Viscoelastic Modelling of Solid Rocket Propellants using Maxwell Fluid Model

摘要

Maxwell fluid model consisting of a spring and a dashpot in series is applied for viscoelastic characterisation of solid rocket propellants. Suitable values of spring constant and damping coefficient were employed by least square variation of errors for generation of complete stress-strain curve in uniaxial tensile mode for case-bonded solid propellant formulations. Propellants from the same lot were tested at different strain rates. It was observed that change in spring constant, representing elastic part was very small with strain rate but damping constant varies significantly with variation in strain rate. For a typical propellant formulation, when strain rate was raised from 0.00037/s to 0.185/s, spring constant K changed from 5.5 MPa to 7.9 MPa, but damping coefficient D was reduced from 1400 MPa-s to 4 MPa-s. For all strain rates, stress-strain curve was generated using Maxwell model and close matching with actual test curve was observed. This indicates validity of Maxwell fluid model for uniaxial tensile testing curves of case-bonded solid propellant formulations. It was established that at higher strain rate, damping coefficient becomes negligible as compared to spring constant. It was also observed that variation of spring constant is logarithmic with strain rate and that of damping coefficient follows power law. The correlation coefficients were 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 developeds .K_2 =K_1+ H× In{(dε_2/dt)l(dε_1/dt)}. Similarly for damping coefficient D also another constant S is introduced and prediction formula is given by D_2= D_1 × {(dε_2/dt)/(dε_1/dt)}~s. Evaluating constants H and S at different strain rates validate this mathematical formulation for different propellant formulations. Stress-strain curves for solid propellants can be generated at those strain rates at which actual testing is not possible. Close matching of test and predicted stress-strain curve indicates propellant behavior as visco-elastic Maxwell fluid.