Non-uniform Void Distribution Research Articles

Temperature-dependent voids and their impact on SMA surface course permeability

This study investigates the water permeability characteristics of newly constructed Stone Mastic Asphalt (SMA) surface course, with a specific focus on the influence of connected voids arising from the compaction temperature during pavement construction. On-site evaluation of the permeability coefficient was performed, followed by core sample extraction from the same locations to investigate the correlation between the permeability coefficient and porosity. Industrial CT scanning was used to identify and separate void regions in the core samples. Three-dimensional digital reconstruction techniques were employed to analyze the morphology and spatial distribution of voids within the core. The connectivity of voids was assessed, providing insights into water infiltration pathways within the SMA course. Additionally, finite element simulation of the pavement temperature field was conducted to investigate the spatially differentiated distribution of voids within the SMA course.The findings reveal that approximately 38.3% of the voids are concentrated within a 1 cm depth below the top surface of the 4 cm-thick SMA course. The aggregation of voids enhances the likelihood of interconnection, facilitating water seepage. Water infiltrates through the open voids on the top surface and flows vertically and horizontally along the interconnected pathways. Notably, at a depth of approximately 2.5 cm, the flow transitions to horizontal spreading, aligning with the primary distribution interval of interconnected voids. The non-uniform distribution of voids is primarily influenced by the compaction temperature. The top and bottom portions exhibit higher void percentages, while the middle portion shows relatively fewer voids, consistent with the observed compaction temperature pattern.

Extrusion-based 3D printing concrete with coarse aggregate: Printability and direction-dependent mechanical performance

Concrete with coarse aggregate in the 3D concrete printing (3DCP) has broad prospects for high strength, low cost and shrinkage. In this study, an extrusion-based 3D printer was designed and utilized to print concrete with the largest aggregate size of 20 mm. Printable concrete with coarse aggregate was designed by different volume ratios of cement to aggregate (C/A). Then the effect of C/A on the printability and direction-dependent mechanical performance was investigated. X-ray micro-computed tomography (X-CT) was used to detect and analyze the voids distribution characteristics of printed specimens. Scanning electron microscope (SEM) investigations of microstructure at the interlayer area were conducted. Results indicated that the initial flowability of printable concrete should be within 178–200 mm, and the recommended printable C/A was within 0.35–0.60. The decrease of C/A improved the maximum printing height and mechanical performance but weakened the shape-stability of the multi-layer structure. X-CT results indicated that reducing excess slurry content caused by the decline of C/A decreased the compactness of the printed structure. The compressive strength and flexural strength of 3D printed specimens showed a direction-dependent characteristic, mainly related to the non-uniform distribution of voids revealed by X-CT. SEM images revealed the “micro-bridging” morphology in the interlayer area and proved that there were carbonation and structural weakening problems at the surface and surrounding of this area.

Two-step heating transient liquid phase bonding of Inconel 738LC

The high-temperature short-time heating step was followed by the low-temperature isothermal solidification step to join IN-738LC superalloy. The shorter bonding time can be applied in comparison to the conventional transient liquid phase process. A dendritic-cell like initial interface was observed which is different from a planar interface of conventional TLP bonds. This led to non-uniform distribution of voids along the joint. By completion of the isothermal solidification, quantity and size of the voids were decreased. A homogenization heat treatment produced the microstructure similar to that of the base metal.

Effect of void cluster on ductile failure evolution

The behavior of a non-uniform void distribution in a ductile material is investigated by using a cell model analysis to study a material with a periodic pattern of void clusters. The special clusters considered consist of a number of uniformly spaced voids located along a plane perpendicular to the maximum principal tensile stress. A plane strain approximation is used, where the voids are parallel cylindrical holes. Clusters with different numbers of voids are compared with the growth of a single void, such that the total initial volume of the voids, and thus also the void volume fractions, are the same for the clusters and the single void. In the comparison it is essential that local void coalescence inside the clusters is accounted for, since this allows for considering the rate of growth of the single larger void that results from coalescence in the cluster. To obtain a parametric understanding, different transverse stresses on the unit cell are considered to see the influence of different levels of stress triaxiality. Also considered are different initial ratios of the void spacing to the void radius inside the clusters. And results are shown for different levels of strain hardening in the material.

Analysis of void formation in thermoplastic composites during resistance welding

The process-induced voids during resistance welding of glass fabric-reinforced polyetherimide was investigated. The mechanisms of void formation in adherends, in particular, the residual volatile-induced voids and the fibre de-compaction-induced voids, were analysed. Due to the non-uniform temperature and stress distributions in the joints during welding, a non-uniform void distribution was observed in the joints with more voids generated in the middle of the joints than at the edges. Welding temperature and pressure were shown to have a large influence on void formation. Increasing of welding pressure was shown to effectively reduce the voids, while the residual moisture-induced voids were found more difficult to be eliminated than the fibre de-compaction-induced voids.

