Void Shape Research Articles

The analysis of damage mechanisms and vibration effects caused by cut blasting under various void shapes

The effect of the void shape on cut blasting is investigated by establishing a damage analysis model for a void using an improved calculation formula for stress on the wall of the void. Additionally, an optimization scheme is provided for the “square void cutting theoretical model.” The vibration effect of the rock mass outside the excavation area is simultaneously monitored, and its validity is substantiated through experimental and simulation-based verification. The findings indicate that the variation of q2sinθ over time aligns with the dynamic loading process of wall stress in holes. Under the influence of longitudinal waves, thin-walled circular damage occurs, and tensile effects from reflected waves are influenced by impedance. In a square void cutting model, two-stage stress waves cause tensile shear damage and inward collapse in the rock mass along hole walls. The explosive energy generated by square holes significantly contributes to fragmentation of rock masses. The circular empty-hole cutting model generates significant vibrations in central areas due to resistance. Vibration velocity in 45° direction for circular holes is lower than that for square voids outside cuts while vibration velocity remains equivalent between circular and square holes at 90° direction.

The role of secondary voids in the mechanism of ductile fracture at a crack tip

The mechanics and mechanisms of ductile fracture, ahead of a blunting crack tip, have been studied extensively. Several computational studies analyzing the effect of initial void volume fraction, void shape, void spatial distribution and the mode of loading (KI,KII etc.) on crack-void interaction and its consequence on the mechanism of fracture have been reported. The influence of small size secondary voids on the failure of ligament between the large primary voids and, hence, on fracture toughness has been analyzed using the Gurson-type homogenized models of ductile fracture. In the present work, the two populations of voids ahead of a crack tip are modeled discretely. A plane strain, central line cracked boundary layer model under small-scale yielding is considered. The role of initial shape and spatial distribution of secondary voids, matrix strain hardening and mode of imposed loading in the mechanism of ductile crack growth initiation and advance is analyzed in detail. For completeness sake, numerical calculations are also performed using a homogenized representation of the secondary voids. The results so obtained are then compared with the predictions based on discrete modeling of the secondary voids. Our numerical studies revealed that plastic flow localization resulting from a small initial volume fraction of favorably distributed secondary voids may alter the path of crack growth initiation and advance, thus, influencing the ductile fracture toughness.

Effects of nozzle geometry and fiber orientation on the tensile strength of 3D printed continuous fiber reinforced composites

In material extrusion (MEX) based 3D printing, inter-filament voids are intrinsic to printing process. The void orientation, volume and shape are affected by multiple factors including the nozzle shape, stacking sequence and printing direction. In this study, the adverse effects of the inter-filament voids on tensile properties and damage modes were investigated numerically on 3D printed acrylonitrile butadiene styrene-carbon fiber (ABS/CF) continuous fiber-reinforced composites (CFRCs). Uniaxial tensile simulations were performed considering various nozzle geometries (circular, square), fiber orientations (θ=0o,30o,45o,60o,90o) relative to loading direction, and a regular stacking sequence of extrudates. The extrudate cross-section was modeled either using elliptical or superelliptical extrudates deposited from a circular or square nozzle, respectively. Excellent agreement was seen when the simulated results were benchmarked against several published experimental and numerical work. Simulated results showed that changing the nozzle shape from circular to square improved the mechanical properties across all fiber angles by lowering the void content by 7−8% and increasing the ultimate tensile strength (σT) by 11−18%, tensile stiffness (ET) by 6−8%, and the tensile failure strains (ϵT,fail) by 1−11%. For superelliptical extrudates the number of observed damage modes also reduced, and this is due to a 37.2% and 58.2% improvement in the inter-filament and inter-layer bond lengths, respectively. Also, when fiber angle became increasingly off-axis to tensile load direction, the strengths, moduli, and failure strains reduced for both circular and square nozzles. The significance of using microstructure geometries and explicitly modeling inter-filament voids for simulating MEX printed CFRCs was highlighted by comparing these results with both analytical calculations and simulated results of homogeneous solid CFRC blocks without voids.

