ArticlePDF Available

# Atomistic-model informed pressure-sensitive crystal plasticity for crystalline HMX

Authors:

## Abstract and Figures

Cyclotetramethylene-Tetranitramine (HMX) is a secondary explosive used in military and civilian applications. Its plastic deformation is of importance in the initiation of the decomposition reaction, but the details of plasticity are not yet fully understood. It has been recently shown that both the elastic constants and the critical resolved shear stress for plastic deformation are pressure sensitive. Since initiation takes place during shock loading, the pressure sensitivity of plasticity is highly relevant. In this work, we examine the pressure-sensitivity of the dynamic mechanical behavior of HMX. To this end, we use an elastic-plastic continuum constitutive model of single crystal HMX in which the anisotropic elastic constants and direction-dependent yield stress are rendered pressure-sensitive. The pressure sensitivity is calibrated based on input from molecular models. We observe that accounting for pressure sensitivity changes significantly the profile of the elastic-plastic wave and the wave propagation speed upon impact. The accumulated dissipation profile and the total dissipation also exhibit profound differences between the simulations that take account of the pressure-dependence of the plastic deformation and the pressure independent counterpart. 2 Ran Ma et al.
Content may be subject to copyright.
A preview of the PDF is not available
... The advantage is a higher fidelity description of the elastic response, but doing so for a material under shock conditions requires knowledge of the pressure and temperature dependence of the elastic coefficients, which in most cases is only available from simulations [15]. Furthermore, the possibility of coupling between the volumetric and deviatoric responses may make it difficult to frame a proper inverse problem for experiments [16][17][18]. ...
... 18: Comparison of black-box neural network architectures trained on monolithic data with our Hamilton-Jacobi hardening elastoplastic framework (introduced in Section 3.2). The black-box models can capture the monolithic loading path (a) but cannot capture any unloading paths (b). ...
... 18: Comparison of hybrid model predictions with FFT simulation data for 3 RVEs from the training data set. The tests conducted are uniaxial unconfined tension (left and middle columns) and pure shear (right column). ...
... The advantage is a higher fidelity description of the elastic response, but doing so for a material under shock conditions requires knowledge of the pressure and temperature dependence of the elastic coefficients, which in most cases is only available from simulations . Furthermore, the possibility of coupling between the volumetric and deviatoric responses may make it difficult to frame a proper inverse problem for experiments (Borja, 2013;Bryant and Sun, 2018;Ma et al., 2021). ...
Preprint
Full-text available
We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of the monoclinic organic molecular crystal $\beta$-HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train the neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g. strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom-line constitutive responses predicted by MD, (2) detailed examination of their stability and uniqueness, and (3) admissibility of the predicted responses with respect to continuum mechanics theory in the finite-deformation regime. We compare the neural networks' training efficiency under different Sobolev constraints and assess the models' accuracy and robustness against MD benchmarks for $\beta$-HMX.
Article
A new finite strain thermomechanical model for the high-rate deformation of the β-polymorph of cyclotetramethylene tetranitramine (β-HMX) has been developed and applied to simulations of plate impact experiments. The crystal plasticity model is based on a model developed previously for RDX (Luscher et al. 2017), which is extended to incorporate deformation twinning. Twinning during normal plate impacts is simulated with a phase-field twin model. First, material parameters governing the kinetics of dislocation slip are calibrated on the subset of simulations which had negative Schmid factors for the twin system. Second, a parametric study of the twin material parameters was performed to find suitable values. The results of the simulations with the phase-field twinning model are reported for impacts on several crystal orientations. We find that the twin growth decreases with increasing distance from the impact surface because of dissipation of the shock front via dislocation-mediated plasticity, and that the simulated interface velocity with and without phase-field twinning do not show appreciable differences. These modeling results suggest that the significance of twinning in β-HMX cannot be determined with traditional loading configurations and diagnostics.
Article
Full-text available
We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of a monoclinic organic molecular crystal known as Octogen (β-HMX) in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g. strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom-line constitutive responses predicted by MD, (2) the robustness of the models measured by detailed examination of their stability and uniqueness, and (3) the admissibility of the predicted responses with respect to mechanics principles in the finite-deformation regime. We compare the neural networks’training efficiency under different Sobolev constraints and assess the models’ accuracy and robustness against MD benchmarks for β-HMX.
