Void Collapse Research Articles

Molecular dynamics study on the nanovoid collapse and local deformation in shocked Cu50Zr50 metallic glasses

The nanovoid evolution is an important part of understanding the physical and mechanical properties of metallic glasses (MGs). Here, the void-included Cu50Zr50 MGs under different shock intensities are investigated by the molecular dynamics simulations, focusing on the characteristics of void collapse, the evolution and correlation of clusters in the collapsed region. The results show that there are two typical mechanisms for the void collapse along the shock direction: the vertical collapse mechanism and the horizontal collapse mechanism. The vertical collapse mechanism is dominated by the hoop stress under the weak shock intensity, while the horizontal collapse mechanism is led by the principal stress along the shock direction under the strong shock intensity. In terms of shock-induced void collapse in the MGs, the plastic deformation mainly concentrates around the void and forms local shear transformation zones. There is very weak activity of the Zr-centered clusters in the shear transformation zones under the weak shock intensity, whereas the Cu-centered clusters appear a strong spatial correlation, and several of them tend to strongly aggregate. When the shock velocity exceeds 1.0 km/s, the Zr-centered clusters also begin to correlate intensely in the shear transformation zones, which corresponds to the horizontal collapse of the void. The results also show that the void defects in the Cu50Zr50 MGs can be almost fixed by long-term shock compression.

Continuum and molecular dynamics simulations of pore collapse in shocked β-tetramethylene tetranitramine (β-HMX) single crystals

The collapse of pores plays an essential role in the shock initiation of high energy (HE) materials. When these materials are subjected to shock loading, energy is localized in hot-spots due to various mechanisms, including void collapse. Depending on the void size and shock strength, the resulting hot-spots may quench or evolve into a self-sustained deflagration wave that consequently can cause detonation. We compare finite element (FE) and non-reactive molecular dynamic (MD) simulations to study the formation of hot-spots during the collapse of an 80 nm size void in a β-tetramethylene tetranitramine energetic crystal. The crystal is shocked normal to the crystallographic plane (010), applying boundary velocities of 0.5 km/s, 1.0 km/s, and 2.0 km/s. The FE simulations capture the transition from viscoelastic collapse for relatively weak shocks to a hydrodynamic regime, the overall temperature distributions, especially at scales relevant for the initiation of HE materials, and the rate of pore collapse. A detailed comparison of velocity and temperature fields shows that the MD simulations exhibit more localization of plastic deformation, which results in higher temperature spikes but localized to small volumes. The void collapse rate and temperature field are strongly dependent on the plasticity model in the FE results, and we quantify these effects.

Modeling the damage evolution and recompression behavior during laser shock loading of aluminum microstructures at the mesoscales

Damage evolution in metals during laser-shock loading (spallation) is a complex phenomenon accompanied by extremely high temperatures, pressures, and strain rates that affect the void nucleation/growth mechanisms. The current modeling efforts at the atomic scales to investigate the evolution of microstructure undergoing the spall failure at the atomic scales are limited to a hybrid atomistic–continuum method that combines the two-temperature model (TTM) with the molecular dynamics (MD) simulations. This manuscript demonstrates this capability by investigating the mechanisms of nucleation/evolution of voids for a nanocrystalline Al system experiencing an ultrafast laser pulse. This capability, however, is unable to model the laser shock response of experimental systems (with grain sizes greater than 100 nm and thicknesses in the microns) as well as the post-spall behavior (damage growth or recompression behavior). This work combines the TTM with the quasi-coarse-grained dynamics (QCGD) method to extend MD-TTM simulations to the mesoscales. The hybrid QCGD-TTM approach retains the laser energy absorption, heat generation/transfer, and microstructure evolution (melting, defects, and damage) behavior predicted by MD-TTM simulations. The QCGD-TTM simulations allow the investigation of the wave propagation behavior, the evolution of microstructure (defects and damage), temperature, and pressure at the time and length scales of laser-shock experiments. The QCGD-TTM simulations reported here investigate the nucleation and post-spall damage evolution behavior during spall failure of sc-Al and 0.5 µm grain-sized pc-Al films with a thickness of up to 2 µm. The QCGD-TTM-predicted damage evolution behavior captures the post-spall behavior observed experimentally and retains the atomistic characteristics of void nucleation and void collapse.

