Young's modulus of isotropic porous materials with spheroidal pores

Based on the Eshelby solution for the single-inclusion problem and Wu's specification of this solution to spheroidal pores, we show that the Eshelby–Wu coefficients for Young's modulus, in contrast to their counterparts for the bulk and shear moduli, are quite insensitive to changes of the Poisson ratio. Therefore the Eshelby–Wu coefficients of Young's modulus can be described (to a very good approximation) by a unique function of the aspect ratio, which is calculated in this paper and for which a master curve is obtained by segment-wise fitting. Also the implementation of the Eshelby–Wu coefficients into the well-known effective medium approximations (Maxwell, self-consistent, differential) and our exponential relation is discussed. Irrespective of the model into which the Eshelby–Wu coefficients are implemented, prolate pore shape affects the porosity dependence of Young's modulus only very weakly, whereas oblate pore shape can lead to an arbitrary reduction of Young's modulus.     

Molecular dynamics simulation study on the structure and properties of polyimide/silica hybrid materials

A type of polyimide/silica (PI/SiO₂) copolymer model was established through the dehydration of tetraethyl orthosilicate molecules (TEOS) and bonding to a silane coupling agent. The content of SiO₂ was controlled by adjusting the number of molecules which bound to the TEOS. Finally, the silica was formed into a hybrid model (hybrid PI/SiO₂) with a small molecule embedded in the PI. The model was optimized by geometric and molecular dynamics and the changes in the model structure, Young's modulus, shear modulus, and glass-transition temperature (T _g) were analyzed. The results showed that the density and cohesive energy density of the composites could be improved by doping SiO₂ in PI. Young's modulus and shear modulus of PI/SiO₂ hybrid materials were higher than undoped PI. The tensile strength reached 568.15 MPa when the doping content was 9%. Therefore, the structure design and content control of SiO₂ was an effective way to improve the performance of a PI/SiO₂ composite. The variation of T _g and tensile strength of PI/SiO₂ hybrid composites is consistent with that of PI/SiO₂ composite synthesized in real experiment, which will be a convenient method for new material design and performance prediction. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47335.     

Influences of evaluation methods and testing load on microhardness and Young's modulus of ZTA and ATZ ceramics

In this work, microindentation tests under different conditions were performed to determine the influence of indentation load on Young's modulus and microhardness of ZrO₂ reinforced with Al₂O₃ particles (ATZ) and Al₂O₃ reinforced with ZrO₂ particles (ZTA).     

Thermal expansion performance and intrinsic lattice thermal conductivity of ferroelastic RETaO4 ceramics

Ferroelastic RETaO₄ ceramics are promising thermal barrier coatings (TBCs) because of their attractive thermomechanical properties. The influence of crystal structure distortion degree on thermomechanical properties of RETaO₄ is estimated in this work. The relationship between Young's modulus and TECs is determined. The highest TECs (10.7 × 10⁻⁶ K⁻¹, 1200°C) of RETaO₄ are detected in ErTaO₄ ceramics and are ascribed to its small Young's modulus and low Debye temperature. The intrinsic lattice thermal conductivity (3.94-1.26 W m⁻¹ K⁻¹, 100-900°C) of RETaO₄ deceases with increasing of temperature due to an elimination in thermal radiation effects. The theoretical minimum thermal conductivity (1.00 W m⁻¹ K⁻¹) of RETaO₄ indicates that the experimental value is able to be reduced further. We have delved deeply into the thermomechanical properties of ferroelastic RETaO₄ ceramics and have emphasized their high-temperature applications as TBCs.     

The determination of the axial Young's modulus of honeycomb specimens under bending

For solid specimens, Young's modulus is commonly determined from straightforward uniaxial tension experiments. However, honeycomb specimens are far more challenging to test in tension, and it is therefore desirable to conduct bending experiments to determine Young's modulus. The premise of this work is that the bending response of honeycomb specimens may be significantly different from that of solid specimens, and therefore it is necessary to establish a sound protocol for the determination of the axial Young's modulus of honeycomb specimens under bending. Toward this goal, we present results of a study that combines experimental, finite element simulation, and classical beam theory approaches. These results confirm that accurate measurements of Young's modulus of honeycombs require careful consideration of the specimen geometry and analysis of the data. We demonstrate that the use of conventional Bernoulli‐Euler's beam theory to interpret the data requires very slender specimens. We also show that less slender specimens can be used if the experimental data is interpreted on the basis of three‐dimensional elasticity theory and numerical simulations. A third option is to use a combination of moderately slender specimens and Timoshenko's beam theory.     

