Theoretical stress mechanism and structural integrity of viscoelastic propellant grains with variable Poisson's ratio

For the propellant grain of solid rocket motors (SRMs) with circular inner surfaces, the generalized Maxwell model (GMM) and the generalized Kelvin-Voigt model (GKV) are used to characterize the relaxation properties of the grain's elastic modulus and the creep properties of Poisson's ratio, respectively. Based on the elastic-viscoelastic correspondence principle, an analytical expression for viscoelastic stress that simultaneously considers the time-dependent nature of elastic modulus and Poisson's ratio is derived. Based on this, a parametric analysis of the stress distribution in the grain under internal pressure is conducted. The results indicate that the hoop stress on the inner surface of the grain is most critical at the beginning of loading. As the thickness of the propellant grain increases, this initial tensile stress decreases moderately, but the duration of tensile stress increases. Increasing the thickness or stiffness of the combustion chamber casing moderately reduces the hoop stress during the initial loading and shortens the duration of tensile stress. Accurate measurement of the creep properties of Poisson's ratio has a significant impact on improving calculation accuracy. The stress calculation results under gradual pressurization are lower than those under instantaneous pressurization. The conclusions provide a reference for analyzing the structural integrity of propellant grains.