten
tial
, ar
e th
e Io
sipe
scu
sh
ear
and ±4
5°te
nsi
lete
sts.
Th
e ap
plic
atio
n o
f th
ese
two
test
s fo
r th
e sh
ear
test
ing
of
wov
en
grap
hit
e/po
lyim
ide
com
posi
tes
at r
oom
an
d el
evat
ed
tem
pera
ture
s w
as
eval
uat
ed
in
this
pr
ojec
t bo
th
expe
rim
enta
lly
and
nu
mer
ical
ly.
Mac
rosc
opic
FEM
Mod
els
of ±
45
° Te
nsi
le
and
Iosi
pesc
u S
hea
r Te
sts
Fin
ite
elem
ent
mes
h o
f ±4
5°
spec
imen
Fin
ite
elem
ent
mes
h o
f Io
sipe
scu
sp
ecim
en.
G.
Ode
gard
, K
. Se
arle
s an
d M
. K
um
osa,
Non
linea
r A
naly
sis
of W
oven
Fab
ric-
Rei
nfo
rced
Gra
phit
e/P
MR
-15
C
ompo
site
s un
der
Shea
r-D
omin
ated
Bia
xial
Loa
ds,
Mec
hani
cs o
f Co
mpo
site
Mat
eria
ls a
nd S
truc
ture
s, V
ol.
7 (2
000)
pp.
129
-152
.
Tow
s
Tow
s
SEM
An
alys
is (
Stag
es o
f D
amag
e in
8
HS
T65
0-3
5/P
MR
-15
)
Stag
es o
f cr
ack
init
iati
on a
nd
prop
agat
ion
in 8
HS
T65
0-3
5/P
MR
-15
at
roo
m t
empe
ratu
re u
nde
r sh
ear
dom
inat
ed in
-pla
ne
load
s.
G.
Ode
gard
, K
. Se
arle
s an
d M
. K
umos
a, N
onlin
ear
Ana
lysi
s of
Wov
en F
abri
c-R
ein
forc
ed G
raph
ite/
PM
R-1
5 C
ompo
site
s un
der
Shea
r-D
omin
ated
Bia
xial
Loa
ds,
Mec
hani
cs o
f Co
mpo
site
Mat
eria
ls a
nd S
truc
ture
s, V
ol. 7
(2
000)
pp.
129
-152
.
M.
Ku
mos
a, G
. O
dega
rd,
D.
Arm
entr
out,
L.
Ku
mos
a, K
. Se
arle
s an
d J.
K.
Sutt
er,
Com
pari
son
of
the ±4
5°O
ff-
Axi
s an
d Io
sipe
scu
Shea
r Te
sts
for
Wov
en
Fabr
ic
Com
posi
te
Mat
eria
ls,
J. C
ompo
site
s Te
chno
logy
&
Res
earc
h, V
ol. 2
4, N
o. 1
(20
02)
pp.
3-16
.
M.
Gen
tz,
D.
Arm
entr
out,
P.
Ru
pnow
ski,
L. K
um
osa,
J.
K.
Sutt
er a
nd
M.
Ku
mos
a, M
ech
anic
al B
ehav
ior
of a
W
oven
Gra
phit
e/P
MR
-15
Com
posi
te a
t R
oom
an
d El
evat
ed T
empe
ratu
res
Det
erm
ined
fro
m t
he ±4
5°Te
nsi
le
and
Iosi
pesc
u S
hear
Tes
ts, C
ompo
site
s Te
chno
logy
& R
esea
rch,
Vol
. 25
(200
3) p
p. 2
2-34
.
8H
S T6
50
-35
/PM
R-1
5;
Iosi
pesc
u V
S. ±
45
°Te
nsi
le T
ests
Shea
r st
ress
es a
t th
e on
set
of in
tral
amin
ar d
amag
e an
d at
th
e m
axim
um
load
s fr
om t
he
±45
ºan
d Io
sipe
scu
tes
ts a
t ro
om a
nd
31
6ºC
tem
pera
ture
s fo
r th
e 8
HS
T65
0-3
5/P
MR
-15
sys
tem
.
T65
0/P
MR
-15
Shea
r St
ress
es a
t th
e O
nse
t of
In
tral
amin
ar
Dam
age
[MP
a]
Shea
r St
ress
es a
t M
axim
um
Lo
ads
[MP
a]
Test
±45
º(b
iaxi
al)
Iosi
pesc
u
(sh
ear)
±45
º(b
iaxi
al)
Iosi
pesc
u
(sh
ear)
at R
T5
6.6
±2
.09
4.8
±1
.38
2.0
±0
.15
10
5.8
±2
.6
at 3
15
ºC3
7.3
±5
.25
9.9
±1
.25
0.8
±6
.07
1.8
±4
.2
G.
Ode
gard
, K
. Se
arle
s an
d M
. K
um
osa,
Non
linea
r A
nal
ysis
of
Wov
en F
abri
c-R
ein
forc
ed G
raph
ite/
PM
R-1
5
Com
posi
tes
unde
r Sh
ear-
Dom
inat
ed B
iaxi
al L
oads
, M
echa
nics
of
Com
posi
te M
ater
ials
and
Str
uctu
res,
Vol
. 7
(20
00
) pp
. 12
9-1
52
..
M.
Ku
mos
a, G
. O
dega
rd,
D.
Arm
entr
out,
L.
Ku
mos
a, K
. Se
arle
s an
d J.
K.
Sutt
er,
Com
pari
son
of t
he ±4
5°O
ff-A
xis
and
Iosi
pesc
u S
hear
Tes
ts f
or W
oven
Fab
ric
Com
posi
te M
ater
ials
, J.