Void number counts as a cosmological probe for the large-scale structure

ABSTRACT Void number count (VNC) indicates the number of low-density regions in the large-scale structure (LSS) of the Universe, and we propose to use it as an effective cosmological probe. By generating the galaxy mock catalogue based on Jiutian simulations and considering the spectroscopic survey strategy and instrumental design of the China Space Station Telescope (CSST), which can reach a magnitude limit $\sim$23 AB mag and spectral resolution $R\gtrsim 200$ with a sky coverage of 17 500 deg2, we identify voids using the watershed algorithm without any assumption of void shape and obtain the mock void catalogue and data of the VNC in six redshift bins from $z=0.3$ to 1.3. We use the Markov chain Monte Carlo method to constrain the cosmological and VNC parameters. The void linear underdensity threshold $\delta _{\rm v}$ in the theoretical model is set to be a free parameter at a given redshift to fit the VNC data and explore their redshift evolution. We find that the VNC can correctly derive the cosmological information, and the constraint strength on the cosmological parameters is comparable to that from the void size function method, which can reach a few per cent level in the CSST full spectroscopic survey. This is because, since the VNC is not sensitive to void shape, the modified theoretical model can match the data better by integrating over void features, and more voids could be included in the VNC analysis by applying simpler selection criteria, which will improve the statistical significance. It indicates that the VNC can be an effective cosmological probe for exploring the LSS.

Effect of void geometry and magnetic anisotropy in controlling the vortex in sub-micron annular Permalloy disc

Ferromagnetic rings, particularly asymmetric Permalloy (Py) rings are recognized as promising configurations for spintronic devices, offering additional degrees of freedom for manipulating magnetic states, especially in vortex configurations. Through micromagnetic simulations, our study explores the impact on magnetization states and spin configuration concerning ring symmetry, aligning with the interest in controlling vortex states for information storage. We initially obtained zero-field spin configurations by varying ring thickness (t), observing a 360° domain wall in rings with t < 12 nm and bi-vortex wall in rings with t ∼36 nm during magnetization reversal. Notably, an extended stability of the global-vortex state was observed in rings with t > 36 nm, indicating the dominance of global-vortex nucleation in thick asymmetric rings during domain wall movement. We investigate the hysteresis loops and spin configurations by varying the in-plane and out-of-plane anisotropy values. Our findings reveal the presence of multiple vortex cores with different polarities and sense of rotations in the ring for the in-plane anisotropy ∼30 to ∼40 kJ m−3. Additionally, a global-vortex with two vortex cores was formed due to demagnetization energy. We analysed the energy profile of stable magnetization states for various t and anisotropy values. Interestingly, the shape of the hysteresis loop changes significantly for the disc containing different shapes of void. Circular and square-shaped geometries suggest that the bi-vortex state is a stable configuration during magnetization reversal in both cases. The study also indicates the stability of the vortex with a square-shaped void geometry up to a sufficiently large field. For the case of triangular-shaped voids, the global-vortex state was favored with even the small fields. The estimated spin canting angles are found to be correlated with the presence of vortex spin configurations. Overall, these results are important for the development of magnetization vortex-based spintronics devices.

Criterion for unhomogeneous yielding of porous materials

A criterion is developed for the unhomogeneous yielding of materials containing arbitrarily oriented ellipsoidal voids. The criterion is built upon classical estimates for pure pressure and pure shear. A data-driven approach is then followed to incorporate the effects of void shape and orientation. A large number of micromechanical unit cell results are used to calibrate the yield criterion. A key feature of the criterion is that it predicts a significant reduction of the effective shear yield strength due to mere void inclination, with the reduction increasing with the void dimension perpendicular to the shear. The coupling between tension and shear deformation results in an apparent rotation of the yield surface, which provides a sound micromechanical basis for predicting void closure in shear among other new features. Once supplemented with evolution equations of relevant internal parameters, the resulting constitutive formulation will enable ductile failure simulations heretofore impossible to carry out on a sound physical basis for general loading conditions.