Calibration-free quantification of interior properties of porous media with x-ray computed tomography

A method is presented for interpreting the values of x-ray attenuation coefficients reconstructed in computed tomography of porous media, while overcoming the ambiguity caused by the multichromatic nature of x-rays, dilution by void, and material heterogeneity. The method enables determination of porosity without relying on calibration or image segmentation or thresholding to discriminate pores from solid material. It distinguishes between solution-accessible and inaccessible pores, and provides the spatial and frequency distributions of solid-matrix material in a heterogeneous medium. This is accomplished by matching an image of a sample saturated with a contrast solution with that saturated with a transparent solution. Voxels occupied with solid-material and inaccessible pores are identified by the fact that they maintain the same location and image attributes in both images, with voxels containing inaccessible pores appearing empty in both images. Fully porous and accessible voxels exhibit the maximum contrast, while the rest are porous voxels containing mixtures of pore solutions and solid. This matching process is performed with an image registration computer code, and image processing software that requires only simple subtraction and multiplication (scaling) processes. The process is demonstrated in dolomite (non-uniform void distribution, homogeneous solid matrix) and sandstone (nearly uniform void distribution, heterogeneous solid matrix) samples, and its overall performance is shown to compare favorably with a method based on calibration and thresholding.

The Discrete Boundary Resistance method for thermal analysis of solid-state circuits and devices

This paper presents a method developed for determining temperature distribution in a semi-analytical way within tri-dimensional solid-state circuits and packaged devices in steady state conditions. The method is an efficient route to investigate large ranging sized structures with an arbitrary complex layout composed of multiple material layers and localized heat sources. The method, called the Discrete Boundary Resistance (DBR), consists in decomposing the structure into layers of different sizes to develop the temperature solution as a Double Fourier Series after subdividing the contact boundaries into discrete elements. The solution is expressed as a function of thermal resistance attached to the contact boundaries connected to a temperature reference. The performance of the method has been studied in regards with a three-dimensional device involving a non-uniform distribution of voids between layers. Computational time was found to be shorter than ones achieved with the Finite Element method.

Bounds and estimates for the effective yield surface of porous media with a uniform or a nonuniform distribution of voids

This paper aims at studying the effects of a nonuniform distribution of voids on the macroscopic yield response of porous media with a rigid-perfectly plastic matrix. For this purpose, a semi-analytical model, recently proposed by Bilger et al. [Bilger, N., Auslender, F., Bornert, M., Masson, R., 2002. New bounds and estimates for porous media with rigid perfectly plastic matrix. C. R. Mecanique 330, 127–132], is extended to more general situations where the local porosity can fluctuate. The microstructure is described by a generalized Hashin-type assemblage of hollow spheres and the distribution of the local porosity is obtained from a three-dimensional simulated microstructure. The matrix layer around the voids is discretized into concentric sub-layers so as to take better into account the plasticity gradient along the radial direction. Classical homogenization techniques then provide new self-consistent estimates and upper bounds for the macroscopic yield surface. These results are compared first to the predictions of the Gurson model and its extensions and then to numerical results derived from three-dimensional Fast Fourier Transform (FFT) calculations carried out with the same material porosity distribution. A good agreement is obtained with the three-dimensional FFT calculations and with Gurson–Tvergaard's predictions even for high triaxiality and without fitting any parameter. Nevertheless, when the heterogeneous distribution of voids tends to form clusters, the proposed model fails to capture the properties of the macroscopic yield surface for large triaxiality factors.

Effects of pressure-sensitivity and plastic dilatancy on void growth and interaction

Hydrostatic stress can affect the non-elastic deformation and flow stress of polymeric materials and certain metallic alloys. This sensitivity to hydrostatic stress can also influence the fracture toughness of ductile materials, which fail by void growth and coalescence. These materials typically contain a non-uniform distribution of voids of varying size-scales and void shapes. In this work, the effects of void shape and microvoid interaction in pressure-sensitive materials are examined via a two-prong approach: (i) an axisymmetric unit-cell containing a single ellipsoidal void and (ii) a plane-strain unit-cell consisting of a single large void and a population of discrete microvoids. The representative material volume in both cases is subjected to physical stress states similar to highly stressed regions ahead of a crack. Results show that oblate voids and microvoid cavitation can severely reduce the critical stress of the material. These effects can be compounded under high levels of pressure-sensitivity. In some cases, the critical stress responsible for rapid void growth is reduced to levels comparable to the yield strength of the material. The contribution of void shape and pressure-sensitivity to the thermal- and moisture-induced voiding phenomenon in IC packages is also discussed.

