This work presents a multiscale modeling framework for predictive simulations of shock-to-detonation transition (SDT) in pressed energetic (HMX) materials. The macro-scale computations of SDT are performed using an ignition and growth (IG) model. However, unlike in the traditional semi-empirical ignition-and-growth model, which relies on empirical fits, in this work meso-scale void collapse simulations are used to supply the ignition and growth rates. This results in a macro-scale model which is sensitive to the meso-structure of the energetic material. Energy localization at the meso-scale due to hotspot ignition and growth is reflected in the shock response of the energetic material via surrogate models for ignition and growth rates. Ensembles of meso-scale reactive void collapse simulations are used to train the surrogate model using a Bayesian Kriging approach. This meso-informed Ignition and Growth (MES-IG) model is applied to perform SDT simulations of pressed HMXs with different porosity and void diameters. The computations are successfully validated against experimental pop-plots. Additionally, the critical energy for SDT is computed and the experimentally observed Ps2τs=constant relations are recovered using the MES-IG model. While the multiscale framework in this paper is applied in the context of an ignition-and-growth model, the overall surrogate model-based multiscale approach can be adapted to any macro-scale model for predicting SDT in heterogeneous energetic materials.

Surrogate models for hotspot ignition and growth rates were presented in Part I, where the hotspots were formed by the collapse of single cylindrical voids. Such isolated cylindrical voids are idealizations of the void morphology in real meso-structures. This paper therefore investigates the effect of non-cylindrical void shapes and void-void interactions on hotspot ignition and growth. Surrogate models capturing these effects are constructed using a Bayesian Kriging approach. The training data for machine learning the surrogates are derived from reactive void collapse simulations spanning the parameter space of void aspect ratio (AR), void orientation ( ), and void fraction ( ). The resulting surrogate models portray strong dependence of the ignition and growth rates on void aspect ratio and orientation, particularly when they are oriented at acute angles with respect to the imposed shock. The surrogate models for void interaction effects show significant changes in hotspot ignition and growth rates as the void fraction increases. The paper elucidates the physics of hotspot evolution in void fields due to the creation and interaction of multiple hotspots. The results from this work will be useful not only for constructing meso-informed macro-scale models of HMX, but also for understanding the physics of void-void interactions and sensitivity due to void shape and orientation.

We investigate the response of polycrystalline HMX 3,5,3,5, under impact loading through a 3-dimensional mesoscale model that explicitly accounts for anisotropic elasticity, crystalline plasticity, and heat conduction. This model is used to quantify the variability in temperature and stress fields due to random distributions of the orientations of crystalline grains in HMX under the loading scenarios considered. The simulations carried out concern the response of fully dense HMX polycrystalline ensembles under impact loading at imposed boundary velocities from 50 to 400 m/s. The polycrystalline ensemble studied consists of a geometrically arranged distribution of bi-modally sized and shaped grains. To quantify the effect of crystalline slip, two models with different numbers of available slip systems are used, reflecting differing characterizations of the slip systems of the HMX molecular crystal in the literature. The effects of microstructure and anisotropy on the distribution of heating and stress evolution are investigated. The results obtained indicate that crystalline response anisotropy at the microstructure level plays an important role in influencing both the overall response and the localization of stress and temperature. The overall longitudinal stress is up to 16% higher and the average temperature rise is only half in the material with fewer potential slip systems compared to those in the material with more available slip systems. Local stresses can be as high as twice the average stresses. The results show that crystalline anisotropy induces significant heterogeneities in both mechanical and thermal fields that previously have been neglected in the analyses of the behavior of HMX-based energetic materials. C 2014 Author(s)

Accurate simulations of the shock response of heterogeneous energetic (HE) materials require closure models, which account for energy localization in the micro-structure. In a multi-scale framework, closure is provided by reaction rate models that account for ignition and growth of hotspots, allowing for prediction of the overall macro-scale sensitivity of a HE material. In the present meso-informed ignition and growth (MES-IG) model, the reaction rate is expressed as a function of shock pressure and morphology of the void field in a pressed energetic material. In MES-IG, the void morphology is quantified in terms of a limited number of parameters: viz., overall porosity, void size, and shape (aspect ratio and orientation). In this paper, we quantify the effects of arbitrary variations in void shapes on meso-scale energy deposition rates. A collection of voids of arbitrary shapes is extracted from scanning electron microscope (SEM) images of real, pressed HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) samples and classified into groups based on their similarity in shapes. Direct numerical simulations (DNS) are performed on the highly contorted “real” void shapes, and the calculated hotspot ignition and growth rates are compared with values predicted by the MES-IG. It is found that while the parameterization of complex void morphologies in terms of orientation and aspect ratio gives fairly good agreement between DNS and MES-IG reaction rates, the intricate details of highly complex void shapes impact hotspot characteristics to a significant extent. This work suggests possible improvements for the prediction of reaction rate in the energetic microstructure by adopting a more detailed description of shapes.

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