r~port il 7035-bal un ~a r ch 1981 - dtic · resume dans le cadre ~'une entente prevoyant...
TRANSCRIPT
UN D ll L
R~PORT 4196/81 IL 7035-BAL ~ARCH 1981
17~~1:!000 \10TOR (,. Ri\1'\ TRL ( Tl R \I I'\ rt , BIT'! \\\I 'I ~h
C. Carrit>r
BUREAU RE CHER CHE El DEVHO PPEMENT MINISTERE DE LA DEFENSE NATIO NALE
CANADA
Centre de Recherches pour Ia Defense
Defence Research Establishment
Valcartier , Qu~bec
NON CL/\SSJFIE
RESE AR CH AN D DEVELO PMENT BRANCH DEPARTMENT O F NATIO NAL DEFENCE
CANADA
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1. REPORT DATE MAR 1981 2. REPORT TYPE
3. DATES COVERED 00-00-1981 to 00-00-1981
4. TITLE AND SUBTITLE 17KS12000 Motor Grain Structural Integrity Analysis
5a. CONTRACT NUMBER
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Defence R&D Canada - Valcartier,2459 de la Bravoure Road,Quebec,Quebec G3J 1X5 ,
8. PERFORMING ORGANIZATIONREPORT NUMBER
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)
11. SPONSOR/MONITOR’S REPORT NUMBER(S)
12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited
13. SUPPLEMENTARY NOTES
14. ABSTRACT
15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as
Report (SAR)
18. NUMBEROF PAGES
71
19a. NAME OFRESPONSIBLE PERSON
a. REPORT unclassified
b. ABSTRACT unclassified
c. THIS PAGE unclassified
Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
·1"
0::..:_
CRDV R-4196/81 DOSSIER: 7035-BAL
Quebec, Canada
UNCLASSIFIED
·17KS12000 MOTOR GRAIN
STRUCTURAL INTEGRITY ANALYSIS
by
C. Carrier
CENTRE DE RECHERCHES POUR LA DEFENSE
DEFENCE RESEARCH ESTABLISHMENT
VALCARTIER
Tel: (41-8) 844-4271
NON CLASSIFIE
DREV R-4196/81 FILE: 7035-BAL
.·
March/mars 1981
.... '
•
UNCLASSIFIED i
RESUME
Dans le cadre ~'une entente prevoyant l'echange de services
entre la Bristol Aerospace Ltd. et le Ministere de la defense nationale,
on a demande au Centre de recherches pout la defense de Valcartier
d'analyser, entre autres, l'integrite structurale du pain de propergol
du moteur-fusee d'apogee l7KS12000. Lars de !'analyse finale, trois
conditions de chargement furent considerees: la contraction thermique,
!'acceleration au lancement, et la mise sous pression a l'allumage.
L'analyste s'est servi de la methode des elements finis et
a applique la technique des variables reduites de l~illiams-Landel
Ferry aux proprietes mecaniques du propergol. (NC)
ABSTRACT
"J"'' 1 As part of a Provision of Services Agreement between Bristol
Aerospace Ltd. and the Department of National Defence, the Defence
Research Establishment, Valcartier was required to perform the structural
integrity analysis of the grain of a solid propellant rocket motor·,
designated as the l7KS12000. Three load cases were considered for
the final analysis: thermal contraction, launch acceleration, and
ignition pressurization.
The analyst used the finite element method and a,pplied the
lhlliams-Landel-Ferry technique of reduced variables. to the propellant
mechanical properties.,(U)
1.0
2.0
3.0
4.0
s.o
·' UNCLASSIFIED
ii
TABLE OF CONTENTS
RESUME/ABSTRACT
NOMENCLATURE
ABBREVIATIONS
INTRODUCTION
GRAIN STRUCTURAL ANALYSES
2.1 Thermal Loading ... 2.2 Acceleration Loading 2.3 Pressurization Loading
FAILURE ANALYSES
3.1 General 3.2 Thermal Loading 3.3 Acceleration Loading 3.4 Pressurization Loading .• ...
DISCUSSIONS
CONCLUSIONS
.
..
i
iv
vi
1
2;
2 25 27
37
37 37 38 39
39
40
6.0 REFERENCES 41
TABLE I
FIGURES 1 to llE
APPENDIX A - WLF Reduced, Variables Equations . . 42
APPENDIX B - 17KS12000 Finocyl Transition Region Structural Analysis - Computer Printouts , . . . . . . . . 43
APPENDIX C-1 - 17KS12000 Booster Cavity Structural Analysis -Computer Printouts . . . . . . . . . . . . . 46
APPENDIX C-2 - 17KS12000 Booster Cavity Axisymmetric Structur-al Analysis - Computer Printouts 48
APPENDIX D - 17KS12000 Axisymmetric-structural Analysis -Thermal 'Loading - Computer Printouts . . . . SO
UNCLASSIFIED iii
APPENDIX E - 17KS12000 Axisymmetric Structural Analysis Acceleration Loading - Computer Printouts. 55
APPENDIX F - 17KS12000 Axisymmetric Structural Anaiysis Pressurization Loading - Computer Printouts . . 58
I
,
·.
