Numerical study of damage in particulate composites during high-strain rate loading using novel damage model
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Materials Science↗
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An Internal Digital Image Correlation Technique for High-Strain Rate Dynamic Experiments
Full-field, quantitative visualization techniques, such as digital image correlation (DIC), have unlocked vast opportunities for experimental mechanics. However, DIC has traditionally been a surface measurement technique, and has not been extended to perform measurements on the interior of specimens for dynamic, full-scale laboratory experiments. This limitation restricts the scope of physics which can be investigated through DIC measurements, especially in the context of heterogeneous materials. The focus of this study is to develop a method for performing internal DIC measurements in dynamic experiments. The aim is to demonstrate its feasibility and accuracy across a range of stresses (up to 650 MPa), strain rates (10 3 - 10 6 s -1 ), and high-strain rate loading conditions (e.g., ramped and shock wave loading). Internal DIC is developed based on the concept of applying a speckle pattern at an inner-plane of a transparent specimen. The high-speed imaging configuration is coupled to the traditional dynamic experimental setups, and is focused on the internal speckle pattern. During the experiment, while the sample deforms dynamically, in-plane, two-dimensional deformations are measured via correlation of the internal speckle pattern. In this study, the viability and accuracy of the internal DIC technique is demonstrated for split-Hopkinson (Kolsky) pressure bar (SHPB) and plate impact experiments. The internal DIC experimental technique is successfully demonstrated in both the SHPB and plate impact experiments. In the SHPB setting, the accuracy of the technique is excellent throughout the deformation regime, with measurement noise of approximately 0.2% strain. In the case of plate impact experiments, the technique performs well, with error and measurement noise of 1% strain. The internal DIC technique has been developed and demonstrated to work well for full-scale dynamic high-strain rate and shock laboratory experiments, and the accuracy is quantified. Here, the technique can aid in investigating the physics and mechanics of the dynamic behavior of materials, including local deformation fields around dynamically loaded material heterogeneities.
36 MATERIALS SCIENCE↗
High-Strain Rate Spall Strength Measurement for CoCrFeMnNi High-Entropy Alloy
In this study, we experimentally investigate the high stain rate and spall behavior of Cantor high-entropy alloy (HEA), CoCrFeMnNi. First, the Hugoniot equations of state (EOS) for the samples are determined using laser-driven CoCrFeMnNi flyers launched into known Lithium Fluoride (LiF) windows. Photon Doppler Velocimetry (PDV) recordings of the velocity profiles find the EOS coefficients using an impedance mismatch technique. Following this set of measurements, laser-driven aluminum flyer plates are accelerated to velocities of 0.5–1.0 km/s using a high-energy pulse laser. Upon impact with CoCrFeMnNi samples, the shock response is found through PDV measurements of the free surface velocities. From this second set of measurements, the spall strength of the alloy is found for pressures up to 5 GPa and strain rates in excess of 106 s−1. Further analysis of the failure mechanisms behind the spallation is conducted using fractography revealing the occurrence of ductile fracture at voids presumed to be caused by chromium oxide deposits created during the manufacturing process.
36 MATERIALS SCIENCE↗
Low viscosity of solid MgO at high pressures and strain rates measured using the laser-driven Richtmyer-Meshkov instability
Solids are often assumed to behave as viscous fluids under high-strain rates. This behavior has been studied experimentally in metals but largely unexplored in brittle ceramic materials. Here, in this study, we present a technique for measuring the viscosity of MgO using time-resolved velocimetry to track the growth rate of a perturbation caused by the Richtmyer-Meshkov instability at the OMEGA EP laser facility. To interpret the results, we use an in-house Eulerian hydrocode to simulate our experiments and model the plastic deformation of solid MgO as a viscous fluid. Results indicate that MgO has a surprisingly low upper bound to its effective viscosity of ∼10 2 Pa s at 175 ± 15 GPa, ∼3500K, and 10 6 −10 7 s −1 strain rate.
Perez, Tyler M. [Johns Hopkins Univ., Baltimore, M↗
Mechanical properties and deformation mechanisms of single crystal Mg micropillars subjected to high-strain-rate C-axis compression
Here, the mechanical properties and deformation mechanisms of single crystal magnesium under c-axis quasi-static and high-strain rate compressions are investigated through in situ scanning electron microscope (SEM) experiments and post-mortem transmission electron microscope (TEM) characterization. The findings revealed that ductility and high rates of hardening are preserved for pillars as large as 15 μm. Furthermore, rate effects result in a mild increase in flow stress with plastic deformations controlled primarily by the slip of type dislocations. Importantly and in contrast to other literature reports, plastic deformation occurs in the absence of twining. As the strain increases and plastic deformation exceeds about 4%, crystal rotation activates basal slip, <$\mathrm{a}$> type dislocations, resulting in a more rate independent flow stress. TEM observation on micropillars compressed at a strain rate of 250/s, revealed the activation of {${11}$$\bar{2}$$\bar{2}$} < $\bar{1}$$\bar{1}23$ > slip systems and high mobility of screw dislocations as major contributors to plastic strains in excess of 10% without fracture. These findings are relevant to the design of lightweight materials used in transportation systems, e.g., selection of material grain size. Moreover, the experimental data here reported provides the materials science community with a unique opportunity to validate discrete dislocation dynamics (DDD) formulations employed in multiscale design of materials.
