Femtosecond Visualization of hcp-Iron Strength and Plasticity under Shock Compression
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36 MATERIALS SCIENCE↗
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Behavior of soda-lime silicate glass under laser-driven shock compression up to 315 GPa
Shock experiments give a unique insight into the behavior of matter subjected to extremely high pressures and temperatures. Understanding the behavior of materials under such extreme conditions is key to modeling material failure and deformation dynamics under impact. While studies on pure silica are extensive, the shock behavior of other commercial silicates that contain additional oxides has not been systematically investigated. To better understand the role of composition in the dynamic behavior of silicates, we performed laser-driven dynamic compression experiments on soda-lime glass (SLG) up to 315 GPa. Using the accurate pulse shaping offered by the long pulse laser system at the Matter in Extreme Conditions end-station at the Linac Coherent Light Source, SLG was shock compressed along the Hugoniot to multiple pressure-temperature points. Velocity Interferometer System for Any Reflector was used to measure the velocity and determine the pressure inside the SLG. The U s –u p relationship obtained agrees well with the previous parallel plate impact studies. Within the error bars, no transformation to the crystalline phase was observed up to 70 GPa, which is in contrast to the behavior of pure silica under shock compression. Our studies show that the glass composition strongly influences the shock compression behavior of the silicate glasses.
36 MATERIALS SCIENCE↗
Unexpected Observation of Disorder and Multiple Phase-Transition Pathways in Shock-Compressed Zr
The response of materials under dynamic compression involves a complex interplay of various deformation mechanisms aimed at relieving shear stresses, yielding a remarkable diversity in material behavior. Here, in this Letter, we utilize femtosecond x-ray diffraction coupled with nanosecond laser compression to reveal an intricate competition between multiple shear-relieving mechanisms within an elemental metal. Our observations in shocked-compressed single-crystal Zr indicate a disorder-mediated shear relaxation at lower pressures. Above the phase-transition pressure, we observe the increasing contribution of structural phase transition in relieving shear stress. We detect not one but three concurrent pathways during the transition from the hcp to a hex-3 structure. These complex dynamics are partially corroborated through multimillion-atom molecular dynamics simulations employing a machine-learned interatomic potential. Our observation of multiple concurrent pathways and disorder during shock compression underscore the far greater intricacies in the dynamic response of metals than previously assumed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime
Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.
36 MATERIALS SCIENCE↗
Evidence of non-isentropic release from high residual temperatures in shocked metals measured with ultrafast x-ray diffraction
Shock experiments are widely used to understand the mechanical and electronic properties of matter under extreme conditions. However, after shock loading to a Hugoniot state, a clear description of the post-shock thermal state and its impacts on materials is still lacking. We used diffraction patterns from 100-fs x-ray pulses to investigate the temperature evolution of laser-shocked Al–Zr metal film composites at time delays ranging from 5 to 75 ns driven by a 120-ps short-pulse laser. We found significant heating of both Al and Zr after shock release, which can be attributed to heat generated by inelastic deformation. A conventional hydrodynamic model that employs (i) typical descriptions of Al and Zr mechanical strength and (ii) elevated strength responses (which might be attributed to an unknown strain rate dependence) did not fully account for the measured temperature increase, which suggests that other strength-related mechanisms (such as fine-scale void growth) could play an important role in thermal responses under shock wave loading/unloading cycles. Our results suggest that a significant portion of the total shock energy delivered by lasers becomes heat due to defect-facilitated plastic work, leaving less converted to kinetic energy. This heating effect may be common in laser-shocked experiments but has not been well acknowledged. High post-shock temperatures may induce phase transformation of materials during shock release. Another implication for the study is the preservability of magnetic records from planetary surfaces that have a shock history from frequent impact events.
42 ENGINEERING↗
Peak states of molybdenum single crystals shock compressed to high stresses
In this work, to determine crystal anisotropy effects at high stresses, peak states behind the plastic shock waves were examined in BCC single crystals. Using plate impact experiments, molybdenum (Mo) single crystals were shock compressed up to 190 GPa elastic impact stress along [100], [110], and [111] orientations. Laser interferometry was used to measure wave velocities and particle velocity profiles at the Mo–LiF window interface. These data were analyzed to obtain in-material quantities in the peak states. The Hugoniots for [100] and [110] orientations were comparable, but the Hugoniot for the [111] orientation was different from the other two orientations. Also, these Mo single crystal Hugoniots display differences from the polycrystalline Mo Hugoniots. Although none of the differences can be considered large, the present results demonstrate that, unlike FCC metal single crystals (Cu, Al), some anisotropy is preserved in Mo single crystal Hugoniots even at high stresses.
