I
THOR L. SMITH]
I
Jet Propulsion Laboratory, California Institute of Technology,
Solid Propellants
...
Elastomeric-Binder and Mechanical-Property Requirements Composite propellants must have dimensional stability as well as rubberli ke properties to ensure reliable performance T , E CURRENT INTEREST in solid propellants for large, high-performance rocket motors stems largely from the development of castable composite propellants that can be case-bonded in thin-walled motor cases. Such propellants are prepared by first dispersing a solid oxidizer and other solid additives in a polymerizable liquid fuel. (Typical oxidizers are potassium perchlorate, ammonium perchlorate, lithium perchlorate, ammonium nitrate, and ammonium picrate.) Prior to incorporation in the liquid fuel, the oxidizer is frequently ground to give the desired particle size ; several grinds may be mixed to give a desired particlesize distribution which influences castability of the propellant mix as well as burning rate and mechanical properties of the cured propellant. After the oxidizer and other additives are uniformly dispersed in the liquid fuel, the thick dispersion or paste is cast into a metal motor case around a centered mandrel which has been inserted to give the desired shape to the dispersion. The dispersion is then cured a t a moderate temperature to produce a rubberlike propellant bonded to the motor case. A single piece of solid propellant is usually called a grain, even though it may weigh several thousand pounds. After cure, the mandrel is removed, leaving an internal perforation or configuration in the grain. When such a case-bonded grain is ignited, the grain burns only on its interior surface. During burning, the unburned portion of the grain insulates the motor case from the extremely hot flame. The motor-case design can therefore be 1 Present address, Stanford Research Institute, Menlo Park, Calif.
776
based on the cold strength of the case material, allowing a marked reduction in case weight. Before the propellant grain is cast, the interior of the motor case is often lined with a thin layer of some elastomeric material, which may be filled with carbon black or some inorganic filler, and is commonly the same as the propellant binder. The uncured liner material is spread over the interior of the case and bonds while curing. The liner helps provide a good bond between the propellant and metal case and also gives some protection to the metal case during the final phase of propellant burning. The internal configuration of a grain is determined largely by the thrusttime program desired of the motor and the ballistic properties of the propellant ; it is commonly star-shaped in cross section, although other configurations are often used. Another method of preparing composite propellants consists of dispersing the oxidizer and other additives into a rubber gum stock by milling or by using special mixers. The resulting mix is extruded to give a propellant grain having the desired configuration; then the grain is cured, the external surfaces of the cured grain often being coated with a layer of some restricting material to prevent burning. The restricted grain is then inserted into a motor case, metal traps often being used for support both before and during flight. This type of grain is called an internal-burning cartridge grain, while the previously discussed bonded grain is called a cast-inplace case-bonded grain. Although the size of extruded grains is limited by the size of available extruders, cartridge and case-bonded grains of unlimited
INDUSTRIAL AND ENGINEERING CHEMISTRY
size can be prepared from castable propellants. Another method of support is to bond the restricted grain to the case. This procedure yields a case-bonded grain, although the term case-bonded ordinarily refers to the cast-in-place type of grain. Propellants for case-bonded grains must have a relatively high ultimate elongation, but they can and usually do have a relatively low modulus and tensile strength. O n the other hand, cartridge grains need not have a high ultimate elongation since they are not bonded to the case, but they must have a high modulus and tensile strength. Such properties are needed to prevent appreciable deformations of the grain under the pressure gradients produced in the rocket motor by ignition and burning of the grain and by flight aceeleration forces. I t is relatively easier to develop a propellant with high modulus and tensile strength than one with high ultimate elongation. Also, the overall performance of a rocket motor containing a cartridge grain is usually lower than that of a motor containing a casebonded grain. Thus, propellants suitable for cartridge grains are less importal it today than they were some years ago.
