Maxwell Fluid Model for Generation of Stress–Strain Curves of Viscoelastic Solid Rocket Propellants

Abstract

AbstractSolid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–strain curve is generated for case‐bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different strain rate. It is observed that change in spring constant, representing elastic part is very small with strain rate but damping constant varies significantly with variation in strain rate. For a typical propellant formulation, when strain rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all strain rates, stress–strain curve is generated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case‐bonded solid propellant formulations. It is observed that with increases in strain rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher strain rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with strain rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any strain rate from that at a reference strain rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K2=(K1‐H)×{ln(dε2/dt)/ln(dε1/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D2=D1×{(dε2/dt)/(dε1/dt)}S. Evaluating constants “H” and “S” at different strain rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–strain curves, which are not attempted by any other researchers.