A nonlinear viscoelastic constitutive model for solid propellant is proposed. Dewetting and cyclic loading effects as well as large deformation are regarded as the main sources of the nonlinear behavior of solid propellant.
In modelling the damage, it is assumed that the time characteristics of the free energy of solid propellant do not change by damage. In this case, the free energy function of the propellant can be regarded as the free energy of the undamaged propellant multiplied by damage functions. In addition, thermorheologically simple behavior is assumed. These assumptions are verified through the stress relaxation tests. Also, the propellant is regarded as homogeneous and isotropic. Damages considered are due to the dewetting phenomena and the nonlinearities in the load-unload cycles. Softening of the solid propellant due to damage is treated by modulus decrease. Viscoelastic dewetting criteria is developed by expanding Vratsanos' elastic dewetting criteria. In the calculation of the modulus decrease, the modulus of void, which is created by dewetting, is modeled with non-zero constant values. This value is calibrated from one test condition and can be used in the other test conditions. The values of adhesion energy between the binder and AP particle, which is used in the dewetting criteria, are obtained by a 180 degree peel test. Nonlinearities during cyclic loading are accounted for by introducing functions of the octahedral shear strain measure. These functions are also calibrated from one test condition and can be used in the other test conditions. In order to represent large deformation effect, Simo's three-dimensional viscoelastic model is adopted and modified to include the general viscoelastic effect in the bulk behavior.
The constitutive equation is implemented into a finite element analysis code for the analysis of experimental tests. A commercial finite element package 'ABAQUS' is used for the analysis and the model is introduced into the code through a user subroutine, UMAT. The analysis is conducted with the auto time increment and convergence criteria supplied by 'ABAQUS'.
To evaluate the model, uniaxial and strip biaxial tests are conducted with several different loading conditions including temperature varying environments. The predicted stress values show good agreement with the measured ones and volume dilatations are slightly underestimated over the wide range of experiments. So, the model can be used in the stress analysis of the propellant grain. The model has the advantages in that the viscoelastic dewetting phenomena are considered directly, damage functions are relatively simple and economic to be implemented in finite element analysis and accurate in the loading conditions that solid propellant grain experience in storage conditions. Especially, the model includes the contributions of each constituent of solid propellant to the stress-strain behavior. So, the model can be used to predict solid propellant behavior with the wide variations of solid propellant compositions frequently occurred.