36 MATERIALS SCIENCE↗
Strongly Anisotropic Thermomechanical Response to Shock Wave Loading in Oriented Samples of the Triclinic Molecular Crystal 1,3,5-Triamino-2,4,6-trinitrobenzene
All-atom molecular dynamics (MD) simulations were used to study shock wave loading in oriented single crystals of the highly anisotropic triclinic molecular crystal 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). The crystal structure consists of planar hydrogen-bonded sheets of individually planar TATB molecules that stack into graphitic-like layers. Shocks were studied for seven systematically prepared crystal orientations with limiting cases that correspond to shock propagation exactly perpendicular and exactly parallel to the graphitic-like layers. The simulations were performed for initially defect-free crystals using a reverse-ballistic configuration that generates explicit, supported shocks. Final longitudinal stress components are between ≈8.5 and ≈10.5 GPa for the 1.0 km s –1 impact speed studied. Orientation-dependent properties are reported including shock speeds, stresses, temperatures, compression ratios, and local material strain rates. Spatiotemporal maps of the temperature, stress tensor, material flow, and molecular orientations reveal complicated processes that arise for specific shock directions. Furthermore, the results indicate that TATB shock response is highly sensitive to crystal orientation, with significant qualitative differences for the time evolution of the stress tensor and temperature, elastic/inelastic compression response, defect formation and growth, critical von Mises stress, and strain rates during shock rise that span nearly an order of magnitude. A variety of inelastic deformation mechanisms are identified, ranging from crumpling of graphitic-like layers to dislocation-mediated plasticity to intense shear strain localization. To our knowledge, these are the first systematic MD simulations and analysis of explicit shock wave propagation along nontrivial crystal directions in a triclinic molecular crystal.
36 MATERIALS SCIENCE↗
Bayesian blacksmithing: discovering thermomechanical properties and deformation mechanisms in high-entropy refractory alloys
Finding alloys with specific design properties is challenging due to the large number of possible compositions and the complex interactions between elements. This study introduces a multi-objective Bayesian optimization approach guiding molecular dynamics simulations for discovering high-performance refractory alloys with both targeted intrinsic static thermomechanical properties and also deformation mechanisms occurring during dynamic loading. The objective functions are aiming for excellent thermomechanical stability via a high bulk modulus, a low thermal expansion, a high heat capacity, and for a resilient deformation mechanism maximizing the retention of the BCC phase after shock loading. Contrasting two optimization procedures, we show that the Pareto-optimal solutions are confined to a small performance space when the property objectives display a cooperative relationship. Conversely, the Pareto front is much broader in the performance space when these properties have antagonistic relationships. Density functional theory simulations validate these findings and unveil underlying atomic-bond changes driving property improvements.
36 MATERIALS SCIENCE↗
Elucidating size effects on the yield strength of single-crystal Cu via the Richtmyer–Meshkov instability
Capturing the dynamic response of a material under high strain-rate deformation often demands challenging and time consuming experimental effort. While shock hydrodynamic simulation methods can aid in this area, a priori characterizations of the material strength under shock loading and spall failure are needed in order to parameterize constitutive models needed for these computational tools. Moreover, parameterizations of strain-rate-dependent strength models are needed to capture the full suite of Richtmyer–Meshkov instability (RMI) behavior of shock compressed metals, creating an unrealistic demand for these training data solely on experiments. Herein, we sweep a large range of geometric, crystallographic, and shock conditions within molecular dynamics (MD) simulations and demonstrate the breadth of RMI in Cu that can be captured from the atomic scale. In this work, yield strength measurements from jetted and arrested material from a sinusoidal surface perturbation were quantified as Y RMI = 0.787 ± 0.374 GPa, higher than strain-rate-independent models used in experimentally matched hydrodynamic simulations. Defect-free, single-crystal Cu samples used in MD will overestimate Y RMI , but the drastic scale difference between experiment and MD is highlighted by high confidence neighborhood clustering predictions of RMI characterizations, yielding incorrect classifications.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Shock response of cobalt-based cemented tungsten carbides at pressures up to 100 GPa
In the present study, shock wave experiments are conducted on General Carbide cemented tungsten carbides with 3.7 wt.% and 6.0 wt.% cobalt binder to determine their shock compression response up to 100 GPa. A three-stage particle velocity profile is observed in the experiments -- an initial elastic-rise to the Hugoniot elastic limit (HEL), an elastic-plastic ramp indicating post-yield hardening, and finally a rise to the peak shocked Hugoniot state. The results of the experiments are used to determine the HEL, shock velocity (U s ) vs. particle velocity (u p ) Hugoniot relationship, and the longitudinal stress vs. specific volume Hugoniot relationship for the two samples. Here, the HEL for the WC 3.7wt% Co and WC 6.0wt% Co samples was determined to be ~4.45 GPa and 3.72 GPa, respectively. The U s – u p relation was determined to be U s = 4.97(0.006)+1. 446 (0.018) u p for WC 3.7 wt.% Co and U s = 4.93(0.006)+1. 454(0.017)u p for the WC 6.0 wt.% Co sample at peak particle velocities>0.75 km/s. For both WC grades, in the particle velocity regime less than ~0.75 km/s, the measured shock wave velocities were found to be larger than those predicted by the linear U s –u p Hugoniot relationship, indicating the two WC samples to preserve substantial strength in the post-yield deformation regime. Both WC grades show a catastrophic drop in shear stress carrying capacity when shocked to longitudinal stresses greater than ~70 GPa.
