Search

High-fidelity constitutive models are critical for accurate meso-scale continuum modeling and prediction of shock initiation of crystalline energetic materials (EMs). While empirically calibrated or atomistic-guided anisotropic elastoplastic models of EM such as cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) capture important micromechanical phenomena (such as dislocation evolution, slip-resistance, and anisotropic elasticity), the computational cost of using anisotropic single-crystal plasticity models can become prohibitive for meso-scale computations of void-collapse and hotspot formation in microstructures. Thermo-mechanically representative, isotropic, pressure, temperature, and rate-dependent material constitutive models are practical alternatives for meso-scale simulations of the shock response of microstructures. To this end, this work constructs physically consistent isotropic plasticity from anisotropic single-crystal plasticity models for HMX and RDX. State-of-the-art crystal plasticity models for HMX and RDX are used to compute the stress states in single crystals oriented in three different directions relative to shocks generated by impact at velocities ranging from 100 to 1000 m/s. Post-shock von Mises stress fields for the three orientations are then used to calibrate the strain-rate hardening coefficient and the reference strain rate for a rate-dependent Johnson–Cook (JC) yield surface model. We compare the pressures and the post-shock von Mises stresses between the JC and the anisotropic models to show that the isotropic computations closely approximate the averaged deformation response of the three different crystal orientations. We then model the interaction of a shock generated by a 500 m/s impact with a 0.5 μm void and show that the pressures and the deviatoric stresses obtained using the isotropic model closely match those computed from anisotropic models for both HMX and RDX. The resulting isotropic J2 plastic flow model for HMX and RDX can be employed to perform meso-scale simulations for energy localization due to shear bands and void collapse in the two materials. [ABSTRACT FROM AUTHOR]

Multi-scale predictive models for the shock sensitivity of energetic materials connect energy localization ("hotspots") in the microstructure to macro-scale detonation phenomena. Calculations of hotspot ignition and growth rely on models for chemical reaction rates expressed in Arrhenius forms; these chemical kinetic models, therefore, are foundational to the construction of physics-based, simulation-derived meso-informed closure (reactive burn) models. However, even for commonly used energetic materials (e.g., HMX in this paper) there are a wide variety of reaction rate models available. These available reaction rate models produce reaction time scales that vary by several orders of magnitude. From a multi-scale modeling standpoint, it is important to determine which model best represents the reactive response of the material. In this paper, we examine three global Arrhenius-form rate models that span the range of reaction time scales, namely, the Tarver 3-equation, the Henson 1-equation, and the Menikoff 1-equation models. They are employed in a meso-informed ignition and growth model which allows for connecting meso-scale hotspot dynamics to macro-scale shock-to-detonation transition. The ability of the three reaction models to reproduce experimentally observed sensitivity is assessed by comparing the predicted criticality envelope (Walker–Wasley curve) with experimental data for pressed HMX Class V microstructures. The results provide a guideline for model developers on the plausible range of time-to-ignition that are produced by physically correct Arrhenius rate models for HMX. [ABSTRACT FROM AUTHOR]

Reactive burn models for heterogeneous energetic materials (EMs) must account for chemistry as well as microstructure to predict shock-to-detonation transition (SDT). Upon shock loading, the collapse of individual voids leads to ignition of hotspots, which then grow and interact to consume the surrounding material. The sub-grid dynamics of shock-void interactions and hotspot development are transmitted to macro-scale SDT calculations in the form of a global reactive "burn model." This paper presents a physically evocative model, called meso-informed sub-grid source terms for energy localization (MISSEL), to close the macro-scale governing equations for calculating SDT. The model parameters are explicitly related to four measurable physical quantities: two depending on the microstructure (the porosity ϕ and average pore size D ¯ v o i d ), one depending on shock–microstructure interaction (the fraction of critical voids ξ c r ), and the other depending on the chemistry (the burn front velocity V h s ). These quantities are individually quantifiable using a small number of rather inexpensive meso-scale simulations. As constructed, the model overcomes the following problems that hinder the development of meso-informed burn models: (1) the opacity of more sophisticated surrogate/machine-learning approaches for bridging meso- and macro-scales, (2) the rather large number of high-resolution mesoscale simulations necessary to train machine-learning algorithms, and (3) the need for calibration of many free parameters that appear in phenomenological burn models. The model is tested against experimental data on James curves for a specific class of pressed 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane materials. The simple, evocative, and fast-to-construct MISSEL model suggests a route to develop frameworks for physics-informed, simulation-derived meso-informed burn models. [ABSTRACT FROM AUTHOR]

