Void Spacing Research Articles

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.

Microstructural evolution and mechanical response of micro-deformation diffusion bonding Ti-6Al-4V with designed interface morphology

This study explicates the microstructural evolution and mechanical response of the Ti-6Al-4 V joints diffusion-bonded with a micro-deformation less than 1%, assisted by pre-designed interface morphology. The interfaces composed of interfacial voids and bonded zones were developed, exhibiting varying bond rates. The interfacial voids evolved from valleys of bonding surfaces, and the bonded zones were derived from comparatively deformed ridges mainly depending on dynamic recrystallization, strain-induced migration of grain boundaries, and diffusion mechanism. The recrystallized α grains was generated due to the nucleation and rotation of sub-grains driven by pile-up of dislocations. Additionally, the diffusion of elements was significantly activated at the deformed zones (herein, referring to the bonded zones), promoting the metallurgical bonding of α / β phase interfaces. The formation of bonded zones supported for sound joining equivalent to the substrate in mechanical properties, confirmed by the void-free joint. Nevertheless, the mechanical properties of the joints were decreased when interfacial voids led to premature failure, and deteriorated more severely with narrowing void spacing. The concentration of stress and strain at void tips induced untimely initiation of cracks, and propagation guided by the trajectory of high stress. The interaction of stress field surrounding adjacent voids was enhanced under narrow spacing (less than 4 times of void length), leading to acceleration of crack initiation and propagation.

Entrained air and freeze-thaw durability of concrete incorporating nano-fibrillated cellulose (NFC)

NanoFibrillated Cellulose (NFC) has consistently proven effective at improving some key properties of cement-based materials. However, till date, the effects of the NFC on the freeze-thaw (F-T) durability of concrete has received little attention. This study aims to fill this gap by first evaluating the fresh, entrained air content of 0.65 and 0.40 water-cement ratio, Plain and Plain +0.1 % NFC concrete mixtures prepared with and without an Air Entrainment Admixture (AEA). Micro computed tomography scan (CT-Scan) was also utilized in investigating the effects of the NFC on the entrained air characteristics of hardened concrete specimens. Thereafter, water-saturation process, F-T durability via, changes in specimen mass, Relative Dynamic Modulus of Elasticity (RDME) were investigated, and strain accumulation was monitored until specimens failed or 300 F-T cycles were attained. Relative to Plain concrete mixtures, test results showed that entrained air content values of Plain +0.1 % NFC mixtures were lower, causing the effective void spacing to significantly increase. However, RDME and strain measurements indicated that F-T internal damage progression in NFC-modified concrete mixtures prepared without an AEA was considerably slower compared to corresponding Plain concrete mixtures. Moreover, the overall F-T performances of air-entrained, Plain and Plain +0.1 % NFC concrete specimens were comparable despite that the latter set of specimens had lower entrained air content, with wider entrained air void spacing. Besides impeding the saturation process of specimen, the NFC enhanced the strain capacity of concrete, and the significant contraction of specimen on exposure to cooling-temperatures was helpful in mitigating expansive F-T damage process. Therefore, for applications where strength reductions associated with air-entrained plain mixtures are undesirable, the NFC will be very beneficial for the production of high-strength and F-T durable concrete.

Study on the influence of fractal dimension and size effect of coarse aggregate on the frost resistance of hydraulic concrete

In cold regions, hydraulic concrete structures are exposed to harsh environmental conditions that greatly impact their durability and safety. The role of aggregates in influencing concrete performance is paramount. This study aims to investigate how the fractal distribution and size of aggregates affect the frost resistance of hydraulic concrete, with air void characteristics, mass loss rate, Elastic Modulus of dynamic, and strength serving as primary references. Two experiment series, fractal distribution influence and aggregate size influence of concrete frost resistance, were conducted to analyze the frost resistance of hydraulic concrete with different aggregates. Based on the fractal theory, four grading fractal distributions were utilized to fractalize aggregate gradation, aiming to investigate the influence of aggregate fractal dimension on the frost resistance of hydraulic concrete. Simultaneously, concrete specimens of fully graded aggregate and wet-screened aggregate were also constructed to simultaneous freeze-thaw cycle tests, the impact of aggregate size on concrete's frost resistance performance was also studied by analyzing the air void structure in the frost-resistant concrete specimens. Results indicate that the specimens exhibit varying frost resistance performance under different aggregate gradation fractals, ranking from strongest to weakest as follows: D=2.5, D=2.3, D=2.1, D=2.7, which is attributed to the differences of air void spacing factors. Increasing aggregate size leads to greater internal structural heterogeneity in concrete, resulting in an increase in defects and weak points. This causes microcracks to develop more rapidly in the transition zone of fully graded concrete during freeze-thaw cycles, leading to more severe damage. The findings of this study can serve as a fundamental scientific basis for the designing and constructing of hydraulic concrete structures in cold areas.

