Function Of Void Size Research Articles

Effects of loading rate on void growth in amorphous glassy polymers

Initiation, growth, and coalescence of microscopic voids are precursors to failure in amorphous glassy polymers. Hence, void growth analysis is important for understanding the failure in these polymers. Under quasi-static conditions, void growth in polymers is well understood; however, a similar analysis under dynamic conditions is not available in the literature. In the present work, we analyse the effect of loading rate on the void growth behaviour using large deformation finite element simulations. An axisymmetric unit cell model of a spherical void is considered for the analysis. The void is subjected to a range of strain rates (10−3s−1 to 105s−1). Remote triaxialities equivalent to uniaxial loading, biaxial loading, and higher triaxiality conditions are considered. Remote mean stresses, which are important from the perspective of void growth, have been characterized as a function of void size, strain rate, and triaxiality. Results show that the critical mean stresses required for unstable void growth increase with increasing triaxiality. Higher loading rates further amplify the critical mean stresses, and the amplification depends upon the material rate sensitivity of polymers. The void growth mechanism does not change because of material rate-sensitivity. During void growth, inertia effects are found to be significant after a strain rate of 103s−1. It is found that inertia increases with increasing triaxiality and increasing void size. It stabilizes the void growth and makes them expand in a more spherical shape, even at low triaxialities.

Partial discharge phenomena within an artificial void in cable insulation geometry: experimental validation and simulation

In the presence of void in cable insulation, repetition of partial discharge (PD) occurrences is one of the main sources of insulation degradation, which may lead to complete breakdown. Therefore, it is important to monitor the condition of cable insulation through PD measurement. Replicating PD measurement on a test object with the presence of a void within cable insulation may help a better understanding of PD characteristics within cable insulation to be achieved. Therefore, in this work, test samples of cable insulation geometry containing an artificial void were prepared in the laboratory for PD experiment. The PD measurements were done as a function of void size and applied voltage. A physical model of PD activities within an artificial void in cable insulation geometry was also designed using finite element analysis method. The model was developed by considering PD occurrences within non-uniform electric field distribution in the void and charge movement along the void surface. The model was applied for simulation of PDs within the void in cable insulation geometry to increase the understanding on PD physical phenomena. This includes the impact of distribution of void surface charge on the distribution of the electric field within the void through comparison with the captured measurement results.

The nature of voids – II. Tracing underdensities with biased galaxies

We study how the properties of cosmic voids depend on those of the tracer galaxy populations in which they are identified. We use a suite of halo occupation distribution (HOD) mocks in a simulation, identify voids in these populations using the ZOBOV void finder and measure their abundances, sizes, tracer densities, and dark matter content. To separate the effects of bias from those of sampling density, we do the same for voids traced by randomly down-sampled subsets of the simulation dark matter particles. At the same sampling density, galaxy bias reduces the total number of voids by ~50% and can dramatically change their size distribution. The matter content of voids in biased and unbiased tracers also differs. Deducing void properties from simulation therefore requires the use of realistic galaxy mocks. We discuss how the void observables can be related to their matter content. In particular we consider the compensation of the total mass deficit in voids and find that the distinction between over- and under-compensated voids is not a function of void size alone, as has previously been suggested. However, we find a simple linear relationship between the average density of tracers in the void and the total mass compensation on much larger scales. The existence of this linear relationship holds independent of the bias and sampling density of the tracers. This provides a universal tool to classify void environments and will be important for the use of voids in observational cosmology.

Molecules: What Kind of a Bag of Atoms?

As discussed by Liang and Dill, Enright and Leitner, and others, proteins are not 3D objects. We study an expanded macromolecular data set ranging from proteins to RNA, lipids, and viruses, and remove surface effects and size bias. Molecules and molecular assemblies with more than 1000 backbone atoms have a volume fractal dimension of D(v) = 2.70 +/- 0.05 by the embedded sphere method and D(v) = 2.71 +/- 0.04 by the ensemble method using radius of gyration as the size measure. The much larger D(v) = 2.89 +/- 0.05 obtained with the average surface radius as the length measure shows that surface corrugation is as extensive as cavity formation. Using a simple "Swiss cheese" model for molecules, we show that the distribution of voids in the interior of molecules cannot be a Boltzmann distribution of void energy as a function of void size. Instead, frustration from imperfect packing builds up with molecular size, allowing larger voids to form in larger molecules. We find that large molecules lie halfway between the extremes of packing for homogeneous objects (D = 3) and Apollonian packing, which accounts for packing of a hierarchy of random-sized objects (D approximately 2.47).

Liquid nucleation of surface-free crystal from nanovoids

According to the classical nucleation theory, an estimation for homogeneous nucleation temperature of liquid from nanovoids within a surface-free bulk material is developed by considering energetic contributions of surface (interface) energy and surface (interface) stress on total Gibbs free energy. The model predicts a kinetic superheating limit temperature T max , which is larger than the corresponding bulk value of T m 0 and is a function of void size. The increase of T max is enhanced as the nanovoid size decreases, which can well explain the molecular dynamics simulation results of melting points T m of argon crystal.

