Multiscale Modeling of Shock Wave Propagation through High Energetic Composites

Abstract

This dissertation studies shock loading of Polymer-Bonded Explosives (PBXs) with varying degrees of microstructural information. PBXs are a class of multi-component solid-state composites consisting of energetic crystals (HMX) embedded in a polymeric binder and are used as propellants, munitions and fuel cell components.

The rapid energy release involves tightly coupled nonlinear interactions between chemistry and mechanics. While the evolution and transfer of chemical energy to thermal and mechanical energy occurs at larger scales, decomposition and energy release take place at the molecular level. Between the molecular and continuum levels, material behavior is governed by the material microstructure; as the shock wave propagates through the energetic material, it is influenced by the particulate matrix interactions.

Typical hydrocodes that are currently used to simulate detonation of energetic composites do not explicitly model material heterogeneities. Continuum methods require the least amount of fidelity and use homogenized material properties. On the other end of the spectrum, Direct Numerical Simulation (DNS) explicitly models the microstructure and requires the highest amount of fidelity. A novel approach is introduced in this work which exploits the attractive features (speed/accuracy) of each method; the First-Order multiscaling approach incorporates micro-scale effects by using volume averaging schemes. A hydrocode was developed to study shock loading of PBXs for all methods.

The Eulerian hydrocode is based on the finite element method. The governing Euler Equations are solved using an explicit, second-order Taylor-Galerkin scheme. The solution procedure includes a high-resolution shock capturing scheme needed for numerical treatment of shocks. Continuum numerical results were validated by comparing to variety of experimental and numerical PBX results. To incorporate material heterogeneity effects, synthetic microstructures were generated using Markov Random Field (MRF) approach, with varying levels of material composition. Initiation of these microstructures and a continuum were studied for four different loading conditions.

Results shown that material behavior is significantly influenced by information from the microscale. In general, a continuum approach is less reactive than material models that include microscale information. For most loading conditions the continuum model was vastly different than the heterogeneous material systems and never achieved pressure, temperature and burn fractions values by those of the heterogeneous material systems. Although the continuum approach includes binder effects through material properties, this inclusion isn't sufficient to fully capture heterogeneous material behavior.

Loading conditions also played a role in material response. Uniformly distributed loading within regions known as ``hot volumes" produced different responses for various material systems. Loading conditions with multiple interactions, not higher hot volumes, were found to have higher pressure and temperature outputs. Binder content affects heterogeneous material performance and safety. HMX heavy materials required less initiation energy and produced the highest temperature and pressure outputs, while binder heavy materials followed the opposite trend. These results showed material performance is at competition with material safety and have implications for material by design.

Finally, First-Order Multiscale modeling showed promise in capturing the influence of heterogeneity on shock loading of PBXs. The multiscale approach compared well to high fidelity DNS results, especially for material systems with reduced heterogeneity, at the fraction of the cost associated with DNS. Applying the methodologies and techniques used in this dissertation to various PBX systems can allow materials to be designed and tailored to specific applications without having to run physical experiments.