Melt-quenched oxide glasses with ultrahigh Young's modulus and small thermal expansion coefficient

The well-known Makishima–Mackenzie relationship, consisting of two terms of the dense packing structure and dissociation energy regarding bonding in constituent oxides, enables fabricating oxide glasses with ultrahigh Young's modulus (∼140 GPa) and a small coefficient of thermal expansion (CTE) (∼4 ppm/K). The effects of increasing MgO and Ta₂O₅ contents in an MgO–Ta₂O₅–Al₂O₃–SiO₂–B₂O₃ glass system using a conventional melt-quenching method are revealed. The essential oxides of Al₂O₃ and Ta₂O₅ are primarily suitable for dense packing structures dominated by a large coordination number of oxygens. The substitution of CaO by MgO results in high dissociation energy when the glass composition falls in the peraluminous regime (Al₂O₃/[MgO + CaO] > 1). A small CTE is realized by increasing the molar ratio of Al₂O₃/MgO. According to magic-angle spinning-nuclear magnetic resonance spectra, mechanically and thermally functional oxide glasses depend on their structures. These findings facilitate the development of glass substrate applications without thermal dilatation.     

Mechanical properties of thin and thick coatings applied to various substrates. Part II. Young's modulus determination of coating materials*

To determine Young's modulus of coating materials when they are applied to substrates, theoretical and experimental analyses are performed. Significant residual stresses are generated within thin and thick coatings applied to substrates. As a result of these stresses, the bi-material strip assumes a certain curvature. The curved beam theory was used to establish the equivalent bending stiffness of bi-layer materials as functions of (a) the initial radius of curvature generated by residual stresses, (b) the mechanical radius of curvature during flexure testing, and (c) mechanical (Young's moduli) and geometrical (widths and thicknesses) characteristics of bi-layered systems. The relevant expression was transformed to a second- or third-order equation in order to calculate Young's modulus of the coating undergoing residual stresses (using models developed in Part I and by Stoney, Röll, and Inoue).     

Effect of Porosity on Structure,Young's Modulus,and Thermal Conductivity of SiC Foams by Direct Foaming and Gelcasting

The study demonstrates the aqueous processing of solid‐state‐sintered SiC foams by gelcasting technique. Aside from increasing strength of green bodies, gelcasting monomers were the source of carbon additive which helped in sintering of SiC foams. Sintered foams with the relative density (RD) between 0.44 and 0.11 were processed by direct foaming of SiC slurries followed by gelcasting and sintering. Structural analysis by X‐ray tomography showed the presence of spherical pores with bimodal pore size distribution and the proportion of large size cell and their interconnectivity increased in low RD foams. SEM study revealed that decreased RD resulted in gradual changes in the strut microstructure from the grains with faceted interface to smooth interfaced grains. The analysis of changes in Young's modulus and thermal conductivity with RD were in agreement with the Ashby model for open cell foams.     

On the nonlinear behavior of Young's modulus of carbon‐bonded alumina at high temperatures

The origin of the nonlinear behavior of the Young's modulus (E) of carbon‐bonded alumina at high temperatures was addressed, based on the microstructural changes observed during processing and their thermo‐mechanical properties. Impulse excitation technique, thermogravimetric analysis, porosity measurement, and scanning electron microscopy were conducted in order to highlight and explain the E behavior. The finite element model of a virtual microstructure was simulated and the results attained are in good agreement with the experimental data. The tests revealed that the Young's modulus of a cured sample heated from room temperature up to 500°C was governed by the release of volatiles. Above this temperature, the thermal expansion mismatch among alumina, graphite, and the carbon matrix is dominant resulting in an increase in the effective Young's modulus. During cooling, crack networks and gaps between alumina particles and the carbon matrix were developed. The former were induced by volatile release and by the graphite's highly anisotropic thermal expansion. The latter was derived by the thermal expansion mismatch between the alumina and the carbon matrix. The closure of the gaps and cracks governed the expansion behavior during the second heating cycle and a nonlinear effective Young's modulus increase as a function of temperature was observed.     

Effects of Orientation on the Properties of Liquid Crystalline Polymers

Abstract

Mechanical properties and thermal behavior of liquid crystalline polymers with mesogene groups in the main chain were studied as functions of jet draw ratio. It is shown that tensile strength F and Young's modulus E increase with draw ratio and the maximum E depends mainly on the chemical structure of chain and F is strongly affected by molecular packing that may be improved by heat treatment. The differential thermal analysis, thermal mechanical analysis and thermal acoustic analysis were used to find the spinning conditions for achieving maximum orientation and annealing conditions for macromolecular reconstructions without disorientation.     

