Rheology of Composite Solid Propellants P. J. BLATZ Aerojet-General Corp., Azusa, Calif.
A composite solid
propellant comprises a resilient binder and a crystalline filler. A rheological study of such a system involves characterization of the binder in terms of its brittle point as well as a measurement o f the reinforcement of the binder b y the filler. A tool used in this study, the method of reducing the data, and the parameters which characterize some typical composite propellants are described.
I
N T H E course of solid propellant development a t the Aerojet-General Corp., it is necessary to investigate a wide variety of propellant properties. These studies include measurements of performance, ballistic parameters, physical parameters such as density and thermal conductivity, and mechanical or rheological parameters such as flexibility and tensile strength. Both experience and theoretical principles dictate what values these parameters must have in order t o satisfy service requirements. The investigation reported here comprised a study of the rheological properties of synthetic linear polymeric binders and propellants filled with various amounts of an inorganic crystalline oxidizer.
16
Bp
f 12 E ! VI W
d 3
8
c K
-W i
t
" 4
0 0
16 24 TIME, M I N U T E S
8
Figure 2.
32
-
Effect o f load on creep of 0.6P1 60F a t 75' F.
span and bottom of the beam. of the span:
R,
40
- 8X -
Subscript m represents the middle
E,
=
Ghym/La
J
=
4bh3yy,/WL3= em/urn
cm= 3WL/2bha
J and
E, are dimensionless; urnhas the dimensions of FL-2. Figure 2 shows a number of typical strain-time curves for a typical propellant formulation a t 75" F. and how they vary with applied load. Each of the propellant formulations being studied includes the following constituents: a linear polymer, indicated
PO 16
Figure 1. Aminco flexometer
2 2 12 a W
5 8 Two instruments were used t o investigate physical propertiesa n Aminco creep flexometer and an Instron tensile-testing machine. Figure l shows the details of the Aminco flexometer. T h e dial gage has been replaced by an extensometer which allows for continuous automatic recording of the instantaneous deflection. The following equations (S) were used t o reduce the measured deflection t o tensile stress and tensile strain at the center of the
April 1956
i &
4
0 10-8
Figure 3.
2 x 106 3 STRESS, DYNES/SQ. CM.
Stress strain curve for R1 a t 75" F.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
x
106
4
x
100
- 8 X - 0.6P1- 60F 721
16 10-7
sp
z
dE
I
I
1
I
,
1
1
I
12 W
En
Y I
3
8
E
z
c $
//I
d M y
4
10-8
10-9 ,
53 4
0 I
2
3 TIME, M I N U T E S
4
0
6
5
Figure 4. Effect of cross-linking agent on creep rate 0.6P1 60F OX, 4 X , 8 X a t and recovery of R1
- 75" - F.
-1.0
0.0 +I .o LOG TIME, M I N U T E S
SP.0
Flexural creep of R1 - 6X - 60F as function of temperature
Figure 7.
0.6P1
( " F.1 -1.0
v
a
I 1 1
~10-9
10
100
r, SECONDS
1000
1
-8.0
$ u ' Y4
-9.0
ln
Figure 5. Effect of oxidizer concentration (yo) on creep of R1 8X 0.6P1 propellants
- -
-1
40
v 13
9 -10.0 30
L. I I - 2.0
-4.0
sg
I
0.0
+P.O
LOG t/K, D I M E N S I O N L E S S
2
7 PO
Figure 8.
Master curve for R,
K
- 6 X - 0.6P1- 60F
v) I-
10
0 5
Figure 6.