.":'··
/
Symbols
UNCLASSIFIED iv
NOMENCLATURE
ay WLF time-temperature shift factor
BFZ Compute3 input mnemonic for the axial body force (lbf/in ) on the propellant
BFZC Compute3 input mnemonic for the axial body force (lbf/in ) on the casing
E
GL
[ i, j 1
(i, j)
R
T
THERM
THERMC
(l c
(l
p
Initial slope modulus (psi)
Effective gage length (3,32 in for JANNAF specimens)
Element i-j
Node i-j
Crosshead speed (in/min)
Temperature (K)
Propellant cure temperature
Zero-strain temperature
Time (min)
Mnemonic for the total thermal contraction (in/in) of the propellant
Mnemonic for the total thermal contraction (in/in) of the casing
Coefficient of thermal expansion (in/in °F) of the casing
Coefficient of thermal expansion (in/in °F) of the propellant
Strain at maximum load (in/in)
A = 1 + Em Extension ratio at maximum load m
a m
'-.-
Standard deviation
UNCLASSIFIED v
Nominal stress at maximum load (psi)
a Radial stress (psi) r
T Maximum shear stress (psi) m
' .
,·
•
---~ • ..
' ,.
-~
UNCLASSIFIED Vi
ABBREVIATIONS
BAL Bristol Aerospace Ltd.
DND Department of National Defence
DREV Defence Research Establishment, Valcartier
HTPB Hydroxyl-Terminated Polybutadiene
NASA National Aeronautics and Space Administration
WLF William-Limdel-Ferry
SCF Strain concentration factor
SF Safety factor
--
UNCLASSIFIED 1
1.0 INTRODUCTION
In early 1979, the National Aeronautics and Space Administration
(NASA) contracted Bristol Aerospace Ltd. (BAL) for the development
of a solid propellant rocket .motor to be adapted as a third-stage
motor to.the Terrier/Black Brant V sounding rocket vehicle. The
projected missions required that the motor contain approximately 700 lb
of a high-energy, HTPB-based propellant. In order to speed up the
developmental work, the contractor decided to use, whenever possible,
inert components of the 17-in Black Brant V motor.
Following a Provision of Services Agreement between BAL and
the Department of National Defence (DND), the Defence Research Establish
ment, Valcartier (DREV), was required to perform the grain internal
ballistics and structural integrity analyses of the projected motor
designated as the 17KS12000.
This report covers the structural integrity analyses of the
17KS12000 propellant grain. The grain anaiysed herein differs from
a preceding design (BAL's DWG 600-03890, dated 10 Oct., 1979): the
port diameter is 4.5 in instead of 4.0 in, and the fins of its booster
cavity are smoothly blended with the cylindrical port. The previous
design was modified after preliminary analyses had indicated that
its safety factor was somewhat low.
The structural integrity investigation included structural
and failure analyses for the three following load cases:·
a.
b.
c.
thermal contraction at the lowest operating temperature
limit ( -10°F);
longitudinal acceleration under launch conditions at
high temperature (15 g n
ignition pressurization
at -10°F).
b at 110 F);
at low temperature (1 000 psi
UNCLASSIFIED 2
The effects of combined'loads were not considered.
A series of two-dimensional, linear, elastic analyses were I
conducted for each load case, using the finite element method. The
critical results of these analyses were subsequently compared td . . I the appropriate failure data. To take into account the thermoviscoelastic
nature of the propellant, its appropriate mechanical properties \c£ , . m cr and E) were treated according to the Williams-Landel-Ferry (WLF)
t:chnique, assuming that t.he time-temperature equivalence p:dncJple
was valid for the highly loaded, HTPB-based propellant.
To summarize the analyses reported herein, let us say that
the modified 17KS12000 des.ign can be considered adequate, since its
minimum strain-based safety factor is 1.71.
This work was performed at DREV between December,
March, 1980, under PCN 21C91, Assistance to BAL.
2.0 GRAIN STRUCTURAL ANALYSES
2.1 Thermal Loading
2 .1 .1 General
1979, and I I
The most severe loading condition this case-bonded, solidi
propellant rocket motor can be subjected to is repetitive low--temperature
cycling. For the analyses reported herein, the thermal stresses\
and strains induced in the propellant grain by the difference between
the coefficients of thermal expansion of the propellant and the kotor . I
case were determined only for a soak of the grain at low temperature.
Cumulative damages due to temperature cycling effects were cover~d by insuring an adequate design safety factor.
UNCLASSIFIED 3
Special attention was given to·:
a) the hoop strain at the inner bore, espacially at the finocyl
transition region,
b) the hoop strain at the star tip of the booster cavity,
c) the stresses at the case-grain termination points,
d) the stresses at the case-grain interface at the motor mid-
length.
The lower operating temperature limit was specified as:
[1]
2.1.2 Heat Transfer Analysis
An elementary heat transfer analysis, not reported herein, in
dicated that the response time of the motor to a temperature drop was
approximately 2 300 min. For the structural analysis, this was consid
·ered as the effective cooling time.
t = 2 300 min cooling (2]
The heat transfer analysis also showed that the usual assumption
of a uniform temperature distribution throughout the grain during
cooling was warranted, for engineering practicality.
2.1.3 Cure shrinkage and Thermal Contraction of the Grain
The effects of the cure shrinkage of the propellant were also
included in the thermal contraction. For that purpose, the thermal
strain calculations were referred to the zero-strain temperature,
T1, which is typically 15°F higher than the cure temperature Tc,
for polybutadiene propellant (Ref. 1). Thus
UNCLASSIFIED_ 4
= 140 + 15 = 155°F (13]
Then, equivalent thermal contractions were .calculated uling
an equivalent temperature change of
With ap
thermal strain
= -10 - (155) = -165°F
and ac taken from Table I, it follows that the
of the propellant is
THERM = a liT p
= 5,86 X -5 10 , X (-165)
. -2 in = -0,967 X 10 in
and that the total strain of the casing is
THERMC = a liT c
= 11.7 X 10-6 X (-165)
[5]
= -}.93 X 10-3 in (6]
in
Properties
Coeff. of Thermal
Expansion
Specific Weight
Young's Modulus
Poisson's Ratio
Thermal Conducti-
vity
Specific lleat
UNCLASSIFIED 5
TABLE I
Relevant Hechanical & Physical Properties
Symbol Unit Casing Propellant
Steel A.MS643S
a in 11.7 X 10-6 s.s6 x 10-s
in°F
y lb 0.283 0,0647 3 in
E psi 29 X 106 (Fig. 1)
v 0.29 0.491 (estimated)
k BTU 3.86 X 10- 4 3.29 X 10-6
in°F s
c BTU 0.31 (estimated) p
lb°F
li'lsulant
RF/B
N.A.
