Thermal Conductivity Constants Research Articles

Phase-field modeling of thermal shock fracture in functionally graded materials

In this paper, the thermo-elastic fracture problems of functionally graded materials (FGMs) are thoroughly investigated based on a modified phase field model. In this model, the material constants and fracture toughness vary along a specified direction, the thermal conductivity and stiffness constants in the damaged regions are degraded by the phase-field variable, and the crack evolution is driven by the variation of elastic energy induced by the thermo-mechanical loading. Therefore, the temperature, mechanical and damage fields are coupled with each other. The validation of the present approach has been checked by comparing the present results with the analytical, numerical, and experimental results in literature. The examples of thermo-elastic tensile fracture and thermal shock cracking of FGMs are performed to investigate the influence of material heterogeneity and external thermal loading. Furthermore, the experimental phenomenon of crack deflection in FGMs has been captured by the present simulations. The present study provides a guidance for understanding the fracture mechanism, material design and safety assessment of FGM structures in engineering practice.

Micro-CT image-based computation of effective thermal and mechanical properties of fibrous porous materials

Fibrous porous materials are extensively employed as heat shielding material for space vehicles and capsules. To predict the performance of these materials using computational modeling at the vehicle/capsule scale, the effective material properties are needed. In this work, the effective thermal conductivity and elastic constants of a carbon fibrous porous material called FiberForm (precursor of PICA) were calculated using a direct image-based approach. In this image-based approach, the microstructures obtained using X-ray computed tomography technique are represented as binary voxel data. Nonlocal interactions are introduced between neighboring voxels. Integro-differential equations, with respect to spatial and temporal dimensions respectively, are developed to govern material thermal and mechanical behaviors. Using this approach, energy-based computational procedures were developed to calculate the effective material properties of fibrous and porous materials irrespective of the periodicity of underlying microstructures. The size of representative volume element was determined by convergence of effective properties with respect to microstructure size.

Influence of variable thermal conductivity and inclined load on a nonlocal photothermoelastic semiconducting medium with two temperatures

The current study explores two-dimensional disturbances in a nonlocal photothermoelastic semiconducting medium with two temperatures by implementing the Green Naghdi-II theory. The thermal conductivity of the medium is assumed to be varying with temperature changes. The formulation is subjected to an inclined mechanical load. A lot of research has been carried out in recent years on photothermoelastic medium, but not much attention has been given to study the dynamical interactions in a nonlocal photothermoelastic medium with two temperatures and variable thermal conductivity under the effect of inclined mechanical load. The analytical solutions of physical field variables such as temperatures, stresses, carrier density and displacement are obtained by using the normal mode analysis method. For a specific material, numerical computations are performed to illustrate the results. The results that were obtained through numerical analysis for the physical quantities are displayed graphically. The comparisons are made among the results obtained by taking into account the different values of time, inclination angle, two temperature parameter, nonlocal parameter, variable thermal conductivity and photothermal elastic constants. Some special cases of interest have been inferred from the present study for validation.

Revisiting thermal transport in single-layer graphene: On the applicability of thermal snapshot interatomic force constant extraction methodology for layered materials

The thermal conductivities of single-/bi-layer graphene and bulk-graphite are obtained using the Boltzmann transport equation (BTE) framework by accounting for three-phonon and four-phonon scatterings. For single-layer graphene, the thermal conductivity and interatomic force constants obtained using temperature-independent finite-difference, and temperature-dependent molecular dynamics-based approaches agree with each other. The use of the thermal snapshot approach to get temperature-dependent force constants results in a non-physical description of interatomic distances for single-layer graphene. The predicted thermal conductivity at room temperature using finite-difference based force constants is 800 W/m K, which is a severe under-prediction of experimentally measured values. For bi-layer graphene and bulk graphite, the thermal snapshot methodology is applicable and thermal conductivity changes by 25% and 5% with temperature-dependent force constants. The effect of four-phonon scattering is less than 10% on the predicted thermal conductivity of bi-layer graphene and graphite, and the obtained thermal conductivities using thermal snapshot methodology are in agreement with the literature. The limitation in the prediction of thermal conductivity of single-layer graphene via the BTE approach stems from non-accountability of temperature-dependence in finite-difference based force constants and non-physical description of interatomic bonds in thermal snapshot based force constants extraction for planar 2-atoms unitcell of single layer graphene.

Thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity and nonlinear finite element analysis

In non-isothermal conditions, numerous experimental and theoretical investigations reveal that the elastic constants and thermal conductivity in piezoelectric solids depend on temperature distribution. This work aims to investigate thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity. The nonlinear time-domain finite element method is developed to directly solve nonlinear finite element governing equations, which maximally avoids the precision losses within the applications of the integrated transformation method. As a numerical example, the developed method is applied to analyze nonlinear transient thermo-electromechanical responses of a two-dimensional orthotropic piezoelectric plate of crystal class mm2. The achieved results reveal that temperature-dependent thermal conductivity and elastic constants remarkably affect the structural dynamic responses, whilst thermal wave or elastic wave will travel faster and the electrical energy harvesting ability is significantly elevated.

Improvement of dielectric properties and thermal conductivity of TPU with alumina-encapsulated rGO

This study focuses on the fabrication of thermoplastic polyurethane (TPU) composites with high thermal conductivity and dielectric constants, which can be used in electronic devices that are able to store charge and dissipate heat. To fabricate the samples, GO was reduced via sonication, and alumina-encapsulated GO particles were prepared with sonication and high-temperature magnetic stirring for 24 h. The TPU composites were fabricated through the melt extrusion process after removing the moistures via oven drying. The storage of charge is enabled by the high dielectric constant obtained from the APTES-treated alumina-encapsulated GO-TPU composites; the heat dissipation characteristics are found from the high thermal conductivity and thermal image camera of the sample. Surprisingly, the tensile and ductile properties of the composite are promising. The thermal conductivity of the APTES treated alumina encapsulated TPU composite is 3.2 times higher than that of the neat TPU. The dielectric property of the GO containing alumina composites is promisingly higher as compared to all other composites investigated.

Computer modeling of systematic processing defects on the thermal and elastic properties of open Kelvin-cell metamaterials

Open-cell metamaterials prepared by additive manufacturing or replica techniques are typically prone to processing defects resulting from limited resolution, strut cross-section variations or internal strut porosity. These defects are expected to cause deviations from the ideal (CAD-based or template-based) target microstructures and thus from the envisaged properties. This paper investigates some of these effects in a quantitative manner. Based on computer-generated open Kelvin-cell (tetrakaidecahedral) alumina-based metamaterials, the effective thermal conductivity and elastic constants, mainly Young’s modulus, are calculated in dependence of the voxel size, strut thinning and strut wall thickness. It is shown that the porosity dependence of smooth, straight and full struts agrees closely to the Gibson-Ashby prediction for open-cell foams, while limited resolution and strut thinning leads to property values that tend to be lower and hollow struts lead to higher property values. The Pabst-Gregorová cross-property relation gives an excellent prediction of the conductivity-modulus correlation in all cases.

Thermoelastic properties of synthetic single crystal portlandite Ca(OH)2 - Temperature-dependent thermal diffusivity with derived thermal conductivity and elastic constants at ambient conditions

Synthetic portlandite single crystals were used to measure thermal diffusivity and elastic constants. The full tensor of elastic constants cijkl is derived by Brillouin spectroscopy at ambient conditions. The resultant aggregate bulk and shear moduli are KS, VRH= 32.2(3) GPa and GVRH= 21.2(2) GPa, respectively. The thermal diffusivity D was measured from −100 ∘C to 700 ∘C parallel [001] and perpendicular [100] to the crystallographic c-axis using laser flash method. The dehydration of the crystals influences the thermal diffusivity determination depending on sample size, orientation and heating rate. Thermal diffusivity and the derived thermal conductivity show a pronounced anisotropy with a maximum perpendicular to the c-axis, i.e. in the plane of the [CaO6] octahedral layers. In the same direction the highest sound velocities (vP and vmean) and longest mean free path length of phonons are determined. The thermal diffusivity as well as the derived thermal conductivity show a distinct temperature dependence.