Com
posi
tes
Tech
nolo
gy &
Res
earc
h, V
ol.
24, N
o. 1
(20
02)
pp.
3-16
.
M.
Gen
tz,
D.
Arm
entr
out,
P.
Ru
pnow
ski,
L. K
um
osa,
J.
K.
Sutt
er a
nd
M.
Ku
mos
a, M
ech
anic
al B
ehav
ior
of a
W
oven
Gra
phit
e/P
MR
-15
Com
posi
te a
t R
oom
an
d El
evat
ed T
empe
ratu
res
Det
erm
ined
fro
m t
he ±
45°
Ten
sile
an
d Io
sipe
scu
Sh
ear
Test
s, C
ompo
site
s Te
chno
logy
& R
esea
rch,
Vol
. 25
(2
00
3)
pp.
22
-34
.
Vis
co-E
last
ic M
eso-
& M
icro
-M
odel
ing
of 8
HS
T65
0-3
5/P
MR
-15
To
un
ders
tan
d th
e ef
fect
of
bi
axia
l an
d sh
ear
dom
inat
ed l
oads
on
th
e fa
ilure
pro
cess
of
eigh
t h
arn
ess
sati
n (
8H
S) T
65
0-3
5/P
MR
-15
, 3
D m
odel
s of
th
e m
eso-
and
mic
ro-
un
it c
ells
wer
e bu
ilt.
The
mag
nit
ude
of
resi
dual
mes
o-an
d m
icro
-str
esse
s in
th
e w
arp
and
fill
tow
s an
d th
e st
ress
es c
ause
d by
pu
rely
m
ech
anic
al
shea
r an
d bi
axia
l lo
ads
wer
e n
um
eric
ally
det
erm
ined
as
a fu
nct
ion
of
the
cool
ing
rate
.
B.
Ben
edik
t, P
. R
upn
owsk
i an
d M
. K
um
osa,
Vis
co-E
last
ic S
tres
s D
istr
ibu
tion
s an
d El
asti
c P
rope
rtie
s in
U
nid
irec
tion
al G
raph
ite/
Pol
yim
ide
Com
posi
tes
wit
h La
rge
Vol
um
e Fr
acti
ons
of F
iber
s, A
cta
Mat
eria
lia,
Vol
. 51
, No.
12
(200
3) p
p. 3
483-
3493
.
P.
Rup
now
ski
and
M.
Ku
mos
a, M
eso-
and
Mic
ro-S
tres
s A
naly
ses
in a
n 8
HS
Gra
phit
e/P
olyi
mid
e W
oven
C
ompo
site
Su
bjec
ted
to B
iaxi
al I
n-P
lan
e Lo
ads
at R
oom
Tem
pera
ture
, Co
mpo
site
s Sc
ienc
e an
d Te
chno
logy
, V
ol. 6
3 (2
003)
pp.
785
-799
.
Vis
co-E
last
o-P
last
ic M
eso-
Mic
ro M
odel
ing
of 8
HS
T65
0-3
5/P
MR
-15
Fin
ite
elem
ent
repr
esen
tati
ons
of u
nid
irec
tion
al (
left
) an
d 8
HS
wov
en (
righ
t)
grap
hit
e/po
lyim
ide
com
posi
tes
for
vis
co-e
last
o-pl
asti
c m
icro
-an
d m
eso-
stre
ss
anal
yses
.
P.
Ru
pnow
ski,
M.
Gen
tz a
nd M
. K
um
osa,
Mec
han
ical
Res
pons
e of
a W
oven
Gra
phit
e/P
olyi
mid
e C
ompo
site
to
In-P
lan
e Sh
ear
Dom
inat
ed B
iaxi
al L
oads
at
Roo
m a
nd E
leva
ted
Tem
pera
ture
s,A
cta
Mat
eria
lia,
Vol
. 52
, N
o.
19 (
2004
) pp
. 560
3-56
13.
Mes
o-&
Mic
ro-
Stre
ss D
istr
ibu
tion
s in
8H
S T6
50
-35
/PM
R-1
5M
eso-
and
mic
ro-s
tres
ses
in t
he
cen
ter
of t
he
tow
in t
he
un
dula
tion
reg
ion
of
8H
S T6
50
/PM
R-1
5 f
or v
ario
us
exte
rnal
in-p
lan
e lo
ads
at r
oom
tem
pera
ture
.
Mes
o-St
ress
es [M
Pa]
Mic
ro-S
tres
ses
[MPa
]
Loa
d ca
seσ X
X(t
rans
. in
-pla
ne)
σ YY
(long
i. in
-pl
ane)
σ ZZ
(tra
ns.
out o
f pla
ne)
σ XZ
(in-
plan
e sh
ear)
Failu
re
Inde
xT
sai-H
ill
σ 1(m
ax.