Void growth in metals: Atomistic calculations

Molecular dynamics simulations in monocrystalline and bicrystalline copper were carried out with LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to reveal void growth mechanisms. The specimens were subjected to tensile uniaxial strains; the results confirm that the emission of (shear) loops is the primary mechanism of void growth. It is observed that many of these shear loops develop along two slip planes (and not one, as previously thought), in a heretofore unidentified mechanism of cooperative growth. The emission of dislocations from voids is the first stage, and their reaction and interaction is the second stage. These loops, forming initially on different {1 1 1} planes, join at the intersection, if the Burgers vector of the dislocations is parallel to the intersection of two {1 1 1} planes: a 〈1 1 0〉 direction. Thus, the two dislocations cancel at the intersection and a biplanar shear loop is formed. The expansion of the loops and their cross slip leads to the severely work-hardened region surrounding a growing void. Calculations were carried out on voids with different sizes, and a size dependence of the stress threshold to emit dislocations was obtained by MD, in disagreement with the Gurson model which is scale independent. This disagreement is most marked for the nanometer sized voids. The scale dependence of the stress required to grow voids is interpreted in terms of the decreasing availability of optimally oriented shear planes and increased stress required to nucleate shear loops as the void size is reduced. The growth of voids simulated by MD is compared with the Cocks–Ashby constitutive model and significant agreement is found. The density of geometrically necessary dislocations as a function of void size is calculated based on the emission of shear loops and their outward propagation. Calculations are also carried out for a void at the interface between two grains to simulate polycrystalline response. The dislocation emission pattern is qualitatively similar to microscope observations.

Jetting and Detonation Initiation in Shock Induced Collapse of Nanometer-Scale Voids

Molecular dynamics simulations have been used to characterize the dynamics of the shock-induced asymmetric collapse of nanometer-scale voids in cubane nitrogen and to characterize how this dynamics couples with local chemistry to increase the shock sensitivity relative to homogeneous initiation. Mesoscopic-scale features of the void collapse correspond well to experimentally observed features of micrometer-scale bubble collapse, including a transition from single to double jetting with an increasing transverse void length. An analytic model is developed for the enhanced shock sensitivity as a function of void size and shape that reproduces the simulation results. At the atomic level, the simulations show vibrational up-pumping of molecules in the jet front because of collisions with the downstream wall followed by bi-molecular reactive dynamics from continued jet impact that triggers the onset of initiation. These results provide important new insights into the coupling of hydrodynamic void collapse and the enhanced shock sensitivity of energetic materials.

Molecular Dynamics Simulation of Dislocation-Obstacle Interactions in Irradiated Materials

The interactions of a dislocation with commonly observed irradiation induced defects such as a stacking fault tetrahedron (SFT) and a void are studied using molecular dynamics (MD) simulation methods. The simulation of an SFT interacting with a dislocation in face centered cubic (FCC) copper (Cu) reveals that an SFT is a strong obstacle against a dislocation motion, with dislocation detachment often involving an Orowan like mechanism. The resulting SFT generally involves a shear step, although partial absorption is also observed in some specific interaction geometries. Dislocation interaction with a void has been studied in body centered cubic (BCC) molybdenum (Mo). The dislocation locally annihilates upon contact with the void and then re-nucleates on the void surface as the dislocation glides past the void. The interaction results in the simple shear of the void by one Burger’s vector. The obstacle strength of the void is measured using conjugate gradient molecular statics (MS) method as a function of void size. A large increase in the obstacle strength is observed for a void size greater than 3 nm in diameter.

Analytical modeling of reservoir effect on electromigration in Cu interconnects

Electromigration (EM) in Cu dual-damascene interconnects with extensions (also described as overhangs or reservoirs) ranging from 0 to 120 nm in the upper metal (M2) was investigated by an analytical model considering the work of electron wind and surface/interface energy. It was found that there exists a critical extension length beyond which increasing extension lengths ceases to prolong electromigration lifetimes. The critical extension length is a function of void size and electrical field gradient. The analytical model agrees very well with existing experimental results. Some design guidelines for electromigration-resistant circuits could be generated by the model.

Target station shielding issues at the spallation neutron source

Recent spallation neutron source shielding activities in support of the neutron beam shutters and the hot cell walls are presented. Existing neutron beam shutters can be replaced with concrete at low power or with concrete and steel at approximately 500 kW of beam power. Potential voids in the hot cell walls are analysed to determine the impact on dose rates as a function of void size. A change in the type of shielding work is noted as the project moved from the early design stages as a 'green field' site to the current stage as a construction project nearing completion, where issues to be addressed are approaching retrofit-type analyses.