Article
The dependence of the components of the elastic stiffness tensors (or elastic constants) of the organic explosives PETN, RDX, CL‐20, DAAF, FOX‐7, and HMX on hydrostatic pressure up to 10 GPa have been computed using dispersion‐corrected density functional theory. We report the evolution of lattice parameters and the non‐zero stiffnesses for the tetragonal, orthorhombic, and monoclinic crystal symmetries. Linear and quadratic dependencies of the components of the elastic stiffness tensors on volumetric compression and hydrostatic pressure are tabulated for use in single crystal plasticity models.
Article
Full-text available
The isothermal second-order elastic stiffness tensor and isotropic moduli of β-1,3,5,7- tetranitro-1,3,5,7-tetrazoctane (β-HMX) were calculated, using the P21/n space group convention, from molecular dynamics for hydrostatic pressures ranging from 10−4 to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite strains on the equilibrated β-HMX crystal at a given pressure and temperature and using the equilibrium stress tensors of the strained cells to obtain the derivatives of stress with respect to strain. For a fixed temperature, the elastic coefficients increase substantially with increasing pressure, whereas, for a fixed pressure, the elastic coefficients decrease as temperature increases, in accordance with physical expectations. Comparisons to previous experimental and computational results are provided where possible.
Article
Full-text available
A mesoscopic constitutive law for 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), an ultra-anisotropic energetic molecular crystal, is proposed and validated on molecular dynamics (MD) simulations. The two dominant deformation mechanisms observed at nanometric scale and limited stress (less than 1 GPa) are a buckling instability and a nonsymmorphic twinning (irreversible) transformation. A thermodynamically consistent continuum model is detailed, with nonlinear elasticity in pressure constructed to reproduce a cold equation of state. The twinning-buckling phase transition observed in MD is modeled by using a phase field by reaction pathway (PF-RP) formalism. In order to validate the present constitutive law, we first study the response of the single crystal under constant-strain-rate uniaxial compressions for various directions in the basal plane and present one-to-one comparisons between MD and PF-RP simulations. As an upscale case for the constitutive law, a large polycrystal is subjected to a shock compression at low velocity and the activation of the twinning-buckling mechanism is discussed.
Article
This paper presents a new thermo-elastic self-consistent formulation to calculate the thermo-mechanical response of polycrystalline aggregates with imperfect interfaces. The new model is based on an improved treatment of the effect of imperfect interfaces on the micromechanical response of the grains compared to pre-existing models. New expressions/algorithms are derived for the effective elastic and thermal properties, localization relations, and calculation of intragranular field fluctuations. In addition, derivation of a novel integral equation for the strain field in a heterogeneous elastic medium subjected to arbitrary thermal strain field and displacement jumps is presented. The new model is applied to study the effective thermo-elastic properties and average field fluctuations as a function of the interface properties for imperfectly-bonded triaminotrinitrobenzene (TATB) polycrystalline granular aggregates. The proposed formulation is general in the sense that it can be extended to other material systems and deformation regimes that require a proper consideration of the effect of imperfect interface properties on the material's thermo-mechanical response.
Conference Paper
Deformation twinning is an active deformation mechanism during loading along certain crystallographic directions of β-cyclotetramethylene tetranitramine (β-HMX). In this work, a finite strain thermomechanical model is extended to include twinning as a deformation mechanism in addition to plastic slip. The stress is derived from the free energy expression including a term representing the equation of state. The crystal plasticity framework is used to divide the total strain into inelastic and elastic component, where the elastic part is used in the expression for the free energy. The twin systems are treated as pseudo slip systems and the shear rate on the twin systems is evaluated in terms of the twin resistance and the projection of the stress tensor. The model parameters were calibrated against a set of plate impact experiments performed on β-HMX by Dick et al. The remaining plate impact experiments are used to evaluate the predictive capability of the model. The quality of the model fits and predictions is discussed from a physical and modeling perspective. Particularly, the role of twin modeling on results is highlighted. The model is used to explore the relationship between the propensity for twinning and crystal orientation.