prin
cipa
l str
ess
in th
e m
atri
x)
Cas
e 1
(∆T
onl
y) o
n co
olin
g64
-119
18-1
0.6
1.1
0.7
3.9
1.2
4.4
4.0
4.6
94
Cas
e 2
(∆T
+TX
)79
-129
16-1
107
Cas
e 3
(∆T
+TZ
)68
145
20-1
102
Cas
e 4
(∆T
+S)I
osip
escu
66-9
819
108
208
Cas
e 5
(∆T
+TX
+TZ
)83
136
170
111
Cas
e 6
(∆T
+TX
+S)
81-1
0717
109
222
Cas
e 7
(∆T
+TZ
+S)
7016
720
109
216
Cas
e 8
(∆T
+TX
+TZ
+S)
+/-4
5 de
g te
st85
158
1811
023
0
∆T
resi
dual
str
esse
s, T
X(Z
) ap
plie
d in
-pla
ne
ten
sion
s al
ong
the
war
p an
d fi
ll to
ws,
S in
-pla
ne
shea
r w
ith
TX
=TZ
=S=
10
0M
Pa
Vis
co-E
last
o-P
last
ic M
eso-
Mic
ro M
odel
ing
of 8
HS
T65
0-3
5/P
MR
-15
0102030405060
0.0%
0.5%
1.0%
1.5%
2.0%
shea
r str
ain
shear stress [MPa]R
T, F
EM
315°
C, F
EM
expe
rimen
tR
Tm
in/
%7
=ε&
min
/%
5=
ε&
315°
C,
315°
C,
min
/%
4.0=
ε&31
5°C
,
The
mac
ro-r
espo
nse
of
th
e co
mpo
site
to
sh
ear
cou
ld
be
accu
rate
ly
pred
icte
d as
a f
un
ctio
n o
f te
mpe
ratu
re a
nd
in-p
lan
e sh
ear
dom
inat
ed
load
s if
th
e ac
tual
com
posi
te a
rch
itec
ture
as
wel
l as
th
e fi
ber
and
mat
rix
prop
erti
es a
re c
onsi
dere
d.
P. R
upn
owsk
i, M
. Gen
tz a
nd
M. K
umos
a, M
echa
nic
al R
espo
nse
of a
Wov
en G
raph
ite/
Pol
yim
ide
Com
posi
te t
o In
-Pla
ne
Shea
r D
omin
ated
Bia
xial
Loa
ds a
t R
oom
and
Ele
vate
d Te
mpe
ratu
res,
Act
a M
ater
ialia
, Vol
. 52
, No.
19
(200
4) p
p. 5
603-
5613
.
Cri
tica
l Iss
ues
The
wea
kest
fra
ctu
re m
ode
in t
he 8
HS
T65
0/P
MR
-15
com
posi
te i
s th
e co
mbi
ned
st
ate
of
stre
ss
con
sist
ing
of
in-p
lan
e sh
ear
and
biax
ial
ten
sion
al
ong
the
war
p an
d fi
ll to
ws.
In
sh
ear
(Ios
ipes
cu
test
),tr
ansv
erse
tow
cra
cks
init
iate
at
appr
oxim
atel
y 9
5 M
Pa
shea
r st
ress
. U
nde
r bi
axia
l sh
ear
dom
inat
ed l
oads
(±
45
° of
f-ax
is),
th
e to
w c
rack
s in
itia
te a
t 5
7 M
Pa
shea
r st
ress
. Thi
s ca
n b
e ex
plai
ned
nu
mer
ical
ly.
Lin
ear
elas
tic
mac
ro-
and
mic
ro-
stre
ss a
nal
yses
can
not
exp
lain
th
e ve
ry c
ompl
ex f
ract
ure
/fai
lure
pro
cess
in
wov
en g
raph
ite/
poly
imid
e la
min
ates
su
bjec
ted
to i
n p
lan
e sh
ear
dom
inat
ed l
oads
. A
lso,
non
-lin
ear
mac
ro-a
ppro
ach
es
are
not
su
itab
le
to
expl
ain
th
e ef
fect
of
bi
axia
l loa
ds a
nd
resi
dual
str
esse
s on
th
e da
mag
e in
itia
tion
str
esse
s.
Vis
co-e
last
o-pl
asti
c an
alyt
ical
an
d FE
M s
tres
s an
alys
es a
re n
eede
d. I
n
part
icu
lar,
th
e ef
fect
of
man
ufa
ctu
rin
g re
sidu
al s
tres
ses
on t
he
failu
re
proc
ess
mu
st b
e co
nsi
dere
d.
The
type
of
frac
ture
an
d th
e cr
itic
al l
oads
will
be
affe
cted
by
phys
ical
an
d ch
emic
al a
gin
g.
Res
idu
al S
tres
ses
and
Tow
Mic
ro-C
rack
ing
Cro
ss-s
ecti
ons
of w
oven
8H
S T
65
0-3
5/P
MR
-15
(le
ft),
4H
S M
40
J/P
MR
-II-
50
(m
iddl
e)
and
4H
S M
60
J/P
MR
-II-
50
(ri
ght)
com
posi
tes
afte
r m
anu
fact
uri
ng
and
post
cu
rin
g
Res
idu
al
stre
sses
in
gr
aph
ite/
poly
imid
e co
mpo
site
s de
pen
d pr
imar
ily o
n:
Vis
co-e
last
o-pl
asti
c st
iffn
ess
prop
erti
es a
nd
CTE
s of
pol
yim
ide
resi
ns
Fibe
r el
asti
c pr
oper
ties
(lo
ngi
tudi
nal
, tra
nsv
erse
, sh
ear)
CTE
s of
fib
ers
(bot
h lo
ngi
tudi
nal
an
d tr
ansv
erse
)M
anu
fact
uri
ng
con
diti
ons
Agi
ng
con
diti
ons
Fibe
r/m
atri
x in
terf
aces
Com
posi
te a
rch
itec
ture
, et
c., e
tc, e
tc.