N.A.
N.A.
N.A.
. -6 4, 9 X 10
N.A.
2.1.4 Thermoviscoelastic Properties of the Propellant
To take into account the thermoviscoelastic nature of the
propellant, the gross data from the uniaxial tension tests conducted
at various crosshead speeds and temperatures were reduced according
to the WLF technique (Ref. 2). Appendix A lists the equations used
to perform these reductions, and Figs. 1 to 3 show the reduced data
with appropriate lower and/or upper limits.
The mechanical properties necessary for the structural analyses
of the thermal loading were calculated as follows: a reduced cooling
time was computed using eqs. A-1 and A-3
.-
" h ' "' h ....
v 0 .... ...,
<::> ....,
... h
' "' h
5
4-
3
2
2.8
,-(.1:::. 2 .. 4-
81:::. 0 .... ...,
<::> 2.0 ....,
1.6
--..... ~ .......... ....._ .....
UNCLASSIFIED 6
I· ;,; .. _, I .,
0 A BATCH 1510 + BAL QC Ll"ITS
----- DESIGN Ll"lTS
\.. 8 ..... .... ..... ......
..... ....... 0 0 ........ -....:! ........................... ~ -i-----...
- 0 0 0 ' 'l- 0
H< .6)515BH18-1 -·- -.
-6 -4- -2 LOC 10<TlAr)
0 2
FIGURE 1 - Reduced Modulus vs Reduced Time
o A BATCH 1510 + QC LI"ITS
A
H(.6)515BH18-1
-6 -4- 0 2
FIGURE 2 - Reduced Stress vs Reduced Time
'
c.J
UNCLASSIFIED 7
o A BATCH 1510 0.6 * QC LINITS
0.'+
0. 2
0.0
----- DESIGN LINS A ... 6 8
oo .!-·-........ 0 00 / * ........ .......
/ ' ' s t .,.. .,.. ~
. .,.. -4 -*
BC.6)515BH18-l
-6 -'+ -2 0 LOGioCT!Ar)
...
--
FIGURE 3 - Maximum·Strain vs Reduced
log t = log t - log <1.r ~
0 0
--
2
Time
log <i.r= -8.86 {T -239) + 3.18 T-137.4
[A-1]
(A-3]
With t = 2 300 min, the estimated cooling time, and T = 250 K, the lower operating temperature limit, we obtain
log!.= ·log 2300-aT
. [-8.86 (250-239) + 3.18 ] 250- 137.4
= 1.05 (7]
At a reduced time of 1.05, the upper limit of the propellant reduced modulus is 2.88 (Fig. 1), hence
E = 639 psi; (8]
_.
UNCLASSIFIED 8
.. j
the lm•er limit of the maximum strain capability is (Fig. 3)
[9]
and the lower limit of the reduced maximum stress is 1.89 (Fig. 2),
hence
am = 54.5 psi. [10]
2.1.5 Finite Element Model
In accordance with the approach commonly~employed throughout . . . I
the solid rocket industry, the modeling of the·three-dimensional
17KS12000 motor grain was done by per~orniing a series of two-diJensional :..:;
analyses, namely:
a) a longitudinal, axisymmetric analysis of the complete grain,.
for which we considered the booster cavity as a cyiidder
whose radius is equal to. that of a circle circumscriBing
the star tips of the boo;ter cavity (Figs. 4a, b, add c).
b) two transverse, plane strain analyses of the booster cavity:
one of the actual cross $ection (Fig. Sa) and the ottier
of the idealized axis~etric ·cross section ,(Fig. Sb)l.
Comparing the results of both analyses permitted us to ~
calculate a strain concentration factor (S,FC) at the fin
tips. This SCF was then applied to the maximum hoop strain
calculated during the first axisymmetric a~alysis .(FJgs ..
4a, b, and c).
.....
·.
•
. UNCLASSIFIED
9
24,00 ..
• ' .:. "
•• 15 • 15 7 15 I 1 • 15 zz.oo
• 1. • 1. 7 .. • .. • .. zo.oo
• 13 • 13· 7 13 I 13 • 13
18,00
• 1Z • 12 7 12• I 1Z • 1Z
u.oo • 11 • 11 7 11 • 11 • 11
1oi,OO • 10 • 10 7 10 • 10 • 10
• • ••• 7 • I 9 • • 12 ,oo
• I 7 I I • 9 I
10,00
• • 7 7 7 • 7 • 7
1,00 • • • •
4,00
z.oo
.oo z.oo 4,00. ..oo e.oo 10,00
FIGURE 4a- Axisynunetric Finite Element Model: Motor Head-End
•a.oo
H,OO ._
u,oo -
02.00 ~
40.00 -'
". 00 -
lh.OO
u. oo r
30,00 -
21,00 ~
20,00 ~
!4.00 ,00
I
UNCLASSIFIED 10
I
5
5 0
5 •
r ., ~r , , r-«-rl!. 3Z " r---.