Improved Mathematical Model of Polluted Insulators nonlinear behaviour Under AC Voltage Based on Experimental Tests

In this paper, an improved mathematical model for flashover behavior of polluted insulators is proposed based on experimental tests. In order to determine the flashover model of polluted insulators, the relationship between conductivity and salinity of solution pollution layer of the insulator is measured. Then, the leakage of current amplitude of four common insulators versus axial, thermal conductivity and arc constants temperature was determined. The experimental tests show that top leakage distance (TLd) to bottom leakage distance (BLd) ratio of insulators has a significant effect on critical voltage and current. Therefore, critical voltage and current were modeled by TLd to BLd ratio Index (M). Also, salinity of solution pollution layer of the insulators has been applied to this model by resistance pollution parameter. On the other hand, arc constants of each insulator in new model have been identified based on experimental results. Finally, a mathematical model is intended for critical voltage against salinity of solution pollution layer of different insulators. This model depends on insulator profile. There is a good agreement between the experimental tests of pollution insulators obtained in the laboratory and values calculated from the mathematical models developed in the present study.

Improved Mathematical Model of Polluted Insulators nonlinear behaviour Under AC Voltage Based on Experimental Tests

In this paper, an improved mathematical model for flashover behavior of polluted insulators is proposed based on experimental tests. In order to determine the flashover model of polluted insulators, the relationship between conductivity and salinity of solution pollution layer of the insulator is measured. Then, the leakage of current amplitude of four common insulators versus axial, thermal conductivity and arc constants temperature was determined. The experimental tests show that top leakage distance (TLd) to bottom leakage distance (BLd) ratio of insulators has a significant effect on critical voltage and current. Therefore, critical voltage and current were modeled by TLd to BLd ratio Index (M). Also, salinity of solution pollution layer of the insulators has been applied to this model by resistance pollution parameter. On the other hand, arc constants of each insulator in new model have been identified based on experimental results. Finally, a mathematical model is intended for critical voltage against salinity of solution pollution layer of different insulators. This model depends on insulator profile. There is a good agreement between the experimental tests of pollution insulators obtained in the laboratory and values calculated from the mathematical models developed in the present study.

Improved Mathematical Model of Polluted Insulators nonlinear behaviour Under AC Voltage Based on Experimental Tests

Abstract—In this paper, an improved mathematical model for flashover behavior of polluted insulators is proposed based on experimental tests. In order to determine the flashover model of polluted insulators, the relationship between conductivity and salinity of solution pollution layer of the insulator is measured. Then, the leakage of current amplitude of four common insulators versus axial, thermal conductivity and arc constants temperature was determined. The experimental tests show that top leakage distance (TLd) to bottom leakage distance (BLd) ratio of insulators has a significant effect on critical voltage and current. Therefore, critical voltage and current were modeled by TLd to BLd ratio Index (M). Also, salinity of solution pollution layer of the insulators has been applied to this model by resistance pollution parameter. On the other hand, arc constants of each insulator in new model have been identified based on experimental results. Finally, a mathematical model is intended for critical voltage against salinity of solution pollution layer of different insulators. This model depends on insulator profile. There is a good agreement between the experimental tests of pollution insulators obtained in the laboratory and values calculated from the mathematical models developed in the present study.

Comparison of Several Thermal Conductivity Constants for Thermal Hydraulic Calculation of Pebble Bed Reactor

There are two type of High Temperature Gas Reactor (HTGR), prismatic and pebble bed. Pebble Bed type has unique configuration because the fuels are randomly distributed inside the reactor core. In term of safety features, Pebble Bed Reactor (PBR) is one of the most promising reactor type in avoiding severe nuclear accidents. In order to analyze heat transfer and safety of this reactor type, a computer code is now under development. As a first step, calculation method proposed by Stroh [1] is adopted. An approach has been made to treat randomly distributed pebble balls contains fissile material inside the reactor core as a porous medium. Helium gas act as coolant on the reactor system are carrying heat flowing in the area between the pebble balls. Several parameters and constants are taken into account in the new developed code. Progress of the development of the code especially comparison of several thermal conductivity constants for a certain PBR-case are reported in the present study.