An
Eva
luat
ion
of
Elas
tic
Pro
pert
ies
and
Coe
ffic
ien
ts
of T
her
mal
Exp
ansi
on o
f G
raph
ite
Fibe
rs
A
met
hod
olog
y h
as
been
su
gges
ted
for
the
eval
uat
ion
of
st
iffn
ess
prop
erti
es (
lon
gitu
din
al,
tran
sver
se a
nd
shea
r) a
nd
coef
fici
ents
of
th
erm
al
expa
nsi
on
(bot
h
lon
gitu
din
al
and
tran
sver
se)
of m
ediu
m (
T65
0-3
5)
and
hig
h (
M4
0J
and
M6
0J)
m
odu
lus
grap
hit
e fi
bers
. Th
e m
eth
odol
ogy
was
su
bseq
uen
tly
use
d to
det
erm
ine
the
stif
fnes
s an
d th
erm
al p
rope
rtie
s of
th
e fi
bers
fro
m t
he
mac
rosc
opic
in
put
data
of
un
idir
ecti
onal
an
d w
oven
com
posi
tes
base
d on
th
e sa
me
fibe
rs e
mbe
dded
eit
her
in
PM
R-1
5 o
r P
MR
-II-
50
pol
yim
ide
resi
ns.
P.
Rup
now
ski,
M.
Gen
tz,
J.K
. Su
tter
and
M.
Kum
osa,
An
Eval
uat
ion
of E
last
ic P
rope
rtie
s an
d C
oeff
icie
nts
of
Ther
mal
Exp
ansi
on o
f G
raph
ite
Fibe
rs f
rom
Mac
rosc
opic
Com
posi
te I
npu
t D
ata,
Pro
ceed
ings
of
the
Roy
al
Soci
ety,
Vol
. 46
1 (
20
05
) pp
. 34
7-3
69
.
P.
Ru
pnow
ski,
M.
Gen
tz,
J. K
. Su
tter
and
M.
Ku
mos
a, A
n Ev
alua
tion
of
the
Elas
tic
Pro
pert
ies
and
Ther
mal
Ex
pan
sion
Coe
ffic
ien
ts o
f M
ediu
m a
nd H
igh
Mod
ulu
s G
raph
ite
Fibe
rs,
Com
posi
tes
Part
A;
App
lied
Scie
nce
and
Man
ufac
turi
ng, V
ol. 3
6 (2
004)
pp.
327
-338
.
T65
0-3
5, M
40
J, M
60
J; E
last
ic P
rope
rtie
s
The
room
te
mpe
ratu
re
prop
erti
es o
f th
e T6
50
-35
, M
40
J an
d M
60
J fi
ber
syst
ems
wer
e m
easu
red
usi
ng
the
thre
e-co
mpo
nen
t os
cilla
tor
reso
nan
ce
met
hod
. Th
e m
acro
-co
effi
cien
ts
of
ther
mal
ex
pan
sion
of
th
e co
mpo
site
s an
d th
eir
nea
t re
sin
s w
ere
obta
ined
by
le
ngt
h
dila
tom
etry
. Th
en,
the
fibe
r pr
oper
ties
w
ere
calc
ula
ted
(re-
calc
ula
ted
for
T65
0-3
5).
2 ⎟⎟ ⎠⎞⎜⎜ ⎝⎛
=n
Lf
Gor
Esp
ecρ
P. R
upn
owsk
i, M
. Gen
tz, J
. K. S
utte
r an
d M
. Kum
osa,
An
Eval
uati
on o
f th
e El
asti
c P
rope
rtie
s an
d Th
erm
al
Expa
nsi
on C
oeff
icie
nts
of
Med
ium
and
Hig
h M
odu
lus
Gra
phit
e Fi
bers
, Co
mpo
site
s Pa
rt A
; App
lied
Scie
nce
and
Man
ufac
turi
ng, V
ol. 3
6 (2
004)
pp.
327
-338
.
Esh
elby
/Mor
i-Ta
nak
a A
ppro
ach
11
11
11
11
[(1)
()(
)][
((
))(
)]
fm
mc
mv
mc
vv
CC
IS
CC
IC
Sf
SI
CC
ff
−−
−−
−−
=−
−−
+−
−−
−
mc
mm
vf
mf
vf
CI
Sf
SC
CC
fα
αα
α+
−−
−−
−=
−)
]())
()(
[(1
1
wh
ere
C f,
C c,
C mar
e th
e st
iffn
ess
mat
rice
s of
th
e fi
bers
, co
mpo
site
an
d re
sin
, res
pect
ivel
y
Sis
th
e Es
hel
by t
enso
r an
d I
is t
he
iden
tity
mat
rix
α f,α
m ,
andα c
are
the
colu
mn
vec
tors
of
the
CTE
s fo
r th
e fi
bers
, m
atri
x an
d co
mpo
site
, res
pect
ivel
y
f vis
th
e vo
lum
e fr
acti
on o
f fi
bers
Mac
ro-
to M
icro
-App
roac
h
Cla
ssic
al e
rror
ana
lysi
s ba
sed
on t
he M
onte
Car
lo m
etho
d ap
plie
d to
th
e in
vers
e Es
helb
y/Ta
naka
-Mor
i m
odel
w
as
empl
oyed
to
com
pute
the
unc
erta
inty
of
indi
rect
eva
luat
ion
of
grap
hite
fibe
r pro
pert
ies.
INPU
T D
ATA
–co
mpo
site
an
d re
sin
prop
ertie
s
OU
TPU
T D
ATA
–pr
obab
ility
di
strib
utio
n fu
nctio
ns (p
df’s
) of
fibe
r pro
perti
es
Mon
te C
arlo
m
etho
d+
Mic
ro-m
echa
nic
mod
el
P. R
upno
wsk
i, M
. Gen
tz, J
.K. S
utt
er a
nd
M. K
um
osa,
An
Eval
uat
ion
of E
last
ic P
rop
erti
es a
nd
Coe
ffic
ien
ts o
f Th
erm
al E
xpan
sion
of
Gra
phit
e Fi
bers
fro
m M
acro
scop
ic C
ompo
site
In
put
Dat
a, P
roce
edin
gs o
f th
e R
oyal
Soc
iety
, Vol
. 461
(20
05)
pp. 3
47-3
69.
