Relative Young’s modulus and thermal conductivity of isotropic porous ceramics with randomly oriented spheroidal pores – Model-based relations,cross-property predictions and numerical calculations

Based on computer-generated digital microstructures with spherical or spheroidal pores (isolated or overlapping) of aspect ratio 1 (spherical), 10 (prolate) and 0.1 (oblate), the relative thermal conductivity and Young’s modulus is numerically calculated and compared to predictions based on generalized effective medium approximations (EMAs) and a recently proposed generalized cross-property relation (CPR). It is shown that, when the aspect ratio is known, generalized power-law and exponential relations provide satisfactory predictions of these two properties without the use of empirical fit parameters. The maximum deviation of these two types of EMA predictions from the true values ranges from ?0.04 to +0.06 relative property units (RPU) for the power-law relation and from ?0.02 to ?0.10 RPU for the exponential relation. However, the generalized CPR results in an even higher accuracy of the predictions, with maximum deviations smaller than 0.01 RPU for the Young’s modulus when the thermal conductivity is known.     

Young’s modulus and thermal conductivity of model materials with convex or concave pores – from analytical predictions to numerical results

The effective Young’s modulus and thermal conductivity of porous materials can be rigorously bounded from above via micromechanical bounds (upper Wiener–Paul bounds and upper Hashin–Shtrikman bounds), and several model relations are commonly used as tentative approximate predictions (Maxwell-type, Coble–Kingery-type, power-law and exponential relations). Based on numerical calculations on computer-generated digital model microstructures, both periodic and random, it is shown that these model relations provide rough approximations that are more or less appropriate for microstructures with essentially convex pores, but are not suitable for microstructures with concave pores. On the other hand, the Pabst–Gregorová cross-property relation provides a very accurate (better than 0.04 relative property units) analytical prediction for the relative Young’s modulus of isotropic porous materials with isometric pores, both convex and concave, when the relative thermal conductivity is known. It is shown that this cross-property relation is the best prediction currently available for isotropic porous materials with isometric pores.     

Phase mixture modeling of the grain size dependence of Young’s modulus and thermal conductivity of alumina and zirconia ceramics

The grain size dependence of Young’s modulus and thermal conductivity of alumina and zirconia ceramics is predicted via phase mixture modeling, using both analytical and numerical approaches. Using typical values for the thickness and properties of the grain boundaries, the equivalent volume fraction of “grain boundary phase” is calculated for a given grain shape. Based on this volume fraction estimate and a rough estimate of the grain boundary properties, the effective properties of the polycrystalline materials are calculated and compared in terms of volume-equivalent sphere diameters. For grains of cubic and tetrakaidecahedral shape excellent agreement is found between numerical calculations and analytical predictions based on the lower Hashin-Shtrikman bound. The grain size dependence is extremely weak for Young’s modulus, but can be more significant for thermal conductivity, especially when the intrinsic conductivity of the material is high. The predictions are compared to literature data.     

Young’s modulus evolution during sintering and thermal cycling of pure tin oxide ceramics

Pure tin oxide (SnO₂) ceramics is well known for its bad sinterability, more precisely for the difficulty to densify without additives by conventional pressureless sintering. This is related to the fact that the sintering mechanisms in pure tin oxide ceramics are non-densifying (surface diffusion at low temperature and evaporation-condensation at high temperature). On the other hand, for the same reason, pure tin oxide ceramics is a very unusual model system that can be used to demonstrate the effects of microstructural changes on effective properties without the otherwise dominating effect of changes in porosity. In this paper we show that pure tin oxide ceramics uniaxially pressed at 50 MPa, pre-sintered at 500 °C and re-sintered at 1000, 1200 and 1400 °C exhibit relative Young’s modulus increases of 30, 70 and 120 % while the porosity remains essentially constant at a value of 51.6 ± 0.7 %.     

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).     

Temperature dependence of Young’s modulus and damping of partially sintered and dense zirconia ceramics

Young’s modulus and damping of partially sintered and almost fully dense zirconia ceramics (tetragonal zirconia polycrystals with 3 mol.% yttria), obtained by firing to different temperatures (range 1000–1400°C), have been determined via impulse excitation, and the evolution of Young’s modulus and damping of partially sintered zirconia with temperature has been monitored from room temperature to 1400°C and back to room temperature. The room-temperature Young’s modulus of the partially sintered materials obeys the Pabst-Gregorová exponential prediction, which is relatively unusual for partially sintered materials. With increasing temperature Young’s modulus decreases, until the original firing temperature is exceeded and sintering (densification) continues, resulting in a steep Young’s modulus increase. During heating and cooling the temperature dependence obeys a master curve with a typical inflection point at approximately 200 °C, the temperature where damping (internal friction) exhibits a maximum. The reasons for this characteristic behavior of doped zirconia are recalled.     