10 TIME, M I N U T E S
15
20
Effect of temperature ( " F.) on creep of
Ri
- 8 X - 0.6PI - 60F
by the symbol R; a trifunctional cross-linking agent, indicated by the symbol X; a low molecular weight plasticizer, indicated by the symbol P; and an inorganic oxidizer indicated by the symbol F . The binder comprises all constituents except the oxidizerfiller, I". The polymer type is distinguished by appending the subscript 1 to the symbol R. I n this particular case and in what follom, the binder, R1, is considered. Furthermore, the effects of varying concentrations of cross-linking agent, plasticizer, and filler are considered, so t h a t a typical formulation is designated completely by specifying the equivalent per cent of cross-linking 728
agent based on the resin, the weight ratio of plasticizer to resin, and the weight per cent of filler in the propellant. For example, R1 - 8X - 0.6P1 - 60F indicates a propellant based on the resin, R I , which is cross linked with 8 equivalent % of a trifunrtional agent, which contains 0.6 by weight as much plasticizer PI as €21 and which contains 60% by weight as filler. The 20-minute strain is plotted against the applied stress in in Figure 3, the deviation from linearity over the range of measurement being indicated by the dashed portion of the curve. The slope of the linear portion corresponds to a Young's modulus of 2 X l o 7 dynes/square em. The effect of the amount of cross-linking agent on the creep rate and recovery of Ri - 0.6P1 - 60F is shown in Figure 4. It appears that something above 4 equivalent 70of cross-linking agent is necessary to ensure an equilibriuni deformation and complete recovery. The interaction between the binder and filler components of the formulation R1 - 8X - 0.6P1 is shonn quantitatively in Figure 5 . I n the absence of any interaction between the two components, the compliance of the propellant should increase with increasing filler concentration. The fact that the compliance
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 4
ROCKET PROPELLANTS Figure 10 shows the temperature dependence of the shift factors associated with the master curve. T h e slope of the log K - T curve passes through a maximum around 6' F. This corresponds t o a maximum activation energy for viscous flov and may be used as a definition of t h e apparent second-order transition point. T h e value of the shift factor a t this so-called brittle point is approximately 4 min. Again this value is typical of many amorphous polymers, filled or unfilled (8). I n summary, a typical propellant based on a cross-linked polymeric binder has been characterized in regard t o its viscoelastic behavior. T h e material obeys Hooke's law up to 12% strain, undergoes a fairly sharp transition from glassy t o rubbery behavior around 0' to 10" F., and displays some interaction between the filler and binder components. The assistance of Donald A. Vogel in this work is acknowledged. Nomenclature 0.1
0.01
5
0
-
(LOG J
40 60 80 95 LOG Jd/(LOG J - LOG J d
PO
Figure 9. Rectified master curve for R1
60F
-6X-
99
99.9
0.6fI-
ern = center tensile strain a t bottom of beam = = = 6 = ym = W =
J h
L
=
center tensile stress a t botton of beam compliance, reciprocal of Young's modulus beam thickness beam width center flexural deflection load span Literature Cited
100
(1) Catsiff, E., Tobolsky, A. V., J . Applied Phys. 25, 1092-7 (1954) (ONR Tech. Rept. 4-13, avail. Princeton Univ. Library,
Princeton, N. J.). (2) Ferry, J. D., Fitzgerald, E. R., J . Colloid Sci. 8, 224 (1953). (3) Timoshenko, S. P., "Strength of Materials," Part I, Chap. 5 , McGraw-Hill, New York, 1953.
f G
RECEIVED for review September 23, 1955.
ACCEPTED February 29. 1956.
1.0
0.1
I
I
-30
-20
0.01
1
I
I
-10 0 10 TEMPERATURE, O F
I PO
I
1
30
40
- 60F - -
Figure 10. Temperature dependence of 6X shift factors associated with R1
0.6Pi 0
Transition point
decreases indicates some interaction. Attempts are under way t o place the interaction concept on a quantitative basis. Figure 6 depicts the temperature dependence of the creep rate of RI - 8X - 0.6P1 - 60F over a range from -40" t o 150" F. Similar data are plotted on log-log paper in Figure 7 for the formulation R1 - 6X 0.6P1 - 60F. B y dividing the time scales of each curve obtained a t a given temperature by an empirically chosen constant, it is possible t o shift the curves into conjunction t o form a single curve known as a master curve. This latter curve (Figure 8) is adjusted so that its inflection point is a t unity on the reduced time scale. The sharpness of the transition from the glassy compliance of 5 X square em./ dyne to the rubbery compliance of 5 X 10-8 square cm./dyne is measured by the dispersion of the straight-line plot (Figure 9) obtained when the sigmoid master curve is rectified on probability paper. The value of the dispersion, 1.6, is typical for most amorphous polymers ( 1 ) and varies from 1 to 2 depending on the amount of filler and the extent of interaction.
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April 1956
View of operator station for fluoroscopic inspection See "Radiographic Inspection of loaded Rocket Motors," page 730
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