T65
0-3
5, M
40
J, M
60
J; “
Fin
al”
Esti
mat
es
E f11
[GP
a]E f
22
[GP
a]G
f12
[GP
a]G
f23
[GP
a]ν f
12C
TE
(lon
g.)
10
-6/K
CTE
(t
ran
s.)
10
-6/K
T65
0-
35
22
4±
3(2
43
)
15
.4±
0.5
(13
.8)
21
.1±
1.1
(23
.1)
5.8
±0
.4(5
.0)
0.4
4±
0.0
2(0
.29
)
-1.1
6±
0.0
5(-
.84
)
13
.3±
0.8
(7.8
)
M4
0J
32
5±
19
(37
7)
10
.8±
0.3
20
.8±
23
.9±
0.1
0.2
2±
0.0
5-2
.0±
0.1
(-.8
3)
8.7
±1
.6
M6
0J
50
0±
2(5
88
)
9.4
±0
.5-
--
-2.0
±0
.2(-
1.1
)
18
.0±
4
() f
rom
lite
ratu
re
Mac
ro-
to M
icro
-App
roac
h;
Lim
itat
ion
s
The
new
ly d
evel
oped
exp
erim
enta
l/n
um
eric
al
met
hod
olog
y is
ex
trem
ely
sen
siti
ve
to
the
accu
racy
of
the
inpu
t m
acro
-dat
a, e
spec
ially
in
th
e ca
se o
f th
e el
asti
c pr
oper
ties
.
How
ever
, u
sin
g th
e m
acro
co
mpo
site
in
put
data
fro
m t
he
osci
llato
r re
son
ance
met
hod
an
d le
ngt
h
dila
tom
etry
in
co
nju
nct
ion
w
ith
EM
T an
d FE
M,
hig
h
qual
ity
esti
mat
es
of
fibe
r pr
oper
ties
wer
e ob
tain
ed.
The
met
hod
olog
y al
so w
orks
ver
y w
ell
wit
h
ther
mal
exp
ansi
ons
of g
raph
ite
fibe
rs.
X-R
ay D
iffr
acti
on T
ests
on
T6
50
-35
/PM
R-1
5
Com
posi
tes
wit
h E
mbe
dded
In
clu
sion
s
Inte
rlam
inar
re
sidu
al
ther
mal
st
ress
es
in
un
idir
ecti
onal
an
d w
oven
(8
HS)
T6
50
-35
/PM
R-1
5
com
posi
tes
wer
e de
term
ined
bot
h e
xper
imen
tally
an
d n
um
eric
ally
as
a fu
nct
ion
of
the
man
ufa
ctu
rin
g pr
oces
s.N
um
erou
s X
RD
mea
sure
men
ts w
ere
mad
e to
de
term
ine
resi
dual
st
rain
s an
d st
ress
es
in
embe
dded
Al
and
Ag
incl
usi
ons
plac
ed i
n f
our
ply
8H
S w
oven
an
d 6
ply
un
idir
ecti
onal
gra
phit
e/P
MR
-1
5 c
ompo
site
s.
B. B
ened
ikt,
M. K
um
osa,
P.K
. Pre
deck
i, L.
Ku
mos
a, M
.G. C
aste
lli a
nd J
.K. S
utt
er, A
n A
nal
ysis
of
Res
idu
al T
her
mal
St
ress
es
in
a U
nid
irec
tion
al
Gra
phit
e/P
MR
-15
C
ompo
site
B
ased
on
th
e X
-ray
D
iffr
acti
on
Mea
sure
men
ts,
Com
posi
tes
Scie
nce
and
Tech
nolo
gy, V
ol. 6
1, N
o. 1
4 (2
001)
pp.
197
7-19
94.
B. B
ened
ikt,
P. R
upn
owsk
i, L.
Ku
mos
a, J
. K. S
utt
er, P
.K. P
rede
cki a
nd M
. Ku
mos
a, D
eter
min
atio
n of
In
terl
amin
ar
Res
idua
l Th
erm
al S
tres
ses
in a
Wov
en 8
HS
Gra
phit
e/P
MR
-15
Com
posi
te U
sing
X-R
ay D
iffr
acti
on M
easu
rem
ents
, M
echa
nics
of
Adv
ance
d M
ater
ials
and
Str
uctu
res ,
Vol
. 9 (
2002
) p
p. 1
-20.
X-R
ay D
iffr
acti
on T
ests
on
T6
50
-35
/PM
R-1
5
Com
posi
tes
wit
h E
mbe
dded
In
clu
sion
s
33
11
22
ψ
ϕ
Diff
ract
ion
Plan
e N
orm
al
ψϕ
εψ
ϕε
ψε
ψϕ
ε
ψϕ
εψ
ϕε
εϕψ
ϕψ
2si
nsi
n2
sin
cos
cos
sin
sin
sin
2si
nsi
nco
s
2313
233
22
22
212
22
110
0
++
+
++
=−
=d
dd
Latt
ice
spac
ing
in u
nst
ress
ed (
d o)
and
stre
ssed
(d ϕ
ψ)
part
icle
s m
easu
red
by X
RD
.