Article
The energetic molecular crystal cyclotetramethylene-tetranitramine (HMX) is used in plastic bonded explosives, and reaction initiation and detonation are usually triggered by plastic deformation. However, the mechanism of plastic deformation in β-HMX, which is the HMX phase stable in ambient conditions, is still a matter of debate. A recent observation that pressure developing under shock conditions inhibits dislocation activity, leaves shear localization as the main deformation mechanism in this crystal at high pressures and strain rates. In this work, the steady state shear band viscosity is evaluated as a function of the applied pressure, temperature, and shear strain rate using atomistic models of the HMX crystal. The viscosity of a fully formed shear band decreases as a power function of the strain rate and decreases linearly with increasing temperature, demonstrating shear thinning and non-Arrhenius behavior. The viscosity increases with increasing pressure. The fully formed band behavior is independent of the crystallographic orientation. It is shown that viscosity can be expressed exclusively in terms of the density of the non-crystalline material in the band, and hence the results can be explained in terms of the excess free volume theory developed for shear bands in other material systems, e.g., metallic glasses. The stress required to nucleate a shear band from a straight pre-existing dislocation is reported as a function of the applied pressure, temperature, and strain rate.
Article
Cyclotetramethylene tetranitramine (β-HMX) is an energetic molecular crystal often used in plastic bonded explosives. Its decomposition reaction may be triggered by plastic deformation. Efforts have been made in recent years to evaluate the mechanisms of plasticity in these crystals and to develop constitutive descriptions that can be used to represent plastic deformation on the microstructural level. In this work, we use atomistic simulations to evaluate the dislocation self-energy, core energy, and line tension in four slip systems previously identified as being the most active. The cores are compact and the anisotropic elasticity solution applies at distances from the dislocation line larger than approximately one Burgers vector. Core energies between 0.3 and 0.5 eV/Å result. The line tension varies rapidly when the character of the dislocation is modified due to the strong elastic anisotropy of the crystal, with maxima at approximately ±40° relative to the screw orientation. The line tension also varies from slip system to slip system. These quantities enter many models of elementary mechanisms of dislocation motion such as cross-slip, dislocation nucleation from stress concentrators, the strength of dislocation junctions and other dislocation structures, and the critical stress for the operation of Frank–Read dislocation sources. The data reported here can be used to evaluate the conditions in which these processes operate and as an input to dislocation dynamics simulations.
Article
The thermomechanical behavior of solids includes dissipative processes such as plastic deformation and fracture. The relative importance of these processes on the response of energetic materials has been a subject of study for many decades due to their significance on ignition and reaction. However, a constitutive model to simulate the anisotropy of the crack patterns and the effect of plastic deformation due to slip in energetic materials is not yet available. Finite strain thermomechanical constitutive equations that couple crystal plasticity, an equation of state, and an anisotropic phase field damage model are presented. The model is implemented in a multiphysics finite element solver and used to simulate recent experiments on β-HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) by Zaug et al. The simulations reproduce qualitatively the crack pattern and the crystal orientation dependence of the observed damage. Specifically, more damage is observed when the crystal is impacted in the (010) direction, while more plastic deformation is observed when the load is applied in the (110) direction. The present model represents a step forward to understand the interplay between plasticity and fracture in shocked β-HMX single crystals. It can be used to gain insights into temperature increase and hot-spot formation under shock.
Article
This manuscript investigates the sensitivity of plastic dissipation expressed in the form of temperature rise to anisotropic elasticity constants and crystal plasticity properties of crystalline β-HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) under impact loading conditions. Parametric sensitivity analyses are performed using a global sensitivity analysis framework to quantify the relative roles of the elasticity constants of the monoclinic β-HMX crystal, as well as to delineate thermal activation and phonon drag induced slip mechanisms that contribute to the nonlinear response. The plastic behavior of β-HMX is modeled using a Crystal Plasticity Finite Element model incorporating the slip mechanisms of thermal activation and phonon drag driven by the evolution of dislocation generation and annihilation. The results of the sensitivity analyses show that the anisotropic elasticity coefficients of the monoclinic crystal have a nominal effect on the energy dissipation and temperature rise, dominated by sensitivities of a few coefficients. Among the two primary slip mechanisms, phonon drag appears dominant within the load rate and amplitude regimes considered in this study.
Conference Paper
The tabletop shock compression microscope is described, along with some recent applications to problems such as the temperature of shocked TATB, hot spots in HMX and detonation on a tabletop in nitromethane (NM).