Sensitivity in polymer-bonded explosives (PBXs) relies on the presence of defects, such as cracks and voids, which create localized thermal energy, commonly known as hotspots, and initiate reactions through various localization phenomena. Our prior research has explored the use of internal gas pressure induced by thermite ignition to generate localized defects for PBX sensitization. However, further research is required to gain a more comprehensive understanding of the defect generation process resulting from internal gas pressure. This study investigates the process of defect generation in PBXs in response to internally induced gas pressure by applying controlled compressed gas to a fabricated cavity within the materials, simulating the gas pressure emitting from thermite. X-ray micro-computed tomography was employed to visualize the microstructure of the sample before and after gas injection. The experiments reveal the significance of gas pressure, cavity shape, temperature, and specimen compaction pressure in the defect generation. Numerical simulations using Abaqus/Standard were conducted to assess the defect generation in mock PBXs under varying gas pressures, cohesive properties, and binder thicknesses. The simulation results demonstrate the substantial influence of these properties on the ability to generate defects in mock PBXs. This study contributes to a better understanding of the factors influencing defect generation in mock PBXs. This knowledge is crucial for achieving precise control over defect generation, leading to improved ignition and detonation characteristics in PBXs. [ABSTRACT FROM AUTHOR]

This paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response. [ABSTRACT FROM AUTHOR]

Heterogeneous energetic materials (EMs) contain microstructural defects such as voids, cracks, interfaces, and delaminated zones. Under shock loading, these defects offer potential sites for energy localization, i.e., hotspot formation. In a porous EM, the collapse of one void can generate propagating blast waves and hotspots that can influence the hotspot phenomena at neighboring voids. Such void–void interactions must be accounted for in predictive multi-scale models for the reactive response of a porous EM. To infuse such meso-scale phenomena into a multi-scale framework, a meso-informed ignition and growth model (MES-IG) has been developed, where the influence of void–void interactions is incorporated into the overall reaction rate through a function, f v − v . Previously, MES-IG was applied to predict the sensitivity and reactive response of EM, where f v − v was assumed to be a function of the overall sample porosity alone. This paper performs a deeper analysis to model the strong dependency of f v − v on other factors, such as void size and shock strength. The improved model for void–void interactions produces good agreement with direct numerical simulations of the HE microstructures and, thus, advances the predictive capability of multi-scale models of the shock response and sensitivity of EM. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) has emerged as a promising approach to achieve energetic materials (EMs) with intricate geometries and controlled microstructures, which are crucial for safety and performance optimization. However, current AM methods still face limitations such as limited densities and inadequate solids loading. To overcome these limitations, we have developed a pressure‐assisted binder jet (PBJ) process that has the potential to allow for the fabrication of intricate EMs while preserving their desired properties. This study aims to investigate the effects of printing parameters on the microstructures and properties of EMs, including density, solids loading, mechanical properties, and heterogeneity. Our results demonstrate that the PBJ process achieves exceptional properties in EMs, including densities up to 83.4 % and solids loading up to 95.4 %, surpassing those achieved by existing AM processes. Furthermore, the mechanical properties of the fabricated EMs are comparable to those achieved using conventional fabrication techniques, including a compressive strength of 3.32 MPa, a Young's modulus of 16.68 MPa, a Poisson's ratio of 0.45, a shear modulus of 5.73 MPa, and a bulk modulus of 21.01 GPa. Various test cases were printed to showcase the ability of the PBJ process to create EMs with complex structures and exceptional properties. Micro‐computed tomography was employed to analyze the influence of printing parameters on the internal composition and microstructures of the printed specimens. [ABSTRACT FROM AUTHOR]

Head-to-head comparisons of multiple experimental observations and numerical simulations on a deconstructed plastic-bonded explosive consisting of an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine crystal embedded in a polymeric binder with a 4 ns duration 20 GPa input shock are presented. Hot spots observed in high-resolution direct numerical simulations are compared with micro-scale shock-induced reactions visualized using nanosecond microscope imaging and optical pyrometry. Despite the challenges and limitations of both the experimental and simulation techniques, an agreement is obtained on many of the observed features of hot spot evolution, e.g., (1) the magnitude and time variation of temperatures in the hot spots, (2) the time to fully consume the crystals (∼100 ns) of size (100–300 μm) employed in this study, and (3) the locations of hot spot initiation and growth. Three different mechanisms of hot spot formation are indicated by simulations: (1) high-temperature hot spots formed by pore collapse, (2) lower temperature hot spots initiated at the polymer–crystal interface near corners and asperities, and (3) high-temperature reaction waves leading to fast consumption of the energetic crystal. This first attempt at a head-to-head comparison between experiments and simulations not only provides new insight but also highlights efforts needed to bring models and experiments into closer alignment, in particular, highlighting the importance of distinctly three-dimensional and multiple mechanisms of the hot spot ignition and growth. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Meso-scale simulations of pressed energetic materials are performed using synthetic microstructures generated using deep feature representation, a deep convolutional neural network-based approach. Synthetic microstructures are shown to mimic real microstructures in the statistical representation of global and local features of micro-morphology for three different classes of pressed HMX with distinctive micro-structural characteristics. Direct numerical simulations of shock-loaded synthetic microstructures are performed to calculate the meso-scale reaction rates. For all three classes, the synthetic microstructures capture the effect of morphological uncertainties of real microstructures on the response to shock loading. The calculated reaction rates for different classes also compare well with those of the corresponding real microstructures. Thus, the article demonstrates that machine-generated ensembles of synthetic microstructures can be employed to derive structure–property–performance linkages of a wide class of real pressed energetic materials. The ability to manipulate the synthetic microstructures using deep learning-based approaches then provides an opportunity for material designers to develop and manufacture pressed energetic materials that can yield targeted performance. [ABSTRACT FROM AUTHOR]