X-R
ay D
iffr
acti
on T
ests
on
T6
50
-35
/PM
R-1
5
Com
posi
tes
wit
h E
mbe
dded
In
clu
sion
s
Alu
min
um
incl
usi
on
Embe
dded
Al i
ncl
usi
ons
betw
een
wov
en p
lies
Embe
dded
Al i
ncl
usi
ons
betw
een
un
idir
ecti
onal
plie
s
Inte
rlam
inar
Res
idu
al S
tres
ses
in 8
HS
T65
0-3
5/P
MR
-15
Com
posi
te
Res
idua
l str
esse
s in
uni
dire
ctio
nal a
nd 8
HS
T650
-35
/PM
R-1
5 co
mpo
site
s w
ere
dete
rmin
edju
st o
n co
olin
g (n
o ex
tern
al lo
ads
appl
ied)
with
ext
erna
l ben
ding
load
s (s
mal
l and
larg
e)
afte
r ag
ing
in N
2an
d ai
r
X-r
ay w
ith
Esh
elby
/Mor
i-Ta
nak
aP
late
th
eory
σ11
[MP
a]σ
22
[MP
a]σ
33
[MP
a]σ
11
[MP
a]σ
22
[MP
a]σ
33
[MP
a]
Lin
ear
elas
tic
70.7
±17
71.1
±17
36.7
±16
94
.09
4.0
0
Vis
co-e
last
ic67
.3 ±
1767
.6 ±
1633
.0 ±
166
3.1
63
.10
Res
idu
al in
terl
amin
ar s
tres
ses
in 8
HS
T65
0-3
5/P
MR
-15
(n
o ex
tern
al lo
ads
and
no
agin
g)
X-R
ay D
iffr
acti
on E
xper
imen
ts o
n G
raph
ite
Fibe
r/P
olyi
mid
e C
ompo
site
s Su
bjec
ted
to A
gin
g
(XR
D)
mea
sure
men
ts o
f re
sidu
al s
trai
ns
in e
mbe
dded
alu
min
um
sp
her
ical
in
clu
sion
s w
ere
perf
orm
ed
to
eval
uat
e th
e re
sidu
al
inte
rlam
inar
str
esse
s in
un
idir
ecti
onal
an
d w
oven
8H
S T6
50
/PM
R-
15
com
posi
tes
subj
ecte
d to
agi
ng
eith
er i
n a
ir o
r n
itro
gen
an
d ex
tern
al b
endi
ng
load
s.
Un
idir
ecti
onal
T6
50
-35
/PM
R-1
5 s
yste
m a
ged
in n
itro
gen
(le
ft)
and
in a
ir (
righ
t) f
or 1
170
hou
rs.
B.
Ben
edik
t et
al.
Det
erm
inat
ion
of I
nte
rlam
inar
Res
idua
l St
ress
es i
n a
Wov
en 8
HS
Gra
phit
e/P
MR
-15
Com
posi
te U
sing
X-r
ay D
iffr
acti
on M
easu
rem
ents
, M
echa
nics
of
Adv
ance
d M
ater
ials
and
Str
uctu
res,
Vol
. 9
(20
02
) pp
. 37
5.
B.
Ben
edik
t et
al.,
, A
naly
sis
of S
tres
ses
in A
lum
inu
m P
arti
cles
Embe
dded
Ins
ide
Un
idir
ecti
onal
and
Wov
en
Gra
phit
e/P
olyi
mid
e C
ompo
site
s Su
bjec
ted
to L
arge
Ben
din
g Lo
ads,
Mec
hani
cs o
f A
dvan
ced
Mat
eria
ls a
nd
Stru
ctur
es, V
ol. 1
1, N
o. 1
(20
04)
pp. 3
1-49
.B
. B
ened
ikt
et a
l., X
-Ray
Dif
frac
tion
Exp
erim
ents
on
Age
d G
raph
ite
Fibe
r/P
olyi
mid
e C
ompo
site
s w
ith
Em
bedd
ed A
lum
inu
m I
ncl
usi
ons,
Com
posi
tes
Part
A,V
ol. 3
5 (2
004)
pp.
667
-681
.
Ou
r N
ew M
odel
of
Agi
ng
in N
itro
gen
Bas
ed o
n:
“Th
e M
ech
anic
al R
espo
nse
of
Eigh
t H
arn
ess
Sati
n
(8H
S) W
oven
T6
50
-35
/PM
R-1
5 A
ged
in N
itro
gen
”by
: P
. R
upn
owsk
i, M
. Gen
tz, D
. Arm
entr
out,
J. K
. Su
tter
an
d , M
. Ku
mos
a pu
blis
hed
in:
Act
aM
ater
ialia
, Vol
. 53
, No.
17
(2
00
5)
pp. 4
55
5-
45
65
.
Ou
r m
odel
has
not
yet
bee
n p
rese
nte
d to
th
is
com
mu
nit
y.
The
Mec
han
ical
Res
pon
se o
f Ei
ght
Har
nes
s Sa
tin
(8
HS)
Wov
en T
65
0-3
5/P
MR
-15
Age
d in
Nit
roge
n
The
mec
han
ical
res
pon
se o
f an
eig
ht
har
nes
s sa
tin
wov
en T
65
0-3
5/P
MR
-15
com
posi
te t
o ag
ing
in
nit
roge
n
at
31
5°C
fo
r u
p to
ap
prox
imat
ely
15
00
hou
rs w
as i
nve
stig
ated
bo
th e
xper
imen
tally
an
d n
um
eric
ally
.
The
agin
g st
ress
es
in
the
com
posi
te
wer
e n
um
eric
ally
pre
dict
ed o
n a
mes
o-sc
ale
usi
ng
the
con
cept
of
a u
nit
cel
l.