36 MATERIALS SCIENCE↗
Full-field quantitative visualization of shock-driven pore collapse and failure modes in PMMA
The dynamic collapse of pores under shock loading is thought to be directly related to hot spot generation and material failure, which is critical to the performance of porous energetic and structural materials. However, the shock compression response of porous materials at the local, individual pore scale is not well understood. This study examines, quantitatively, the collapse phenomenon of a single spherical void in PMMA at shock stresses ranging from 0.4 to 1.0 GPa. Using a newly developed internal digital image correlation technique in conjunction with plate impact experiments, full-field quantitative deformation measurements are conducted in the material surrounding the collapsing pore for the first time. The experimental results reveal two failure mode transitions as shock stress is increased: (i) the first in situ evidence of shear localization via adiabatic shear banding and (ii) dynamic fracture initiation at the pore surface. Numerical simulations using thermo-viscoplastic dynamic finite element analysis provide insights into the formation of adiabatic shear bands (ASBs) and stresses at which failure mode transitions occur. Further numerical and theoretical modeling indicates the dynamic fracture to occur along the weakened material inside an adiabatic shear band. Finally, analysis of the evolution of pore asymmetry and models for ASB spacing elucidate the mechanisms for the shear band initiation sites, and elastostatic theory explains the experimentally observed ASB and fracture paths based on the directions of maximum shear.
42 ENGINEERING↗
Characteristics of Fluid‐Solid Interaction Constitutive Models Within Poroelastodynamics at Higher Strain‐Rates and Large Deformations Implemented in 1D
The large deformation, mixed formulation, finite element (FE) modeling approach presented in Irwin et al. 2024 is extended herein to include improved constitutive models for representing dynamic solid-fluid interactions at higher strain rates (𝒪(10 2 −10 3 )s −1 ) and larger overpressure magnitudes (𝒪(10 2 )kPa) within a biphasic soft porous material using Theory of Porous Media (TPM) at finite strain. Specifically, these constitutive modeling improvements are the following: (i) a more physically robust constitutive model for pore fluid seepage velocity via inclusion of pore fluid viscous stress, and (ii) a modified deformation-dependent-permeability model and updated hyperelastic constitutive model better suited for handling larger volumetric compressions and extensions. The novelty of the present work is mainly the contribution (i): inclusion of pore fluid viscous stress at higher strain-rate and large deformations, which requires 𝐶 1 continuity in the weak formulation, accomplished by employing Hermite cubic interpolation functions within a mixed nonlinear poromechanical finite element formulation. In (ii), the model is updated to weakly enforce solid phase incompressibility, such that this assumption is not violated numerically, which provides improved numerical stability for achieving larger overpressure magnitudes on 𝒪(10 2 ) kPa, which were not achievable with the previous Kozeny–Carman model in Irwin et al. 2024. Also in (ii), the volumetric part of the solid skeleton free energy function is modified to ensure proper bounds on the solid skeleton Jacobian of deformation 𝐽 s related to incompressibility of the solid phase. Uniaxial strain, unidirectional flow examples at higher strain rates (𝒪(10 2 −10 3 )s −1 ) and larger deformations (up to 0.2 (or 20%) nominal axial strain) demonstrate the improved physical representation—and numerical stability—of these constitutive model improvements.
