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Micromechanics of Spray-On Foam Insulation
Brett A. Bednarcyk* 3 Jacob Aboudi* Steven M. Arnoldi Senior Scientist Professor Research Engineer
Roy M. ~ullivani Research Engineer
Understanding the therm*mechanical response of the Space Shuttle k ternal Tank spray- on foam insulation (SOFI) material is critical, to NASA's Return to Flight effort. This closed- cell rigid polymeric foam is used to insulate the metallic Space Shuttle External Tank, which is at cryogenic temperatures immediately prior to and during lift off. The shedding of the SOFI during ascent led to the loss of the Columbia, and eliminating/minimizing foam lass from the tank has become a priority for NASA as it seeks to resume scheduled space shuttle missions. Determining the nature of the SOFI material behavior in response to both thermal and mechanical loading plays an important role as any structural modeling of the shedding phenomenon k predicated on knowledge of the constitutive behavior of the foam.
In this paper, the SOFI material has been analyzed using the High-Fidelity Generalized Method of Cells (HFGMC) micromechanics model, which has recently been extended to admit a triply-periodic 3-D repeating unit cell (RUC). Additional theoretical extensions that mere made in order to enable modeling of the dosed-cell-fok material include the ability to . represent internal boundaries witbin the RUC (to simulated internal pores) and the ability to impose an internal pressure within the simulated pores. This latter extension is crucial as two sources contribute to significant internal pressure changes within the SOFI pores. First, gas trapped in the pores during the spray will expand or contract due to temperature changes. Second, the pore pressure will increase due to outgassing of water and other species present in the foam skeleton polymer material. With HFGMC's new pore pressure modeling capabilities, a nonlinear pressure change within the simulated pore can be imposed that accounts for both of these sources, in addition to stmdar&-thermal and mechanical loading;
The triply-periodic HFGMC micromechanics model described above was implemented within NASA GRC's MAC/GMC software package, giving the model access to a range of nonlinear constitutive models for the polymeric foam skeleton material. A repeating unit cell architecture was constructed that, while relatively simple, still accounts for the geometric anisotropy of the porous foam microstructure and its thin walls and thicker edges. With the lack of reliable polymeric foam skeleton materia1 properties, many simulations were executed aimed at backing out these material properties. Then, using these properties, predictions of the thermemechanical behavior of the foam, including calculated internal applied pressure profiles, were performed and compared with appropriate experimental data.
*Ohio Aerospace Institute, Ohio Aerospace Institute, NASA GRC, 21000 Brookpark Rd., Cleveland, USA 44135
f Mechanics and L f i g Branch, NASA Glenn Research Center, MS 49/7,21000 Brookpark Rd., Cleveland, USA 44135
$Corresponding Author; Contact Email: bednarcyk0oai . org
https://ntrs.nasa.gov/search.jsp?R=20070005861 2020-05-26T06:39:07+00:00Z
Micromechanics of Spray-On 1 Foam Insulation
Brett A. Bednarcyk and Jacob Abuudi O M Aemwce Insmfe a e d e n d , OH
dl Steven M. Amold and Roy M. Sullivan NASA Gimn Rwwm Center, C l e M , OH -.
I ---. w,y
Multi-Scale Approach to Modeling ET Foam Insulation A
m E a c h e ! m m t m b a m t b o m ~ , ~ l pmperlleq W h W , and
L: I ~ l ~ m ~
k 1 Fuam FEA
I Level HFGMC AnaWb of Foun
. - + - .. -. - -f--IC-L3..W-..-.--rC--r *. .
'HFGMC Mimmechanirn Model: Geometry and Approach
. > ; .
,, Sbbdl. may Eontain any nraterial. -- Q T ~ ~ ( W )
1 1 '
lnlemalmRtmwm --- i ,
HFGMC Micromechani& Model: Basic Equations
h p t y s u ~ ~ subjected b Internal p m n : P'*) ConsWuthre equation Mhln each &&ell W h g inebstlc and thermal streins:
@(mW = d.*) .(" - r l 1 4 ) - f i B P T ) f l ( M d assumed In each subcell:
Unknorm t e r n in asb suboell, d$' determld via impellion of sqrYlbriurn. I continuity, and petidcity equations in an average (Integral) sense
R w l b in system d linear w m k equatbns for u n k m terms: W = f +g
K - Contalm gewnstry and themKrmechanid property inhnmth u - ~ ~ u u n k n a w t e m ( ~ ~ ) ) f - Cantalm applied mkr and tempemhue I- g - Contelrw im&a of Inelastic stmlns and - ofep!m of prer#iums, #m
HFGMC Micromechanics Model: Basic Equations
Sohrlng the s p b m of eqimtbns establishes the b l h t b n rehth: = A(++ A ~ ~ A T + A'(* + ~ f l m /
Mechanicrd f
fhennel I r d w c l m - conesntration eoncenbation lntemelpeBMa tema va&r wtctor --
llm &Wml average stma In Ute matwkl-filled subcells are related to the average w ~ ~ b y : 1 a=- C ddrplrdm
D m rm* m-R Above equatrons allow Wlishment of constitutive equation fw p m s material:
E = ~ E - ( ~ " A T +$)-d
Where, I c =- C ddp lr &*)A(*) p ddrp I, [C'*)A*~ - r"'
D m (m* www I -f . - --I d># I? [dm*- v=GL
Dm CM- , bC'."**m
--.