Why cosmic voids matter: mitigation of baryonic physics

We utilize the Magneticum suite of state-of-the-art hydrodynamical, as well as dark-matter-only simulations to investigate the effects of baryonic physics on cosmic voids in the highest-resolution study of its kind. This includes the size, shape and inner density distributions of voids, as well as their radial density and velocity profiles traced by (sub-) halos, baryonic and cold dark matter particles. Our results reveal observationally insignificant effects that slightly increase with the inner densities of voids and are exclusively relevant on scales of only a few Mpc. Most notably, we identify deviations in the distributions of baryons and cold dark matter around halo-defined voids, relevant for weak lensing studies. In contrast, we find that voids identified in cold dark matter, as well as in halos of fixed tracer density exhibit nearly indistinguishable distributions and profiles between hydrodynamical and dark-matter-only simulations, consolidating the universality and robustness of the latter for comparisons of void statistics with observations in upcoming surveys. This corroborates that voids are the components of the cosmic web that are least affected by baryonic physics, further enhancing their use as cosmological probes.

Failure analysis of unidirectional CFRP composites with the coupled effects of initial fibre waviness and voids under longitudinal compression

This research delves into the failure mechanisms exhibited by unidirectional Carbon Fiber Reinforced Polymer (CFRP) composites under longitudinal compression, while considering the interplay of three types of manufacturing-induced defects: initial waviness of fibres, void volume fraction, and void size. The study employs 3D high-fidelity intact representative volume element (RVE) models, incorporating the initial waviness of fibres and voids based on Micro-CT imaging. A novel algorithm is proposed to generate more accurate 3D void shapes, departing from conventional circular or triangular approximations. The results highlight the substantial influence of the initial waviness angle on the reduction of predicted compressive stiffness and strength. The volume and size of voids play a significant role in determining damage initiation within the composites. The failure mechanisms of the composite under the coupled effects of initial waviness of fibres and voids are discussed, exhibiting reasonable agreement with experimental observations.

Numerical study of voids geometry effects on sandstone’s mesoscopic fracture Mechanism: Insights from acoustic emission and moment tensor inversion

In the field of rock mechanics, the study of void shape on the mechanical properties and fracture mechanisms of sandstone is crucial for the progression of rock engineering practices. In this study, PFC3D is utilized to conduct numerical simulations of uniaxial compression on intact rock and brittle rocks containing five different shapes of voids (including circular, inverted U-shaped, trapezoidal, rectangular, and square). By employing acoustic emission and moment tensor inversion techniques, the microscopic fracture mechanisms of rocks with different void shapes are revealed. Our key findings reveal: (1) The PFC3D’s Soft-Bond Model is adept at simulating acoustic emissions with high accuracy, facilitating an authentic reproduction of the uniaxial compression process in sandstone, including the nonlinear compaction stage. (2) The presence of hole defects markedly undermines the structural strength and deformability of the sandstone, with circular holes having minimal impact, whereas rectangular holes exert the most significant detriment. (3) A thorough analysis of fracture mechanisms demonstrates that specimens with hole defects primarily undergo initial tensile, remote cracks, V-shaped notch, and shear fractures, with shear fractures being pivotal in leading to specimen failure by rapidly evolving into macroscopic fractures that merge with V-shaped notches. (4) Acoustic Emission (AE) analysis highlights the distribution of tensile stress around the upper and lower extremities of the holes and shear stress along the left and right sidewalls, establishing shear stress as the dominant factor in the failure of specimens with hole defects.