Effect of a nonuniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis

This study investigates the overall and local response of porous media composed of a perfectly plastic matrix weakened by stress-free voids. Attention is focused on the specific role played by porosity fluctuations inside a representative volume element. To this end, numerical simulations using the Fast Fourier Transform (FFT) are performed on different classes of microstructure corresponding to different spatial distributions of voids. Three types of microstructures are investigated: random microstructures with no void clustering, microstructures with a connected cluster of voids and microstructures with disconnected void clusters. These numerical simulations show that the porosity fluctuations can have a strong effect on the overall yield surface of porous materials. Random microstructures without clusters and microstructures with a connected cluster are the hardest and the softest configurations, respectively, whereas microstructures with disconnected clusters lead to intermediate responses. At a more local scale, the salient feature of the fields is the tendency for the strain fields to concentrate in specific bands. Finally, an image analysis tool is proposed for the statistical characterization of the porosity distribution. It relies on the distribution of the ‘distance function’, the width of which increases when clusters are present. An additional connectedness analysis allows us to discriminate between clustered microstructures.

The use of X-ray computer tomography to investigate particulate interactions within opencast coal mine backfills

Restoration of opencast coal sites frequently involves the controlled compaction of heterogeneous arisings, and accurate prediction of the settlements associated with such backfill is difficult. Attention has previously focussed on improving the specifications used to control backfilling as a way of both reducing the magnitude of the settlements and improving their predictability. However, there still exists a large degree of uncertainty about the fundamental particulate interactions that occur within a fill. The range of mechanisms previously considered to be influential on creep behaviour is described. A current research programme is investigating the use of X-ray computer tomography (CT) as a means of nondestructively observing particle interactions during settlement, in conjunction with both long-term creep tests and short-term compressibility tests. The principles of this radiographic technique, which is relatively new to geotechnical engineering, are described, and findings are presented that illustrate the potential of the method. Interim findings indicate that large particles are distributed on an apparently random basis within a fill, and the nonuniform distribution of voids is clearly demonstrated. Moreover, the results presented conflict to some degree with the general consensus of opinion that particle crushing is a major mechanism in the settlement process. Rather, local collapse into small voids left by compaction, and relative sliding and rotation of particles, seem to be the dominant factors for a range of compaction efforts. Particle splitting is discernible on some sections, but this mechanism appears to be less significant than others. Research is continuing into the time dependency of the observed mechanisms, the effects of moisture content changes and the effects of heterogeneous initial particle strengths.

Ductile fracture of materials with high void volumefraction

In the present paper, axisymmetric cell models containing one or two voids and athree-dimensional cell model containing two voids have been used to investigate void size andspacing effect on the ductile fracture in materials with high initial void volume fraction. They areperformed for round smooth and round notched specimens under uniaxial tension. The examplematerial used for comparison is a nodular cast iron material GGG-40 with initial void volumefraction of 7.7%. The parameters considered in this paper are void size and shape foraxisymmetric cell models containing a single void, and void distribution pattern foraxisymmetric and 3D cell models containing two voids of different sizes. The results obtainedfrom these cell models by using FEM calculations are compared with the Gurson model, theGurson–Tvergaard–Needleman model, the Rice–Tracey model and the modified Rice–Traceymodel. It can be stated that the influence of void size and void spacing on the growth in volumeof voids is very large, and it is dependent on the distribution of voids. Using non-uniform voiddistribution, the results of axisymmetric cell models can explain how a void can grow in anunstable state under very low stress triaxiality at very small strain as observed in experiments.Calculations using cell models containing two voids give very different results about the stableand unstable growth of voids which are strongly dependent on the configuration of cell model.

Influence of void nucleation and growth on deformation localization in tensile sheet specimen

The deformation localization in a tensile sheet specimen is analyzed based on the lower bound constitutive equations for porous materials proposed by the present author. The non-uniform void distribution effect is characterized by the initial imperfection band model. Emphasis is given to the influence of the microscopic damage evolution on the localization mode and the value of critical strain. These analyses are then applied to predict the strain to localization and the instability band orientation of a tensile sheet specimen of AISI4340 steel. Good results are obtained.

均質性を仮定した気液２相流中の翼に及ぼすボイド率分布の理論効果

Reactor coolant pump performance under two-phase flow condition has been recognized to be an important area of concern in nuclear reactor safety analysis. Nonuniform void distribution at the inlet of such a pump due to the suction pipe bend can have a significant effect on the impeller blade characteristics.From such circumstances, this paper aims firstly to propose an analytical method of solution for the two dimensional thin hydrofoil placed in liquid-gas two-phase flow assumed to be incompressible and homogeneous, and secondly to clarify the effect of void fraction distribution, which exponentially changes in the direction normal to free stream, on the hydrodynamic characteristics of hydrofoil.