Enabling improved cycling stability of hollow SnO2/C composite anode for lithium-ion battery by constructing a built-in porous carbon support

Owing to the cooperative effect of well-defined interior voids and conductive and flexible carbon coating, the hollow nanostructural SnO2/C composites exhibit significantly improved electrochemical performance over their pure nanostructured SnO2 counterparts, and hence attracts increasing research interests. However, the potential collapse of SnO2 inwards interior voids and subsequent agglomeration will diminish the cycling stability of hollow SnO2/C composites and hence needs to be further improved. Herein, to reduce the excess void space and block agglomeration of the SnO2 inwards interior voids, a cubic hollow SnO2/C composite with a built-in porous carbon support yolk has been designed and constructed successfully. As a result, thus as-constructed composite with a novel architecture displays significantly improved cycling stability as comparison to the similar hollow SnO2@C composite without a built-in porous carbon, delivering 788 and 588 mAh g−1 at 200 and 1000 mA g−1 after 550 and even 900 cycles, respectively. The results obtained here could pave the way for properly improving the cycling stability of other hollow metal oxides/carbon composites for advanced lithium-ion battery anodes.

Mechanical response and deformation mechanisms of porous PZT95/5 ceramics under shock-wave compression

A series of plate impact experiments were performed to investigate the shock response of porous PZT95/5 ceramics. Based on the measured free surface velocity profiles, the influences of impact velocity and porosity on the shock response of porous PZT95/5 ceramics were explored. Then, the shock response of porous PZT95/5 ceramics was numerically simulated by using the discrete element method (DEM) based on flat-joint bonded contact model to analyze the microscopic deformation mechanisms. The simulation results of the free surface velocity profiles agreed well with experimental results. The macroscopic deformation process of porous PZT 95/5 ferroelectric ceramics under shock-wave compression can be divided into four stages: elastic deformation, cracks spread deformation, void collapse deformation and Hugoniot state. The microscopic deformation mechanisms of porous PZT95/5 ceramics under shock-wave compression could be mainly attributed to the nucleation and growth of large numbers of shear cracks and tension cracks around voids, as well as the collapse of voids in ceramics.

High-pressure preference for reduced water content in porous zinc aspartate hydrates.

The zinc aspartate (ZnAsp2) complex, a common dietary supplement, preferentially crystallizes as the dihydrate (ZnAsp2·2H2O) from aqueous solution. Under normal conditions the dihydrate easily transforms into the sesquihydrate (ZnAsp2·1.5H2O). The dihydrate crystal structure is triclinic, space group P1, and the sesquihydrate is monoclinic, space group C2/c. However, their structures are closely related and similarly consist of zinc aspartate ribbons parallel to pores accommodating water molecules. These porous structures can breathe water molecules in and out depending on the temperature and air humidity. High pressure above 50 MPa favours the sesquihydrate, as shown by recrystallizations under pressure and compressibility measured by single-crystal X-ray diffraction up to 4 GPa. This preference is explained by the reduced volume of the sesquihydrate and water compressed separately, compared with the dihydrate. The sesquihydrate undergoes an isostructural phase transition when the voids collapse at 0.8 GPa, whereas no phase transitions occur in the dihydrate, because its pores are supported by increased water content.

Macro-scale sensitivity through meso-scale hotspot dynamics in porous energetic materials: Comparing the shock response of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) and 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX)

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 Ps and void size Dvoid. 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.

Micromechanics-based damage model for liquid-assisted healing

This work presents a damage evolution framework including liquid-assisted healing. The model incorporates contributions from void size, void pressure, surface tension and liquid pressure. Experimental motivation for the damage-healing model is provided with in-situ melting experiments, where the evolution of the void distribution under monotonic tension is illustrated. The damage evolution is based on nucleation and growth of voids, which are modeled in a unified creep and plasticity framework. The proposed damage formulation introduces a void collective, which computes the void distribution in the material and allows to describe void collapse using the Rayleigh-Plesset equation. The necessary conditions for healing are discussed with use of model results. Particularly, the role of external load during healing, the dependence on liquid viscosity and surface tension are investigated.

Evaluation of reaction kinetics models for meso-scale simulations of hotspot initiation and growth in HMX

