Spherical harmonics method for computing the image stress due to a spherical void
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Materials Science↗
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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↗
Dimensionality effects in void-induced explosive sensitivity
Here, the dimensionality of defects in high explosives controls their heat generation and the expansion of deflagrations from them. We compare the behaviour of spherical voids in three dimensions to that of circular voids in two dimensions. The behaviour is qualitatively similar, but the additional focusing along the extra transverse dimension significantly reduces the piston velocity needed to initiate reactions. However, the reactions do not grow as well in three dimensions, so detonations require larger piston velocities. Pressure exponents are seen to be similar to those for the two-dimensional system.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The predicted shapes of voids and Xe bubbles in UO 2
Morphology is a fundamental attribute when investigating voids and bubbles in UO 2 . Here we use molecular dynamics and Monte Carlo simulations to predict the lowest energy shapes for voids and bubbles in UO 2 . The energies of the {100}, {110} and {111} surfaces have been calculated and used to predict the equilibrium void shape from Wulff construction. This equilibrium shape is compared to low energy faceted voids exhibiting different relative proportions of each family of terminating surfaces. It is found that the equilibrium Wulff shape does not represent the lowest energy morphology for nm void sizes at temperatures between 300 K and 1200 K. Furthermore, the lowest energy faceted voids are slightly more energetically favourable than spherical voids, and as Xe is added, and bubble pressure increases, the faceted morphology becomes even more favourable than the spherical shape.
36 MATERIALS SCIENCE↗
Role of grain boundary crystallography on void growth in FCC metals
The growth of an isolated spherical void at and near a grain boundary or a triple junction is studied by means of full-field crystal plasticity simulations with explicit representation of the void. To examine the fundamental aspects of void/grain boundary interactions in these cases, a three-dimensional large-strain elasto-viscoplastic fast-Fourier transform (LS-EVP-FFT) model with axisymmetric tensile periodic boundary conditions was developed. We employ this model to reveal the role of crystallography (grain orientations, grain boundary misorientation and inclination angle with respect to the largest component of the applied stress) and type of loading on void growth. It was found that grain orientation was the primary crystallographic feature governing void growth in strain-rate controlled simulations. For strains small enough to not significantly alter the local geometry, the overall growth of the void in bicrystal boundaries was not strongly affected by grain boundary inclination angle. The relative amount of void growth experienced within each grain in a bicrystal or tri-crystal was strongly dependent on the grain boundary inclination angle. We found a subset of orientations that exhibit faster void growth in bicrystal boundaries than inside the constituent single crystals. Last, we show that when placed primarily in one grain but near the grain boundary, void growth was similar to void growth when placed at the grain boundary. Furthermore, the growing void remained in the original grain and did not grow into the other grain, regardless of crystallographic character.
36 MATERIALS SCIENCE↗
The Impact of Void-finding Algorithms on Galaxy Classification
We explore how the definition of a void influences the conclusions drawn about the impact of the void environment on galactic properties using two void-finding algorithms in the Void Analysis Software Toolkit: Voronoi Voids (V 2 ), a Python implementation of ZOnes Bordering On Voidness (ZOBOV); and VoidFinder, an algorithm that grows and merges spherical void regions. Using the Sloan Digital Sky Survey Data Release 7, we find that galaxies found in VoidFinder voids tend to be bluer and fainter and to have higher (specific) star formation rates than galaxies in denser regions. Conversely, galaxies found in V 2 voids show less significant differences when compared to galaxies in denser regions, less consistent with the large-scale environmental effects on galaxy properties expected from both simulations and previous observations. These results align with previous simulation results that show V 2 -identified voids “leak” into the dense walls between voids because their boundaries extend up to the density maxima in the walls. As a result, when using ZOBOV-based void-finders, galaxies likely to be part of wall regions are instead classified as void galaxies, a misclassification that can be critical to our understanding of galaxy evolution.
cosmic web↗
Encapsulant Void Breakdown Voltage Modeling & Experiments
For high voltage electrical devices, prevention of high voltage breakdown is critical for device function. Use of polymeric encapsulation such as epoxies is common, but these may include air bubbles or other voids of varying size. The present work aimed to model and experimentally determine the size dependence of breakdown voltage for voids in an epoxy matrix, as a step toward establishing size criteria for void screening. Effects were investigated experimentally for both one-dimensional metal/epoxy/air/epoxy/metal gap sizes from 50 μm to 10 mm, as well as spherical voids of 250 μm, 500 μm, 1 mm and 2 mm sizes. These experimental results were compared to modified Paschen curve and particle-in-cell discharge models; minimum breakdown voltages of 6 - 8.5 kV appeared to be predicted by 1D models and experiments, with minimum breakdown voltage for void sizes of 0.2 - 1 mm. In a limited set of 3D experiments on 250 μm, 500 μm, 1 mm and 2 mm voids within epoxy, the minimum breakdown voltages observed were 18.5 - 20 kV, for 500 μm void sizes. These experiments and models are aimed at providing initial size and voltage criteria for tolerable void sizes and expected discharge voltages to support design of encapsulated high voltage components.