Dispersion and Spatial Distribution of Air Voids or Microspheres in Assessing Frost Resistance of Concrete

Abstract The standard spacing factor developed by Powers is typically used to evaluate the quality of the air void system in hardened concrete, but it does not always correlate with durability of the concrete. Several air void spacing equations, which are also applicable when polymeric microspheres are used in place of air entrainment, have been proposed because of the need for a more robust and comprehensive basis to evaluate the quality of the air void system. However, the spacing parameters provided by the various proposed equations, when used as sole measures in predicting the frost resistance of concrete, do not seem to do any better than the standard spacing factor. Dispersion and spatial distribution have been shown to be effective ways of describing air void or microsphere systems in hardened concrete because they have been quantified to establish criteria to assess the frost resistance of concrete. In this paper, dispersion and distribution factors are further elaborated upon to explain how they characterize zones that are protected by air voids or microspheres in the concrete. Criteria to assess the durability of concrete under rapid cycles of freezing and thawing based on the dispersion and distribution factors are linked to the exposure classes defined in the ACI 318 Code and in the recently proposed Unified Durability Guidance in ACI Committee Documents.

Investigating the Effects of Modified Interlayer Spacing within Mixed Metal Oxide Cathode Materials for Next-Generation Aqueous Rechargeable Zinc-Ion Batteries

Aqueous rechargeable zinc-ion batteries (ZIBs) are a promising addition to the current energy storage landscape, particularly supporting the decarbonization of the power sector as a low-cost, high safety alternative to lithium-ion batteries. Unfortunately, the relative infancy of ZIBs means that there are a limited number of reported cathode materials, and a divisive understanding of the operating principles for those which have been reported including Mn- and V-oxides. The large solvation shell of the working cation (Zn2+) imparts several design requirements for cathode material development, specifically the need for sufficient void space for Zn2+ intercalation, further limiting the materials which have been reported. Looking to other well-established battery chemistries, we considered the use of layered mixed metal oxides (MMOs) with Mn due to its known electrochemical activity within the operating voltage of aqueous ZIBs. We developed several MMO cathodes with tuned interlayer distance to achieve the larger void spacing capable of accommodating Zn2+. We investigated the impact of composition on the structural and electrochemical properties of 15+ different MMO materials. We determined that interlayer spacing plays critical role in electrochemical performance and that there is an optimal composition to provide enhanced specific capacity to the battery. Considering the narrow range of reported ZIBs cathodes, in this study we proposed several new materials that expand the scope of viable cathodes for next generation ZIBs and provides direction for future researchers to accelerate new material development for this technology.

Atomistic Simulations of Dislocation-Void Interactions in Concentrated Solid Solution Alloys

This paper investigates the interaction of edge dislocations with voids in concentrated solid solution alloys (CSAs) using atomistic simulations. The simulation setup consists of edge dislocations with different periodicity lengths and a periodic array of voids as obstacles to dislocation motion. The critical resolved shear stress (CRSS) for dislocation motion is determined by static simulations bracketing the applied shear stress. The results show that shorter dislocation lengths and the presence of voids increase the CRSS for dislocation motion. The dislocation–void interaction is found to follow an Orowan-like mechanism, where partial dislocation arms mutually annihilate each other to overcome the void. Solute strengthening produces a ‘friction stress’ that adds to the Orowan stress. At variance with classical theories of solute pinning, this stress must be considered a function of the dislocation line length, in line with the idea that geometrical constraints synergetically enhance the pinning action of solutes. Modifying the equation by Bacon, Kocks and Scattergood for void strengthening to account for the solute hardening in CSAs allows one to quantitatively predict the CRSS in the presence of voids and its dependency on void spacing. The predictions show good agreement with the simulation data without invoking any fit parameters.