The
Mec
han
ical
Res
pon
se o
f Ei
ght
Har
nes
s Sa
tin
(8
HS)
Wov
en T
65
0-3
5/P
MR
-15
Age
d in
Nit
roge
n
Vis
coel
asti
c, a
ge s
tiff
enin
g, a
nd
volu
met
ric
shri
nka
ge
effe
cts
wer
e co
nsi
dere
d in
th
e si
mu
lati
ons
to
desc
ribe
th
e m
ech
anic
al
beh
avio
r of
th
e n
eat
PM
R-1
5 p
olyi
mid
e in
th
e co
mpo
site
su
bjec
ted
to a
gin
g at
31
5°C
.
To
veri
fy
the
nu
mer
ical
pr
edic
tion
s,
the
stre
ngt
h
and
stif
fnes
s of
th
e co
mpo
site
w
ere
mea
sure
d as
a f
unct
ion
of
agin
g ti
me
usi
ng
the ±4
5°te
nsi
le t
est.
Vis
coel
asti
c P
rope
rtie
sof
PM
R-1
5
A s
erie
s of
mec
han
ical
2 h
lo
ng
rela
xati
on t
ests
at
27
5,
30
0, 3
25
an
d 3
50°
C w
ere
perf
orm
ed u
nde
r co
nst
ant
disp
lace
men
t to
obt
ain
st
ress
es a
nd
stra
ins
as a
fu
nct
ion
of
tim
e (σ
(t)
and
ε(t)
).Th
en, a
n o
ptim
izat
ion
te
chn
iqu
e w
as e
mpl
oyed
to
dete
rmin
e th
e re
laxa
tion
m
odu
lus
E(t)
for
eac
h t
est
(upp
er r
igh
t). S
ubs
equ
entl
y,
a m
aste
r cu
rve
was
co
nst
ruct
ed (
low
er r
igh
t)an
d th
e h
oriz
onta
l th
erm
al
shif
t fa
ctor
s w
ere
obta
ined
.
Age
Sti
ffen
ing
& S
hri
nka
ge o
f P
MR
-15
Wh
en a
pol
ymer
s is
ph
ysic
ally
age
d it
s vi
scoe
last
ic
resp
onse
ch
ange
s as
a f
un
ctio
n o
f ag
ing
tim
e.
Typi
cally
, th
e re
laxa
tion
pro
cess
slo
ws
dow
n w
ith
ag
ing.
Th
is a
ge s
tiff
enin
g ef
fect
in P
MR
-15
can
be
mod
eled
by
shif
tin
g th
e ti
me
scal
e in
its
visc
oela
stic
m
odel
.Con
sequ
entl
y,,
t.
∫⋅
−=
klijk
lij
dt
Ct
0
)(
))(
)((
)(τ
ετ
ψψ
σ
whe
re∫
=t
hd
at
0
)(
)(
ττ
ψ
Age
Sti
ffen
ing
& S
hri
nka
ge o
f P
MR
-15
a h in
th
e pr
evio
us
con
stu
tive
equ
atio
n is
a
hor
izon
tal a
gin
g sh
ift
fact
orta
ken
fro
m
[Kam
vou
ris,
J. E
., R
ober
ts, G
. D.,
Per
eira
, J.
M.,
and
Rab
zak,
C.,
(19
97
), “
Ph
ysic
al a
nd
Ch
emic
al A
gin
g Ef
fect
s in
PM
R-1
5 N
eat
Res
in”,
AST
M S
TP13
02, p
p. 2
43
-25
8. ]
The
agin
g sh
rin
kage
str
ain
rat
e fo
r P
MR
-15
w
as d
eter
min
ed f
or t
imes
ran
gin
g fr
om 0
to
30
0 h
an
d w
as f
oun
d to
be
-23
.4·1
0-6/h
. Th
e sa
me
rate
was
ass
um
ed in
th
e ag
ing
sim
ula
tion
s of
th
e co
mpo
site
for
up
to
10
00
h.
Vis
coel
asti
c P
rope
rtie
sof
PM
R-1
5
Long
ter
m r
elax
atio
n cu
rve
with
and
w
ithou
t ag
e st
iffen
ing
(left
)
•A
ge s
tiff
enin
g st
ron
gly
affe
cts
the
shap
e of
th
e re
laxa
tion
fu
nct
ion
s in
th
e co
nsi
dere
d ti
me
ran
ge a
nd
ther
efor
e ca
nn
ot b
e n
egle
cted
in t
he
com
puta
tion
s of
str
esse
s in
th
e ag
ed c
ompo
site
.
•A
n a
gin
g m
odel
wit
hou
t ag
e st
iffe
nin
g w
ould
un
dere
stim
ate
the
agin
g st
ress
es in
th
e co
mpo
site
app
roxi
mat
ely
by a
fac
tor
of t
wo.
Agi
ng
Expe
rim
ents
Twen
ty-t
wo
spec
imen
s w
ith
th
e fi
bers
alig
ned
at
±45
°fr
om t
hei
r lo
ng
axis
wer
e w
ater
jet
cut
from
a
com
posi
te p
anel
. Th
e di
men
sion
s of
th
e sp
ecim
ens
wer
e 1
53
.5 x
25
.4 x
5.3
4 m
m. F
ollo
win
g w
ater
jet
cutt
ing
the
spec
imen
s w
ere
drie
d in
a v
acu
um
at
11
0°C
for
24
h.
The
spec
imen
s w
ere
plac
ed in
an
ove
n in
a s
tati
c n
itro
gen
atm
osph
ere
at r
oom
tem
pera
ture
. Th
e te
mpe
ratu
re o
f th
e ov
en w
as r
ampe
d at
5°C
per
m
inu
te u
nti
l 31
5°C
was
rea
ched
. O
nce
th
e is
oth
erm
al a
gin
g te
mpe
ratu
re w
as a
chie
ved,
th
e ag
ing
tim
e st
arte
d. F
rom
th
e tw
enty
spe
cim
ens
fou
r sp
ecim
ens
each
wer
e ag
ed a
t 2
88
, 62
4, 9
58
, 1
29
6, a
nd
15
35
h.