Compositional and Structural Atomistic Study of Amorphous Si–B–N Networks of Interest for High-Performance Coatings

We explore by computational modeling the effects of boron–nitrogen (BN) composition on the thermal and mechanical properties of amorphous silicon–boron–nitride (Si–B–N), a synthetic ceramic material with superior thermal protection, mechanical attributes, and oxidation resistance at high temperatures. Network-derived Si–B–N models optimized with ab initio molecular dynamics serve as input structures for classical molecular dynamics simulations. Atomistic Green–Kubo simulations on relaxed supercells and structural relaxations on strained cells are used to screen the thermal and mechanical properties of a collection of network structures with low enthalpies of formation. We find that when the material is composed of well-mixed parts rather homogeneously spread within the material, the thermal conductivity and elastic constants are isotropic and exhibit a weak dependence on composition and network structure. In contrast, when separation into BN-rich layers occurs, the material exhibits anisotropic behavior, ...

Experimental and modeling of thermal and dielectric properties of aluminum nitride-reinforced polybenzoxazine hybrids

The effects of aluminum nitride (AlN) loading and size on the thermal conductivity of bisphenol A-aniline-based polybenzoxazine resin were studied. The experimental data of the thermal conductivity, CTE, and dielectric constants of these hybrids were compared with those predicted using various models. The morphological analysis revealed the formation of AlN conductive chains in the polybenzoxazine matrix. The thermal conductivity values of these hybrids gradually increased as the AlN fillers content increased and their sizes decreased. The highest thermal conductivity value reached 7.89 W m−1 K−1 at 60 vol% of 50 nm AlN. At the maximum AlN loading, the CTE values of these hybrids were reduced by 75 %, while their dielectric constants are raised by almost 45 %. The TG results showed significant improvements in the thermal degradation properties of these composites by adding the AlN filler; moreover, the Agari semiempirical model well-fitted the thermal conductivity experimental data of these materials.

Uncertainty Analysis of Melting and Resolidification of Gold Film Irradiated by Nano- to Femtosecond Lasers Using Stochastic Method

A sample-based stochastic model is presented to investigate the effects of uncertainties of various input parameters, including laser fluence, laser pulse duration, thermal conductivity constants for electron, and electron–lattice coupling factor, on solid–liquid phase change of gold film under nano- to femtosecond laser irradiation. Rapid melting and resolidification of a free-standing gold film subject to nano- to femtosecond laser are simulated using a two-temperature model incorporated with the interfacial tracking method. The interfacial velocity and temperature are obtained by solving the energy equation in terms of volumetric enthalpy for control volume (CV). The convergence of variance (COV) is used to characterize the variability of the input parameters, and the interquartile range (IQR) is used to calculate the uncertainty of the output parameters. The IQR analysis shows that the laser fluence and the electron–lattice coupling factor have the strongest influences on the interfacial location, velocity, and temperatures.

Decay of solutions for a mixture of thermoelastic solids with different temperatures

We study a system modeling thermomechanical deformations for mixtures of thermoelastic solids with two different temperatures, that is, when each component of the mixture has its own temperature. In particular, we investigate the asymptotic behavior of the related solutions. We prove the exponential stability of solutions for a generic class of materials. In case of the coupling matrix B being singular, we find that in general the corresponding semigroup is not exponentially stable. In this case we obtain that the corresponding solution decays polynomially as t−1/2 in case of Neumann boundary condition. Additionally, we show that the rate of decay is optimal. For Dirichlet boundary condition, we prove that the rate of decay is t−1/6. Finally, we demonstrate the impossibility of time-localization of solutions in case that two coefficients (related with the thermal conductivity constants) agree.