Improving structural damage tolerance and fracture energy via bamboo-inspired void patterns

Bamboo has a functionally-graded microstructure that endows it with a combination of desirable properties, such as high failure strain, high toughness, and a low density. As a result, bamboo has been widely used in load-bearing structures. In this work, we study the use of bamboo-inspired void patterns to geometrically improve the failure properties of structures made from brittle polymers. We perform finite element analysis and experiments on 3D-printed structures to quantify the effect of the shape and spatial distribution of voids on the fracture behavior. The introduction of periodic, uniformly distributed voids in notched bend specimens leads to a 15-fold increase in the fracture energy relative to solid specimens. Adding a gradient to the pattern of voids leads to a cumulative 55-fold improvement in the fracture energy. Mechanistically, the individual voids result in crack blunting, which suppresses crack initiation, while neighboring voids redistribute stresses throughout the sample to enable large deformation before failure.

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.

A criterion for the coalescence of three-dimensional voids

A micromechanics-based yield criterion is developed to model void coalescence of three-dimensional voids under combined tension and shear. The analysis treats a cylindrical cell containing a coaxial cylindrical cavity, both having an elliptic cross section. Limit analysis is employed to first derive a criterion for homothetic cells. The model is then generalized to incorporate independent void spacing ratios (non-homothetic cells) The model predictions are assessed against finite-element based limit analysis on similar geometries. The effects of relative void spacing and void shape on effective yielding are investigated. In tension, the results indicate an increase in the coalescence stress with increasing in-plane anisotropy for both homothetic and non-homothetic cells. The new criterion is chiefly motivated by modeling shear failure. The extent to which the shear limit load reduces when shearing perpendicular to the largest transverse void dimension, as compared with shearing parallel to it, is discussed.

Experimental and numerical evaluation of the influence of voids on sound absorption behaviors of 3D printed continuous flax fiber reinforced PLA composites

This study aims to quantitatively analyze the effects of voids on sound absorption properties of 3D printed continuous flax fiber reinforced PLA composites (CFFRCs). Three kinds of flax yarns with different linear density were employed to prepare CFFRCs via 3D printing technology. The sound absorption performances of these composites were measured using the impedance tube based on the two-microphone transfer function method. The microstructure morphologies including cross-sections of flax yarns, voids shape and distributions of the composites were observed via ultra-depth microscope and micro-computed tomography to reconstruct the exact structures in simulation. Mercury intrusion porosimetry was applied to measure the voids dimensions of CFFRCs. The influence of voids on sound absorption mechanisms of CFFRCs were revealed based on thermoviscous acoustics theory by conducting the simulation in COMSOL software. The experimental results demonstrated that CFFRCs exhibited excellent sound absorption coefficients (close to 1) within the frequency range of 150–350 Hz and 350–550 Hz, resulting from the voids inside and between the flax yarns respectively. With the increase of linear density (diameter of the yarn), the contents of voids inside and between the flax yarns both increased. The dimensions of voids inside the flax yarns improved while those between flax yarns remained unchanged. The existence of the voids between the flax yarns resulted in a decrease in the sound absorption coefficient of CFFRCs, while more voids inside flax yarns led to the increase of the sound absorption frequency. Numerical results indicated that voids between the flax yarns contributed to a more uniform change in sound speed, reducing sound absorption performance. Whereas, voids inside the flax yarns could improve viscous friction of soundwaves due to narrow structures, enhancing sound absorption capabilities. This study is anticipated to provide a guidance for the design of integration of structure and function of 3D printed CFFRCs.