Mechanical a n d Ballistic Properties of Propellants Mechanical Properties Required for Case-Bonded Grain. Strains are induced in a case-bonded grain during propellant cure, temperature cycling, and motor ignition. The total strain a t any point in the grain is determined by these factors, although elastic strains may be partially relieved by stress a
P L A S T I C S A N D E L A S T O M E R S IN R O C K E T S
Good tensile elongation i s the prime mechanical property required of propellant grains for case bonding. Shear strength and modulus of the grain can be rather low, but the grain must creep appreciably during storage. The ideal binder should have low glass temperature, should exhibit high elongation over a wide temperature range, should be cross-linked preferably through stable primary valence bonds, and should not crystallize spontaneously during storage at any temperature. The uncured binder material should be a liquid which cures with minimum heat release and shrinkage and without evolution of gases. The binder should dissolve little or no oxidizer and should be chemically stable for long periods in close contact with the oxidizer. Other factors to be considered in weighing the relative merits of potential binders are oxygen balances, viscosity prior to cure, and density. It i s improbable that a binder which fulfills all of these requirements will be found; however, in developing new propellants, these factors should be considered.
relaxation and permanent deformation or plastic flow of the propellant. The maximum strain that the case-bonded grain will withstand depends on temperature, time (or strain rate), and thermal history. However, predicting conditions under which a grain will not crack is an extremely complicated and difficult problem, even when classical stress analysis is utilized, because stress concentration points exist on the inner perforation of the grain. Further, the grain is often bonded at the head and aft end of the motor, which results in the introduction of triaxial stresses. Thus, instead of an exact analysis of the conditions that a grain can withstand, only some qualitative and semiquantitative considerations can be presented. Grain cure is accompanied by a volume decrease or shrinkage. Prior to the formation of a three-dimensional molecular network in the binder-Le., before the gel point is reached during the polymerization-strains induced by shrinkage can be relieved by viscous flow. However, after the gel point is reached and the grain is well bonded to the case, further shrinkage induces strains in the grain which cannot be relieved except by rupture of primary valence bonds. After the grain becomes bonded, its outside circumference is fixed ; shrinkage now produces strains which are maximum around the perforation of the grain. When a case-bonded grain is cooled below ita curing temperature, strains are produced for essentially the same reason that strains are produced by propellant shrinkage during cure. Since
the coefficient of thermal expansion of propellant is roughly 10 times that of metal, shrinkage of the metal case is negligible compared to the propellant shrinkage. Propellant shrinkage produces tensile strains which are a maximum around the internal perforation of the grain. For a tubular grain, the strain is a function of Poisson's ratio for the propellant, the thermal expansiop coefficients of the metal and propellant, ( b / a ) 2 , where b and a are the outer andinner radii of the grain, and the number of degrees that the propellant is cooled below the curing temperature. I t is assumed that the modulus of the case material is large compared with that of the propellant, which assures that stresses in the grain do not modify the dimensions of the case. For internal configurations more complex than the tubular grain, much greater strains may exist at stressconcentration points. Ideally, to obtain the minimum strain during temperature cycling, the grain should be cured and case-bonded a t a temperature midway between the temperature extremes encountered during cycling. This procedure, however, is usually not possible because somewhat elevated temperatures are ordinarily required for propellant cure. Even though a grain withstands rather rapid temperature cycling, it may crack during prolonged storage at temperatures below the cure temperature because the ultimate elongation is not a unique function of temperature but also depends on the experimental time scale. For example, suppose that a propellant has an ultimate elongation of 15% at
160" F. and an elongation of 30T0 a t 0" F. when measured at a strain rate of 1.0 min.-' Now, suppose that a specimen of this propellant is stretched at 0" F. and held at 20y0 elongation. The specimen will not rupture immediately but may rupture after some period. This delayed rupture is predictable qualitatively by viscoelasticity theory, which indicates that if a material ruptures rather quickly under a given strain at some elevated temperature, it will rupture under the same strain at a lower temperature but after a much longer elapsed period. Such a conclusion is reached by considering the temperature dependence of the internal viscosity of the sample. If primary bonds are broken at the elevated temperature because of purely thermal effects or if primary bonds break and reform at the lower temperature, the conclusion may have to be modified. Strains are also produced in a casebonded grain by motor ignition. During the ignition period, the pressure in the motor chamber increases rapidly to its equilibrium or operating value, which usually is between 200 and 1000 p.s.i., depending upon motor design. This pressurization produces strains in the grain which are a maximum around its inner perforation. For a tubular grain, it has been shown by using standard stress analysis techniques that
