Minimum Solid Area Model Research Articles

Influences of the solid load on the microstructure and compressive behavior of Fe2O3 scaffolds manufactured by freeze-casting using stearic acid as dispersant agent

Porous materials manufactured by freeze-casting are demonstrating potential application as oxygen carriers for the production and purification of hydrogen, or anode material for lithium-ion batteries. However, to obtain the required pore morphology and sufficient mechanical strength, the suspension processing parameters must be controlled. Fe2O3 nanoparticles/camphene suspensions were fabricated using stearic acid as the dispersant agent showing a low-viscosity (130 mPa·s) with a high solid volume fraction (0.3). Suspensions show a shear-thinning behavior according to the Sisko model and a maximum packing fraction of 0.569 estimated from a zero porosity sample. A modified Krieger and Dougherty model was introduced to incorporate the influence of the particle-aspect ratio. The Fe2O3 scaffolds manufactured by freeze-casting shown a gradient pore size along the freezing direction, which was diminished with the solid volume fraction, the compression strength was improved with the pore size reduction and fitted according to the minimum solid area model.

Preparation and characterization of porous alumina ceramics using sunflower seed shells as fugitive material

Abstract Porous alumina ceramics were prepared through the space holder technique, using ground sunflower seed shells as a fugitive material and uniaxial pressing for forming the green ceramics. Influences of the sunflower seed shell content on the shrinkage of the green bodies and porosity of sintered products were evaluated. The prepared ceramics were characterized for mechanical properties using the Brazilian disk test, and the porosity effect on the measured strength was determined. The microstructure was characterized by SEM. The sunflower seed shell content was varied from 0 to 60 wt%. Porosities within 29.9-71.0 vol% were achieved, and the strength of the obtained alumina ceramics decreased accordingly from 59.7 to 4.0 MPa. Additional samples, prepared with different compaction pressure, were characterized for electrical properties and showed high electrical insulation capability, which increased with porosity. Mechanical and electrical data were discussed based on theoretical models, namely the Gibson-Ashby model and/or the minimum solid area model.

Influence of porosity on the mechanical behaviour of single phase β-TCP ceramics

Processing and mechanical behaviour of fine grained (diameter ≈0.5–3µm) and pure β-TCP materials with different levels of porosity (up to 19%) is described. Pores with diameters, d50 ≈13–14µm were formed fromcorn starch during sintering. Comprehensive mechanical characterisation –Young´s modulus, strength and toughness– has been done paying special attention to toughness determined in stable fracture tests. The dependence of Young´s modulus and strength with porosity was well fitted to the minimum solid area models while toughness values did not. The competitive processes occurring during fracture impede the degradation of toughness associated to the decrease in Young´s modulus as porosity increases. Materials present similar values of the critical energy release rate GIC, which describes crack initiation. A maximum of the specific fracture energy, GF, which averages crack propagation, has been obtained for the material with the highest porosity.

Investigations on Material and Mechanical Properties, Air‐Permeation Behavior and Filtration Performance of Mullite‐Bonded Porous SiC Ceramics

A theoretical relation between processing parameters and porosity (29–56%) of mullite‐bonded porous SiC ceramics was derived and validated with experimental data. Porosity‐dependent variation of fracture strength (9–34 MPa) and elastic modulus (7–28 GPa) was explained by the minimum solid area model. At room temperature, the Darcian, k1 (1.2 × 10−13–1.6 × 10−12 m2) and the non‐Darcian, k2 (4.6 × 10−9–2.7 × 10−7 m) permeability coefficients showed linear variation with porosity. Tests conducted up to 650°C indicated an increase in k1 with temperature and a reverse trend for k2. Airborne NaCl nanoparticle filtration tests showed good performance of SiC ceramics with fractional collection efficiency of >99% at 46–56% porosity levels.

