Info

"Polybutadiene binder with reduced aluminum and ammonium perchlorate; data are from four different 5-gallon mixes.

Source: Data taken with permission of the AIAA from Ref. 11-23.

"Polybutadiene binder with reduced aluminum and ammonium perchlorate; data are from four different 5-gallon mixes.

Source: Data taken with permission of the AIAA from Ref. 11-23.

wide, with —65°F and +160°F or 219 K and 344 K often being the lower and upper extremes expected during motor exposure. Propellant grains must be strong enough and have elongation capability sufficient to meet the high stress concentrations present during shrinkage at low temperature and also under the dynamic load conditions of ignition and motor operation. The mechanical properties (strength, elongation) can be increased by increasing the percent of binder material in the propellant, but at a reduction in performance.

Structural Design

The structural analysis of a typical case-bonded grain has to consider not only the grain itself but also the liner, insulator, and case, which interact structurally with the propellant grain under various loading conditions (see Chapter 9 or Ref. 11-1). The need to obtain strong bonds between the propellant and the liner, the liner and the insulator, or the insulator and the case is usually satisfied by using properly selected materials and manufacturing procedures to assure a good set of bonds. Liners are usually flexible and can accept large strains without failure, and the vehicle loads can be transmitted from the case (which is usually part of the vehicle structure) into the propellant.

When the propellant is cured (heated in an oven), it is assumed to have uniform internal temperature and to be free of thermal stresses. As the grain cools and shrinks after cure and reaches an equilibrium uniform ambient temperature (say, from —40 to +75°F), the propellant experiences internal stresses and strains which can be relatively large at low temperature. The stresses are increased because the case material usually has a thermal coefficient of expansion that is smaller than that of the propellant by an order of magnitude. The stress-free temperature range of a propellant can be changed by curing the motor under pressure. Since this usually reduces the stresses at ambient temperature extremes, this pressure cure is now being used more commonly.

The structural analysis begins when all loads can be identified and quantified. Table 11-6 lists the typical loads that are experienced by a solid propellant motor during its life cycle and some of the failures they can induce. Some of these loads are unique to specific applications. The loads and the timing of these loads during the life cycle of a solid propellant rocket motor have to be analyzed for each application and each motor. They depend on the motor design and use. Although ignition and high accelerations (e.g., impact on a motor that falls off a truck) usually cause high stresses and strains, they may not always be the critical loads. The stresses induced by ambient environmental temperature cycling or gravity slumps are often relatively small; however, they are additive to stresses caused by other loads and thus can be critical. A space motor that is to be fired within a few months after manufacture presents a different problem than a tactical motor that is to be transported, temperature cycled, and vibrated for a long time, and this is different yet from a large-diameter ballistic missile motor that sits in a temperature-conditioned silo for more than 10 years.

TABLE 11-6. Summary of Loads and Likely Failure Modes in Case-Bonded Rocket Motors

Load Source

1. Cool-down during manufacture after hot cure

2. Thermal cycling during storage or transport

3. Improper handling and transport vibrations

4. Ignition shock/pressure loading

5. Friction of internal gas flow in cavity

6. Launch and axial flight acceleration

7. Flight maneuvers (e.g., antimissile rocket)

8. Centrifugal forces in spin-stabilized projectiles/missiles

9. Gravity slump during storage; only in large motors

10. External air friction when case is also the vehicle's skin

Description of Load and Critical Stress Area

Temperature differential across case and grain; tension and compression stresses on grain surfaces; hot grain, cool case Alternative hot and cold environment; critical condition is with cold grain, hot case; two critical areas: bond-line tensile stress (tearing), inner-bore surface cracking

Shock and vibration, 5 to 30g0 forces during road transport at 5 to 300 Hz (5 to 2500 Hz for external aircraft carry) for hours or days; critical failure: grain fracture or grain debonding Case expands and grain compresses; axial pressure differential is severe with end-burning grains; critical areas; fracture and debonding at grain periphery Axially rearward force on grain