Interaction of extended dislocations with nanovoid clusters

Voids of nanoscale dimensions in irradiated metals can act as obstacles to dislocation motion and cause strengthening. In this work, nanovoid strengthening and the influences of void size, void spacing and material properties, such as stacking fault energies, on dislocation bypass mechanisms are investigated using Phase Field Dislocation Dynamics, a three-dimensional mesoscale model that predicts the minimum energy pathway taken by discrete dislocations. A broad range of face centered cubic metals (copper, nickel, silver, rhodium, and platinum) and nanovoid sizes and spacings are treated, altogether spanning void size–to–dislocation stacking fault width ratios from less than unity to ten. Material γ-surfaces, calculated from ab initio methods, are input directly into the formulation. The analysis reveals that the critical bypass stress scales linearly with the linear void fraction, effective isotropic shear modulus, and ratio of the intrinsic to unstable stacking fault energies. With only a few exceptions, the critical stress is controlled by the stress required for the leading partial to impinge the voids (to move within range of the attractive image stress field of the void). When the void diameter is nearly an order of magnitude greater than the stacking fault width, the mechanism determining critical strength shifts to the stress for the dislocation to breakaway after partially cutting the void. This situation corresponds to that treated by line tension models and is realized here for Pt, with a sub-nanometer stacking fault width.

X-ray micro-tomographic imaging and modelling of saline ice properties in concrete frost salt scaling experiments

Frost salt scaling of concrete is related to cyclic freezing and melting of a few millimeter thick deicer solution on the surface of the concrete. It is almost absent when pure water is freezing and reaches a maximum at a so-called pessimum concentration that for NaCl is around 3%. Different mechanisms have been suggested to explain this pessimum and frost salt scaling in general, ranging from the transport of moisture and growth of ice within the pore space of concrete (“cryogenic suction”) to crack formation in the saline ice layer followed by spalling off the surface (“glue-spall”). Though in these theories the saline ice layer, that forms in concrete frost salt scaling experiments, plays a major role, so far little is known about its properties. We present a characterisation and an analysis of the microstructure of this saline ice layer by means of 3D X-ray microtomography. We found that the morphology of the saline ice is very similar to young, columnar sea ice, with lamellae of ice and brine oriented in the direction of freezing. On the basis of the microscopic 3D image data, we formulated percolation-based models of macroscopic properties (e.g., strength, thermal expansion coefficient, porosity metrics) relevant for different proposed frost salt scaling mechanisms. Model results and observations suggest that the ice growth velocity, direction and confinement, have a major impact on the pore structure of saline ice, thereby governing both mechanical and transport properties. These properties in turn are expected to affect proposed frost salt scaling mechanisms of concrete. The microstructure length scales in the ice-brine composite (lamellar spacing, pore width) are comparable to those for concrete (air void spacing and size), suggesting complex poro-mechanical interaction at the interface of concrete and saline ice. The results highlight the importance of studying saline ice properties to improve predictions of frost salt scaling processes.

Ductile failure and damage localization in Al6061‐T6 characterized by in situ X‐ray computed tomography and neural network segmentation

AbstractDamage initiation and localization in uniaxial tension tests of an Al6061‐T6 alloy are evaluated and quantified using in situ X‐ray computed tomography and a neural network segmentation strategy. This segmentation strategy offers significant advantages over traditional thresholding in quantifying microstructural and damage evolution metrics. Void nucleation was observed to occur throughout the deformation process, whereas void volume did not grow significantly until later stages of deformation. Localized analysis determined that void nucleation begins in and around the necked region during the early stages of deformation, whereas limited damage nucleation occurs outside of the neck until late stages of deformation. Lastly, inhomogeneities in void and particle spacing in the initial undeformed state of the material are observed to correlate well with the location of damage localization and necking during deformation. These results provide new insights into the ductile failure of Al alloys and how preexisting defects influence damage and rupture.

Fracture behavior and mechanical properties of Ti-6Al-4V joints diffusion-bonded with pre-designed interfacial voids

This study focuses on the effects of interfacial voids on the mechanical properties and fracture behavior of the diffusion-bonded Ti-6Al-4 V joints. The joints with regular interfacial voids were designed and developed at 850 °C for 20 min. The initiation and propagation of cracks were illustrated through an in-situ tensile test, and the evolution of stress-strain field around interfacial voids was revealed via finite element models. The preferred propagation path of cracks was the edge of the earliest plastic zone where the coupled stress field was concentrated between adjacent interfacial voids. Spacing and size of interfacial voids significantly affected stress concentration around the voids, leading to premature nucleation of cracks at the tips of interfacial voids. The influence of spacing on strength and plasticity of the joint followed power laws. The joint strength reached 95 % of that of the base material when the spacing of interfacial voids was relatively 4 times length of interfacial voids, and the plastic deformation of the joint occurred. The joint fractured prematurely with a remarkable decrease of the plasticity when the length of interfacial voids was beyond 50 μm, and the joint strength decreased.

