A Directional Damage Constitutive Model for Stress-Softening in Solid Propellant

Solid propellants are particulate composite with a light crosslinked elastomeric binder that is filled with a high concentration of energetic solid aggregates. Solid propellants are often considered as highly nonlinear elastomeric materials, with elastic behavior resulted from its binder and plastic behavior from its energetic particles. The study of the microstructure and mechanical properties of solid propellant is of crucial importance for its design, safety evaluation, and lifetime prediction of solid fuel carriers. Due to dependency on the mechanical behavior of solid propellant on its elastomeric binder material, the constitutive model proposed for rubber-like material can often be generalized to predict the nonlinear behavior of solid propellant. They exhibit strain rate dependency, finite elasticity, and strong stress softening and strain residual (permanent set). The stress softening effect in the first cycle (Mullins effect) has been described as the result of network rearrangement and chain scission. The mechanical behavior of elastomer undergoing stress softening is usually modeled by adopting a damage function, already defined by many models, and implement it into a 3D element which often provides a good agreement with experimental data, although residual strains are neglected. As this damage functions are often purely phenomenological, model accuracy highly depends on the fitting procedure, and most models could not predict the softening outside the fitted range. Several physical-based models have described the stress softening in elastomers through different mechanisms such as bond rupture, molecule slipping, and filler rupture. Due to the complexity of such modeling approaches, some of these physically-based models still use phenomenological parameters to simplify the description of the damage. Purel micromechanical models mostly have too many material parameters which make them hard to use, or they have limited ability in predicting both stress-softening and strain residual.  Therefore, a micro-mechanical model with a limited number of fitting parameters can be significantly relevant in FE approaches. This paper focuses on developing a model, which can predict the stress softening and strain-residual mechanism of the solid propellant. This micromechanical model for solid propellant was proposed based on the network evolution theory. The motivation of this study is the lack of a micro-mechanical model that can describe both the stress softening effect and permanent set in quasi-static behavior of propellants. The simplified network-evolution model with only five parameters is a simple micro-mechanical model that can capture both stress softening effect and permanent set. Besides the simplicity and reduced fitting procedure, the model was validated against several experimental data and illustrated good agreement in small and large deformations, which makes the proposed model a suitable option for commercial and other applications.