1 -.:..... , 1_. J1
0 -!.!' ~ -_JO_. 0
• 29 • • • 21
. -....r·-..t·-r·~· ~J. • '' r'-..Jt..l:·~~ 1 .... ~ ...t lze
7 . ~· r 7. • 7 Z7 • 7
5 • _. .
7 • • 20 . ~· 5 ll_5 " 25 ' 25 • 2' • 5
5 lz. • Z4 7 24 • Z4 • 24'
--
• 23 • lz,
5 lz 2 • 2Z 7 22 • 22 • 2Z
5 lzo • 20 ""' . ' 20 • 20 • lzo
·s- 1~ . .. 7 .. . .. . " 5 11 0 II 7 II I 11 • 11
'•1w7~~·~1 ~7 ~~7~1~7--~1 •1w7~-J·~17, I • I I I I
! ! ' ! ! I I
2.oo c.oo •• oo a.oo
.
""'- .
.
-
.
.
-
i '
FIGURE 4b -Axisymmetric Finite Element Model:
10.00 I Motor Mid-Section
I
~-
5'9.00
se.oo
57.00
ss.oo
54.00
53.00
sz.oo
51.00
so._oo
4'9.00
• 48.00
s.oo •• oo
UNCLASSIFIED 11
7.00 a.oo 1o.oo
FIGURE 4c- Axisymmetric Finite Element Model: Motor Nozzle-End
c)
UNCLASSIFIED 12
a circumferential, plane stress analysis of the inner surface . I of the port, at the finocyl transition region (Fig. 6),
to compute the SCF at this particular location. ThiJ . I SCF was then applied to the transition hoop strain computed
during the first axisymmetric analysis to evaluate t~e actual maximum strain in this area.
AMG032 and AMG033' Partls The analyses were performe_d using
of a package written by Rohm &.Haas Ltd. (Ref. 3) for grain strJctural
analysis using the finite element method.
2. 1. 6 Results
1) The SCF at the finocyl transition was comp~ted as
2)
SCF = max. strain (5,10] max. strain [1,1]
= 0.13568 = 1.487 (11] 0.091245
where 5,10 and 1,1 stand for the appropriate elements. . . .
Pertinent pages of the computer outputs are included as
Appendix B, and ,.Pigs. • 7a and b illustrate the results.
When extrapolated to the surface, the plane strain analysis
of the actual cross section of the motor cavity (Fig.l Ba
and Appendix C-1) indicated a maximum strain of 0.037r42
for the element [1,2] (See note p. 20). A similar analysis
of the idealized axisymmetrix booster cavity (Fig~ 8bl
and Appendix C-2) yielded a maximum strain of .0.00888~
for the element [1,1]. Therefore,
SCF = 0.037742 = 4.25 0.008884
[ 12]
'
.. •
·~·
6.00
~. 00
r.oo
...
•
UNCLASSIFIED 13
' '
''
''
FIGURE Sa - Finite Element Model of the Booster Cavity Cross Section •
..oo
. .
,.oo
... oo
z.oo
••• s.oo
UNCLASSIFIED 14
• •
• . . I 1 2 I 3 I
7.00
..
) ~-.
7 3 5 •
• 7 •• • • 5
4 I 5 I h I . :T t
•.oo
FIGURE Sb - Finite Element Model of the Axisymmetri~ Booster Cavity
I
-.
..
'
- ./.'
44.50"
44.00
43.00
42.50
42.00
4 1 • 50
4 I .00
40.50
40.00
39.50
-1.00 -.50
UNCLASSIFIED 15
192 193 194 19
182 1 83 184 18
172 1 7 3 1H 17
16 2 163 164 16
15 2 1 53 154 15
1H 10 1U 10
13 2 133 1~ 13
12 2 12 3 12 ;i12
1' 3 4~ 1
11 2 1!. 1V 1
1" 3 1" 4 105 ,n. ul.' 0
l1 n 2
9 2 9
8 2 •
7 2 7
6 2 6
5 2 5
• 2 •
3 2 3
2 2 2
1 2 1
.oo
_,:. • 4 • 5 q_6
3
4. 54 3
~, \Y 3 '
4 '\
3 4 L
3 5 4 • 5
3 4 • • 5
3 3 4 3 5
3 2 4 2 5
3 1 4 1 5
.so 1.00
8
7
7
5
•
3
2
1
1.50 2.00
FIGURE 6 - Finite Element Model of the Finocyl Transition Region
40. so I" .. I •• + I + I
40.30 I I
1 ' ' • '-······
40. I 0
•• •• - + +
31.10 1 ' '
3<1.70
.co .zo ·"
'
UNCLASSIFIED 16
. ' I I • • I + I I I
3 ' ...... !.. ••••••..•.•.
• • .. :
3 , I
1
·" ·"
' I : ' 'I ' I •• I I + I I I I I -I I
• 2 5 2
-•• + ' ' i !1 !
• 1· i 5 1 ··-----1
-
1 I I I
I .00 I • 20 ' 1 • 4 0 1 • 8 0
FIGURE 7a - Finocyl Transition Stresses/Displacements (2-3 ~n away from the Fin Tip)
43.20 1
43.00
'q ' a ' ! ' ' '
• :i • q 0 :I + +· \I + !I
'I ·I .:~ .. " 1..!3
1-a-- . " -•..
·~ II ' ·, ! 7\
' 17 ' ' " I I +. \ +· +. I ..... J . 1Z l .1 - -
irr=: ----~ -\ \
" ' 3~ ! + '
" + ' \ ·~· + \ .