Young’s modulus evolution during heating,re-sintering and cooling of partially sintered alumina ceramics

The Young modulus of partially and fully sintered alumina ceramics, obtained by firing to different temperatures (range 1200–1600°C), has been determined via impulse excitation, and the evolution of Young’s modulus of partially sintered alumina with temperature has been monitored from room temperature to 1600°C. As expected, the room-temperature Young modulus of the partially sintered materials is lower than all theoretical predictions. With increasing temperature Young’s modulus decreases, until the original firing temperature is exceeded and sintering (densification) continues, resulting in a steep Young’s modulus increase. During heating and cooling the temperature dependence obeys a master curve for alumina, unless the temperature of the original firing is excessively low.     

Measuring the Young’s modulus of polystyrene-based composites by tensile test and pulse-echo method

In this study, the pure polystyrenes (PS) with different molecular weights (3.5 × 10⁵ and 5.0 × 10⁵) have been modified by the chemical modification with succinic anhydride (SA), maleic anhydride (MA), and phthalic anhydride (PhA). The modified polystyrenes (MPS) have been mixed with the pure PS with the molecular weight of 2.3 × 10⁵ in weight % ratio 90:10, 80:20, and 70:30. Young’s modulus of obtained composites has been measured mechanically by the tensile test and ultrasonic method at frequency of 5 MHz. Further, the values of Young’s modulus measured by both methods have been compared with each other. From the results, a significant difference has not been found between the values of Young’s modulus of both methods. As a result it can be stated that measuring the Young’s modulus of these materials by the ultrasonic methods is more sensitive and economical than the mechanical methods.     

Young׳s modulus,hardness and thermal expansion of sintered Al2W3O12 with different porosity fractions

Owing to their unusual thermal expansion properties ceramic phases from A₂M₃O₁₂ family have potential for applications as thermal expansion controlling fillers inside soft matrices or as materials with high thermal shock resistance when prepared in monolithic forms. In spite of this, the consolidation routes for achieving bulk forms with adequate microstructure and their mechanical and thermal properties are scarcely known and rarely studied. A prelaminar study on sinterability of Al₂W₃O₁₂, a low thermal expansion phase, was accomplished for the temperature range between 850 °C and 1000 °C. Sintered samples with the porosity fraction between 0.1 and 0.25 were produced and their Young׳s moduli, hardness and thermal expansion studied through nanoidentation and dilatometry. Acoustic emission was employed for studying of microcrack formation during heating and cooling of sintered samples. Sintering study showed that the temperatures higher than 1150 °C may lead to the decomposition of tungstate due to WO₃ evaporation, while the sintering at the temperature of 850 °C provokes only small changes over grain size distribution. Hardness and Young׳s modulus decrease linearly in porosity range between 0.1 and 0.25. Young׳s modulus for fully dense Al₂W₃O₁₂ was calculated to be 70 GPa, illustrating that the phases from A₂M₃O₁₂ family are considerable softer than traditional ceramics. Microcrack formation was observed on cooling and heating, as well, causing the discrepancy between the intrinsic coefficient of thermal expansion (CTE), measured in powder form, and the CTE measured in bulk form. The key feature for future development of A₂M₃O₁₂ phases for thermal shock resistance applications is the better understanding of sintering processes in order to improve microstructure and reduce influence of microcracks over mechanical and thermal properties.     

Young׳s modulus,Vickers hardness and indentation fracture toughness of alumino silicate glasses

A wide range of alumino silicate glasses with different network modifier ions (Li, Mg, Na, Ca, Zn, La, Ba, Sr, and Pb) was prepared. The glasses were studied with respect to their mechanical properties: Poisson׳s ratio, Young׳s modulus, Vickers hardness and indentation fracture toughness. These properties were mostly affected by the field strength of network modifier ions. All determined properties increase with increasing field strength of the network modifier ions. The mixed modifier alumino silicate glasses with zinc and magnesium show a positive deviation from linearity with two maxima. Lanthanum containing glasses show larger values of mechanical properties for higher lanthanum concentrations. For magnesium alumino silicate glasses the mechanical properties get smaller with increasing SiO₂ concentration; an effect of the magnesium concentration is not observed. Furthermore, if up to 9 mol% MgO is replaced by MgF₂ the mechanical properties are not significantly affected. Compared to models predicting Young׳s moduli of all studied glass compositions, significant deviations are found.     

