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10"7 10"6 10"5 lO"4 10-3 10-2 10"1 10° 101 102 103 104 105 106 107

FIGURE 11-23. This stress-relaxation modulus master curve for a particular composite solid propellant is constructed from manipulated data taken from a number of uniaxial tensile tests at constant strain rate but different temperatures. (Reproduced with permission of United Technologies Corp., Chemical Systems from Ref. 11-27.)

ER (5 yr) = 65 psi at 70 °F Er (5 yr) = 67 psi at 48 °F ER (2 mo) = 88 psi at 23 °F Er (0.1 sec! = 3150 psi at 23 °F

Usually, several different grain loading and operating conditions need to be analyzed. Such a structural analysis is useful for identifying locations of maximum stress or strain and to any structural members or grain sectors that are too weak or too heavy, but these analyses have not always been successful. The choice of the best analysis tool and the best pseudo-viscoelastic compensation factors will depend on the experience of the stress analyst, the specific motor design conditions, the complexity of the motor, the geometry, and suitable, available, valid propellant property data.

In a case-bonded motor, special provision is required to reduce the stress concentrations at the grain ends where the case and grain interface, especially for motors expected to operate satisfactorily over a wide range of temperatures. Basically, the high stresses arise from two primary sources. First, the physical properties, including the coefficient of thermal expansion of the case material and the propellant, are grossly dissimilar. The coefficient of expansion of a typical solid propellant is 1.0 x 10~4 m/m-K, which is five times as great as that of a steel motor case. Secondly, the aft-end and head-end geometries at the grain-case juncture often present a discontinuity, with the grain stress theoretically approaching infinity. Actually, finite stresses exist because viscoplastic deformations do occur in the propellant, the liner, and the case insulation. Calculating the stress in a given case-grain termination arrangement is usually impractical, and designers rely on approximations supported by empirical data.

For simple cylindrical grains the highest stresses usually occur at the outer and inner surfaces, at discontinuities such as the bond surface termination point, or at stress concentration locations, such as sharp radii at the roots or tips of star or wagonwheel perforations, as shown in Fig. 11-16. Figure 11-24 shows a stress relief flap, sometimes called a boot, a device to reduce local stresses. It is usually an area on the outside of the grain near its aft end (and sometimes also its forward end), where the liner material is not sticky but has a non-adhesive coating that permits the grain to shrink away from the wall. It allows for a reduction of the grain at the bond termination point. It moves the location of highest stress into the liner or the insulation at the flap termination or hinge. Normally, the liner and insulation are much stronger and tougher than the propellant.

Parametric studies of propellant and case-bond stresses of a typical grain-case termination design (Fig. 11-24) reveal the following:

1. Flap length is less significant than the thickness of the insulation or the separate flap boot, if one is used, in controlling the local level of stresses at the grain-case termination.

2. The distribution of stresses at the grain-case termination is sensitive to the local geometry; the level of stress at the case bond increases with web fraction and length-to-diameter ratio under loading by internal pressure and thermal shrinkage.

3. As the L/D and web fraction increase, the inner-bore hoop stress and the radial stress at the grain-case bond increase more rapidly than does the vaily

FIGURE 11-24. The asterisks in the bottom simplified diagram denote potentially critical failure areas. The top sketch is an enlargement of the aft termination region of the grain and shows a boot or stress relief flap.

Flap (unbonded length), no adhesion between liner and insulation

Case insulation

•Grain liner

Case (insulated on inside)

•Grain termination

FIGURE 11-24. The asterisks in the bottom simplified diagram denote potentially critical failure areas. The top sketch is an enlargement of the aft termination region of the grain and shows a boot or stress relief flap.

'Head end of perioral ion

Star-shaped perforation

Perforation

'Perforation tip

Flap (unbonded length), no adhesion between liner and insulation

Case insulation

Case (insulated on inside)

'Head end of perioral ion

'Perforation tip

Perforation

•Grain liner

•Grain termination

Star-shaped perforation grain-case termination stress under internal pressure and thermal shrinkage loads.

4. The radial case-bond stress level at the grain-case termination is much larger than the case-bond shear stress under axial acceleration loading as well as under internal pressure and thermal shrinkage loading.

Aging of propellants in rocket motors refers to their deterioration in the physical properties with time. It is caused by the cumulative damage done to the grain (such as by thermal cycling, and load applications) during storage, handling, or transport. It can also be caused by chemical changes with time, such as the gradual depletion (evaporation) of certain liquid plasticizers or moisture absorption. The ability to carry stress or to allow elongation in propellants diminishes with cumulative damage. The aging limit is the estimated time when the motor is no longer able to perform its operation reliably or safely (see Refs. 11-28 and 11-29). Depending on the propellant and the grain design, this age limit or motor life can be betwen 8 and 25 years. Before this limit is reached, the motor should be deactivated and have its propellant removed and replaced. This refurbishing of propellant is routinely done on larger and more expensive rocket motors in the military inventory.

With small tactical rocket motors the aging limit is usually determined by full-scale motor-firing tests at various time periods after manufacture, say 2 or 3 years and with an extrapolation to longer time periods. Accelerated temperature aging (more severe thermal cycles) and accelerated mechanical pulse loads and overstressing are often used to reduce the time needed for these tests. For large rocket motors, which are more expensive, the number of full-scale tests has to be relatively small, and aging criteria are then developed from structural analysis, laboratory tests, and subscale motor tests.

Many of the early grains were cartridge loaded and kept the grain isolated from the motor case to minimize the interrelation of the case and the grain stresses and strains resulting from thermal expansion. Also, upon pressuriza-tion the case would expand, but the grain would shrink. The case-bonded grain presents a far more complex problem in stress analysis. With the propellant grain bonded firmly to the case, being a semirubbery and relatively weak material, it is forced to respond to case strains. As a result, several critically stressed areas exist in every case-bonded motor design; some are shown with an asterisk in Fig. 11-24.

The varying nature of the stress analysis problem is brought about by the physical character of propellant; in general terms, solid propellant is relatively weak in tension and shear, is semielastic, grows softer and weaker at elevated temperatures, becomes hard and brittle at low temperatures, readily absorbs and stores energy upon being vibrated, degrades physically during long-term storage because of decomposition and chemical or crystalline changes, and accumulates structural damage under load, including cyclic load. This last phenomenon is shown graphically in Fig. 11-25 and is particularly important in the analysis of motors that are to have a long shelf-life (more than 10 years).

FIGURE 11-25. Representation of the progress in cumulative damage to the bond between the grain and the case in a case-bonded rocket motor experiencing a hypothetical stress history. (Adapted from Ref. 11-30.)

No a priori reason is known for materials to exhibit cumulative damage, but propellants and their bond to case material exhibit this trait even under constant load, as shown in Fig. 11-26. Valid theories and analytical methods applicable to cumulative damage include a consideration of both the stressstrain history and the loading path (the material effected). The most important environmental variables affecting the shelf life of a motor are time, temperature

Time to failure, hr

FIGURE 11-26. Time dependent reduction of the propellant-liner-insulator bond strength when subjected to constant load at 77°F. (From Ref. 11-31.)

Time to failure, hr

FIGURE 11-26. Time dependent reduction of the propellant-liner-insulator bond strength when subjected to constant load at 77°F. (From Ref. 11-31.)

cycles, propellant mass, stress (gravity forces for large motors), and shock and vibration. Failure due to cumulative damage usually appears as cracks in the face of the perforation or as local "unbonds" in case-bonded motors.

The strength of most propellants is sensitive to the rate of strain; in effect they appear to become more brittle at a given temperature as the strain rate is increased, a physical trait that is important during the ignition process.

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