··- -r-- - "7 ,.,~-------· · . ..._ " • " 7 " I \ •• ., •• ., " 50 + • \+ +· + .. +· \... •... ··- ·:·- -.·-...., .J... 10 r- ·+ . '· ;· ... • •.. --;:- 10 . s •. {3-
_____ , -- -z r.;--· 3 1 : : I i t;· -
I 1 I . ' I ' ,. I
:: li u I •• I --~ + I 7 • J
I ' I ol ~·+. " ~--+
I I I L ~
'
1T FIGURE 7b - Finocyl Transition Stresses/Displacements (at the Fin
I
... '· 20 1 • 4 0 ·" ... ••• ... I .00 1. eo
Tip)
'
t.oo
•••
•••
' 10 +.
--------
5.50
I
UNCLASSIFIED 17
1 1
\
'38 \ 35
t t ' 1
" +
' 1
\ \ \ \
\ ·, \ ·.
\ ·. \ ' \' \\
. " +
I \
i • t
FIGURE Sa - Booster Cavity Cross Section: Stresses/Displacements (at the Fin Tip)
c,oo
2,00
.oo s.oo
UNCLASSIFIED 18
I 1 +
2 3
I 1 \ 1
+ +
• 3
~1 v ' 2 •
~1 .. :.,
t z •
J.,Oit
\U +
~ .. +
r • 5 •
lu ~ .. v· + ;
• 5 • z r 2 I
l" t" r· t" 4 I I 1 • 1 r 1
I •. oo
FIGURE 8b - Booster Cavity Axisymmetric Cross Section: Stresses/Displace-ments I
UNCLASSIFIED 19
3) The main results of the axisymmetric analysis of the complete
grain (Figs. 9a, b, c, d and e, and Appendix D) were the
following:
a)· when ·extrapolated to the surface, the inner bore hoop
strain, approximately at the motor mid-length, was
evaluated as
E (5;1_7] = 0.0905 max [ 13]
b) when extrapolated to the surface, the hoop strain at
the finocyl transition was 0.079. With the appropriate
SCF calculated in eq. U, it became
Emax [4,26] = 1.487 x 0.079
= 0.117 (14]
c) after.extrapolation, the hoop strain at the fin tip
was computed as 0.0055. With the.SCF calculated by
eq. 12, the maximum strain was
Emax [6,34] = 0.0055 x 4.25
= 0.0234 (15]
Note: Extrapolated according to the equation
7.00 I· I· I
• • • &.oo
s.oo
4.00
J.oo
z.oo
1.oo
••• 1 1
••• 1.00 z.oo
8
•
J.oo
UNCLASSIFIED 20
•
7
•
c.oo s.oo &.oo
FIGURE 9a- Thermal Loading Stresses/Displacements:
• • 31
•
7.00
Motor
I I· ' 5
35 • ' •
" • ·' 3
2
aloo q.oo
I H~ad-End
~·
.·
2 q. 0'0 J 5 ',q
-
28.00
27.00 5 11i
.
26.00
5 1~
25.00
• 24 .oo IJ 5
23.00 -5 ,J
22.00 I
••• 1 • 0 0 2.00
+
+
+
UNCLASSIFIED 21
I' .. • "
.. . .. +
• :a
.. ... +
• ,·1
.. ' • 4 ' +
' • 1~.
' ,., ', 4 4
+ +
- .• IJ,
I· 1.H
1 8
1 1
1 i •
' , l. J.oo c.oo s.oo
8 r,. q t I q
" . .. -+ +
8 18 • 18
" .. + +
8 11 • 11
... . .. + +
-8 " • "
; 45 '. 47 + +
8 15 • 15
7 .oo e.oo
FIGURE 9b -·Thermal Loading Stresses/Displacements: Motor Mid-Section
44.00
41.00
•
UNCLASSIFIED 22
e..oo
FIGURE 9c -Thermal Loading Stresses/Displacements: Region
'
•• . + '
., ;t
I
·U ..
I
7
I .. I • I f I
T .00
·Finocyl
I a.oo . •.oo
T I .. rans1t1on I
10.50
so.oo
••.so
••.ao
41.10
41.00
47 .so
47 .oo 4.10 &.oo
I I
''I:~ I I 1 I 0 I i
,' I I I 1 I I
s.so e..oo
UNCLASSIFIED 23
• •
e. .so T.oo
'"' ..
T.IO
' • • -------
1.ao
·2• .+
I I I
' I I
·1.10 •• oo
FIGURE 9d - Thermal Loading Stresses/Displacements: Booster Cavity Fin Tip
51.50
57 .oo
s•.so
s~.oo
as.so
ss.oo
u.so
s•.oo •• so s.oo s."so
·UNCLASSIFIED 24
' . r-- --1--
i i·
• ll· -··•· .·.·I· ..
I
I • •
I
!' 6 .oo •.so•
.
{ ' + f
' ' '
1 • . -~
J .oo
... , + , .
• 7.50.
FIGURE 9e- Thennal Loading Stresses/Displacements:
. ;.!'"
I •• __ ._
I .. I ,
e.oo
Motor
:u
·-
,, • I
. ~-..
. .
... .
... . . ..
