Fabrication, Microstructural Characterisation and Mechanical Properties of Glass Compacts Containing Controlled Porosity of Spheroidal Shape

Addition of hollow glass microspheres to a glass powder and densification of the mixture by hot-pressing is shown to be an attractive technique to fabricate porous glass compacts with isolated porosity of controlled shape. The microspheres are deformed in viscous state under the uniaxial pressure during matrix densification, leading to spheroidal pores dispersed in the glass matrix. By changing the hot-pressing parameters, it is possible to manipulate the shape of the pores, i.e., to change their axial ratio. Pore axial ratios between 1 and 0.1 were obtained, with porosity volume fractions of up to 0.35. The mechanical properties of the porous glass compacts (Young's modulus and flexure strength) were determined and the influence of pore content, shape and orientation on the measured property values was discussed. It was observed that pores acted as fracture origins. The fabricated porous materials, containing spheroidal pores of well-defined shape and orientation, are shown to be very useful to test the validity and prediction capability of theoretical models. Other possible application areas of these porous materials with closed, isolated pores are discussed.     

Failure Variability in Porous Glasses: Stress Interactions,Crack Orientation,and Crack Size Distributions

Fracture behavior of porous glass is investigated through a combined finite element–fracture mechanics approach. In contrast to earlier studies, here, simulations embody flaw size distributions in addition to pore–pore stress interactions and crack orientation along pore surfaces. Fracture strength of porous glass shows a steep decrease up to 20% porosity and then levels off due to interacting pores. Weibull modulus varies because of the decreased probability of interactions in microstructures containing less than 2% porosity or the smallest pore diameter =48  μm. Weibull modulus strongly depends on crack size distributions for porosity less than 2% and pore–pore stress interactions for porosity greater than 5%.     

Mechanical properties of porous ceramics in compression: On the transition between elastic,brittle, and cellular behavior

This paper deals with the uniaxial compression behavior of porous ceramics within a wide range of porosity, varying from 30 to 75 vol%. The load–displacement curves recorded on porous alumina samples showed a transition between a typical brittle behavior at porosity fractions below 60 vol% and a damageable, cellular-like behavior, at higher porosity fractions. This transition in fracture mode was confirmed by in situ compression tests in an X-ray tomograph. Based on a simple model taking into account the competition between the crack length initiating from spherical pores and the mean distance between pores, the porosity at which the transition took place was estimated. The influence of the pore size also depended on the volume fraction of pores: no size effect was noted at the lowest porosity whereas a statistical effect on the size of the solid walls was observed at higher porosity, with an increase in fracture strength with small pores.     

Impact of doping on the mechanical properties of acicular mullite

Acicular mullite (ACM) is a highly porous ceramic with a needlelike microstructure. Next-generation ACM-based diesel particulate filters will require porosities >60%, making optimizing ACM's mechanical properties a key area of interest. A prior study determined that, for the range of microstructures evaluated, the elastic modulus, strength, and fracture toughness were largely functions of total porosity and not needle or pore size, consistent with the Gibson–Ashby foam model. Therefore, alternate strengthening and toughening methods were sought. Doping the ACM precursor with either MgO or Nd₂O₃ produced ACM microstructures that appeared similar but had differing bulk mechanical properties. The mechanical properties of the mullite needles, the intergranular glassy phase, and the mullite–glass interface of the ACMs were investigated, but no major differences were found. Using X-ray computed tomography, a 3D imaging technique, it was found that MgO-doping of the ACM created a less uniform, and thus weaker, microstructure than Nd₂O₃-doping.     

Optimal design on the mechanical and thermal properties of porous alumina ceramics based on fractal dimension analysis

In order to investigate the relationship between pore structure and thermal conductivity as well as mechanical strength, porous alumina ceramics (PAC) with various pore structures were fabricated, using starch as the pore‐forming agent. Fractal theory was employed to characterize the pore size distribution more accurately than ever used parameters. The results show that the increase in starch content in PAC leads to an enhanced porosity, a higher mean pore size, and reduced fracture dimension, thermal conductivity and strength. The fractal analysis indicated that the fractal dimension decreases gradually and reaches its minimum value with increasing the starch content up to 25 wt%, but the further incorporation results in an opposite trend. It is suggested from micro‐pore fractographic analysis that the optimization of both thermal insulation performance and mechanical strength are positively correlated with the increase in the mean pore size and proportion of 2‐14 μm pores but negatively corrected with the porosity. These results provide a new perspective and a deeper understanding for fabrication of PAC with both excellent thermal insulation and mechanical performance.     