Meso-scale modeling of heterogeneous energetic materials requires accurate description of the chemical reaction model that governs the decomposition of solid energetic crystals to gaseous products. For HMX, various 1-step and multi-step Arrhenius based chemical kinetic models are available; these chemical kinetics models for HMX have been calibrated against macro-scale experimental data under different ranges of pressure and temperature conditions, which may lie outside the ranges that arise during void collapse. Therefore, depending on the reaction model, the predicted meso-scale hotspot initiation and growth behavior can vary. Here, we examine the effects of five global HMX reaction kinetics models on predictions of void collapse induced hotspots, viz. the Henson-Smilowitz 1-step (HS1), Menikoff 1-step (M1), Tarver-Nichols 3-step (TN3), Henson-Smilowitz 9-step (HS9) and a 7-step extended Brill-Yetter model (BYS7). Variations in the hotspot behavior predicted using the different models are observed to be significant. A detailed examination of the individual reaction mechanisms of each of these global chemistry models is undertaken to provide insights and understanding of the reaction steps that lead to the differences in the predicted hotspot behavior. For the temperature regime relevant to the void collapse generated hotspots, the differences in the hotspot behavior are attributed to the orders of magnitude variations in the reaction rates that govern the maximum energy release during HMX decomposition. The paper shows that the issue of a suitable kinetics model, even for the commonly used HMX material, remains unsettled.

The latest development and the new extended capabilities of the GENII-LIN soil transfer model

Some years ago, we started developing an enhanced soil transport model, where short life nuclide contributions were accurately accounted, Teodori (2017). The aim was to extend the code capabilities to handle incidental release of contaminant to soil, by evaluating exposure since the very beginning of the contamination event, before the radioactive decay chain equilibrium is reached. In this years those new capabilities have been widely extended: the leaching model has been reworked in a more physically based manner, by using a more sophisticated formulation for the transfer rate; the soil compartment number has been increased, by introducing an intermediate layer; bioturbation by animals now also affects downward transfer of materials, by modifying the leaching constant and by void collapse; plant transfer contributes to contaminant redistribution through all soil depth by plant recycle.

Hotspot formation due to shock-induced pore collapse in 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX): Role of pore shape and shock strength in collapse mechanism and temperature

The shock to detonation transition in heterogeneous high energy density solids starts with the spatial localization of mechanical energy into so-called hotspots that form due to the interaction between the leading wave and microstructural features and defects. We used large-scale molecular dynamics to characterize the hotspots resulting from the shock-induced collapse of cylindrical voids and elongated cracks focusing on the effect of shock strength, defect shape, and size. The temperature fields resulting from the collapse of cracks elongated along the shock direction show significantly higher sensitivity to both shock strength and size than cylindrical voids. Cracks 80 nm in length result in temperatures almost three times higher than voids 80 nm in diameter, reaching values corresponding to the ideal case of isentropic recompression of a gas. The molecular dynamics trajectories reveal the atomic origin of this contrasting behavior. While circular voids undergo a transition from viscoelastic pore collapse to a hydrodynamic regime with increasing shock strength, shock focusing in elongated cracks results in jetting and vaporization which, upon recompression, leads to increased heating.

Strength and compressibility of sedimented ash beds treated with chemical columns

This paper reports the strength and compressibility properties of sedimented ash beds treated with chemical columns. Sedimented model ash beds were prepared by simulating the natural sedimentation process in a laboratory environment and allowing them to undergo consolidation under the self-weight for a period of 30 days. Then, the ash beds were treated with three different configured chemical columns of sodium hydroxide (NaOH) with a concentration of 18 M for 60 days. After the 60 days of treatment, the in-situ dry unit weight, moisture content, bearing resistance, collapse potential, compressibility properties, and pore structure at different locations of the treated ash beds were examined. The contours of the bearing resistance were found to be bell-shaped with larger spreading towards the bottom end of the columns. The magnitude of the strength development was found to diminish rapidly with an increase in the radial distance from the column surface. After 60 days, the void ratio and collapse potential values in the column’s peripheral region of the ash beds treated with full, ½, and 1/4 columns were found to be 0.89, 0.93, and 0.95 and 0.75%, 0.89%, and 0.97%, respectively, compared to 1.64 and 7.46% of an untreated ash bed. These changes were attributed to the development and distribution of reaction products, which are functions of the column configuration and sampling location. The void ratio gradually increased with an increase in the radial distance from the chemical column. The decrease in void ratio was attributed to the blockage of the capillary pores by the reaction products. Primarily sodium- and calcium-based reaction products were observed along with hybrid compounds of sodium-calcium-based alumino-silicates. These reaction products encapsulated the ash particles within the matrix structure, thus modifying the bearing resistance, collapse potential, and compressibility properties of the sedimented ash beds. The morphology of the stabilized ash specimens showed a mixture of partially reacted ash particles, semi-crystalline structures, and reacted gel phase as the geopolymerization products.