Agi
ng
Expe
rim
ents
The
±4
5°
ten
sile
tes
ts w
ere
perf
orm
ed a
t ro
om t
empe
ratu
re a
t a
rate
of
1 m
m/m
in.
un
til f
ailu
re.
Two
room
tem
pera
ture
ten
sile
tes
ts a
t 0
ag
ing
tim
e w
ere
perf
orm
ed a
nd
a m
inim
um
of
th
ree
room
tem
pera
ture
ten
sile
tes
ts a
t al
l ot
her
agi
ng
tim
es w
as p
erfo
rmed
.
Du
rin
g th
e ±4
5°te
sts,
aco
ust
ic e
mis
sion
(A
E)
was
mon
itor
ed b
y a
D9
21
5 s
enso
r fr
om
Ph
ysic
al A
cou
stic
Cor
p. (
PA
C)
Agi
ng
Expe
rim
ents
Res
ult
s fr
om t
he
±45
ºex
peri
men
ts o
n t
he
aged
com
posi
te s
peci
men
s in
clu
ded:
(1)
the
ult
imat
e st
ren
gth
of t
he
±45
ºspe
cim
ens,
(2
) st
ress
at
the
init
iati
on o
f in
tral
amin
ar
dam
age
as d
eter
min
ed b
y A
E,(3
) th
e sh
ear
mod
ulu
s
All
as a
fu
nct
ion
of
agin
g ti
me
at 3
15°
C.
Agi
ng
Expe
rim
ents
34567
0288
624
958
1296
1535
Aging Time (hr)
Modulus (GPa)
20
30
40
50
60
70
80
90
100
0288
624
958
1296
1535
Aging Time (hr)
Stress (MPa)
Ultimate Strength
Onset of A.E.
•B
etw
een
0 a
nd
28
8 h
of
agin
g ti
me
the
mod
ulu
s in
crea
sed
appr
oxim
atel
y 1
2%
. Th
en, t
he
mod
ulu
s w
as u
nch
ange
d w
ith
in t
he
vari
abili
ty o
f th
e m
easu
rem
ents
.
•Th
e u
ltim
ate
shea
r st
ren
gth
was
un
chan
ged
as a
fu
nct
ion
of
agin
g.
•A
gin
g di
d n
ot a
ffec
t n
otic
eabl
y th
e on
set
of in
tral
amin
ar d
amag
e.
Mod
elin
gTh
e Es
hel
by/M
ori-
Tan
aka
mod
el
was
em
ploy
ed
to
obta
in
the
visc
oela
stic
pr
oper
ties
an
d sh
rin
kage
of
the
tow
s.
Then
, th
e pr
oper
ties
of
the
tow
s w
ere
intr
odu
ced
into
a
mes
o u
nit
-cel
l re
pres
enti
ng
the
com
posi
te
(see
ri
ght)
. Su
bseq
uen
tly,
ag
ing
was
si
mu
late
d u
sin
g th
e u
nit
-ce
ll an
d th
e m
eso-
stre
sses
an
d st
rain
s in
th
e co
mpo
site
w
ere
dete
rmin
ed
as
a fu
nct
ion
of
tim
e.
Mod
elin
g R
esu
lts
Num
eric
al in
-an
d ou
t-of
-pla
ne
shrin
kage
str
ains
(*)
as a
fu
nctio
n of
agi
ng a
t 31
5°C
*)
not
yet
exp
erim
enta
lly v
erif
ied)
.
Shea
r st
ress
vs.
she
ar s
trai
n di
agra
ms
and
the
shea
r m
odul
i at
315°
C be
fore
and
aft
er a
ging
for
10
00 h
ours
.
Mod
elin
g R
esu
lts
0102030405060708090
010
020
030
040
050
060
070
080
090
010
00Ag
ing
time
[hr]
Transverse stress [MPa]
cool
ing
stre
ss (6
4 M
Pa)
agin
g st
ress
(v
isco-
elas
tic m
odel
)
agin
g st
ress
(e
last
ic m
odel
)
The
max
imum
tra
nsve
rse
stre
ss in
the
tow
s (a
bove
)af
ter
agin
g fo
r 10
00 h
ours
at
315°
C, a
s de
term
ined
fro
m t
he m
odel
, w
as a
ppro
xim
atel
y 85
PM
a(u
pper
lim
it, c
ould
be
even
low
er!)
.Af
ter
cool
ing
with
out
agin
g th
e st
ress
is a
ppr.
64
MPa
.
Con
clu
sion
s
Agi
ng
in n
itro
gen
at
31
5°C
for
up
to 1
50
0 h
ours
had
a
very
sm
all e
ffec
t on
th
e st
ren
gth
, on
set
of
intr
alam
inar
dam
age,
an
d th
e sh
ear
mod
ulu
s of
8H
S T6
50
-35
/PM
R-1
5.
The
stre
ss r
elax
atio
n in
PM
R-1
5 t
hat
tak
es p
lace
at
elev
ated
tem
pera
ture
su
bsta
nti
ally
red
uce
s ag
ing
stre
sses
in t
he
com
posi
te.
The
agin
g st
ress
es in
side
th
e to
ws
wer
e m
uch
sm
alle
r th
an t
he
cool
ing
stre
sses
aft
er t
he
man
ufa
ctu
rin
g cy
cle.
Ou
r n
um
eric
al p
redi
ctio
ns
agre
ed w
ell w
ith
th
e ex
peri
men
tal r
esu
lts.