+
+
(1 - 2 v ) ( l (1 - Y e 2 )
P)
E,t
XI
where eid and eod are the hoop strains at the inside and outside of the grain, Y and vc are Poisson's ratio for the propellant and the motor case, E, and E are the modulus of the motor case material and the propellant, and t is the thickness of the case. For more complicated internal geometries, stressconcentration factors can be used to modify the value of e i d calculated by means of Equation 1 for the tubular grain. T h e tensile strength or, more precisely, the shear strength of a grain, can be quite low and need only be sufficiently great to enable the grain to withstand flight acceleration forces. A rough estimate of the shear strength required can be made by assuming that a grain is supported entirely by the outside wall of the case and receives no support from the head and aft ends of the motor. The equation applicable to such conditions is
where S is the shear strength, m the mass of the propellant, a the maximum flight acceleration, r the radius of the case, I the length of the grain, and g the graviVOL. 52,
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PROPELLANT
4 Typical case-bonded
rocket motor. The drawing shows the motor case, liner, an internal star-configuration case-bonded grain, igniter, and the rocket expansion nozzle with a graphite insert
COMBUSTION CHAMBER
I GRAPHITE INSERT
L!
NOZZLE
tational constant. For a wide variety of conditions, a shear strength of 10 p.s.i,, which corresponds roughly to a tensile strength of 30 p.s.i,, is sufficient to prevent rupture of the grain. Thus, as a rough rule, a tensile strength of 50 p.s.i. should be adequate for most rocket applications, e\ en allowing a margin of safety. Modulus of the propellant can be relatively low and need only be large enough to assure that flight acceleration forces do not deform the grain sufficiently to modify the internal ballistics. If a propellant has sufficient tensile strength, it is usually true that the modulus will also be adequately large. Another requirement of the casebonded grain is that it not creep appreciably during storage; otherwise the internal configuration of the grain may be changed sufficiently to affect the internal ballistic properties adversely. The star points or other protrusions of a grain are most susceptible to creep during prolonged motor storage. Propellant Mechanical Properties. In brief, the mechanical properties are influenced largely by the volume fraction of oxidizer, the viscoelastic properties of the elastomer binder, and the adhesion between the binder and filler particles. Because of the viscoelastic nature of the binder. the modulus and ultimate mechanical properties (the tensile strength and ultimate elongation) of propellants depend markedly on temperature and strain rate a t which they are measured. The modulus and the tensile strength increase as the temperature is decreased or the strain rate increased, However, the ultimate elongation may either increase or decrease with increasing strain rate. depending on the temperature and the range of strain rate covered. As discussed elsewhere ( 7 , Z ) , a change of temperature is quantitatively equivalent to a certain change in strain rate. Thus. master curves can often be constructed from which the ultimate properties can be predicted at any strain rate and any
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temperature above the glass temperature. This data-reduction procedure seems to be applicable to composites having an amorphous elastomer binder which does not crystallize. Creep behavior of composite propellants is qualitatively similar to unfilled elastomers, except that the quasi-equilibrium compliance (reciprocal of the modulus) depends on the oxidizer content. However, under certain loading conditions, adhesion between the binder and oxidizer particles may break, which leads to vacuole formation around oxidizer particles. Once this process begins, it usually continues, and the deformation increases exponentially with time until a test specimen breaks. At high temperatures, or equivalently at low strain rates, propellants have an equilibrium or quasi-equilibrium modulus. This modulus depends on the modulus of the unfilled binder and the volume fraction of oxidizer. Also, the modulus is influenced by the particle size distribution, although little information is available on the effect of this factor. The mechanical properties are also affected by the adhesive strength between the binder and oxidizer. The