How the coarse fraction influences the microstructure and the effective thermal conductivity of alumina castables – An experimental and numerical study

This study investigates the particle size distribution's effect on the microstructure and effective thermal conductivity (ETC) of alumina castables. The ETC was measured by the transient plane source method and predicted numerically based on a two-scale model describing the structure on a fine and coarse scale. The prediction considered particle and pore size distributions, porosity (around 20%) and grain morphology. The microstructure was investigated by scanning electron microscopy. For a constant fines content, increasing the coarse grain fraction while decreasing the medium fraction enhanced sintering of the matrix. Small pores (≤250 nm) increased the sintering activity. The densest castable contained the most small pores. The particles’ and pores’ contributions to the sintering activity led to intensified microcracking and a decreased ETC. The numerical model did not consider constituents ≤500 nm like the small pores and microcracks and the calculated ETC values consequently deviated from the measured values.     

Ultrasonic measurement of Young’s modulus MgO/C refractories at high temperature

The paper deals with the elastic behavior of MgO/C refractories used in BOF at temperatures up to 1400°C in air or inert atmosphere. Measurements have been made by the way of a high temperature ultrasonic technique. Heating-cooling cycles and long time aging in the range 700–1400°C show strong variations of Young’s modulus which have been interpreted with the aid of XRD analysis, SEM observations and EDS analysis. Carbon oxidation and sintering of MgO particles are found to be responsible of the major parts of the measured evolutions. ©     

Microstructure and Young’s modulus evolution during re-sintering of partially sintered alumina-zirconia composites (ATZ ceramics)

Partially and fully sintered alumina-zirconia composites (ATZ ceramics), with porosities decreasing from 53.5 to 1 %, have been prepared by uniaxial pressing and firing at 1000–1500 °C and characterized by the Archimedes method and mercury intrusion porosimetry. Young’s modulus has been measured via the impulse excitation technique at room temperature, resulting in an almost exponential porosity dependence (which is unusual for partially sintered ceramics in which the microstructure is dominated by concave pore surfaces), and at elevated temperatures up to 1500 °C during heating and cooling, resulting in a temperature master curve with a low-temperature inflection point around 200 °C (accompanied by a damping maximum). Both results confirm previous findings for zirconia and are typical for zirconia-containing ceramics. When the original firing temperature is exceeded, sintering and densification continues, albeit with a temperature lag when the sintering activity (specific surface area) is reduced as a consequence of previous firing.     

Thermal batteries with ceramic felt separators – Part 2: Ionic conductivity,electrochemical and mechanical properties

In this Part 2, the ionic conductivity of molten salt electrolytes, the electrochemical properties of single cells containing a ceramic separator infiltrated with an electrolyte, and the mechanical strength of the electrolyte layer are compared with those of the conventional pellet-pressed structure. The ionic conductivity for the molten electrolyte is higher than that of the previous report for both LiCl-KCl and LiF-LiCl-LiBr electrolytes, which is explained by the decrease in contact resistance using a graphite electrode instead of stainless steel. The electrochemical performance of the single cells containing a ceramic felt separator assembled with Li(Si)/FeS₂ electrodes shows longer operating time to a cut off voltage of 1.3 V compared to the conventional MgO-contained single cell. In addition, the flexural strength of the electrolyte layer with the ceramic felt separators is in the range of 2.80–6.29 kgf cm⁻², which is incomparable to that (=0.01 kgf cm⁻²) of the pellet-pressed conventional separator. These findings suggest that the ceramic felt separator can be an alternative to mitigate the current problems of pellet-pressed structure in thermal batteries, enhancing the mechanical strength and electrochemical properties.     

Effect of β to α phase transformation on microstructure and thermal conductivity of SiC ceramic densified with Y2O3-MgO additives in argon

SiC ceramic was fabricated by spark plasma sintering of β-SiC powder and Y₂O₃-MgO additives in argon. The effects of β→α phase transformation of SiC on microstructure and thermal conductivity of densified bulks were systematically investigated, in comparison to the counterparts using α-SiC as starting powder. The β→α phase transformation led to a “unimodal to bimodal” transition in grain size distribution. After sintering at 1850 ^oC, the incomplete β→α phase transformation induced the appearance of β/α heterophase boundary with strong effect of phonon-scattering. After sintering at 2050 ^oC, the completion of β→α phase transformation resulted in enlarged grains and disappearance of β/α heterophase boundary in SiC ceramic. The lattice oxygen content was decreased primarily by enhanced grain growth and oxygen picking-up of sintering additives, and possibly some contribution from β→α phase transformation. The optimized microstructure enabled SiC ceramic to obtain a remarkable increase in thermal conductivity from 126 to 204 W/mK after the replacement of α-SiC by β-SiC as starting powder and the accomplishment of β→α phase transformation.     