Implementing Stiffening and Creep Modets need to be relatively simple, but capture primary effects Elastic Stifbnina Constitutive Model IChen and Sabb. 1981):
- Bdk MO~U~US: K(E,) = KO + K,8, + ~d vokrmdrlcstrain: ~ . = e ~ ~ f E , + € ~
-ShearModulus: ~ ( p , & ) = ~ , + 4 p + A &
1 1 J2 =yS,S, P = ~ ( % +%+@u)
- Fw slmpllcity reduce b two parameters, s%t K, = 4 =O
mian-Viscous C m e ~ Model for Palmers 1Ashbv and Jones. 1 M k
P- = ~ a e * / ~ Q = Creep activation energy
A = Creep coefficient
Creep and Stiffening Model for Skeleton Material % -- . , w;
we. "
-0IlIyrnsik €"causes -1ng Creep strain does not c o n M ~ t D ~ ~
-Creep highly dependent on timdbading lab
- ~Tem~ependsnce of m p aulmwk through Arrhenius eq.
*AddMonal temp dependence of Go and
o 0.01 am 0.0s 0.w 0.05 om am 0.0s & not shourn in chart
TmhkSWn
- - . ---
Model Variables
Geometrv
- Wall ThMness Treat&sftxed - Edge l l i i n e s s - --- Unit Cell Dlswetbtion 1
Material Prowrties - Elastic: bm, v, = 0.4 - Efastic Stiffening: K, , A, A#em@ b determine to - C w p : A, Q achieve W agreement
- 4 - Themral Epansion: .. - . .-- , - . +g-:< b . 4 < , , - A ..,,.: -:
-.,,a,,
-----
Geometry - BX 265 ~ X I
- ,
Face I Wail
- .
om
Rise Dlredon
-.-. R,,=R,,=1,36 . - . .. -.- .
. , .. .* * i .-. . . 0
(Bx-265 Aub law data provided by B. Lerch, NASA GRC) - , ,
Room Temp Loading and 15 s Creep
70 m
Assumed $me W i n g ~asnotchedtest
80
50 E,=270MPa(39Irsl) ,
u A = 0.001 W MPEI" 8-I
i : (0.00715 ksl-l s;') Q = 10,000 Jlmole
K,=7500MPe(tOMksi) 20 4=30
10 MmbR -CoolDormbD-320F
0 0 0.01 om 0.03 0.01 om om
m n
C
Cool Down to -320 F mraction of many effeds
- '%- - Porepmwrechange - CTE and CTE tempdependence - Gwp: due to Arrhenius tern
Temp. change rate (signMeantly a f k b weep)
& b m ~ d e ~ n d e n ~ e : a
Utll ld E vs. T data
1 -320 F vs. gS F 4 E i m s e by 46% Assume linear in#lease in skelebn m a t e r i a l E , ~ ~ o o m m p t o ~
E = ~ ~ [ 1 - ( 0 . ~ ~ 1 1 5 T-')AT]
a x l a m 0 ZOOmmO = E. [I - (0.001 175 OF-') AT] rorrll*.m
Cool Down to -320 F n ~ressum chanae: - Assume no phage transfer of voOatiles from m m temp to ayo - ~sswne -1-ps c m b d b n of air in pms
,, =ern= (O.W11979g/a)(8.314J/de-K) ( l ~ c e f M, 28.8g/mk m3
= (345.8 Pa/K)AT = (0.0279 p s i / ' ~ ) A T
UsddaEefromSouthm ResearchtobadrwtCTE (1 atm data)
4 b 1 - a a * u - m a l , im 9
------m ~ l . ~ - n r I I X w ( n l l l l P l h & V a r l
a ~ r r u # u
CTE and CTE Temp-Dependence
*Assumed llnsar CTE bemp.dependence
* W = ~ F ) = C ~ = 120x1 0% (87x1 OSF)
a= %[I -(0.03 * C ~ ) A T ]
=%[I-(0.00167 P)M]
~Note:Usedpwe
- - - pst3um estlfn8tes Imiudlng vdatiles above
Tmp#r tur (F) mom temp
Prediction of Southern Research Vacuum Data
Test
Codbocryoertlertm
Pull vacuum
HaBo125F
W b 7 5
R e k a vacuum - pl -w W r n W M ~ r n I 0 n I I T sm 1 1m 4 In -UJl 3 1910 419 0 1.19 4 m tS I I&* S lmm IB 1 all I t lrn s a I&o 7 L l l l fS 117 W
Cool Down to -320 F utrmbb.r*smu
---M-
ml am m bm L.*w
Last item needed is cool down rate (temperature vs. time) First tried linear temp. vs. time
_.*I' - . . ' ' , , . . ,
Zoo1 Down to -320 FWmiL , - .