pressure and the extent to which the combustion gases expand on passing out the rocket nozzle, it is customary to report values of specific impulse at a chamber pressure of 1000 p.s.i., with the gases expanded to sea-level pressure. The specific impulse can be calculated from thermodynamic data using the equation,
factors which affect the adhesive strength and the conditions under which the adhesive bond fails both influence propellant mechanical behavior, especially in large deformations. Ballistic-Property Considerations. The single most important ballistic property of a propellant is its specific impulse, Zap. In terms of experimentally measurable quantities, the specific impulse is given by the equation,
bustion products, p. the chamber pressure, and p. the exhaust pressure. Thus. to obtain high performance, the flame temperature should be high and the average molecular weight of the exhaust products should be low. A useful equation for rating the overall performance of a rocket motor is the so-called burnt-velocity equation. This equation gives the final velocity of a motor fired in the absence of aerodynamic drag and gravity and is expressed as :
where F is the thrust or force measured during the static firing of a rocket motor, and t is the time required to burn I$’, pounds of propellant. Since the impulse varies with the chamber
INDUSTRIAL AND ENGINEERING CHEMISTRY
I,,
= -
g
4” ~
m
where g is the gravitational constant. and AH is the change in heat content for a propellant mass m in going horn its initial unburned state in the rocket motor to its final state as it leaves the rocket nozzle. This equation is cxact provided that exit pressure of the gas equals the external pressure, velocity of the molecules in the chamber is small compared with their exit velocity, and the process is adiabatic, steady -state, and involves one-dimensional flow. If the gases are perfect and chemical reactions do not occur during the expansion process, then Equation 4 can be where T , is the adiabatic flame temperature, M the average molecular weight of the combustion gases, y the average ratio of the specific heats of the tom-
where u is the final or burnt velocity: W , the weight of the propellant, and
P L A S T I C S A N D E L A S T O M E R S IN ROCKETS W,, the empty weight of the rocket motor-i.e., W, W,,, equals the initial weight of the motor. This equation shows that the final velocity can be increased by increasing either the propellant specific impulse or the ratio of propellant weight to empty weight of the motor. Further, for a given grain design and motor case, an increase in propellant density will increase the burnt velocity, because this increase allows more pounds of propellant to be confined in the available volume. Thus, an increase in propellant density is equivalent to an increase in specific impulse, although the quantitative relation between these factors will depend on the particular missile system being considered. The specific impulse of a propellant depends on the thermodynamic properties of the binder and oxidizer and the relative amounts of each which are present. T o analyze the effect of such factors in more detail, consider a hypothetical propellant containing ammonium perchlorate and a hydrocarbon binder (CHe),. Straightforward thermodynamic calculations show that maximum performance is obtained when the propellant contains about 90% by weight of ammonium perchlorate, which corresponds to about 8OY0 by volume. Both weight 7 0 and volume 7 0 of oxidizer are important to consider, because specific impulse depends on the weight %, but castability and the mechanical properties of the final propellant depend largely on the volume %. Because the closest possible packing of uniform spheres is about 74% by volume, it might appear impossible to prepare the hypothetical propellant. However, with a certain particle-size distribution of ammonium perchlorate, it should be possible to add 80% by volume, although the resulting mix might be difficult to cast. Further, the resulting propellant would undoubtedly have poor mechanical properties, especially in ultimate elongation. Two solutions to the problem exist: The per cent of oxidizer can be decreased until the castability and the mechanical properties are satisfactory, although this decrease in oxidizer will reduce the specific impulse of the propellant. Or, another binder can be selected which contains some oxygene.g., ( C T H ~ O ) ~as; a rule, the more oxygen in the binder, the less is the amount of oxidizer required to achieve the maximum performance for a particular binder-oxidizer system. However, the greater the oxygen content of a CHOtype binder, the less favorable is the heat of formation of the binder, so that the maximum specific impulse is decreased somewhat. A reasonably good indication of the
