(227g) Micromechanics Simulations of the Viscoelastic Properties of Pbx-9501 by Material Point Method

An understanding of the viscoelastic properties of PBX-9501 is critical to the understanding and prediction of the response of these materials to external stimuli, particularly mechanical shocks. Due to the explosive nature of PBX-9501 experimental testing is difficult and expensive. Unfortunately, existing theoretical approaches that have been successfully applied to more conventional composites have not been successful for PBX-9501. Numerical simulations that explicitly consider the composite microstructure are expected to play a more important role in predicting mechanical response of PBX-9501 than they play in the studies of conventional composites. Such homogenization simulations of PBX-9501, however, are complicated by a number of factors including: (a) the need to realistically represent PBX-9501 microstructure with a broad distribution of filler sizes from fine particles of one micron to large particles approaching one millimeter in diameter, necessitating the use of a huge number of small computational elements; (b) complicated geometries of HMX particles; (c) the need to predict PBX-9501 viscoelastic response over times ranging from picoseconds to seconds.

In this study, the viscoelastic properties of the highly filled plastic-bonded explosive PBX-9501 are studied by two-dimensional dynamic Material Point Method (MPM) simulations utilizing plasticized polymer binder and crystalline HMX constituent properties taken from experiment. The upper bound for the composite properties is estimated from iso-displacement boundary conditions, whereas the lower bound is estimated from iso-stress boundary conditions. A homogenized or “dirty” binder approach is utilized to handle the multiple length scales involved in MPM simulations of highly-filled composites with a broad distribution of filler particle sizes. The idea behind the homogenization approach is that mechanical properties of the binder can be replaced with an effective (homogenized) binder containing the smallest particle and used in larger-scale simulations where only the larger particles are explicitly represented, requiring much coarser resolution and, therefore, significantly less computational time. The procedure is repeated until the homogenized binder represents the response of the binder and all but the largest particles, which are still represented explicitly. Results of this final simulation yield the homogenized properties of the composite. Multiple time scale challenges are addressed by conducting a series of simulations in which the speed of sound of the composite is systematically varied by adjusting material point masses. This approach is used to predict the homogenized time-dependent shear modulus of PBX-9501 from nanoseconds to milliseconds yielding good agreement with experimental data.

This work is funded by the University of Utah Center for the Simulation of Accidental Fires and Explosions (C-SAFE), funded by the Department of Energy, Lawrence Livermore National Laboratory, under subcontract B341493.