Inertial load mostly axial; shear stress at bond line; slump deformation in large motors can reduce port diameter High side accelerations cause unsymmetrical stress distribution; can result in debonding or cracks High strain at inner burning surfaces;

cracks will form Stresses and deformation in perforation can be minimized by rotating the motor periodically; port area can be reduced by slump

Heating of propellant, liner and insulators will lower their strengths causing premature failure. Induces thermal stresses

Furthermore, the structural analysis requires a knowledge of the material characteristics and failure criteria: namely, the maximum stress and strains that can safely be accepted by the propellant under various conditions. The failure criteria are derived from cumulative damage tests, classical failure theories, actual motor failures, and fracture mechanics. This analysis may be an iterative analysis, because the materials and geometry need to be changed if analysis shows that the desired margins of safety are exceeded.

Ideally, the analysis would be based on a nonlinear viscoelastic stress theory; however, such an approach is still being developed and is not yet reliable (see Ref. 11-1). An analysis based on a viscoelastic material behavior is feasible, relatively complex, and requires material property data that are difficult to obtain and uncertain in value. Most structural analyses today are based on an elastic material model; it is relatively simple and many two- and three-dimensional finite element analysis computer programs of this approach are available at rocket motor manufacturing companies. Admittedly, this theory does not fit all the facts, but with some empirical corrections it has given approximate answers to many structural grain design problems. An example of a two-dimensional finite element grid from a computer output is shown in Fig. 11-22 for a segment of a grain using an elastic model (see Refs. 11-24 and 11-25).

With elastic materials the stress is essentially proportional to strain and independent of time; when the load is removed, the material returns to its original condition. Neither of these propositions is valid for grains or their propellant materials. In viscoelastic material a time-related dependency exists between stresses and strains; the relationship is not linear and is influenced by the rate of strain. The stresses are not one-dimensional as many laboratory tests are, but three-dimensional, which are more difficult to visualize. When the load is removed, the grain does not return to its exact original position. References 11-26 and 11-27 and Chapters 9 and 10 of Ref. 11-1 discuss three-dimensional analysis techniques and viscoelastic design. A satisfactory analysis technique has yet to be developed to predict the influence of cumulative damage.

Various techniques have been used to compensate for the nonelastic behavior by using allowable stresses that have been degraded for nonlinear effects and/or an effective modulus that uses a complex approximation based on laboratory strain test data. Many use a modified modulus (maximum stressstrain at maximum stress or erm/em in Fig. 11-21) called the stress relaxation modulus Er in a master curve against temperature-compensated time to failure, as shown in Fig. 11-23. It is constructed from data collected from a series of uniaxial tests at constant strain rate (typically, 3 to 5%) performed at different temperatures (typically -55 to +43°C). The shifted temperature TJT is shown in the inset on the upper right for 3% strain rate and sample tests taken at different temperatures. The factor X in the ordinate corrects for the necking down of the tension sample during test. The small inset in this figure explains the correction for temperature that is applied to the reduced time to failure. The empirical time-temperature shift factor aT is set to zero at ambient temperatures (25°C or 77°F) and graphically shifted for higher and lower temperatures. The master curve then provides time-dependent stress-strain data to calculate the response of the propellant for structural analysis (see Ref. 1121 and Chapter 9 of Ref. 11-1).

Sleeve

End ring

Sleeve

End ring

Grain

Annular grooves

FIGURE 11-22. Finite element analysis grid of the forward end of a cast grain in a filament-wound plastic case. The grain has an internal tube and annular grooves. The top diagram shows the model grid elements and the bottom shows one calculated strain or deformation condition. (Reprinted with permission from A. Turchot, Chapter 10 of Ref. 11-1).

Grain

Annular grooves

FIGURE 11-22. Finite element analysis grid of the forward end of a cast grain in a filament-wound plastic case. The grain has an internal tube and annular grooves. The top diagram shows the model grid elements and the bottom shows one calculated strain or deformation condition. (Reprinted with permission from A. Turchot, Chapter 10 of Ref. 11-1).

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