(assuming linear time vs. temp.) ", , - .: > ' :BTf$t-! .;'+ +!-:,'-;$ f " ,-
, ,
o 0.01 1.02 am 0.04 aw o.w 0.07 aoe Stdn
--
Transient W-lr t Transfer in Cylinder B ..: Hmtmwm
rv2T(r,t) ==? f
J c = l O b S ~ =41.5% k c m
:'-,m k =- w
m 'C
k In' ihZ r= - = 6.Mx loq- 3 0.00103- a
-n. 195
~ ( r , , ) =T, -2(T, - T , ) Z = ~ ( ~ rt/$) rl 4 J , ( 4
Evaluate drlg J,, J, Beam1 f u n d m of lhe l* ldd Mathematim
4. nth positive zem of J,
. ,,
Transient Heat Transfer in cylinder Also perbrrned ABAQUS FEA heat transfer analyses:
DC308 Bridi 1 - 1
I W L - -.I- --.-Ic-r- -*----
J % m Z ~ L - - - AE~T- I I I -
1 A* - - ... --. - - - - -
n w*=-z-----
- -. #A'-- , L.. .h . I .
a ; ;.*,;u.:.>. '?ma*,* ,.r.
Transient Heat Transfer in Cylinder ABAQUS Temp Rofiles
m
0
- g a
I-.. . ---
-I 50
-2m
Transient Heat Transfer in Cylinder AMPUS Temp M l e s vs. Adytlcal Temp Frofilm r ) :I{$,
50
0
i' g -roo
+
-150
a . t OF+-.-+u 0 3 0.4 M Ad 0.7
7 , - O 2 ... >C A:. I- r n ~ k ( h L )
Transient -- - .---- Heat Transfer in Cylinder , . . 3.T"" RJ1Vp.Lill? V
Average Temp vs. T l m 26j
0 z
1 - 5
i4* 4 450 ." .
-m 0 to0 200 900 & IKK) 6M 7M W
lime I*) - ,. - ..
m
Cool Down to -320 F I 0
' Y
60
50
340
! 30 cn
20
\
10
." :'o 0 0.01 0.02 0.03 0.04 0.05 0.08
Stmln
r
Cool Down to -320 F Inconsistent with Southern Research Data
70
60
50
= $40
I- 10
10
rc.4 0
0 0.01 0.02 0. W 0.01 0.05 ROB SWn d
' 6<+ :y m, - \,-
I * ,
. ' I , '
Re-calibrate CTE TO -
Q = 283ttwlC (15.ClWlF)
0 0.01 0.02 0.03 0.04 0.08 0 . a Strain
Full Smooth Tensile Test Simulation 70
80
50
= g m r-
20
10
0 0 0.01 0.02 0.03 0.04 0.W 0.08
8traln
I GRC Thermal Expansion Data (~eb. 2006)
l h r a v l m d - B k d r 3
oa
038
RP
als
a1
am
0 0 I w 1 9
-m
- n C l o l ~ l TIC I m-
-tc lolBrrmWI -TE I M m
Elevated Temperature Pore Pressure Estimates
70
80
5%
I - I
#I
10 0 S D l W 1 5 4 2 0 0 2 5 0 5 0 0 9 5 0
T m m u n IF)
. . . . , , . -. .
0 20 10 80 80 100 1M 140 1BO Tempraturn (C)
--. 1' :* .-:; *1- --'C
aaq$& Conclusion $ev&2 * kt
NASA,uAl ImMAc s u h enhanced to enable m of foams wilh:
**nits anafysis '
- Intern1 p r e pre#ure n'
- EWmaterMsWlenlq - ~ l a w ~ m e t e r l a l c ~ e e p
' L%A~
Model attempts to captum 1 'Lorder mechanisms -\ " < 1 . E
. . : : q f
Model can do a masonawe job of simulating foam material thermo- mechanical behavior - QuIteafewpnmetersmustbe~autdIoambstdata - M i m powerful when eansthent-IM dda are avalhble
' f - - I ' L : - 7 . I -
-& -- * -* -r . 0: I oOE nelj :a% x : ' ar
-. - OB U ~ J t 4 0 t p f . ~ ~
. . . . . -