Characterization of Ti–6Al–4V alloy foams synthesized by space holder technique

Ti–6Al–4V foams, biomedical candidate materials, were synthesized by powder metallurgical space holder technique as a result of evaporation of magnesium to achieve desired porosity content. Final products contained porosities in the range ∼43–64% with an average macropore size between 485 and 572 μm and a lamellar type Widmanstätten microstructure composed of α-platelets and β-laths. Unlike the case of bulk Ti–6Al–4V alloy tested under compression loading, compression stress–strain curves of manufactured Ti–6Al–4V foams were similar to those of elastic–plastic foams, which contain a linear elastic region; a plateau stage; and a densification stage. In the plateau region deformation bands perpendicular to the compression axis were developed and cell collapsing took place together with the buckling and fracture of some of the cell walls and edges in a ductile manner. Calculated elastic modulus and yield strength were in the range 1.42–14.7 GPa and 28.2–150 MPa, respectively, and the foam mechanical properties were found to be dependent on micro porous cell wall properties, which in turn depends on neck size between powder particles. Around 330 MPa yield strength value was calculated for porous cell walls by the use of Ti–6Al–4V alloy powder samples sintered in loose and compacted conditions, which were utilized to simulate the cell wall structure of foams. In addition, overall mechanical properties of foams were investigated considering macro porosity fraction, p macro, and the yield strength of foams exhibited a power law dependence, similar to commonly used minimum solid area models, in the form of A * (1 − p macro) n , where the proportionality constant “ A” was found to be the yield strength of micro porous cell walls.

Mechanical behaviour of porous hydroxyapatite

The aim of the study was to investigate the role of microstructure and porosity on the mechanical behaviour of sintered hydroxyapatite. Hydroxyapatite disks with four different porosities were used in this investigation. With a nanoindentation system, elastic modulus, hardness, contact stress–strain relationship, energy absorption and indentation creep behaviour were investigated. The elastic modulus and hardness of hydroxyapatite exhibited an exponential relationship (e − bP ) with the porosity P, which is similar to Rice’s finding with the minimum solid area model. High porosity samples showed more substantial inelastic behaviour, including higher energy absorption, no linear elastic region in the contact stress–strain curve and some indentation creep behaviour. We conclude that porous microstructure endows hydroxyapatite with inelastic deformation properties, which are important in a material for bone substitution usage.

Mechanical Properties of Magnesia–Spinel Composites

The mechanical properties of magnesia–spinel composite ceramics, which are candidate materials for supporting solid oxide fuel cells, have been measured as a function of porosity (up to 30%) and temperature (up to 900°C). The theory for the ring‐on‐ring test has been re‐examined to resolve an inconsistency in the literature. The Young's modulus shows an exponential dependence on porosity that is in agreement with the expectation of minimum solid area models. Fracture toughness, fracture energy, and flexural strength are all approximately proportional to Young's modulus. The mechanical properties are not greatly dependent on temperature, but there is a detectable increase in fracture toughness with temperature, which could be due to some limited plasticity.

Fracture strength of porous ceramics: stress concentration vs minimum solid area models

In this study, we have reviewed recently published strength-porosity data of porous ceramics, and compared these data with those computed from both the minimum contact solid area (MCA) and the pore stress concentration effect (SCE) models. We observed that the theoretical data (MCA model) matched better the experimental results of ceramics in the low volume fraction porosity range (P 0.25), the SCE model better predicts the experimental results. African Journal of Science and Technology Vol. 5(2) 2004: 19-27

Apparent Electrical Conductivity of Porous Titanium Preparedby the Powder Metallurgy Method

Porous titanium is produced by the powder metallurgy method. Dependenceof the electrical conductivity on the porosity and pore size isinvestigated and the experimental results are compared with a number ofmodels. It is found that the minimum solid area model could besuccessfully applied to describe the relationship between the electricalconductivity and the porosity of porous titanium. This kind ofconductivity increases with increasing pore sizes.

Use of normalized porosity in models for the porosity dependence of mechanical properties

The use of normalized porosity in models for the porosity dependence of mechanical properties is addressed first for the frequently used power law expression for such dependence, i.e., E/E0 = (1−P)n where E is the property of interest at any volume fraction porosity (P) and E0 is the value of E at P = 0. Normalizing P by PC, the value of P at which the property of interest inherently goes to zero, giving E/E0 = (1−P/PC)n, clearly calls attention to the importance of PC values < 1 (e.g., potentially as low as ∼ 0.2), a fact long known but inadequately recognized. Serious problems from the arbitrary use of both n and PC as fitting parameters with little or no guidance as to the dependence that n and PC (which is microstructurally sensitive) have on the type of porosity are shown. Further, porosity normalization of the power law model indicates at best limited compression of different porosity dependences into a single universal porosity dependence function and little distinguishing of property dependences as a function of the type of porosity. However, normalized porosity of minimum solid area (MSA) models gives a single universal porosity dependence. The difference in responses to P normalization of the two modeling approaches is attributed to their being based respectfully on little or no pore character and on detailed pore character. Thus, P normalization may be a valuable tool for evaluating porosity models, but must be applied in a more rigorous fashion, i.e., PC determined primarily by measurement and correlation with the type of porosity (as with MSA models) and not as an arbitrary fitting parameter as used in the evaluations of the power law model.

