Theoretical modeling of thin binder interphases in highly filled PBX composites together with the closed form expression of the effective isotropic moduli of a simplified PBX model

Binder interphases inside the highly filled polymer bonded explosives (PBXs) are irregularly distributed and extremely thin, but play an essential role in affecting the overall moduli and explosive performance of such heterogeneous media. In the present paper, a spring-type interface model, which was physically equivalent to these practical layers within a fixed error bound, was briefly derived, at first taking account of the fact that the stiffness of the binder material was much lower than that of the explosive crystals. Hereafter, a simplified PBX model consisting of a spherical explosive particle bonded to an infinite explosive matrix by the spring-type interface is designed, and its effective isotropic moduli were analytically determined via the generalized self-consistent scheme. The upper and lower bounds of these moduli were also derived based on the elasticity extremum principles of minimum potential and minimum complementary energies. These explicit expressions can be applied to predict the preliminary elastic properties of highly filled PBXs as benchmarks to validate numerical evaluations and so forth. Eventually, some discussions were made on the size-dependent effect of PBXs with the aid of the simplified model.