Measurement of thermal conductivity,viscosity and density of ionic liquid [EMIM][DEP]-based nanofluids☆

This article studied experimentally the effect of multi-wall carbon nanotubes(MWCNTs)on the thermo physical properties of ionic liquid-based nanofluids.The nanofluids were composed of ionic liquid,1-ethyl-3-methylimidazolium diethylphosphate [EMIM][DEP],or its aqueous solution[EMIM][DEP](1)+ H_2O(2)and MWCNTs without any surfactants.The thermal conductivity,viscosity and density of the nanofluids were measured experimentally.The effects of the mass fraction of MWCNTs,temperature and the mole fraction of water on the thermo physical properties of nanofluids were studied.Results show that the thermal conductivity of nanofluids increases within the range of 1.3%–9.7% compared to their base liquids,and have a well linear dependence on temperature.The viscosity and density of the nanofluids exhibit a remarkable increase compared with those of the base liquids.Finally,the correlation of the effective thermal conductivity and viscosity of the nanofluids was made using the models in the literatures.     

Thermal conductivity of binary ceramic composites made of insulating and conducting materials comprising full composition range – Applied to yttria partially stabilized zirconia and molybdenum disilicide

The thermal diffusivity and conductivity of dense and porous binary composites having an insulating and conducting phase were studied across its entire composition range. Experimental evaluation has been performed with MoSi₂ particles embedded into yttria partially stabilized zirconia (YPSZ) as prepared by spark plasma sintering (SPS). The thermal diffusivity of the composites was measured with Flash Thermography (FT) and Laser Flash Analysis (LFA) techniques. Subsequently, the thermal conductivity was determined with the measured heat capacity and density of the composites. The actual volume fraction of the conducting phase of the composites was determined with image analysis of X-ray maps recorded with scanning electron microscopy (SEM). The phases present and their density were determined with X-ray diffractometry (XRD) using Rietveld refinement. The thermal diffusivity increases with increasing volume fraction of MoSi₂. Porosity reduces the thermal diffusivity, but the effect diminishes with high volume fractions MoSi₂. The thermal diffusivity as a function of the MoSi₂ volume fraction of the YPSZ composites is captured by modelling, which includes the porosity effect and the high conductivity paths due to the percolation of the conductive phase.     

Acoustical,damping and thermal properties of polyurethane/poly(methyl methacrylate)-based semi-interpenetrating polymer network foams

In the present study, the interpenetrated polymer networks (IPN) foams of polyurethane (PU) and poly(methyl methacrylate) (PMMA) with different ratio of PU/PMMA (i.e. 85/15, 75/25 and 65/35) were prepared using the polymerisation process. The acoustical, damping and thermal properties of synthesised IPN foams with regard to different compositions were studied. As indicators of effective damping capability, viscoelastic parameters including loss factor (tan δ), glass transition temperature (T_g) and effective damping interval (tan δ?>?0.3) were also determined. The results show that the T_g shifted to higher temperature ranges, and the damping temperature range (tan δ?>?0.3) increased when the IPN was formed. The sound absorption coefficient results show that because of the formation of IPN, the sound-absorbing capacity of prepared samples increased at a certain frequency, and the resonance frequency shifted to lower frequencies by increasing the PMMA content in IPN foams.     

A generalized Young’s equation for contact angles of droplets on homogeneous and rough substrates

Using Gibbs’ method of dividing surfaces, the contact angle of a drop on a flat homogeneous rough non-deformable solid substrate is investigated. For this system, a new generalized Young’s equation for the contact angle, including the influences of line tension and which valid for any dividing surface between liquid phase and vapor phase is derived. Under some assumptions, this generalized Young’s equation reduces to the Wenzel’s equation or Rosanov’s equation valid for the surface of tension.     

Microstructure,mechanical properties and thermal conductivity of (Ti0.5Nb0.5)C–SiC composites

A series of (Ti_0.5Nb_0.5)C-x wt.% SiC (x = 0, 5, 10, 20) composites were prepared by spark plasma sintering. Dense microstructures with well‐dispersed SiC particles were obtained for all composites. With the increment of SiC content, the Vickers hardness, Young's modulus and fracture toughness increase monotonically. An optimized flexural strength of 706 MPa was achieved in (Ti_0.5Nb_0.5)C-5 wt.%SiC composite. (Ti_0.5Nb_0.5)C-20 wt%SiC composite exhibits the highest fracture toughness of 6.8 MPa m^1/2. The crack deflections and the suppression of grain growth were the main strengthening and toughening mechanisms. Besides, (Ti_0.5Nb_0.5)C-20 wt%SiC composite exhibit the highest thermal conductivity of 45 W/m·K at 800 °C.