Analytical investigation of the influence of various void shape and spacing on the load-bearing behavior of concrete hollow core slabs

Analytical investigation of the influence of various void shape and spacing on the load-bearing behavior of concrete hollow core slabs

Effect of Low Atmospheric Pressure on Bubble Stability of Air-Entrained Concrete

The effect of low atmospheric pressure of the environment on the air content and bubble stability of air-entrained concrete was investigated in Beijing and Lhasa. The results indicate that the reduction of atmospheric pressure can weaken the air-entraining capability of air-entraining agents (AEAs). The air content of fresh concrete decreased by 9%–39% when the atmospheric pressure dropped to 64 kPa. The bubble stability of concrete mixed at a low atmospheric pressure becomes worse. Within 50–55 min after mixing, the air content of concrete mixed at a low atmospheric pressure decreases greatly, and the void spacing factor increases obviously. The concrete mixed at a low atmospheric pressure will lose more air content when vibration time increases, leading to the decrease of air content and the increase of the spacing factor, which are more significant than the concrete mixed at normal atmospheric pressure. On the basis of the experiment results in this study, the type of AEAs must be carefully selected, and the vibration time must be strictly controlled to ensure that the air content of concrete will meet the design requirements in low atmospheric pressure areas.

Shape and Size of Particles Scaled from Concrete Surfaces during Salt Frost Testing and Rapid Freeze/thaw in Water

Abstract Thickness (T), Length (L), Width (W) and size distribution of scaled concrete particles in frost testing were measured. T (mm) increases with particle size surprisingly similarly for different concrete qualities and frost test methods. 2T/(L+W) reduces as function of size and is lowest for the largest particles of the salt scaling test: 0.1 – 0.15 but increases if large aggregate particles scale. Particle size distributions from salt frost testing peak for particles of 1-2 mm. The particles are flakier compared to particles from freeze/thaw in water which also have flatter size distribution no matter type of concrete or degree of damage. Scaling in water is not so efficiently reduced by air voids despite protecting very efficiently against internal damage and scaling in salt frost testing. Comparisons with T predicted by the glue spall model (≈3/4 × ice thickness) and the air void dependent (≈3× critical air void spacing) model proposed by Fagerlund are difficult due to the size dependent flake thickness. Image analysis could well describe shape. Further studies of concrete flake thickness scaled at varying thickness of ice layers are proposed.

Determining the air void efficiency of fresh concrete mixtures with the Sequential air method

The Sequential Air Method (SAM), AASHTO TP 118, is the only test that can quantify the air void volume and spacing in fresh concrete but using the results to design a concrete mixture can be challenging. This work introduces a new tool that uses the outputs from the SAM to determine how different ingredients or changes to the environment impact the volume and spacing of the air void system. This tool is known as the Efficiency Chart. The Efficiency Chart can help producers create more reliable and consistent air void systems that also meet the suggested freeze thaw requirements. The Efficiency Chart is made by using 227 diverse concrete mixtures to establish an upper and lower bound of performance. To show the usefulness of this method several examples are presented to show how different admixtures and cements impact the air void systems. Agreement is shown between the predictions of the Efficiency Chart and the results from a hardened air void analysis (ASTM C457). Because the SAM can evaluate fresh concrete, the concrete industry can use the Efficiency Chart to help design and troubleshoot the air void systems in their concrete mixtures.

Trans-scale multi-physics coupling finite element model of concrete during freezing and thawing

This paper presents a trans-scale finite element model based on hydraulic-thermal-mechanical coupling equations of porous medium to simulate the behavior of concrete during freezing and thawing. Unlike previous models that regard concrete as homogeneous material, this paper aims to establish a macro-size concrete model with detailed micro-structure, the aggregates (mm) and air voids (μm) are randomly generated by the Monte Carlo method, and the interfacial transition zones (μm) with random thickness are built around the aggregates. The capillary pores (nm) of concrete is expressed by the relationship between the percentage of frozen ice and the radius of capillary pore. The simulation results reveal the mechanism of air voids protecting the concrete from freezing and thawing damage, and the mechanical field shows the freezing and thawing damage occurs preferentially at the interfacial transition zone, because the stress concentration due to the irregular distribution of aggregates and water resistance of aggregates. The temperature boundary conditions were also varied to study the influence of the temperature change rate on hydrostatic pressure and volume stress. The effect of the cement paste's pore structure, including the spacing of air voids, on the ability of concrete to resist freezing and thawing is presented.