Formability of sheet metal with heterogeneous damage

During sheet metal forming operations, internal damage occurs as a result of nucleation, growth and coalescence of cavities around particles, inclusions or second phase. In this work, this phenomenon is experimentally studied by relative density change measurements and scanning electron microscope observations in a dual-phase steel sheet. It is observed that the distribution of cavities is not homogeneous. A model of plastic flow localization is proposed taking account of a non-uniform void distribution. The results show a substantial reduction in the formability of the sheet as well as anisotropic effects due to the heterogeneous distribution of voids.

Finite elements in non-associated plasticity—axisymmetric necking in void-containing materials

Numerical procedures for the solution of large strain non-associated elasto-plasticity problems by the finite element method are presented. Both the Cartesian and natural finite element formulations are discussed in detail. As an example of the theory of plasticity without normality rule, a plasticity of void-containing metals is considered. The paper closes with a numerical study of necking in an axisymmetric specimen with initial imperfections resulting from a non-uniform distribution of voids.

Hindrance of Grain Growth in Al2O3 by ZrO2 Inclusions.

Alumina and Al2O3/ZrO2 (1 to 10 vol%) composite powders were mixed and consolidated by a colloidal method, sintered to >98% theoretical density at 1550°C, and subsequently heat‐treated at temperatures up to 1700°C for grain‐size measurements. Within the temperature range studied, the ZrO2 inclusions exhibited sufficient self‐diffusion to move with the Al2O3 4‐grain junctions during grain growth. Growth of the ZrO2, inclusions occurred by coalescence. The inclusions exerted a dragging force at the 4‐grain junctions to limit grain growth. Abnormal grain growth occurred when the inclusion distribution was not sufficiently uniform to hinder the growth of all Al2O3 grains. This condition was observed for compositions containing ≤2.5 vol% ZrO2, where the inclusions did not fill all 4‐grain junctions. Exaggerated grains consumed both neighboring grains and ZrO2, inclusions. Grain‐growth control (no abnormal grain growth) was achieved when a majority (or all) 4‐grain junctions contained a ZrO2 inclusion, viz., for compositions containing ≥5 vol% ZrO2. For this condition, the grain size was inversely proportional to the volume fraction of the inclusions. Since the ZrO2 inclusions mimic voids in all ways except that they do not disappear, it is hypothesized that abnormal grain growth in single‐phase materials is a result of a nonuniform distribution of voids during the last stage of sintering.

Plastic flow localization due to non-uniform void distribution

I nfinite band calculations indicate that the process of flow localization in voided solids is highly sensitive to non-uniformity in void distribution. In this paper, a model is proposed for an elastic-plastic solid with an excess of voids in a disk-shaped cluster embedded in a uniform background distribution. The model is used to study the effect of a void cluster on plastic flow localization. Substantial reductions in ductility due to nonuniformity only occur for quite large clusters when the triaxiality of the overall stresses is low, as in uniaxial tension. At higher stress triaxialities, a small cluster can be severely deleterious.

Effect of helium on void swelling in molybdenum

Simultaneous irradiation of molybdenum with helium and heavy ions (Ta 3+) using a dual beam facility resulted in continued void nucleation in molybdenum to high dose levels, but the added helium had no measurable effect on the void swelling or swelling rate when compared with results for heavy ion irradiation without helium. Pretreatment by neutron irradiation or preinjection with helium resulted in no significant microstructural changes compared to no pretreatment. Also the temperature dependence of swelling was essentially unchanged when helium was added to the irradiation. The lack of a strong helium effect was attributed to the high inherent void nucleation rate in molybdenum. The overall swelling rate was similar to that observed for neutron irradiation and correlated well with the microstructural features that were observed. At the highest temperature and dose (1475 K and 40 dpa), simultaneous helium and heavy ion irradiation did result in a very nonuniform void distribution; thus, helium may have a greater effect on the microstructure at temperatures above those reported here.

Recovery capability of multifilamentary superconductors with non-uniform void distribution

The effects of several abnormal conditions resulting from a possible non-uniform void distribution in a multifilamentary and cabled superconductor on the cryogenic recovery capability of a triplex, a seven strand bundle and a 19 strand bundle were studied. For a triplex, if only one of the three strands was cooled, the maximum recoverable initial normal temperature is reduced by 1/3 of the value for the nominal case in which all the three strands are cooled equally. If the outer six strands of a seven strand bundle were cooled and the center one was not cooled, the recovery capability of this bundle is just slightly below that of the nominal triplex. If only the outer 12 strands of a 19 strand bundle were cooled, the bundle would not recover once it is driven normal. The effects of the cold and stagnant helium located in the space between the strands and of the insulation thickness are small.