Dynamic response of ductile materials containing cylindrical voids

The fracture of ductile materials is often the result of the nucleation, growth and coalescence of microscopic voids. In this thesis, we mainly focus on the dynamic void evolution in porous media containing cylindrical voids. This study covers a problem that is of particular interest in many areas of research (e.g. development of shock mitigation devices for civil or military applications). Owing to the development of additive manufacturing, the processing of porous material with cylindrical voids is an option to create lightweight materials having interesting properties in terms of energy dissipation. Therefore, our work aims at describing the dynamic response of architectured materials such as honeycomb structures. In dynamic loading, microvoids sustain an extremely rapid expansion which generates strong acceleration of particles in the vicinity of cavities. These micro-inertia effects are known to play a significant role in the macroscopic response and the development of damage in porous media. In fact, the overall macroscopic stress is found to be the sum of two contributions: a static term (micro-inertia independent term) and a dynamic term (micro-inertia dependent term), the latter being related to the microstructure (e.g. size and aspect ratio of voids). In our work, a cylindrical shell is adopted as a Representative Volume Element (internal and external radii a and b, length 2l) for the porous material. The static term is derived from a yield function available in the literature. The dynamic stress is evaluated analytically using a trial velocity field for cylindrical voids combined with the multi-scale approach developed in the literature in LEM3. It is shown that the dynamic stress is scaled by the mass density, two characteristic lengths of the voids, the porosity, the macroscopic strain rate tensor and the time derivative of the strain rate tensor. An important outcome of the model is the differential lengthscale effect which exists between in-plane and out of plane components of the macroscopic stress. Namely, it is observed for axisymmetric loading that in-plane dynamic stress components are only related to the void radius a while the out of plane stress component is linked to a and the length of the RVE, l. In the thesis, we present the dynamic response of the porous medium when subjected to various loading conditions: spherical loading, axisymmetric plane strain loading, uniaxial loading and biaxial loading. While for plane strain loading under quasi static condition, the overall axial stress is spherical, in dynamic conditions, the inertia contribution hinders the overall stress tensor from being spherical. Another important result of the proposed theory is the effect of the void length, which does not exist in quasi static conditions where the overall response is solely modulated by the porosity. The case of thin cylinders under dynamic loading reveals a peculiar damage kinetics. In fact, the damage developed in such porous materials results from an increase of the void radius and a reduction of the external radius. The void collapse for uniaxial as well as for biaxial loadings are new observations. The analytical model predictions are validated based on comparisons with finite element calculations (Abaqus/Explicit).

Crystal plasticity based investigation of micro-void evolution under multi-axial loading conditions

The present work investigates the effects of stress state and crystallographic orientation of the principal stress axes on the growth behaviour of micro-voids embedded in an aluminium alloy single crystal. Cubic unit cells with a spherical void located at their centre are relied upon to study the behaviour of the porous FCC single crystal under multiaxial loading conditions. A physics-based crystal plasticity constitutive model is used to describe crystallographic slip around the voids. Special emphasis is placed on quantifying the ductile behaviour of the porous material, where the description of the stress state requires the use of two dimensionless parameters: the stress triaxiality and the so-called Lode parameter. A detailed investigation is carried out to study the effect of the crystallographic orientation of the principal stress axes for a given stress state on the behaviour of the voided single crystal. The results show that the Lode parameter has a strong effect on single crystal void growth at low triaxialities, as well on void coalescence strains. A general relation is proposed to determine the void coalescence strain, a measure of the material ductility, in terms of a novel equivalent loading parameter which depends, in turn, on the stress state and the relative orientation of the principal stress axes. A transitional state has been identified from void failure mechanism maps where neither void collapse nor void coalescence occurs when the stress state in the porous single crystal varies from high to low triaxialities.

Dynamic stress-strain response of high-energy ball milled aluminium powder compacts

Ball milling is a bulk powder manufacturing process used in the creation of dispersion strengthened and nanostructured materials. Fundamentally, these powders have not been dynamically characterized in a green state prior to hot consolidation. The understanding of high strain-rate compaction on void collapse and particle interaction for such systems can help the development of predictive models for impact events of porous metallic structures that may be employed as energy absorbers, reactive structures, and intermetallic materials. This study investigates high strain-rate impact of porous green compacts of as-received and high-energy ball milled (HEBM) aluminium powders characterized under dynamic compression using a split-Hopkinson pressure bar (SHPB) in a passive confinement configuration. The plastic deformation of the powder compacts and crush up were shown to be strain-rate insensitive within the strain rate range of 1000–2100 s−1 and as a result, were modelled adequately with a second order P-α model. The as-received aluminium and HEBM aluminium powders appear to have the same strain-hardening coefficient and strength index as solid aluminium after yielding. The respective stress-strain responses of green compacts follow the same trend but differ only in strength as result of porosity and pre-strain experienced prior to dynamic compression. The HEBM powder was found to be twice as strong as the untreated as-received aluminium powder.