-~
UNCLASSIFIED 25
d) the shear stress at the forward case-grain termination
was
T [8,1]=21.7psi r-z
[16]
e) the case-grain interfacial stress at the mid-length of
the motor was estimated as
2.2 Acceleration Loading
2 . 2 . 1 General
a [8.17] = 41 psi r
[17]
During the ascent of a solid rocket vehicle, high shear stresses
are normally induced at the forward termination point of the case
and grain. It is particularly important here-because the 17KS12000
is a third-stage motor left unpressurized during acceleration; pressur
ization would of course induce a hydrostatic compression field, thus
enhancing the load carrying capability of the propellant. The axial
deformation (or slump) is also worth being considered.
High-temperature acceleration is more severe than low-temperature
acceleration because of the reduced bond strength capability and shear
modulus.
2.2.2 Input data
1) The propellant mechanical properties were calculated as
follows. Assuming that acceleration would last one minute,
i.e. the combined burning times of the first and second stages,
2)
3)
UNCLASSIFIED 26
and that the motor temperature at launch would be T = j i0°F I
(316.3 K), a reduced time was calculated, using eqs. A-1 and I
A-3:
log t = log t - log ~ aT
[A-1]
= log 1 - [-8.86(316.3-239) + 3.18] 316.3-137.4
= 0.65
At that reduced time, it was possible to infer from
1, 2, and 3
[ 18]
FigJ.
E
E m
0 m
With the specified axial
pellant specific weight,
force BFZ of 0.0647 x 15
= 353 psi [ 19]
=
=
0.205 [20]
73.5. psi [21]
acceleration (15 gn)·and the pro-
0.0647 lb /in3 (Table I), a bod~
m . I = 0.9705 lbf/in3 was input as one
of the propellant physical properties. I
The payload weight was assumed to be 450 lb . A body folce m '
of 450 x 15 = 6750 lbf was thus applied at no~e 9,1, thel
assumed payload/motor junction. Node 9,44 was considered as
the attachment point ~f the motor to the secortd stage. I
UNCLASSIFIED 27
4) Since the specific weight of steel is 0.283 lbm/in 3 (Table
I), a body force BFZC of 0.283 x 15 = 4.25 lbf/in.3 was input
as one of the casing material properties.
2.2.3 Computer Analysis
A single longitudinal, axisymmetric, finite element analysis (AMGO
32) was performed with the model previously used for the thermal loading
stress analysis (Fig. 4), but applying the appropriate data calculated
above.
Pertinent pages of the computer printouts are included as Appendix
E; ·Figs. lOa and b illustrate the main results.
2.2.4 Results
1) The shear stress at the forward case-grain· termination was
computed as
Tr-z [8.1] = 5.0 psi [22]
2) The axial slump, which is maximum at the forward end of th·e
inner bore node, 1,1, was
az (1,1) = 0.120 in [23]
2. 3 Pressurization Loading ·
2.3.1 General
The ignition pressurization induces a compressive hydrostatic
stress throughout the grain with a superimposed tensile hoop stress and
strain at the inner bore.
•• oo
1.oo
c.oo
z.oo
1.00
••• ••• 1.00
' ,,
UNCLASSIFIED 28
,, ,, • ~ ''~r::;;;;;;;..--
z.oo J.oo · 4.00 s.oo
I I • 5
._1 • r · .. ~
• • oo 7.00 I ... i . 9.00
FIGURE lOa - Acceleration Loading Stresses/Displacements: Motor Head-End
415.00 '
44.oo f-
r
42.00
41.00
40.00
n.oo
II .oo
.oo 1.00
' '
UNCLASSIFIED 29
~ '
·~
./ ' 0 ·~
'l I I
·-.it.
~ •
' 0 .. 0
~ '· ..
• '-. 0 .......
' '-.0
. " '0 .
' OL
I I I
I I :I II I• I
z.oo • • oo 15.00
'-.
0
o' I ' - 0
I " I I .. .. '· . I I "' .. • • • •
~.I ' I ... ..
• • I
' I
"' .. ~· .,
' • ·, ~.I "...' ..
·:,
•• . ~ . 'I
,. •• . ~.
I I I I I
•• oo r.oo •• oo
FIGURE lOb -Acceleration Loading Stresses/Displacements: Finocyl Transition Region
-
•• oo
UNCLASSIFIED 30
I '
·""'
' I
The hoop strain at the inner bore and the str~sses at the termi-
nation points of the grain were considered critical.' The_analy~is - -- I
was based on the mechanical properties determined at low temperature
(-10°F).
2. 3. 2 Input .data
1) Assuming an ignition pressure rise time
10- 3 min) at T = 10°F (250 K) a reduced
from eqs. A-1 and A-3 ;•.
~-
of 100 ms (1.67 x - -I --' . time was calculated
log _..!. = log t - log ~ [A-1}
•
-"
~ ~
2)
= log 1.67 x 10-3 [~8.86'(250-239) + 3.18]..,...--
250-137.4 I
= -5.09_ (24}.
With that reduced time, Figs. 1, · 2 and 3 show the following
mechanical properties for the propellant: .,... ~ ~-
E = 7330 psi (25}
em = 0.40 . (26}
om = 284.5 psi [27}l
It was (conservatively) assumed that the ignition prelsure -~ • c . -_ • I
(1 000 psi) would induce an axial force of 1 000 x IT x
(8. 537) 2 = 229 000 lbf in the casing. That was input at
node 9,1.
c..oo
s.oo
c.oo
J.oo
z.oo
1.00
•••
-1.00
••• I .oo r.oo
UNCLASSIFIED 31
c.oo s.oo ..oo e.oo
FIGURE lla -Pressurization Loading Stresses/Displacements: Motor Head-End
... oo
29.00 5 ·,~
i i '
21.00 ':[· ... , __
I ' I '
. ' 1l !