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oxidizer-to-binder weight ratio required for optimum performance can be obtained by balancing the combustion products to '/z CO, '/z COZ, and HzO. Any chlorine and nitrogen in the binder and oxidizer are assumed to go to hydrogen chloride and nitrogen. When two different binders are considered for use with one oxidizer, the binder with the more positive heat of formation (AH,) should yield a propellant with the greater optimum performance (provided the average molecular weights of the combustion products from both binders are about the same), because an increase (positively) in the heat of formation tends to increase the flame temperature. Likewise, when several oxidizers are considered with one binder, the oxidizer with the most positive heat of formation should give a propellant with the greatest optimum performance. After the optimum weight oxidizer has been determined, the densities of the binder and oxidizer can be used to calculate the volume yo oxidizer, which gives a rough indication of the castability of the system and of whether or not reasonably good mechanical properties can be expected of the propellant. When a relatively small amount of oxidizer is required, a binder with a high density is desirable to increase the density of the propellant. On the other hand, when a relatively large amount of oxidizer is required, a binder with low density is desirable to improve cast-
ability and propellant mechanical properties. Ordinarily, however, the common oxidizers have greater densities than most binders, so that the maximum amount of oxidizer yields the greatest propellant density. Other ballistic properties, such as burning rate and its pressure and temperature sensitivity, are also important, but effect of the binder on these properties is usually not predictable. Properties Desired of Elastomeric Binders
To satisfy the various requirements for case-bonded grains, a partially polymerized liquid fuel is desirable, because it cures with a minimum of shrinkage and heat release. Also, viscosity of such a liquid fuel can be adjusted by varying the degree of polymerization. The viscosity should not be so high as to render it difficult to disperse the oxidizer uniformly in the fuel and to cast the final mix at a reasonable rate under gravity or under a moderate pressure. On the other hand, the viscosity should not be so low as to allow the oxidizer to settle rapidly in the uncured mix. The uncured propellant mix should have a reasonable long pot life and should cure completely a t relatively low temperatures-Le., a t temperatures less than 200' F. and preferably less than lGOo F. The curing reactions should not
1
TUBULAR
ROD AN0 TUBE
DOUBLE ANCHOR
TIME --D
TIME
-
TIME --D
STAR
MULTI-FIN
DUAL COMPOSITION
TIME --D
TIME -+
TIME
-+
Internal configurations and the resulting thrust-time curves. Configuration of the grain is determined largely b y the thrust-time program desired of the motor, and ballistic properties of the propellant VOL. 52, NO. 9
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evolve volatile products, because these products may produce voids in the propellant or may lead to an undesirably long cure-time if the rate of the curing reaction is diffusion controlled. When the oxidizer is appreciably soluble in the binder, certain problems can conceivably arise. For example. casting may be more difficult, and the cured propellant may have undesirable mechanical properties and nonreproducible or otherwise undesirable ballistic properties. However, it is also possible that some solubility of the oxidizer in the binder could produce some desirable properties. The binder should be chemicallystabIe in the presence of the oxidizer; otherwise, deterioration in propellant mechanical and ballistic properties mav occur during storage of the propellant at elevated temperatures. How.ever, except in accelerated aging tests, propellants are not ordinarily subjected to storage for long periods at temperatures much above 100' I;. In addition to storage stability, a propellant should not detonate easily when subjected to shock or impact. Although few quantitative correlations exist between the mechanical properties of cured unfilled binders and those of the propellants, certain mechanical properties seem desirable in a binder. For example. the unfilled binder should deform to an exceedingly large extent when subjected to a relatively low stress. Such ease of deformation is desired. because the binder dispersed among the oxidizer particles is highly deformed when a heavily loaded propellant is only slightly deformed. If a large force is required to produce this high deformation, the adhesive bonds between the binder and oxidizer particles will break. producing vacuoles. Ordinarily, when vacuoles begin to form around oxidizer particles as a sample is stretched, the stress-strain curve passes through a maximum and often shows a sharp yield point. With a binder which has a high modulus as well as a high ultimate elongation, the propellant may have a yield value at an elongation of about 5y0 but an elongation at break of as great as 100%. During elongation between 5 and loo%, the binder continues to pull away from oxidizer particles. while the stress remains relatively constant. Past experience has indicated that such propellant properties are not desirable. and the design of a case-bonded grain from such a propellant must be based on the elongation at the yield point. One possible method of delaying the yield phenomenon is to increase the strength of the binder-to-oxidizer adhesion. However, little apparently is known about the factors which influence the adhesion in propellants and the amount by which the adhesion can