42 ENGINEERING↗
Nonlinear ultrasonic response of voids and Cu precipitates in body-centered cubic Fe
Interpreting nonlinear ultrasonic signals detected in nondestructive evaluation of radiation damage needs the knowledge of the correlation between defects and nonlinearity. In this work, molecular dynamics simulations are performed to study the effect of distributed vacancies, voids, Cu atoms, and Cu precipitates on nonlinear ultrasonic response in body-centered cubic (bcc) Fe. The nonlinearity parameter calculated from the second harmonic amplitude in the perfect lattice is 2.73. Vacancies are found to increase the nonlinearity. Surprisingly, clusters of vacancies in the form of spherical voids show an opposite effect. This finding can be used to conveniently distinguish vacancies from voids in the material. Unlike vacancies, individual Cu atoms decrease the nonlinearity. Clustering of Cu atoms into Cu precipitates further decrease the nonlinearity. Interestingly, precipitates with a diameter of 2 nm and larger exhibit a similar effect despite their different structure and coherency with the Fe matrix.
Setyawan, Wahyu↗
Effect of void positioning on the detonation sensitivity of a heterogeneous energetic material
We show although it is well-established that voids profoundly influence the initiation and reaction behaviors of heterogeneous energetic materials such as polymer-bonded explosives (PBX) and propellants, there has been little study of how void location in different constituents in the microstructures of such materials affect the macroscale behavior. Here, we use three-dimensional (3D) mesoscale simulations to study how void placement within the reactive grains versus the polymer binder influences the shock-to-detonation transition (SDT) in a polymer-bonded explosive. The material studied here has a microstructure comprised of 75% PETN (pentaerythritol tetranitrate) grains and 25% HTPB (hydroxyl-terminated polybutadiene) polymer binder by volume. Porosities up to 10% in the form of spherical voids distributed in both the grains and polymer are considered. An Arrhenius reactive burn relation is used to model the chemical kinetics of the PETN grains under shock loading, thereby resolving the heterogeneous detonation behavior of the PBX. The influence of void location on the shock initiation sensitivity of the material is quantitatively ranked by comparing the predicted run distance to detonation (RDD) for each sample. The analysis includes inherent quantification of uncertainties arising from the stochastic variations in the microstructure morphologies and void distributions by using statistically equivalent microstructure sample sets (SEMSS), leading to probabilistic formulations for the RDD as a function of shock pressure. The calculations reveal that the location of voids in the composite microstructure significantly affects the RDD. Specifically, voids exclusively within the grains cause the PBX to be more sensitive (having shorter RDD) than voids in the polymer binder. Unique probabilistic relationships are derived to map the probability of observing RDD for each void location material case, allowing for prediction of initiation behavior anywhere in the shock pressure – RDD space. These findings agree with trends reported in the literature.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
PRECIPITATES AND VOIDS IN CUBIC SILICON CARBIDE IMPLANTED WITH 25Mg+ IONS
This study reports on the formation of 25Mg-bearing precipitates and voids in cubic phase silicon carbide (3C-SiC) single crystals implanted to 9.6×1016 25Mg+/cm2 at 673 K and subsequently annealed at 1073 and 1573 K for 2, 6 and 12 h in an Ar environment. Unidirectionally aligned tetrahedral precipitates are observed around the Mg profile peak, many of which are likely cubic MgC2 and tetragonal Mg2Si particles or their precursor structures. There is also evidence that suggests a possible formation of core (MgC2)-shell (Mg2Si) structure in some of the large precipitates. In addition, small spherical voids are observed near the surface, along with the larger faceted voids in the region of maximum vacancy concentration. 25Mg segregation takes place with a dominant fraction of small atomic clusters. The study provides important results needed to fully assess SiC for potential fusion applications.
Jiang, Weilin↗
Coupled phase field damage and crystal plasticity analysis of intragranular fracture: The role of crystallographic orientation and voids
Damage evolution in engineering metal alloys at the grain scale exhibits significant microstructural heterogeneity and anisotropy. These heterogeneities create local hotspots for stress and strain localization, leading to void nucleation. Crystal orientation influences the active slip systems around voids, affecting lattice rotation and potentially forming discontinuities. At low triaxiality, voids may change shape due to lower stress, rotation, elongation, and coalescence. At high triaxiality, the correlation between crystal orientation and void growth rate becomes stronger, resembling the behavior observed in isolated single crystals. Therefore, understanding the effects of crystal orientation, heterogeneous strain, and defect evolution is crucial for single crystal fracture characterization. Here, in this work, a coupled phase-field damage (PFD) and crystal plasticity (CP) model is implemented within a finite element framework to analyze crystal deformation and failure. The CP method employs a dislocation density-based constitutive model, while intragranular failure is modeled using an anisotropic PFD method. The PFD model considers both the stored energy due to elastic stretching and the energy release due to defect formation and crack formation. A single crystal Al2219 with an intracrystalline spherical void is chosen to analyze fracture. The study finds that fracture propagation is strongly correlated with crystal orientations. This coupled CP-PFD model provides accurate failure prediction in crystalline materials by incorporating the effects of crystal orientations and existing voids. This study demonstrates how the local microstructure and defects influence plastic deformation and failure mechanisms in metal alloys.