I I '
s 1 u.oo
'· 1
s lis 2 2 .oo I
••• I eOO 2.oo
UNCLASSIFIED 32
• I· • ---- -----
I I I t· I -r· i 1 I I.
• •
-r· i t1 I I
• '
1" I t' I
.. • •
1" t· • Is
I, J ...
·- I
I I I
I I
' ~~ . -I
I I
' '
. ' •
' s
4.00 s.oo
T . .. -- .•. .. -
-v· • I . ---
1"' I '
t' I ..
t· • ~. J.oo
FIGURE llb -Pressurization Loading Stresses/Displacements: Mid-Plane
~'
I • ... -
I _t.,
I . " -1 .. .
I . " I
t' .
I
-• 16 I '
\i' I • " I 1.oo •.oo
I Motor
..
u.oo
••.oo
u:.oo
t1.00
•••••• 1-
s•.oo
• sa.oo ••• 1.00
r
•
• • I
~ I
2.00
• 3.00
UNCLASSIFIED 33
-r
• •
I y •
1'
1'
• •
1' ' .
.... ···. " . ... oo s.oo t..oo
• 7 • 7
1' • •
7' • b. •lu
l.oo a.oo •.oo
FIGURE llc - Pressurization Loading Stresses/Displacements: Finocyl Transition Region
so.so
so.oo
4•.so
48.50
48 .oo
.u.so
417.00 4.50 s.oo
FIGURE lld -
I I I
I I: I;
;It'~ ! ! I I I .,
I I I 1 I I
&.so •• oo
UNCLASSIFIED 34
1'
r------1
I I
"
-r
1' I I
! I I I I
8 ,, .
-------- i I
t: I 5 • 5
I / 1'
• I ' I, / -r I I I
II I I
' 'I
--...:::_ '
-'I' }
I c.oo •.so •.oo
I Pressurization Loading Stresses/Displacements: Booster Cavity Fin Tip
57.50
s7.oo
u.so
sa.oo
u.so
54.00
c.so s.oo s.&o
UNCLASSIFIED 35
r..oo
... ' ... ..:. • " r.:7;'\ I;_~· ~ .. 7 .J~·
- . --\I
.. 7' -p·· 1'~· ---- . .\\ -;.~ ,. -,.. . \
-t 07 \ '
. ~~1~ :_ ·~~.;-~ .,_ ~ \' I 'f 44 . ~ ---- -' .• -· ·-·---· -------------, .. . ,,, 'lh . '
II 11
7 .o_o 7.so •• oo •• so
FIGURE lle - Pressurization Loading Stresses/Displacements: Motor Nozzle-End
•.oo
UNCLASSIFIED 36
2.3.3 Computer Analysis
' I
Applying the data calculated above to the model previously used . . I for the thermal loading structural analysis, we performed an ax~sym-
metric finite element analysis (AMGO 32).
The strain concentration factors·. computed· for the structural . - I
analysis of the thermal loading were applied, as required.
Pertinent pages from the computer outputs are
Appendix F; Figs. lla, b, c, d, and e illustrate the
2. 3. 4 Results
1) After an appropriate extrapolation to the
bore hoop strain at the mid-length of the
as
Emax [5,17] = 0.00584
included in . I
ma1n results.
surface, tJe inner I motor was computed
[28]
2) When extrapolated·· to the surface, the hoop strain at the
finocyl transition was calculated as 0.0514. With the SCF
of eq. 11, it became
E (4,26] = 1.487 X 0.0514 max
= 0.0764
.,
UNCLASSIFIED 37
3) After extrapolat{on to the surface, the calculated hoop
·strain at the .fin tip was 0.0080. With·the appropriate
SCF. of eq. 12, it became
Emax [6,34] = 4.25 x 0.0080
= 0.0340 [30]
4) The maximum shear stress at the forward termination of the
case-grain was calculated·as
Tr-z [8,1] = 132.3 psi [31]
3.0 FAILURE ANALYSES
3.1 General
Because of the various unknowns associated with the structural·
analyses, specifically with the propellant behavior and .the failure
criteria, a minimum safety factor (SF) of 2.0 is desirable; it is usual
ly based on the mean properties of an unaged propellant minus 3cr.
When the statistical properties of the propellant are not available,
it may be conservatively" considered that lcr = 10% of the relevant
property (Ref. 1).
3.2 Thermal Loading
1) Under the stated conditions, the lower limit of the maximum
strain capability was E = 0.20 (eq. 9). The maximum strain m
calculated at the finocyl transition region was 0.117 (eq.
14). Therefore, the strain-based safety factor is
2)
UNCLASSIFIED 38
SF = 0.20 1 71 0.117 = 0 [32]
The shear stress at the· forWard case-grain termination was
calculated as 21.7 psi (eq. 16). The maximum. allowaJle
shear stress is usually considered 1:~ be 10% of _the iniaxial
tension failure stress (Ref. 1). Since a = 54.5 psi m
(eq. 10},
and the
T = 0.70 X 54:5 = 38.2 psi m
SF = ~;: ~ = l. 76
(33]
(34]
3.3 Acceleration Loading
1) The maximum shear stress·expected was calculated as 5.0
psi (eq. 22). Using eq. 33, since am = 33 .. 5 (eq. 21), the
maximum admissible shear stress is ~
' : -Tm = 0.70 X 73.5
= 51.5 psi (35]
Therefore, the
SF 51.5 10.3 = --= 5.0 (36]
2) The maximum slump calculated, 0.120 in, (eq. 23) is deemed
acceptable.