36 MATERIALS SCIENCE↗
Enhanced mobility of dislocation network nodes and its effect on dislocation multiplication and strain hardening
Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been developed, but its lack of atomistic resolution leaves open the possibility that certain key mechanisms may be overlooked. Here, by comparing large-scale Molecular Dynamics (MD) with DDD simulations performed under identical conditions we uncover significant discrepancies in the predicted strength and microstructure evolution in BCC crystals under high-strain rate conditions. These are traced to unexpected behaviors of dislocation network nodes forming at dislocation intersections, that can move in ways not previously anticipated as revealed by MD. Once these newfound freedoms of nodal motion are incorporated, DDD simulations begin to closely match plastic evolution observed in MD. This additional mechanism of motion whereby non-screw dislocations can change their glide plane profoundly affects fundamental processes of dislocation multiplication, recovery and storage that define strength of metals.
36 MATERIALS SCIENCE↗
On the role of geometrically necessary dislocations in void formation and growth in response to shock loading conditions in wrought and additively manufactured Ta
This study investigates the role of geometrically necessary dislocations (GNDs) and microstructure on void nucleation and growth in wrought and additively manufactured (AM) tantalum subjected to high-strain rate loading. Multi-modal 3D data was collected using TriBeam tomography to calculate GND densities and their spatial relationship to voids. A microstructural comparison between the wrought and AM samples identified distinct void shapes and locations, with intragranular voids and more spherical voids frequently observed in the AM dataset. Results indicate that voids preferentially form at both high-angle grain boundaries and low-angle subgrain boundaries, the latter of which are frequently observed in the AM material. Through a radial distribution analysis of all voids in the datasets, significant GND localization to near-void-surface regions was observed in both samples. 3D crystal plasticity simulations were employed to extend the experimental observations, revealing higher void growth rates in [111] oriented grains when compared to [001] grains. The simulations also suggest that GNDs can be generated as part of the void growth process, with more GND accumulation for growth in a [111] grain than a [001] grain. These findings provide valuable insights into the links between nanoscale void nucleation, mesoscale void growth, and microstructural effects in dynamically loaded tantalum.
36 MATERIALS SCIENCE↗
Observation and Modeling of Dynamic Fracture Behaviors of Battery Cell Under Impact Loading Using Enhanced Representative Volume Element Concept
The burgeoning electric automobile industry has increased interest in battery safety. Battery cells experience significant mechanical stress during operation, including the impact of accidents and vibrations from driving. The potential for thermal runaway reactions in battery cells raises safety concerns. Although numerous researchers have defined the dynamic behavior of battery cells and proposed numerical models to describe it, few studies have focused on the high-strain rate mechanical impact phase correlated with the onset of fracture. In this study, we describe the dynamic behavior of pouch battery cells and propose a modeling method to study their mechanical failure under impact situations. Impact tests are conducted at various velocities and heights. To overcome numerical issues commonly encountered under rapid deformation scenarios, a new finite element model is developed based on the representative volume element model. The proposed approach efficiently simulates continuous crack propagation and brittleness behavior during impact by permitting the individual behavior of the cell components. Therefore, engineers can reliably design safer electric vehicle battery cells by measuring the properties of the cell components.
ENERGY STORAGE↗
Quasi-static and dynamic response of a Cu/Nb composite following equal channel angular extrusion
The article presents a study of the plastic properties of a Cu–18%Nb composite following equal channel angular extrusion under both low- and high-strain rate loadings. The microstructures are characterized by optical and scanning electron microscopy as well as electron backscatter diffraction. Comparisons are also made with a Cu–50%Nb laminate made by accumulative roll bonding. Textures obtained within the respective phases in the extruded composite closely mimic those previously reported for the pure components alone (Cu, Nb). Grain sizes of the major phase (Cu) exhibit broad distributions, due largely to partial recrystallization during the extrusion process. Further re-crystallization is obtained within localized deformation bands produced at high strain rates (3 × 10 3 s –1 ). While the degree of anisotropy and the strain rate sensitivity of the composite response are similar to those of pure Cu after extrusion, the strength levels of the composite are somewhat greater, falling broadly between those obtained in the pure components after extrusion to comparable plastic strains. Furthermore, the implications for selection of composite composition and processing for achieving higher strengths are briefly discussed.