42 ENGINEERING↗
Effect of Topology on Transient Dynamic and Shock Response of Polymeric Lattice Structures
Architected cellular materials, such as lattice structures, offer potential for tunable mechanical properties for dynamic applications of energy absorption and impact mitigation. In this work, the static and dynamic behavior of polymeric lattice structures was investigated through experiments on octet-truss, Kelvin, and cubic topologies with relative densities around 8%. Here, dynamic testing was conducted via direct impact experiments (25–70 m/s) with high-speed imaging coupled with digital image correlation and a polycarbonate Hopkinson pressure bar. Mechanical properties such as elastic wave speed, deformation modes, failure properties, particle velocities, and stress histories were extracted from experimental results. At low impact velocities, a transient dynamic response was observed which was composed of a compaction front initiating at the impact surface and additional deformation bands whose characteristics matched low strain-rate behavior. For higher impact velocities, shock analysis was carried out using compaction wave velocity and Eulerian Rankine–Hugoniot jump conditions with parameters determined from full-field measurements.
36 MATERIALS SCIENCE↗
New dynamic diamond anvil cell for time-resolved radial x-ray diffraction
The dynamic diamond anvil cell (dDAC) is a recently developed experimental platform that has shown promise for studying the behavior of materials at strain rates ranging from intermediate to quasi-static and shock compression regimes. Combining dDAC with time-resolved x-ray diffraction (XRD) in the radial geometry (i.e., with incident x-rays perpendicular to the axis of compression) enables the study of material properties such as strength, texture evolution, and deformation mechanisms. This work describes a radial XRD dDAC setup at beamline P02.2 (Extreme Conditions Beamline) at DESY’s PETRA III synchrotron. Time-resolved radial XRD data are collected for titanium, zirconium, and zircon samples, demonstrating the ability to study the strength and texture of materials at compression rates above 300 GPa/s. In addition, the simultaneous optical imaging of the DAC sample chamber is demonstrated. The ability to conduct simultaneous radial XRD and optical imaging provides the opportunity to characterize plastic strain and deviatoric strain rates in the DAC at intermediate rates, exploring the strength and deformation mechanisms of materials in this regime.
47 OTHER INSTRUMENTATION↗
A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening
A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.
42 ENGINEERING↗
High-speed x-ray phase contrast imaging and digital image correlation analysis of microscale shock response of an additively manufactured energetic material simulant
The performance of energetic materials subjected to dynamic loading significantly depends on their micro- and meso-scale structural morphology. The geometric versatility offered by additive manufacturing opens new pathways to tailor the performance of these materials. Additively manufactured energetic materials (AMEMs) have a wide range of structural characteristics with a hierarchy of length scales and process-inherent heterogeneities, which are hitherto difficult to precisely control. It is important to understand how these features affect AMEMs’ response under dynamic/shock loading. Therefore, temporally and spatially resolved measurements of both macroscopic behavior and micro- and meso-level processes influencing macroscopic behavior are required. In this paper, we analyze the shock compression response of an AMEM simulant loaded under several impact conditions and orientations. Furthermore, x-ray phase contrast imaging (PCI) is used to track features across the observed shock front and determine the linear shock velocity vs particle velocity equation of state, as well as to quantify the interior deformation fields via digital image correlation (DIC) analyses. Photon Doppler velocimetry is simultaneously used to measure the particle velocities of the specimens, which are consistent with those obtained from x-ray PCI. The DIC analyses provide an assessment of the average strain fields inside the material, showing that the average axial strain depends on the loading intensity and reaches as high as 0.23 for impact velocities up to 1.5 km/s. The overall results demonstrate the utility of x-ray PCI for probing “in-material” equation of state and interior strains associated with dynamic shock compression behavior of the AMEM simulant.
3D printing↗
Inelastic equation of state for solids
In this study, a complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration energy contributions. Inelasticity is introduced through the nonlinear equations of finite strain plasticity which utilize the temperature dependent Johnson–Cook yield model. Material failure is incorporated into the model by a coupling of the damage history variable to the energy potentials. The numerical evaluation of the IEOS requires a nonlinear solution of stress, temperature and history variables associated with elastic trial states for stress and temperature. The model is implemented into the ALEGRA shock and multi-physics code and the applications presented include single element deformation paths, the Taylor anvil problem and an energetically driven thermo-mechanical problem.
42 ENGINEERING↗
Machine learning visualization tool for exploring parameterized hydrodynamics
We are interested in the computational study of shock hydrodynamics, i.e. problems involving compressible solids, liquids, and gases that undergo large deformation. These problems are dynamic and nonlinear and can exhibit complex instabilities. Due to advances in high performance computing it is possible to parameterize a hydrodynamic problem and perform a computational study yielding $\mathscr{O} (TB)$ of simulation state data. We present an interactive machine learning tool that can be used to compress, browse, and interpolate these large simulation datasets. This tool allows computational scientists and researchers to quickly visualize 'what-if' situations, perform sensitivity analyses, and optimize complex hydrodynamic experiments.
97 MATHEMATICS AND COMPUTING↗