L-303 - Mixing Rules for Energetic Materials: Coefficient of Thermal Expansion and Relationships with Elastic Modulus placed Under Review

An important issue with energetic composites is the lack of experimental measurements of their properties. Alternatively, mechanical and physical properties may be estimated from known values of the constituent materials using mixing rules available in the literature. This approach has been previously described by Schrama and Der Weduwen, who studied the electrical and mechanical properties of energetic composites, respectively, and provided recommendations about models that could be used. Continuing this theme, this report considers mixing rules applicable to the prediction of the coefficient of thermal expansion and elastic modulus, in particular the bulk modulus.

A wide variety of models are reviewed, applied to energetic and non-energetic composites, and compared to experimental data. It is shown that the rule of mixtures and Kerner’s rule provide good estimations, with the average error not exceeding 10%. It may be deduced that the interaction commonly observed between filler and matrix has no effect on the coefficient of thermal expansion in the case of energetic composites.

Following these results, and since Der Weduwen’s conclusions stipulate that the precision of the models for the prediction of elastic modulus were not satisfactory, the product of the coefficient of thermal expansion and the bulk modulus is investigated. Experimental data, even if insufficient and debatable, are compared with calculated values furnished by several relationships. Furthermore, a new model for the prediction of the bulk modulus is derived and other empirical relations are provided based on different data in the literature. This new model, as well as an empirical relation, display better performance than the shifted logarithmic sum rule recommended by Der Weduwen.

The first recommendation is to use the rule of mixtures when estimating the coefficient of thermal expansion and the second is to use either the newly derived model or the empirical equation specifically derived from Kel F-TATB composites to predict the bulk modulus. Further experimentation is also recommended to better verify these two models.