36 MATERIALS SCIENCE↗
High pressure suppression of plasticity due to an overabundance of shear embryo formation
Abstract High pressure shear band formation is a critical phenomenon in energetic materials due to its influence on both mechanical strength and mechanochemical activation. While shear banding is known to occur in a variety of these materials, the governing dynamics of the mechanisms are not well defined for molecular crystals. We conduct molecular dynamics simulations of shock wave induced shear band formation in the energetic material 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) to assess shear band nucleation processes. We find, that at high pressures, the initial formation sites for shear bands, “embryos”, form in excess and rapidly lower deviatoric stresses prior to shear band formation and growth. This results in the suppression of plastic deformation. A local cluster analysis is used to quantify and contrast this mechanism with a more typical shear banding seen at lower pressures. These results demonstrate a mechanism that is reversible in nature and that supersedes shear band formation at increased pressures. We anticipate that these results will have a broad impact on the modeling and development of high-strain rate application materials such as those for high explosives and hypersonic systems.
36 MATERIALS SCIENCE↗
An Eulerian crystal plasticity framework for modeling large anisotropic deformations in energetic materials under shocks
Here, 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.
42 ENGINEERING↗
Static and shock compression studies of eutectic high-entropy alloy AlCoCrFeNi 2.1 to ultrahigh pressures
The high-entropy alloy with composition AlCoCrFeNi 2.1 , additively manufactured with the laser powder-bed fusion technique, has a far-from-equilibrium BCC/FCC eutectic nanolamellar structure. We studied the high-pressure response of this alloy under both static compression and high-strain rate shock compression. The response to static compression using a diamond anvil cell was studied at pressures up to 302 GPa with synchrotron x-ray diffraction at the advanced photon source. The high-pressure FCC-only phase of the EHEA previously observed by Pope et al. [AIP Adv. 13, 035124 (2023)] is found to be stable up to the highest pressure achieved in this study with a volume compression of V/V 0 = 0.587 at ambient temperature. The shock experiments were performed by using GEKKO XII lasers at the Institute of Laser Engineering, Osaka University. The principal Hugoniot equation-of-state of the EHEA was measured up to a pressure of 515 GPa and a compression of V/V 0 = 0.613. Additionally, the thermal equation of state of the EHEA was measured up to 6.2 GPa and 1623 K using a large-volume Paris–Edinburgh cell to obtain the temperature dependence of bulk modulus and thermal expansion coefficients. The melting temperature for EHEA AlCoCrFeNi 2.1 at a pressure of 5.6 GPa was measured to be 1648 ± 25 K. These results can be used to refine stochastic (or special) quasi-random structure (SQS) models for high-pressure high-temperature behavior of high-entropy alloys.
36 MATERIALS SCIENCE↗
Understanding Microstructural Effects on Dynamic Performance Towards the Development of Shock Metamaterials
With the recent advances in additive manufacturing (AM), long-range periodic lattice assemblies are being developed for vibration and shock mitigation components in aerospace and military applications with unique geometric and topological structures. There has been extensive work in understanding the static properties associated with varying topology of these lattice architectures, but there is almost no understanding of microstructural affects in such structures under high-strain rate dynamic loading conditions. Here we report the shock behavior of lattices with varying intrinsic grain structures achieved by post process annealing. High resolution 316L stainless steel lattices were 3D printed by a laser-powder bed fusion machine and characterized by computed tomography. Subsequent annealing resulted in stress-relieved and recrystallized lattices. Overall the lattices had strong cubic texture aligning with the x-, y- and z-directions of the build with a preference outside the build direction (z). The recrystallized sample had more equiaxed polygonal grains and a layer of BCC ferrite at the surface of the structure approximately 1 grain thick. Upon dynamic compression the as-deposited lattice showed steady compaction behavior while the heat-treated lattices exhibit negative velocity behavior indicative of failure. We attribute this to the stiffer BCC ferrite in the annealed lattices becoming damaged and fragmenting during compression.
36 MATERIALS SCIENCE↗
Resolving the Martensitic Transformation in Q&P Steels In-Situ at Dynamic Strain Rates Using Synchrotron X-ray Diffraction
Herein the dynamic deformation response of two quenching and partitioning (Q&P) steels was investigated using a high strain rate tension pressure bar and in-situ synchrotron radiography and diffraction. This allowed for concurrent measurements of the martensitic transformation, the elastic strains/stresses on the martensite and ferrite, and the bulk mechanical behavior. The steel with the greater fraction of ferrite exhibited greater ductility and lower strength, suggesting that dislocation slip in ferrite enhanced the deformability. Meanwhile, the kinetics of the martensitic transformation appeared similar for both steels, although the steel with a greater ferrite fraction retained more austenite in the neck after fracture.