Analysis of Electromigration-Induced Void Motion and Surface Oscillations in Metallic Thin-Film Interconnects

AbstractAn analysis is presented of electromigration-induced migration and oscillatory dynamics of morphologically stable void surfaces based on self-consistent numerical simulations of morphological evolution of voids in metallic thin films. As the morphological stability limit is approached, the migration speed of a stable void deviates substantially from being inversely proportional to the void size, a well-known result that is rigorously valid in an infinite conductor with isotropic material properties. A non-linear shape function that includes both current crowding and diffusional anisotropy effects is used to rescale properly the void migration speed resulting in a universally valid relationship for the migration speed as a function of void size. Furthermore, in grains characterized by high symmetry of surface diffusional anisotropy, our analysis predicts the onset of stable time-periodic states for the void surface morphology that correspond to waves propagating on surfaces of voids that migrate along the metallic film at constant speeds.

Electromigration-driven motion of morphologically stable voids in metallic thin films: Universal scaling of migration speed with void size

The dependence on void size of the migration speed of morphologically stable voids that translate along metallic thin films due to surface electromigration is analyzed in finite-width films through self-consistent numerical simulations taking surface diffusional anisotropy into account. It is shown that, as the morphological stability limit is approached, the void migration speed deviates substantially from being inversely proportional to the void size. A nonlinear “shape function” that includes both current crowding and diffusional anisotropy effects is derived and incorporated into the well-known theoretical result that is valid for infinite-conductor domains and isotropic surface diffusivity. Rescaling the void migration velocity with the corresponding, numerically evaluated shape function results in a universally valid relationship for the migration speed as a function of void size. This result is important in understanding electromigration-induced void dynamics in metallic interconnect lines.

Microstructural characterization of XLPE electrical insulation in power cables: determination of void size distributions using TEM

In an effort to progress in our understanding of the ageing mechanisms of high voltage cables submitted to electrical and thermal stresses, we present a quantitative study of voids, the defects which are considered to be partly responsible for cable failure. We propose a method based on large data sets of transmission electron microscopy (TEM) observations of replicated samples allowing for the determination of void concentration distribution as a function of void size in the mesoscopic to microscopic range at any point in the cable insulation. A theory is also developed to calculate the effect of etching on the apparent size of the voids observed. We present the first results of this sort ever obtained on two industrial cables, one of which was aged in an AC field. Results clearly indicate that a much larger concentration of voids occur near the inner semiconductor compared to the bulk of the insulation, independently of ageing. An effect of ageing can also be seen near the inner semiconductor, resulting in an increase in the total void internal surface area and a slight shift of the concentration curve towards larger voids, with the peak moving from about 40 nm to about 50 nm.

Evolution and Distribution of Surface Voids Affecting Char Burning Rates at Diffusion-Limited Conditions

Research has indicated that the accurate calculation of char burning rates at diffusion-limited conditions requires consideration of the effects of voids (gaps in the continuous surface of burnable material that are deeper than their surface radius) on the particle burning area. Experimentally, void area distributions as a function of void size can be quantified using scanning electron microscopy and digital processing of quenched char particle images. Modeling void area distributions is problematic, even assuming voids behave as pores, because of initial surface imperfections and effects of combustion on surface morphology. This work examines the effects of factors that affect general pore formation for their effect on voids larger than 1 μm, such as heterogeneous combustion, devolatilization, and particle size and how these factors influence the calculation of diffusion limited burning rate from temperature and image data. Void distributions were predicted using an established pore distribution model, with and without the effects of pore combination. Results indicate that void distributions roughly follow expected pore behavior through devolatiltzation, but not after ignition, with void area fraction increasing with increasing coal volatile content and particle heating rate, but not significantly affected by oxygen concentration or initial particle size. Further, analytical pore models provide reasonable approximations for void distributions in the calculation of particle burning rates from temperature and image data.

Void Sizes in Granular Soils

In an earlier paper, the writer presented a simple stochastic model of the grain and pore structure in cohesionless soils and similar materials. Equations that very adequately predict the void ratio as a function of grain-size distribution were derived. In this technical note, the stochastic model is used to find the distribution of void volume as a function of void size (void-chord length). An evaluation of laboratory tests shows that both the bubbling pressure of a soil and the size of the largest grain that can pass through the voids of a soil in a base-filter compatibility test can be correlated with the calculated mean void chord of the soil.

Atomic relaxations around vacancy clusters in molybdenum and their effects on trapped-positron lifetime.

The relaxations of first- and second-nearest-neighbor shells of atoms around a monovacancy and around voids corresponding to the removal of 9, 15, 27, and 51 atoms in molybdenum have been calculated by minimizing the total energies with respect to atomic displacements. The energies are obtained by using the tight-binding scheme within the moments and continued-fraction formulation. The sign of the atomic displacements (inward or outward) of both the nearest and next-nearest neighbors varies with the size of the void. In addition, the displacements exhibit oscillations as a function of void size and do not appear to converge to atomic relaxations characteristic on surfaces even for the largest void studied. The relaxation of the first-nearest neighbor has a significant effect on the lifetime of positrons trapped in monovacancies, bringing theory to much better agreement with experiment. This effect, however, diminishes and becomes insignificant as voids grow in size.