Isothermal and adiabatic Young's moduli of alumina and zirconia ceramics at elevated temperatures

The elastic moduli (Young's moduli) of alumina and zirconia ceramics with porosities ranging from almost dense (2–3%) to highly porous (46–52%), the latter prepared with starch as a pore-forming agent, have been measured via impulse excitation and four-point bending tests from room temperature up to more than 1200 °C. It is shown that, independent of the temperature and the material, the porosity dependence of the Young's modulus is well predicted by our exponential relation and that, irrespective of porosity, the temperature dependence follows a master curve that is characteristic of the material (for alumina exhibiting a decrease with a gradually growing tangent slope and for zirconia exhibiting a steep decrease with an inflection point at moderately elevated temperatures below 400 °C). Differences between isothermal (static) and adiabatic (dynamic) values are negligible as long as the materials are purely elastic (i.e. at temperatures below approximately 1000 °C).     

Effect of glassy bonding materials on the properties of LAS/SiC porous ceramics with near zero thermal expansion

Near zero thermal expansion porous ceramics were fabricated by using SiC and LiAlSiO₄ as positive and negative thermal expansion materials, respectively, bonded by glassy material. The coefficient of thermal expansion value of a desired porous composite can be easily controlled by choosing the appropriate ratios of the different phases. It was shown that some of LiAlSiO₄ was decomposed to LiAlSi₂O₆ and LiAlO₂, some of LiAlSiO₄ reacted with SiO₂ to form LiAlSi₂O₆ during sintering. With increasing the content of glassy materials, the reaction between LiAlSiO₄ and SiO₂ was accelerated. The Young's modulus increased due to the neck growth between the SiC grains. The 52.5 vol% LiAlSiO₄ (LAS)/SiC ceramics with ∼36% porosity had a combination of near zero coefficient of thermal expansion ∼0.39 × 10⁻⁶ K⁻¹ at room temperature and relatively high Young's modulus ∼59 GPa.     

Microscopically-viewed relationship between the chain conformation and ultimate Young's modulus of a series of arylate polyesters with long methylene segments

Relationship between the chain conformation in the crystal lattice and the ultimate Young's modulus has been discussed on the basis of the crystal structural information revealed by the X-ray diffraction analysis for a series of arylate polyesters with long methylene segments (–[–COC₆H₄CO–O(CH₂)_mO–]_n–). The X-ray structural analysis revealed that the molecular chains take the all-trans-zigzag conformations for all of the even-numbered polyesters and their model compounds as well as the odd-numbered polyesters with the methylene segmental length longer than (CH₂)₁₄. These chain conformations have been correlated well to the ultimate Young's modulus along the chain axis or the crystallite modulus E_c, which has been estimated experimentally by the X-ray diffraction method under a constant stress and also predicted theoretically using the X-ray-analyzed crystal structures on the basis of the molecular mechanics method. The E_c was found to show the minimum at around m = 4–6 and increased gradually with an increment of m and approached the crystallite modulus of polyethylene, 235 GPa (X-ray value) ∼ 316 GPa (calculate) at an infinite m value. This behavior of E_c as a function of the number of methylene segmental units m was reasonably interpreted by developing the theoretical equation of E_c for a simplified zigzag chain model composed of a repetition of two linear rods representing the benzene–ester and methylene segmental parts respectively. These findings may promise that the mechanical property of arylate polyester can be controlled by adjusting the methylene segmental length m.     

Mechanical properties,thermal expansion performance and intrinsic lattice thermal conductivity of AlMO4 (M=Ta,Nb) ceramics for high-temperature applications

The vital thermo-mechanical properties of thermal and environment barrier coatings (TBCs/EBCs) include high hardness, low Young's modulus, matching thermal expansion coefficients (TECs) with substrate and low thermal conductivity. The effect of distortion degree of crystal structure on thermo-mechanical properties of AlMO₄ (M=Ta, Nb) ceramics are assessed in this work. AlMO₄ ceramics display modest TECs and no phase transformation is detected from room temperature to 1200?℃. The experiment thermal conductivity can be dropped further as the theoretical minimum thermal conductivity of AlTaO₄ and AlNbO₄ is 1.48?W?m^?1 K^?1 and 1.05?W?m^?1 K^?1, respectively. The temperature dependent phonon thermal diffusivity of AlMO₄ ceramics has been confirmed; the intrinsic lattice thermal conductivity is determined. The extraordinary thermo-mechanical properties make it clear that AlMO₄ ceramics are suitable for high-temperature applications.     