The effect of the shape and size of the pores on the mechanical properties of porous HAP-based bioceramics

In this study, the influence of the shape and size of the pores on the mechanical properties of the obtained porous HAP-based bioceramics was investigated. The porous HAP-based bioceramics were obtained starting from spherical calcium hydroxyapatite powder, obtained by hydrothermal syntheses. The number of shapeless inter-agglomerate pores decreased and amount of spherical intra-agglomerate pores increased on increasing the sintering temperature from 1100 °C to 1250 °C. The shape of pores also changed with thermal treatment of specimens; the small pores remained spherical while the larger pores became more spherical in shape, as was proved by image analysis. A three-dimensional, finite element unit cell model was applied to evaluate the influence of pore shape on the mechanical strength of HAP ceramics. By analyzing the effect of the shape of pores to the fracture toughness of sintered porous HAP bioceramics, it was observed that the more spherical the pores were, the tougher became the bioceramics. After sintering at 1250 °C for 2 h, measured toughness was 1.31 MPa m^1/2, which is a relatively high value for this type of bioceramics.     

Numerical Simulation of Viscous Sintering by a Periodic Lattice of a Representative Unit Cell

In this paper numerical simulations of the viscous sintering phenomenon are presented, i.e., of the process that occurs (for example) during the densification of a porous glass heated to such a high temperature that it becomes a viscous fluid. The numerical approach consists of simulating the shrinkage of a two-dimensional unit cell which is in some sense representative for the porous glass. Hence it is assumed that the microstructure of the glass can be described by a periodic continuation in two directions of this unit cell. In this way it is possible to obtain insights into the viscous sintering process with respect to both pore size and pore distribution of the material. In particular this model is able to examine the consequences of microstructures on the evolution of the pore size distribution. The major finding is that the pores vanish in order of size one after another-the smallest pores first, followed by the larger ones. Moreover, it is shown that pores with concave boundary parts may initially grow before they start shrinking at a later stage.     

Conductivity of porous materials with spheroidal pores

Models predicting the conductivity of porous materials with spheroidal insulating pores are summarized and a new model, based on our exponential relation, is proposed. Using the well-known single-inclusion solution for spheroids, Maxwell coefficients (“intrinsic conductivities”) are calculated in dependence of the pore aspect ratio for isotropic microstructures with randomly oriented spheroidal pores, and implemented into the three traditional effective medium approximations (Maxwell-type, self-consistent, differential) and our exponential relation. As expected, all models predict that prolate pore shape has a very small influence on the porosity dependence, while oblate pores affect the porosity dependence of conductivity significantly. However, the self-consistent predictions are linear and imply spurious percolation thresholds, whereas Maxwell-type and differential models (power-law relations) are known to provide predictions that are unrealistically high for the special case of spherical pore shape. Thus, our exponential relation seems to be currently the most suitable relation for implementing the single-inclusion solution for spheroids.     

油井土、废玻璃基多孔陶瓷的制备及结构表征

利用油井土、废玻璃作为主要原料,同时以碳酸钙作为造孔剂,通过控制烧结过程,最终制备多孔陶瓷材料,并利用XRD、SEM等对样品进行结构表征。本研究的目的是为了研究油井土、废玻璃、碳酸钙的比例以及烧结温度对孔隙率、机械强度、体积密度、吸水率、微观结构和结晶程度的影响。结果表明样品A3呈现大孔均匀的微观结构,是通过添加35wt％油井土、40wt％废玻璃、20wt％碳酸钙、5wt％硅酸钠在较低的烧结温度下来获得,其孔隙率、抗压强度、抗弯强度、体积密度和吸水率的值分别为52．38％、4．43 MPa、12．59 MPa、1．07 g／cm3和29．56％。并观察到其机械强度、吸水率和微观结构（孔径及孔径分布）有良好的相关性。     

Estimating thermal conductivities and elastic moduli of porous ceramics using a new microstructural parameter

