A Review of Propellant Grain Structural Analysis Methods,
HERCULES INC MAGNA UT BACCHUS WORKS
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Nonlinear propellant behavior in combination with finite grain deformation is usually the primary cause of inaccuracy in grain integrity analysis. Stresses and strains for the motor are typically calculated with linear theories, whereas the allowables are measured in laboratory tests under nonlinear conditions. Acceptable nonlinear viscoelastic finite viscoplastic finite element codes are not yet available. Therefore, the practicing grain structural analyst uses linear theories, or attempts to estimate nonlinear effects with various engineering approaches. Some nonlinear approximations are surprisingly accurate but there are many pitfalls in the use of such approximations. Solutions to the 1-D plane strain cylinder problem are quite useful in grain structural analyses. The loading conditions of most structural concern are usually thermal cooling shrinkage and ignition pressurization. For tactical motors, thermal loading has typically dominated because of wide temperature limits and metal cases. On the other hand, strategic motors with narrow temperature limits and composite cases are typically design-limited by pressure loading conditions. There is an equivalence relationship between stresses and strains for uniform thermal and pressure loading conditions. Both can be viewed as case displacement loading conditions. Strain distributions in the grain are similar for both loading conditions. Stress distributions are also similar after the applied pressure is added to the normal stresses as a hydrostatic component.