Modeling mesoscale energy localization in shocked HMX, Part II: training machine-learned surrogate models for void shape and void–void interaction effects

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

Damage and hotspot formation simulation for impact–shear loaded PBXs using combined microcrack and microvoid model

A physically–based damage–hotspot formation framework incorporating multiple stress–state motivated evolution–modes of microcracks and microvoids is developed to study the overall damage behavior of polymer–bonded explosives (PBXs). Localized heating sub-models of shear–crack friction and void collapse hotspot mechanisms are described to predict impact–shear ignition of PBXs. Several features of microdefect evolution under a combined shear and compression loading are predicted as follows. (i) Crack growth causes an elasticity deterioration and softening response; (ii) void distortion begins at the yield point and ends at the softening point; (iii) the softening stage will be interrupted if the increasing lateral pressure is sufficiently large to inhibit crack growth; and (iv) void collapse occurs if the lateral pressure continually increases to a critical high value. Simulated results of a punched PBX charge show that shear–crack friction heating plays a critical role in ignition under low–velocity impact (<400 m/s). Under high–velocity impact (>400 m/s), the heating due to void collapse dominates ignition because the timescale to void hotspot formation (~1 μs) is considerably shorter than that of crack hotspots (~10 μs).

Multiscale Approach to Shock to Detonation Transition in Energetic Materials

AbstractIn this work we present a multiscale approach for coupling the dynamics of void collapse at the microscale to simulations at the mesoscale. We solve the reactive Euler equations, with the energy equation augmented by a power deposition term. The reaction rate at the mesoscale is modelled using a pressure‐dependent power law. The deposition term is based on previous simulations of void collapse, modelled at the mesoscale as hot‐spots. The equation of state was previously calibrated for PBX 9501. The run‐to‐detonation distance is calculated as part of the numerical solution procedure. Results for 1‐D, 2‐D homogeneous, and 2‐D heterogeneous medium are presented, and show good agreement to experimental data.

Sinkhole occurrence monitoring over shallow abandoned coal mines with satellite-based persistent scatterer interferometry

Unexpectedly occurring sinkholes caused by shallow submerged voids are one of the key problems of intensively built-up post-mining areas. Five percent of Poland’s territory is still under the influence of post-mining deformation. Impending sinkholes, which tend to develop randomly over very large areas, cannot be detected by using traditional geophysical methods. Moreover, geodetic measurement methods like Global Positioning System (GPS) analyses, tachymetry, laser scanning, or photogrammetry may be useful only for the registration of the dimensions and locations of sinkholes that have already occurred. Here, we investigate an area in Upper Silesia, Poland, where 345 sinkholes were recorded over a period of more than 20 years (1992–2013). Most of the events occurred in intensively built-up areas, and thus, these sinkholes posed a direct threat to the population. In the test area, 11 sinkholes were detected with a maximum depth of 16 m and maximum dimension of 25 m. The root cause of sinkhole formation was the collapse of post-mining shallow voids. We used satellite radar technology to detect and monitor ground movements potentially associated with the impending sinkholes. The findings showed that the application of Persistent Scatterer Interferometry can support the identification of zones where sinkholes will occur, given adequate spatio-temporal sampling. A stack of Envisat Synthetic Aperture Radar (SAR) images acquired between March 2003 and August 2010 was used in the analysis, and the results confirmed that precursory ground movements were detectable at an early stage of sinkhole development. The land subsidence rate observed prior to sinkhole collapse was not constant in time. Accelerated ground movements within 100 m of an observed sinkhole were detected. We conclude that satellite measurements may provide significant support in the early identification of areas prone to sinkhole occurrence.

Molecular dynamics study on void collapse in single crystal hcp-Ti under hydrostatic compression

Molecular dynamics simulations were performed to investigate the void collapse in single crystal hcp-Ti under hydrostatic compression. The principal mechanisms of deformation are identified. In the early stage, the dislocations nucleate at the intersections of facets, four slip systems (1/3<112¯0>{11¯00}, 1/3<112¯0>{11¯01}, 1/3<112¯3¯>{11¯01} and 1/3<112¯0>{0002}) are activated. As deformation continues, non-planar loops form, and the perfect dislocation decomposition occurs only on the basal plane. Effects of void sizes on mechanical respond are also investigated, and the results show that the stress decreases as the initial void size increases, while the dislocation density increases as the initial void size increases. What’s more, dislocation detachment occurs by chance.