:
3.4 Pressurization Loading·
UNCLASSIFIED 39
a. It is generally accepted that.pressurized biaxial tests,
used to evaluate port cracking during ignition pressurization,
yield a maximum t.ensiie strain 2 .S time.s higher than the
standard uniaxial test. Thus, from eq·. 26,
' 2-D e:max = 2.5 X 0.-4 = 1.0 (37)
Since the maximum induced strain has been evaluated as
0.0764 (eq. 29), it follows that
SF = 1.0 . 0.0764 = 13.1 (38)
b. The maximum shear stress calculated at the forward termina
tion of the case-grain was 132.3 psi (eq. 31). Since the
maximum admissible shear stress can be estimated as
Tm = 0.70 x (am= 284.5) = 199.2 psi (39)
(eqs. 33 and 27), then
SF = 199.2 132.3 = l.Sl [ 40)
4.0 DISCUSSIONS
It is generally agreed throughout the rocket industry that strain
based safety factors are the best acceptance criteria; indeed, for
viscoelastic materials, strains and displacements are usually more ex
actly predicted than stresses (Ref. 1). Therefore, only strain-based
SF will be considered critical herein.
UNCLASSIFIED 40
The minimum strain-based SF computed-· is 1. 71 (eq. 32) under
conditions of thermal loading. This is somewhat low1er then thJ
generally recommended SF, but it is sufficiently clo~e to 2. 0 Jhat · - . - I
no problem is anticipated, when the rationale behind such an acceptable
SF (see para. 3.1) is understood.
In regard to the- minimum ·stress"based SF of 1.51, calculated
for the pressurization loading analysis, it is somewhat low butl not
considered critical because of the conservative assumption mad~ regarding the input data. Indeed, by merely choosink the lowerll
limit of the modulus, instead of·the upper limit, we'would obtain
a SF of approximately 4.0, insfead of 1.51, indicati~g that the\
actual SF is likely around 2. 7; this is considered more realistlic
and more acceptable.
5.0 .CONCLUSIONS
Since the estimated strain-based safety factor is 1. 71,_ the
modified 17KS12000 motor grain appears structurally adequate fo~ -
the three load cases considered (thermal, acceleratibn, and preksuriza
tion loadings).
UNCLASSIFIED 41
6.0 REFERENCES
1. Fitzgerald, J .E .• and Hufferd, W.L.·, "Handbook for the Engineering
Structural Analysis of Solid Propellants'', Chemical
Information Agency, !Silver Springs, Md., May 1971.
Pub. No. 214) UNCLASSIFIED
Propulsion
(CPIA
2. Williams, M.L, Landel, R.F. and Ferry, J.D. "The Temperature
Dependence of Relax~tion Mechanisms in Amorphous Polymers
and other Glass-forming Liquids". J.Am. Chern. Soc., ·vol. 77,
p. 3701-3707, 1955,; '
3. Becker, E. B., and Brisbane, J .J. "Application of the Finite Ele
ment Method to Stress Analysis of Solid Propellant Rocket Grains".
Rohm· & Haas Ltd., Special Report· S-76, Vol. 1 & 2, Nov. 1965. UNCLASSIFIED
. .
UN(:LASSIFIED 42
APPENDIX A
~ I ..
WLF Reduced Variables Equations .i ·
1. Reduced Time
with
log~
2. Reduced Modulus
3. Reduced Stress
log ....!. [A-l]
~
t: duration. of applipaqon of
the load .(in minu~es). For . - !
constant strain-rate testing !
GL t =- E R m
with GL = 3.32 in
= -8.86(T-239) + 3.18 T-137 4
1 E 297 og T
lGg cr A 297 m m T
[A-2]
[A-·3]
[A-4)
[A-S)
•
:
·.
'
'
.,
UNCLASSIFIED 43
APPENDIX B
17KS12000
Fin~cyl Transition Region
· Structural Analysis ..
'computer Printouts
:
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UNCLASSIFIED 46
APPENDIX C-1
17KS12000
Booster Cavity Structural Analysis
Computer Printouts
'
·' l·-• ...._
.,
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UNCLASSIFIED 48
APPENDIX C-2
17KS12000
Booster Cavity
Axisymmetric Structural Analysis
Computer Printouts
I jl ce&ROINATES 8 T A t s s E 9 I 8 T R A I N S -'NGLE X y X y AX I A~ z I HEAR hY P1A)CJMUM MJNI1'1U"' MAX SHEAR
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UNCLASSIFIED so
APPENDIX D
17KS12000
•
Axisymmetric Structural Analysis 1 ;
Thermal Loading
Computer Printouts
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UNCLASSIFIED 55
APPENDIX E
17KS12000
Axisymmetric Structural Analysis
-. Acceleration Loading.
Computer Printouts
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UNCLASSIFIED 58
APPENDIX F
17KS12000
~ !
Axisimmetric structural Analysis
Pressurization Loading
Comp~ter Printouts
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REPORT NO: \ ,~;~- ::·:;:;~;; DREV REPORT 4196/81
TITLE: 17KS12000 motor grain rolructural integrity analysis.
DATED: March 1981
AUTHOR: C. Carrier
SECURI'l'Y GRADING: UNCLASSIFIED Initial dislri but ion May 1981.
1- DSIS Report Collection Plus distribution 1- Microfiche Section (unbound copy)
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CRAD 1- DACS D/CRAD/L 1- D!-K:S D/CRAD/D D/CRAD/P 6- Brintol DTA(A) DTA(L) DTA(M) DST(OV) DST(OV)-2 DST(OV)-3 DGAEM DGMEM.
;icrospace Ltd.
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