36 MATERIALS SCIENCE↗
AA2024/SiC metal matrix composites simultaneously improve ductility and cracking resistance during elevated temperature deformation
Here this study uses the stir-casting technique to combine a semi-solid AA2024 alloy directly with finely-sized β-SiC p embedded as a powder or with mechanically alloyed granules as a delivery agent. Liquid-state primary fabrication tends to form agglomerates of reinforcement particles, whereas rolling better distributes the composite constituents. Sub-micron reinforcements of low volume fractions do not significantly increase the hardness of the composite materials. Uniaxial tensile testing at elevated temperatures over a wide range of strain rates showed simultaneous increases in the ductility and crack resistance of AA2024 + SiC p granules embedded as a powder when compared to the non-reinforced control material at lower strain rates, with the same toughness as the control material. The maximum engineering strain of 252.7 ± 19.2% was observed in AA2024/SiCp at a strain rate of 10 -4 s -1 . This improvement in properties is attributed to grain refinement in the MMCs, leading to pinning events during the straining and ductility increases. The resultant impediments to grain growth and crack propagation allow the fine-sized reinforcements to control dynamic microstructural changes during fatigue. Cube {001}<100> is a dominant texture component in AA2024, whereas the Goss {011}<100> and S {123}<634> components mainly represent the texture of the discontinuously reinforced aluminum matrix.
36 MATERIALS SCIENCE↗
Using Particle Image Velocimetry to Determine Turbulence Model Parameters
The primary parameter of a standard k-ϵ model, C μ , was calculated from stereoscopic particle image velocimetry (PIV) data for a supersonic jet exhausting into a transonic crossflow. This required the determination of turbulent kinetic energy, turbulent eddy viscosity, and turbulent energy dissipation rate. Image interrogation was optimized, with different procedures used for mean strain rates and Reynolds stresses, to produce useful turbulent eddy viscosity fields. The eddy viscosity was calculated by a least-squares fit to all components of the three-dimensional strain-rate tensor that were available from the PIV data. This eliminated artifacts and noise observed when using a single strain component. Local dissipation rates were determined via Kolmogorov’s similarity hypotheses and the second-order structure function. The eddy viscosity and dissipation rates were then combined to determine C μ . Considerable spatial variation was observed in C μ , with the highest values found in regions where turbulent kinetic energy was relatively low but where turbulent mixing was important, e.g., along the high-strain jet edges and in the wake region. This suggests that use of a constant C μ in modeling may lead to poor Reynolds stress predictions at mixing interfaces. A data-driven modeling approach that can predict this spatial variation of C μ based on known state variables may lead to improved simulation results without the need for calibration.
42 ENGINEERING↗
Design, characterization and shape recovery behavior of 3D/4D printed shape memory polymers (SMPs)
Shape memory polymers (SMPs) represent a paradigm shift in material science, uniquely capable of undergoing reversible shape transformations triggered by external stimuli, positioning them as pivotal in developing next-generation biomedical devices, aerospace components, and adaptive structures. Extensive research has been done on SMPs with a major focus on high-temperature programming methods, which can limit energy efficiency and applicability with temperature-sensitive materials. Additionally, while various SMP blends have demonstrated great potential, limited work has been done on the suitability for 3D printing these materials, particularly under high-strain and ambient temperature programming conditions. In this study, a three-component optimized SMP composition was evaluated by 3D printing via the Material Extrusion (MEX) technique and investigating its ambient temperature-programming behavior at high strains. The SMP formulation studied was a tailored blend of thermoplastic polyurethane (TPU), polycaprolactone (PCL), and an octadecane diol-based copolymer (OBC) that exhibits robust shape memory behavior, high strain tolerance, and efficient force generation. Rigorous thermal, mechanical, and shape recovery analyses, along with optimized printing parameters and consistent shape recovery rates of up to 90%, were achieved under dynamic mechanical analysis (DMA), even under ambient programming conditions. This work demonstrates the SMP composition’s potential for adaptive, self-deployable systems with 4D printing characteristics ideal for bio-inspired structures and artificial muscle fibers.
Sudan, Kavish [University of Louisville, KY]↗
Uncertainty bounds for multivariate machine learning predictions on high-strain brittle fracture
Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive. The cost increases even more if multiple simulations are needed to account for the randomness in crack length, location, and orientation, which is inherently found in real-world materials. Constructing a machine learning emulator can make the process faster by orders of magnitude. There has been little work, however, on assessing the error associated with their predictions. Estimating these errors is imperative for meaningful overall uncertainty quantification. In this work, we extend the heteroscedastic uncertainty estimates to bound a multiple output machine learning emulator. Overall, we find that the response prediction is accurate within its predicted errors, but with a somewhat conservative estimate of uncertainty.
36 MATERIALS SCIENCE↗