In situ growth and shrinkage of coated voids in aluminium

Voids can be detrimental to the mechanical and electrical properties of materials but may also find applications in catalysis and plasmonics. Key to the performance of materials containing voids are the sizes and morphologies of the voids, which can be tuned by heat treatment. The present work investigates the morphological evolution of voids, with solute segregation at their surfaces, in an aluminium‑copper‑tin alloy during in situ heating in a transmission electron microscope (TEM). These voids exhibited complex morphological changes that included growth or shrinkage, in contrast to voids in pure Al, which all shrank and disappeared (as reported in an earlier study). Without electron irradiation, the voids never grew. Nearly one fourth of the voids grew under certain heating and electron irradiation conditions, showing distinct growth stages. Growth and shrinkage of the voids both occurred primarily along the surface of the Sn particles to which they were attached. The voids exhibited faceting as they grew and gained morphological isotropy while they shrank. The growth and shrinkage fronts were both found to be primarily the curved surfaces and not the facets at the void surfaces. Growth followed by shrinkage led to a well-defined rounded triangular shape, in projection, with smooth boundaries. This work is, to the best of our knowledge, the first to characterise the growth of nanoscale voids in aluminium using in situ heating TEM. The dual effect of heating and electron irradiation could be utilised to switch the voids between growth and shrinkage to manipulate the void size and shape. This work provides useful insights into tuning void morphologies in the development of advanced materials such as for applications in engineering, catalysis and plasmonics.

Porous Crystalline Organic Cages Made by Design

AbstractShape‐persistent organic cages are an intriguing class of molecular porous materials. Through hierarchical molecular design, size and shape of the intrinsic molecular voids are controlled by dynamic covalent chemistry, while pore structure and topology are governed by noncovalent alignment in the solid state. However, the predictable and reliable crystallization of organic cages is still challenging since long‐range superstructures are solely based on weak and rather unidirectional supramolecular interactions. In this tutorial review, we provide a general classification of porous solid‐state materials and discuss specific design principles regarding the dynamic covalent reactions, the small‐molecule building blocks and solid‐state engineering. Furthermore, we introduce the most important analytical techniques for porous materials with a special focus on organic cages.

The effect of mechanical compaction on the soil water retention curve: Insights from a rapid image analysis of micro-CT scanning

Soil hydrological and agricultural properties are highly affected by the soil water retention characteristics, which are closely related to the void size distribution and structure of the soil. Agricultural lands are often faced with the challenge of soil compaction, which alters the size, shape, connectivity, and morphology of soil voids. To determine the water retention curve and other hydrological and agricultural functions of un-compacted and compacted sandy soils, we used micro-CT techniques and image analysis procedures in both two and three dimensions. We found that these techniques were reliable, as they were validated against physical measurements and empirical physically-based models, and provided a relatively simple and fast way to characterize the key features of soil hydrological and agricultural properties. The findings highlight the impact of compaction on the soil void size distribution, resulting in increased water holding capacity, greater water availability for root uptake, and reduced hydraulic conductivity. We also discussed the differences between the two and three-dimensional analyses, highlighting the better ability to characterize soil hydrological and agricultural functions and soil water retention curve using the three-dimensional image analysis approach.

The impact of initial fabric anisotropy on cyclic liquefaction behavior with polygonal particles using the discrete element method (DEM)

Liquefaction is one of the most significant phenomena that can occur in soil during an earthquake. The destructive effects of this phenomenon on earth structures have captured the attention of many geotechnical engineers. Additionally, the gradual increase in pore water pressure during the cyclic loading induced by the propagation of earthquake waves, known as cyclic liquefaction, is a crucial factor that might lead to the complete loss of shear strength in soils. A better understanding of cyclic liquefaction is essential for improving earthquake hazard analysis and mitigating structural damage. Factors influencing liquefaction behavior include particle size, particle grading, and soil fabric. By “soil fabric,” we refer to the arrangement and positioning of particles with each other, particle shape, and the shape of voids among particles. This research aims to focus on the effects of fabric anisotropy on cyclic liquefaction of granular soils with angular particles. To carry out this investigation, the discrete element method has been employed. In the discrete element method, the geometry of particles and, generally, the soil fabric can be considered. In this research, specimens with varying particle orientation angles were produced and subjected to cyclic loading tests under undrained conditions. By examining the stress paths of specimens during cyclic loading, it is observed that the initial fabric and inherent anisotropy significantly influence the behavior of the specimens. Inherent anisotropy leads to varying numbers of cycles required for the initial liquefaction of each specimen. Furthermore, it is observed that as the particle orientation angle increases, the localization of axial strains shifts from tensile to compressive directions. The effect of inherent anisotropy plays a substantial role in the initial liquefaction (ru = 1). If the liquefaction of specimens is of interest at lower values of ru, the effect of inherent anisotropy can be disregarded.