Thermal conductivity,elastic modulus,and coefficient of thermal expansion of polymer composites filled with ceramic particles for electronic packaging

The effective thermal conductivity, elastic modulus, and coefficient of thermal expansion of epoxy resins filled with ceramic fillers like silica, alumina, and aluminum nitride were determined. The data obtained was compared with theoretical and semitheoretical equations in the literature that are used to predict the properties of two phase mixtures. It was found that Agari's model provided a good estimate of the composite thermal conductivity. The Hashin‐Shtrikman lower bound for composite modulus fits the modulus data fairly well at low concentrations of the filler. Also, it was found that the coefficients of thermal expansion of the filled composites lie in between Schapery's upper and lower bounds. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 3396–3403, 1999     

The Use of Thin Film Thermocouples to Determine the Thermal Conductivity and Young's Modulus of Coatings and Interfaces

Linear and differential thin film thermocouples, typically 500-1000Å thick, were fabricated on flexible polymer and paper substrates by thermal evaporation. Both types of thermocouples had thermal sensitivities of approximately 4 μ V/°C, for temperatures between 20°C and 40°C, on the paper and polymer-coated paper substrates. The transverse thermal conductivity (k^t), i.e., thermal conductivity in the direction perpendicular to the plane of the films, of polyimide (Kapton-H®) films, of a clay-coated paper, and of a polystyrene coating on paper were determined by depositing linear thermocouples on both sides of the films and raising the temperature of one junction and measuring the heat flux and, at equilibrium, the temperature of the other junction. Shear and Young's moduli of the polymer films were estimated from the measured thermal conductivity values, assuming the Debye model of thermal conductivity.     

Reliability studies of gelcast fused silica between organic and inorganic binder systems

Fused silica ceramics was prepared by using conventional organic binder, mathacrylamide‐N,N′‐methylenebisacrylamide (MAM‐MBAM) system by gelcasting process. Mechanical properties of green bodies were studied as a function of solid loading varying from 60 to 72 vol%. After evaluating the green body mechanical properties, the samples were densified at different sintering temperature from 1200 to 1450°C with definite intervals of 50°C and subjected to flexural strength analysis. Variation in flexural strength with sintering temperature was observed and correlated with the quantity of devitrification of fused silica during sintering. Quantification of devitrified cristobalite was carried out by using 20 wt% rutile (TiO₂) as an internal standard by X‐ray diffraction. It was found that, as the cristobalite content increased, flexural strength decreased. Reliability studies were carried out for the samples having maximum flexural strength with and without crystalline content. Reliability studies have shown that for this organic binder system the sample sintered at 1300°C is crystalline free and most reliable product. The mechanical properties and reliability of this product processed with organic binder are compared with inorganic binder system. Results indicate that the sample fabricated using inorganic binder system is exhibiting high Weibull modulus and thus better reliability.     

Elastic anomalies in tridymite- and cristobalite-based silica materials

Cristobalite and tridymite are the main SiO₂ phases in silica bricks, a widespread refractory product. The elastic properties of cristobalite at room temperature have been extensively studied, because it is known for auxetic behavior, i.e. negative Poisson ratios, whereas the elastic properties of tridymite are essentially unknown. Here we show that silica brick materials, consisting almost entirely of tridymite and cristobalite, exhibit remarkable anomalies in the temperature dependence of the Young modulus: in the intermediate temperature range between approximately 50 and 250 °C these materials become very compliant, with stiffness minima of around 60% of the room temperature values, with a broad transition region at the low-temperature end, a sharp transition at the high-temperature end and a precisely reproducible hysteresis during heating and cooling. Furthermore, it is shown that Young's moduli at around 800 °C can be more than three times as high as the room temperature values.     

A Two‐Step Method Based on Micromechanical Models to Predict the Young's Modulus of Polymer Nanocomposites

A two‐step method is suggested to predict the Young's modulus of polymer nanocomposites assuming the interphase between polymer matrix and nanoparticles. At first, nanoparticles and their surrounding interphase are assumed as effective particles with core–shell structure and their modulus is predicted. At the next step, the effective particles are taken into account as a dispersed phase in polymer matrix and the modulus of composites is calculated. The predictions of the two‐step method are compared with the experimental data in absence and presence of interphase and also, the influences of nanoparticles size as well as interphase thickness and modulus on the Young's modulus of nanocomposites are explored. The predictions of the suggested model show good agreement with the experimental data by proper ranges of interphase properties. Moreover, the interphase thickness and modulus straightly affect the modulus of nanocomposites. Also, smaller nanoparticles create a higher level of modulus for nanocomposites, due to the large surface area at interface and the strong interfacial interaction between polymer matrix and nanoparticles.