Aluminum alloy↗
Geometric dependence of transport and universal behavior in three dimensional carbon nanostructures
Carbon nanostructures with the spherical voids exhibit interesting temperature and magnetic field dependent transport properties. By increasing the void size, the structures are tuned from metallic to insulating; in addition, the magnetoresistance (MR) is enhanced. Here, our investigation in the magnetic fields (B) up to 18 T at temperatures (T) from 250 mK to 20 K shows that at high temperatures (T > 2 K), the MR crosses over from quadratic to a non-saturating linear dependence with increasing magnetic field. Furthermore, all MR data in this temperature regime collapse onto a single curve as a universal function of B/T, following Kohler's rule. Remarkably, the MR also exhibits orientation insensitivity, i.e., it displays a response independent of the direction on the magnetic field.
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↗
Effect of Proximity of Features on the Damage Threshold During Submicron Additive Manufacturing Via Two-Photon Polymerization
Two-photon polymerization (TPP) is a laser writing process that enables fabrication of millimeter scale three-dimensional (3D) structures with submicron features. In TPP, writing is achieved via nonlinear two-photon absorption that occurs at high laser intensities. Thus, it is essential to carefully select the incident power to prevent laser damage during polymerization. Currently, the feasible range of laser power is identified by writing small test patterns at varying power levels. Here in this paper, we demonstrate that the results of these tests cannot be generalized, because the damage threshold power depends on the proximity of features and reduces by as much as 47% for overlapping features. We have identified that this reduction occurs primarily due to an increase in the single-photon absorptivity of the resin after curing. We have captured the damage from proximity effects via X-ray 3D computed tomography (CT) images of a non-homogenous part that has varying feature density. Part damage manifests as internal spherical voids that arise due to boiling of the resist. We have empirically quantified this proximity effect by identifying the damage threshold power at different writing speeds and feature overlap spacings. In addition, we present a first-order analytical model that captures the scaling of this proximity effect. Based on this model and the experiments, we have identified that the proximity effect is more significant at high writing speeds; therefore, it adversely affects the scalability of manufacturing. The scaling laws and the empirical data generated here can be used to select the appropriate TPP writing parameters.
36 MATERIALS SCIENCE↗
The impact of void environment on AGN
ABSTRACT We study the population of active galaxies in void environment in the Sloan Digital Sky Survey. We use optical spectroscopic information to analyse characteristics of the emission lines of galaxies, accomplished by WHAN and BPT diagrams. Also, we study Wide-field Infrared Survey Explorer(WISE) mid-IR colours to assess active galactic nucleus (AGN) activity. We investigate these different AGN classification schemes, both optical and mid-IR, and their dependence on the spatial location with respect to the void centres. To this end, we define three regions: void, the spherical region defined by voidcentric distance relative to void radius (distance/rvoid) smaller than 0.8, comprising overdensities lesser than −0.9, an intermediate/transition shell region (namely, void-wall) 0.8 < distance/rvoid < 1.2, and a region sufficiently distant from voids, the field: distance/rvoid > 2. We find statistical evidence for a larger fraction of AGN and star-forming galaxies in the void region, regardless of the classification scheme addressed (either BPT, WHAN, or WISE). Moreover, we obtain a significantly stronger nuclear activity in voids compared to the field. We find an unusually large fraction of the most massive black holes undergoing strong accretion when their host galaxies reside in voids. Our results suggest a strong influence of the void environment on AGN mechanisms associated with galaxy evolution.
79 ASTRONOMY AND ASTROPHYSICS↗
Are we living near the center of a local void?
The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2-point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structure of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.
79 ASTRONOMY AND ASTROPHYSICS↗
Quasi-brittle porous material: Simulated effect of stochastic air void structure on compressive strength
Highlights: • A simulation procedure to study the effect of porosity on the compressive strength of a quasi-brittle material is introduced • Based on the simulated results, the relationship between compressive strength and air void fraction (porosity) is presented. • A linear relationship was achieved between the cubic root of porosity and the simulated compressive strength. The effect of porosity comprised of spherical air voids on the compressive strength of quasi-brittle material was studied via simulations. The simulated porous structures were based on pore size distributions of two mortar samples measured by X-ray microtomography. While the simulation method set practical limits on the size of sample, the base of the statistics was established by simulating 128 small structures generated by sampling from pore structures of two mortars. By studying the application of the classical strength-porosity formulas to the simulated data, a new simple model was formed. A linear relationship was achieved between the cubic root of air void fraction (porosity) and the simulated compressive strength. The reasons for scattering of simulated strength around fitted trend remained unresolved in this study; no clear dependence on pore number or other distribution properties was observed. With the presented simulation approach, the dependence of compressive strength on porosity is achieved independently of disturbances that occur in experimental studies creating understanding of compressional behavior of low porosity materials.
36 MATERIALS SCIENCE↗