Impact of atomization gas on characteristics of austenitic stainless steel powder feedstocks for additive manufacturing

Given the complexity of the laser-material interactions prevalent in powder bed fusion additive manufacturing, the need for tight control of alloy composition in the metal powder feedstock is leading to the use of specific gases during atomization. These changes in atomization gas also impact powder flow and packing. In order to identify the magnitude of this impact, two nitrogen atomized and one argon atomized 316 L austenitic stainless steel powders with similar size distributions were characterized using traditional powder characterization tools and rotating drum and annular shear rheological tools. While the traditional characterization tools and particle size measurements did not differentiate between the powders, these rheological tools allowed connections between the particle morphologies and rheological properties and powder performance to be identified. In particular, the argon atomized powders displayed higher aspect ratios, which translate into more spherical morphologies, and improved flow, defined by lower avalanche angles, when tested in the rotating drum. On the other hand, these differences in flow properties were not captured in the corresponding basic flow and specific energy measurements made with the annular shear tools. Variations in the powder packing properties and internal powder porosity in the different powder lots decreased the powder mass and introduced increased uncertainty in the force and torque measurements. The void spacing between loosely packed powders was also measured and showed how changes in particle size distribution and morphology impacted both packing density and permeability. Larger void spacing produced higher permeability values, indicating greater gas flow through the loosely packed powder.

Interaction of Void Spacing and Material Size Effect on Inter-Void Flow Localization

Abstract The ductile fracture process in porous metals due to growth and coalescence of micron scale voids is affected not only by the imposed stress state but also by the distribution of the voids and the material size effect. The objective of this study is to understand the interaction of the inter-void spacing (or ligaments) and the resultant gradient-induced material size effect on void coalescence for a range of imposed stress states. To this end, three-dimensional finite element calculations of unit cell models with a discrete void embedded in a strain gradient-enhanced material matrix are performed. The calculations are carried out for a range of initial inter-void ligament sizes and imposed stress states characterized by fixed values of the stress triaxiality and the Lode parameter. Our results show that in the absence of strain gradient effects on the material response, decreasing the inter-void ligament size results in an increase in the propensity for void coalescence. However, in a strain gradient-enhanced material matrix, the strain gradients harden the material in the inter-void ligament and decrease the effect of inter-void ligament size on the propensity for void coalescence.

Image-based restoration of the concrete void system using 2D-to-3D unfolding technique

Hardened air void analysis provides essential information of concrete freeze–thaw durability based on the size and spacing of air voids in the material. As the physical freeze–thaw experiment is time-consuming and costly, the characteristics of concrete air voids are often deemed as a proxy of the freeze–thaw performance. This analysis is typically done by measuring the 2D air void intersections on polished samples, but the current interpretation of the 2D void characters does not accurately capture the 3D characteristic of the actual voids. To solve this problem, a 2D-to-3D unfolding technique from stereology can be used. However, the unfolding analysis is known to be sensitive to several factors, such as void population and size, along with a binning scheme, where improper unfolding can largely bias the prediction of the actual concrete void system. This study investigates the optimal strategy of unfolding analysis for concrete. The investigation is carried out on both idealized void systems to interrogate the influence of the critical factors individually and real concrete samples with varying levels of air entrainment to assess the concrete-specific impacts. The concrete void system is studied based on a stereological model emulating the intersected 3D air voids on the surface of polished concrete. The results highlight that, for unfolding concrete voids, logarithmic binning scheme is far more accurate to linear binning. The low unfolding error of the concrete samples indicates that the proposed methodology enables an accurate restoration of 3D void size distribution.

Exploring subtle features of yield surfaces of porous, ductile solids through unit cell simulations

A general computational technique for deriving macro yield surfaces from unit cells with a given microstructure has been proposed in a companion paper (Chouksey, M., Keralavarma, S. M., Basu, S., 2019, “Computational investigation into the role of localization on yield of a porous ductile solid,” Journal of the Mechanics and Physics of Solids, 130,pp. 141–164). Using this technique, macro yield surfaces for porous ductile solids, represented by cuboidal unit cells containing ellipsoidal voids, have been generated and compared with suitable analytical yield criteria. These yield surfaces exhibit vertex-like features when the principal directions of the macro stress coincides with the axes of the ellipsoidal void. In this work, we study the effects of void spacing and orientation with respect to the principal directions nα (α∈[1,3]) of the macro stress. Subtle changes in the yield surface are revealed when its traces are plotted on octahedral or meridional section planes in stress space. Further, the possibility of utilizing the computational framework to automatically generate complete macro yield surfaces by sampling the entire macro stress space, for a given microstructure, is demonstrated with examples where the space of applied macro stress states are limited by suitable assumptions.