Mechanical properties of tape cast nickel-based anode materials for solid oxide fuel cells before and after reduction in hydrogen

The processing of solid oxide fuel cells (SOFCs) often involves co-sintering of multi-layered stacks. In the case of SOFCs incorporating Ni-based anodes, hydrogen reduction of the anode usually takes place during the first service cycle of operation or conditioning. Initial reduction causes changes in the chemistry, microstructure and properties of the Ni-based anode material, which in turn induce mechanical stresses in the cell. In this study the elastic moduli, biaxial strength and fracture toughness of unreduced (NiO-YSZ) and reduced (Ni-YSZ) anode were determined as functions of porosity. Elastic properties were determined by impulse excitation at ambient temperature. Biaxial strength and fracture toughness were determined at ambient temperature by the ring-on-ring and double torsion test methods, respectively. It was found that the mechanical properties of unreduced and reduced Ni-based anode materials depend strongly on porosity. Property–porosity trends were found to be in good agreement with prediction of the minimum solid area model. Results presented in this study show that the elastic moduli and biaxial strength of the Ni-based anode material decreases after reduction in hydrogen while fracture toughness increases after reduction due to formation of ductile Ni-metal phase.

Minimum solid area models applied to the prediction of Young's modulus for cancellous bone.

In developing models for the mechanical behavior of cancellous bone, accurate prediction of Young's modulus as a function of the pore fraction and morphology is a requirement. Previous workers have suggested models which provide good statistical fits, but most of these models are highly idealized, with no treatment of the actual morphology of the porosity. In the field of engineering ceramics, simple minimum solid area models have been developed over the past four decades to describe the mechanical properties of porous structural ceramics. This paper applies these models to data for cancellous bone, and it is shown that one, developed specifically for high porosity materials, gives realistic predictions of tissue modulus and a good statistical fit to well-established data. This model should prove to be useful in biomechanical analyses involving cancellous bone tissue.

The influence of the microstructure on the hardness of sintered hydroxyapatite

Abstract The Vickers hardness, H V , was measured for 42 sintered monophase hydroxyapatite (HAP) specimens having volume fraction porosities, P, that ranged from 0.02 to 0.31 and average grain sizes between 1.7 μm and 7.4 μm. The H V versus porosity behavior of the sintered HAP specimens were successfully described by the exponential function of porosity, H V = H 0 exp(– bP ), where the least-squares fit values of the zero-porosity hardness H 0 and the constant b were 6.00±0.7 GPa and b =6.03, respectively. The function H V = H 0 exp(− bP ) is consistent with a minimum solid area model proposed by Rice. In contrast to the strong dependence of hardness on porosity, there was no clear trend of hardness as a function of grain size, for the grain size range included in this study.

Porosity dependence of mechanical properties of porous sintered SiC. Verification of the minimum solid area model

Porosity dependence of mechanical properties of porous sintered SiC. Verification of the minimum solid area model

Comparison of physical property-porosity behaviour with minimum solid area models

An extensive survey of the porosity dependence of (room temperature) physical properties shows that mechanical properties and electrical and thermal conductivity, i.e. properties dependent on the local flux or fields in the material, follow minimum solid area models. This is shown extensively for elastic properties and tensile (flexure) strength, but consistency with other properties, e.g. compressive strength, hardness, electrical and thermal conductivity is also shown. Although data for ceramics is most extensive, data for rocks, metals, and carbon are included, since the consistency of these, especially of metals with ceramics, provides important support for the minimum solid area concept. While porosity characterization is generally minimal, expected model trends with pore character are corroborated by correlating processing and resultant expected pore character with porosity-property results. It is argued that properties dependent on mass should be better fit by a linear, i.e. rule of mixture, relationship between such properties and porosity. Support for this is shown in dielectric constant-porosity data.