The response of a wide class of heterogeneous energetic materials (HEs) to loads is determined by dynamics at the meso-scale, i.e., by physicochemical processes in their underlying microstructure. Structure–property–performance (S–P–P) linkages for such materials can be developed in a multi-scale framework, connecting the physics and thermophysical properties at the meso-scale to response at the macro-scale. Due to the inherent stochasticity of the microstructure, ensembles of microstructures are required to conduct meso-scale simulations to establish S–P–P linkages. Here, a deep neural network-based method called deep feature representation is applied to generate a range of material microstructures from heterogeneous energetic materials to metal foams and metallic mixtures. The method allows for the generation of stochastic microstructures using a single real microstructure as the input and is not limited to low packing density or topological complexity of solids. In its application to pressed energetic materials, we show that qualitative and quantitative features of real (i.e., imaged) microstructures are captured in the synthetic microstructures. Therefore, a stochastic ensemble of synthetic microstructures can be created for use in reactive meso-scale simulations to relate the microstructures of HEs to their performance. While the focus is on pressed HE microstructures, we also show that the method is general and useful for generating microstructures for in silico experiments for a wide range of composite/multiphase materials, which can be used to establish S–P–P linkages. [ABSTRACT FROM AUTHOR]

Material models for single-crystal β-HMX are systematically examined in the context of continuum pore-collapse simulations. Continuum predictions using five different isotropic material models are compared head-to-head with molecular dynamics (MD) predictions for a 50 nm cylindrical pore in β-HMX subject to a range of shock strengths. Shock waves were generated using a reverse-ballistic configuration, propagating along [010] in the MD simulations. The continuum models are improved hierarchically, drawing on temperature- and pressure-dependent MD-derived material parameters. This procedure reveals the sensitivity of the continuum predictions of pore collapse to the underlying thermophysical models. The study culminates in an MD-calibrated isotropic rate- and temperature-dependent strength model, which includes appropriate submodels for the temperature-dependent melting point of β-HMX [M. P. Kroonblawd and R. A. Austin, Mech. Mater. 152, 103644 (2021)], pressure-dependent shear modulus [A. Pereverzev and T. Sewell, Crystals 10, 1123 (2020)], and temperature-dependent specific heat, that produces continuum pore-collapse results similar to those predicted by MD. The resulting MD-informed model should improve the fidelity of simulations to predict the detonation initiation of HMX-based energetic materials containing micrometer-scale pores. [ABSTRACT FROM AUTHOR]

The sensitivity of an energetic material is strongly influenced by its microstructure. This work distinguishes the roles played by the microstructure (i.e., the meso-scale) in the macro-scale shock sensitivity of two different materials: TATB and HMX. To quantify sensitivity, we develop a meso-informed energy deposition model for a porous TATB material, following procedures from the previous work on HMX. Simulations of reactive void collapse in TATB are employed to calculate the rate of initiation and growth of hotspots. These rates are expressed as surrogate models, expressing meso-scale (hotspot) quantities of interest as functions of shock strength P s and void size D v o i d . The hotspot ignition and growth rate surrogates for TATB are compared with those for HMX, providing insights into meso-scale physics underlying shock sensitivity of these two energetic materials. The surrogate models are then used in a meso-informed ignition and growth (MES-IG) model to close macro-scale simulations of the shock response of porous TATB. We also obtain the run-to-detonation distances and generate Pop-plots to quantify macro-scale sensitivity. It is shown that Pop-plots for HMX-based energetic materials accord with behavior observed in experimental studies; however, there is a significant discrepancy between MES-IG predictions and experiments for TATB; the causes for this difference between HMX and TATB are discussed, pointing to areas for future work. [ABSTRACT FROM AUTHOR]

This study investigates the capabilities of a diffuse interface immersed boundary method in the simulation of fluid flow over an oscillating flat-plate airfoil at moderately high Reynolds numbers where interacting unsteady vortical flows control the flow behavior. The recently developed and modified Smoothed Profile Method (SPM) is adopted as a diffuse interface immersed boundary solver to model the fluid-structure interaction (FSI) problem. While in general diffuse interface methods are simpler to implement relative to sharp-interface methods (SIMs), they have been thought to lose accuracy in the simulation of moderate Reynolds number flows. The simulation results show that the lift coefficient and vorticity contours from SPM match well with experiments. Moreover, our detailed analysis of the vorticity fluxes at the airfoil leading edge and the comparison with experiments also show that SPM can be used for moderate Reynolds number external aerodynamics problems applicable to micro-air vehicles. [ABSTRACT FROM AUTHOR]