Measuring Propellant Stress Relaxation Modulus Using Dynamic Mechanical Analyzer

Structural analysis of solid rocket motors is challenging for several reasons, but the most important of these is the complex behavior of the propellant. The mechanical response of a solid propellant is time and temperature dependent. The complexity of the mathematical analysis of the propellant depends on the loading conditions, but for some loading situations, the linear viscoelasticity assumption is reasonable. In particular, linear viscoelasticity is perhaps the most appropriate material behavior description for use in the simulations of stresses related to storage conditions. Typically, simulations use a viscoelastic model in the form of a Prony series and a Williams-Landel-Ferry (WLF) equation. The parameters in these models are derived from stress relaxation experiments, making the stress relaxation experiment a key viscoelastic test, analogous to the tensile test for linear elastic materials.

A typical set of stress relaxation tests is performed at several discrete temperatures that cover a range of temperatures anticipated by the fielded motor. At each of the selected temperatures, the specimen is deformed with approximately a single step in strain, which is then held constant for the duration of the test. While held at this constant strain, the stress decays over time due to relaxation of the rubbery elastomer. During this portion of the test, the stresses are measured, and the ratio of stress to applied strain is determined. This ratio is termed the stress relaxation modulus ER. Using time-temperature superposition, the set of curves at the various temperatures can be shifted horizontally relative to each other to form a master curve. The translation of the curves takes a specific mathematical form, viz., the WLF equation. From this master curve, the Prony series at any given temperature can be calculated, and the calculation can be incorporated into finite element analyses along with the WLF equation, making linear viscoelastic analysis of rocket motors possible.