Porous ceramics are numerically constructed based on the convexity of the void phase: microstructures with convex pores are representative of isolated or randomly overlapping spherical pores, while particulate materials with non-convex pores are composed of randomly overlapping, partial overlapping or partially sintered solid spheres. Finite element simulations show that, given the porosity, thermal conductivities and elastic moduli for convex porosity are larger than the values for non-convex pores. These conditions are not well described by solely porosity. By contrast, this study proposes a new microstructural parameter, <lp2>/(<ls2>+<lp2>), to estimate thermal conductivities and elastic moduli for both convex and non-convex pores. <ls2> and <lp2> are respectively mean-square solid chord length and mean-square pore chord length of cross-sections, which can be conveniently extracted from SEM images combined with chord length distributions of solid and void.     

Sensitivity of fracture strength in porous glass

We investigated the effect of porosity and crack size distributions on the fracture behavior of porous glass through a combined finite element and fracture mechanics method. Simulations showed that the effect of crack size distributions on the change in fracture strength with porosity decreases as the pore size to crack size ratio increases. For a pore size to crack size ratio of >∼4, the average failure initiating crack size decreases with increasing porosity. Two regions were defined to describe the relationship between porosity and fracture strength: Region I for porosity less than 20 vol.% and Region II for porosity greater than 20 vol.%. Simulation results were directly compared to the porous glass experiments from the literature.     

Modeling changes of fractal pore structures in coal pyrolysis

Coal pyrolysis processes are numerically investigated in mathematically produced coal pore models which simulate real coal pores in the parameters of the porosity and fractal dimension. The simulations include FG-DVC chemical reaction model, gas molecular diffusion in pores, energy conservation model and coal swelling model. Numerical results are verified by experimental results qualitatively, and they revealed that both the porosity and volatile contents of the parent coal can affect the fractal dimension of the final char pores after pyrolysis linearly. A formula to predict the fractal dimension of char pores from its parent coal properties is obtained by curve fitting in numerous results.     

Correlations between pore structure parameters and gas permeability of corundum porous materials

Corundum porous materials with different contents of calcium hexaluminate formed in situ were prepared using pure calcium aluminate cement as the calcium source. The surface fractal dimensions of the porous materials were calculated based on the experimental data of mercury intrusion. Correlations between pore structural parameters and the permeability coefficients k₁ and k₂ of the porous materials were then studied based on the grey system theory. The results showed that pores in the corundum porous materials have great fractal characteristics. The surface fractal dimension was a significant pore structural parameter that reflected the complexity of pore shape, pore surface, and pore-size distribution, which had the maximum correlation coefficient with the permeability of this type of porous materials. The apparent porosity and pore-size distribution had relatively high correlation coefficients to the permeability as well. Increasing the apparent porosity and the volume percentage of larger pores, and decreasing the volume percentage of smaller pores all benefited the permeability of the porous materials. In addition, the mean pore size and median pore size showed lower correlation coefficients to the permeability—especially for porous materials with a wide pore-size distribution.     

Effect of closed pores on dielectric properties of 0.8Na0.5Bi0.5TiO3-0.2K0.5Bi0.5TiO3 porous ceramics

Porous 0.8Na_0.5Bi_0.5TiO₃-0.2K_0.5Bi_0.5TiO₃ ceramics are fabricated via the pore-forming agent method with polymethyl methacrylate (PMMA) and stearic acid (SA) as pore forming agents, and microstructure observations demonstrate that the porosity, pore shape, and pore sizes can be controlled by the synthesis technology. The dielectric properties of porous ceramics are found not only correlated to the pore-matrix composite model, but also have a significant grain-size effect. Based on the Zener Theory, pining forces exerted by pores on the grain boundary are calculated, to explain the shape effect of pores on grain boundary migration. A phase-field simulation is carried out to investigate pore shape effect on the grain size regulation in porous polycrystalline, and simulation results are in good agreements with experiential results as well as theoretical calculations. Thus, a modified equation is proposed to predict the effective permittivity of the porous piezoelectric ceramics by considering effects of porosity, pore shape and grain size.     

Elastic Properties of Model Porous Ceramics

The finite-element method (FEM) is used to study the influence of porosity and pore shape on the elastic properties of model porous ceramics. Young's modulus of each model is practically independent of the solid Poisson's ratio. At a sufficiently high porosity, Poisson's ratio of the porous models converges to a fixed value independent of the solid Poisson's ratio. Young's modulus of the models is in good agreement with experimental data. We provide simple formulas that can be used to predict the elastic properties of ceramics and allow the accurate interpretation of empirical property–porosity relations in terms of pore shape and structure.     