Modeling vacancy-induced porosity in compositionally-graded complex alloys

A phase-field model of the void evolution is developed to investigate the vacancy-induced Kirkendall porosity within diffusion couples under isothermal annealing conditions. This model encapsulates a comprehensive computational framework for multicomponent diffusion, non-equilibrium vacancy diffusion, voids nucleation, and growth — integrating considerations for surface anisotropy and morphological instability. This novel thermodynamically consistent methodology combines the phase-field model with the vacancy diffusion model and uses thermodynamic and atomic mobility parameters defined by CALPHAD approach. The generalized nature of the method enables us to include both non-equilibrium and equilibrium vacancies, covering all cases of non-ideal/ideal sinks and sources for vacancies, whether at dislocations or void surfaces. Moreover, the model can deal with compositionally complex alloys such as Ni-based superalloys. Along with the full model, a fast variant is also suggested, providing long-time simulations at the experimentally relevant time and space scales valuable for both academic and industrial contexts. The model’s efficacy was demonstrated through precise simulation of voids evolution in a model AlCoCrTa/Ni diffusion couple, mirroring the experimental outcomes observed in the CMSX-10/Ni diffusion couple at 1525 K after 192 h of annealing. This encompassed accurate replication of diffusion profiles and tomographic analysis of voids. A very good agreement with the experimental data was observed, particularly in the distribution of pore volume-fractions and the delineation of void shapes.

The void characteristics of cement emulsified bitumen mixture under microwave heating by X-ray computed tomography

Excessive void content is an essential reason for the poor road performance of cement emulsified bitumen mixture (CEBM), while incorporating steel slag with high microwave responsiveness into CEBM and followed by microwave heating may be an effective method to reduce void content. To verify this hypothesis, this paper investigated the effect of microwave heating on the void characteristics of CEBM using X-ray computed tomography. The study mainly focused on the distribution characteristics of different-sized voids, the distribution uniformity of voids, and the shape characteristics of voids. The results revealed that the number of different-sized voids decreased significantly after microwave heating, especially the number of small-sized voids decreased the most. The reduction in void number improved the distribution uniformity of longitudinal and radial voids. However, it reduced the distribution uniformity of voids between the inner and outer sections of the specimen. Through the analysis of aggregate movement characteristics, it was found that the increase in the separation degree of inner and outer voids was due to the larger-sized aggregates being more efficiently distributed on the outer section of the specimen. Additionally, microwave heating reduced the complexity of void shapes. The reduction of void number and the improvement of void characteristics by microwave heating are expected to enhance the structural durability of CEBM, thereby improving its road performance.

Elastic properties and compressive mechanical behaviour of closed-cell porous materials: Effect of microstructural morphology

This paper studies the effect of different combinations of morphological parameters of porous closed-cell materials on their elastic properties and mechanical behaviour. Three-dimensional representative volumes of porous media with different polyhedral void shapes are investigated, considering variation of statistical realisations of morphological features, such as shape, size and distribution of pores. Description of morphology of each investigated representative volume is formalized using second- and fourth-order correlation functions. The effective properties of representative volumes are calculated with finite-element analysis. Additionally, samples of the studied models were additively manufactured with polystyrene, using fused filament fabrication (FFF/FDM) 3D-printing technique, and subjected to compression. Experimental results for elastic mechanical properties and distributions of strain fields on the surface of the samples, obtained with micro-DIC (digital image correlation), are compared with results of numerical finite-element computations. This is accompanied by analysis of internal-stress distributions to assess the mechanical state of the structures. Patterns and trends observed in mechanical responses of porous materials depending on their different morphological parameters are outlined and discussed.