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be varied. I n fact, it is not clear whether or not strong adhesion is actually desirable. When the binder itself has a relatively low modulus and ultimate elongation, it would seem likely that the propellant would have increased elongation if the adhesive bonds were rather weak and broke continuously during the stretching of a propellant specimen. Such a continuous rupturing of the adhesive bonds might relieve local stress concentrations in the propellant specimen and thus increase the elongation. However, additional studies are needed to determine more precisely the basic factors that influence propellant mechanical properties. iVhen high elongation (greater than 20 to 30%) is desired of a propellant at some low temperature, the unfilled binder must have an even lower glasstransition temperature. The addition of filler to a binder apparently always increases the glass temperature, although the magnitude of the increase may depend on the volume fraction and surface area of the filler and possibly on the specific nature of the binder and filler. The maximum elongation of unfilled binders at a moderate strain rate (about 3 min.-I) often occurs some 20" to 40" C. above the glass temperature. Thus, the glass temperature of a propellant binder should be about 30' C. or more below the lowest temperature at which the propellant will be used. A low glass temperature for the propellant is especially needed, because at low temperatures, the high strain rates produced by motor ignition decrease the elongation of a propellant rather markedly. The tensile strength and ultimate elongation of both elastomers and propellants usually decrease monotonically with increasing temperature at temperatures sufficiently above the glass temperature. Thus, when a propellant is not to be used at low temperatures, a binder should be chosen \chose glass temperature is just low enough to give the propellant adequate mechanical properties to meet the requirements at the lowest operating temperature. This should lead to an improvement in mechanical properties in the high-temperature range. TVhen a binder contains significant amounts of oxygen or polar groups, the glass temperature is quite often higher than desired. T o improve the lowtemperature mechanical properties of propellants containing such binders, plasticizers may be employed. Either low-energy conventional plasticizers or high-energy plasticizers, such as the nitroglycerin in double-base propellants, may be used. When high-energy plasticizers are used in the binder, less solid oxidizer is required to achieve optimum performance. Ideally, it seems best to omit plasticizers whenever possible. Large amounts
I N D U S T R r A l AND ENGINEERING CHEMISTRY
of plasticizer not only reduce the propellant tensile strength at a given temperature but also may possibly lead to difficulties in case-bonding and to other complications associated with plasticizer migration. However, such problems are probably not basic; they can be circumvented in various ways and decrease as the amount of plasticizer is reduced. A binder should not crystallize when stored or when deformed highly. This latter condition is undesirable because a binder which crystallizes when highly deformed may crystallize spontaneously if stored in the appropriate temperature range. Such crystallization is undesirable because it produces a marked reduction in the elongation of a propellant. To determine whether or not an elastomer or binder in a propellant will crystallize spontaneously is not a simple task. Crystallization is often a slow process and is preceded by an induction period. Further, an optimum remperature exists for crystallization which is not easy to locate initially; and the more the temperature is displaced from the optimum temperature. the longer is the period required for cry stallization to occur. If a propellant binder can crystallize, it is safe to use the propellant only at temperatures above the thermodynamic melting point for the crystallites. The elastomeric binder in a propellant should be cross-linked, preferably through stable primary valence bonds, to minimize permanent deformation or creep of a propellant grain Creep of propellants is more complex than the creep of unfilled binder. In addition to the mechanism responsible for creep of the unfilled binder, creep of propelants is modified by the reinforcing adhesion between binders and oxidizer particles. However. under certain conditions, these adhesive bonds can break and increase the creep rate. Acknowledgment
The author wishes to thank John I. Shafer and John Wiley & Sons, Inc., for permission to use the illustrations. References (1) Landel, R . F., Smith, T. L., "Viscoelastic Properties of Rubberlike Composite Propellants and Filled Elastomers," Division of Paint, Plastics, and Printing Ink Chemistry; 136th Meeting, ACS, September 1959. (2) Smith, T. L., J . Polymer Sct. 32, 99 (1958).
RECEWED for review October 28, 1959 ACCEPTED March 21, 1960
Work done under contract No. NASw-6, sponsored by the National Aeronautics and Space Administration.