Viscosity of Porous Glasses

Viscosity of porous glasses has been derived from the elastic stress analysis, using the viscous analogy. Viscosity as a function of porosity has been estimated for spherical as well as for arbitrary pore geometry. Since the pore geometry changes during sintering, a shape factor that varies with pore geometry has been considered to predict the viscosity–porosity relationship. Viscosity as a function of porosity was measured on cordierite-type glass by isothermal sinter-forging experiments and data showed good agreement with the analysis. Experimental data from literature on viscosity as a function of porosity on two other glasses also show good agreement with the analysis.     

Microstructure,mechanical behavior and flow resistance of freeze-cast porous 3YSZ substrates for membrane applications

Freeze-cast porous 3YSZ with different porosities were characterized as mechanical load carrying supports for oxygen transport membrane applications. Porosity influence on mechanical properties, i.e. elastic modulus and fracture stresses was assessed with biaxial ring-on-ring bending tests. The flow resistance was characterized in terms of the pressure drop using different gases to reveal the effect of the porous support on the accessing of the inlet gas flow to the functional dense membrane layer. Both properties were discussed in terms of the influence of porosity and pore structure, and compared with the properties of porous 3YSZ produced via pressing and sintering.     

Three-dimensional structure analysis by X-ray micro-computed tomography of macroporous alumina templated with expandable microspheres

The three-dimensional (3D) structures of macroporous alumina, produced by a novel method that combines gel casting with expandable polymeric microspheres as a sacrificial templating material, have been characterised by X-ray micro-computed tomography (μ-CT). The grey-scale intensity tomogram data produced by the X-ray μ-CT was segmented into porous and solid phases and the individual pores were identified. We compared two-dimensional slices of the analysed data with the corresponding scanning electron microscopy images and showed that the structural features of the pores were well reproduced in the X-ray μ-CT images. 3D visualisations of the pore structure and the pore network were also shown. The open porosity obtained from X-ray μ-CT corresponded well with the porosity derived from mercury porosimetry for pores larger than the voxel dimension (3 μm). The quantitative analysis also yielded information on the spatial variations in porosity and the number of connected neighbours of pores. The 3D data was used to relate the calculated permeability to the open porosity.     

Modeling of Young’s modulus and thermal conductivity evolution of partially sintered alumina ceramics with pore shape changes from concave to convex

Numerical calculations of the effective (relative) Young’s modulus and thermal conductivity have been performed for porous model materials on computer-generated digital microstructures with a transition from concave to convex pore shape. The results are compared to the case of purely concave and convex pores (isolated or overlapping). It is shown that the Pabst-Gregorová cross-property relation for isotropic porous materials with isometric pores gives an excellent prediction of effective (relative) properties for materials with a transition from concave to convex pore shape. With accuracy better than 0.010 relative property units (RPU) this prediction is far better than the prediction by any other cross-property relation currently known. For the intermediate (concave-convex) microstructures the accuracy of this cross-property relation is better than that for microstructures with purely concave pores (accuracy better than 0.034 RPU) and, surprisingly, even better than for purely convex pores (accuracy better than 0.011–0.013 RPU).     

Processing and properties of low cost macroporous alumina ceramics with tailored porosity and pore size fabricated using rice husk and sucrose

The present study demonstrates a cost effective way to fabricate porous ceramics with tailored microstructures using rice husk (RH) of various range of particle sizes as a pore former and sucrose as a binder as well as a pore former. Sample microstructures reveal randomly oriented elongated coarse pores and fine pores (avg. size 4 μm) created due to burnout of RH and sucrose, respectively. Porous alumina ceramics with 20–66 vol% porosity and 50–516 μm avg. pore size (length), having isolated and/or interconnected pores, were fabricated using this process. Mechanical properties of the porous samples were determined as a function of porosity and pore microstructure. The obtained porous ceramics exhibited flexural strength of 207.6–22.3 MPa, compressive strength of 180–9.18 MPa, elastic modulus of 250–18 GPa and hardness of 149–18 HRD. Suggested application area includes thermal, filtration, gas purging etc.