Thermal Conductivity, Heat Capacity, and Elastic Constants of Water-Soluble Polymers and Polymer Blends

We use time-domain thermoreflectance (TDTR), and the generation and detection of longitudinal and surface acoustic waves, to study the thermal conductivity, heat capacity, and elastic properties of thin films of poly(vinyl alcohol) (PVA), poly(acrylic acid) (PAA), polyacrylamide (PAM), poly(vinylpyrrolidone) (PVP), methyl cellulose (MC), poly(4-styrenesulfonic acid) (PSS), poly(N-acryloylpiperidine) (PAP), poly(methyl methacrylate) (PMMA), and a polymer blend of PVA/PAA. The thermal conductivity of six water-soluble polymers in the dry state varies by a factor of ≈2, from 0.21 to 0.38 W m–1 K–1, where the largest values appear among polymers with a high concentration of hydrogen bonding (PAA, PAM, PSS). The longitudinal elastic constants range from 7.4 to 24.5 GPa and scale linearly with the shear elastic constants, suggesting a narrow distribution of Possion’s ratio 0.35 < ν < 0.40. The thermal conductivity increases with the average sound velocity, as expected based on the model of the minimum thermal c...

Mechanical properties of a diamond–copper composite with high thermal conductivity

Abstract Using pressureless infiltration of copper into a bed of coarse (180 μm) diamond particles pre-coated with tungsten, a composite with a thermal conductivity of 720 W/(m K) was prepared. The bending strength and compression strength of the composite were measured as 380 MPa. As measured by sound velocity, the Young's modulus of the composite was 310 GPa. Model calculations of the thermal conductivity, the strength and elastic constants of the copper–diamond composite were carried out, depending on the size and volume fraction of filler particles. The coincidence of the values of bending strength and compressive strength and the relatively high deformation at failure (a few percent) characterize the fabricated diamond–copper composite as ductile. The properties of the composite are compared to the known analogues — metal matrix composites with a high thermal conductivity having a high content of filler particles (~ 60 vol.%). In strength and ductility our composite is superior to diamond–metal composites with a coarse filler; in thermal conductivity it surpasses composites of SiC–Al, W–Cu and WC–Cu, and dispersion-strengthened copper.

Thermal Conductivity and Elastic Constants of PEDOT:PSS with High Electrical Conductivity

Mixtures of poly(3,4-ethylenedioxythiophene) and polystyrenesulfonate (PEDOT:PSS) have high electrical conductivity when cast from aqueous suspensions in combination with a high boiling-point cosolvent dimethyl sulfoxide (DMSO). The electronic component of the thermal conductivity of these highly conducting polymers is of interest for evaluating their potential for thermoelectric cooling and power generation. We find, using time-domain thermore- flectance measurements of thermal conductivity along multiple directions of thick (>20 μm) drop-cast PEDOT films, that the thermal conductivity can be highly anisotropic (Λ∥ ≈ 1.0 W m −1 K −1 and Λ⊥ ≈ 0.3 W m −1 K −1 for the in-plane and through- plane directions, respectively) when the electrical conductivity in the in-plane direction is large (σ ≈ 500 S cm −1 ). We relate the increase in thermal conductivity to the estimated electronic component of the thermal conductivity using the Wiedemann−Franz law, and find that our data are consistent with conventional Sommerfeld value of the Lorenz number. We use measurements of the elastic constants (C11 ≈ 11 GPa and C44 ≈ 17 GPa) of spin-cast PEDOT films and through-plane thermal conductivity (Λ⊥ ≈ 0.3 W m −1 K −1 ) of drop-cast and spin-cast films to support our assumption that the phonon contribution to the thermal conductivity does not change significantly with DMSO composition.

Asymptotic expansion homogenization for multiscale nuclear fuel analysis

Engineering scale nuclear fuel performance simulations can benefit by utilizing high-fidelity models running at a lower length scale. Lower length-scale models provide a detailed view of the material behavior that is used to determine the average material response at the macroscale. These lower length-scale calculations may provide insight into material behavior where experimental data is sparse or nonexistent.This multiscale approach is especially useful in the nuclear field, since irradiation experiments are difficult and expensive to conduct. The lower length-scale models complement the experiments by influencing the types of experiments required and by reducing the total number of experiments needed. This multiscale modeling approach is a central motivation in the development of the BISON and MARMOT fuel performance codes. These codes seek to provide more accurate and predictive solutions for nuclear fuel behavior.One critical aspect of multiscale modeling is the ability to extract the relevant information from the lower length-scale simulations. One approach, the asymptotic expansion homogenization (AEH) technique, has proven to be an effective method for determining homogenized material parameters. The AEH technique prescribes a system of equations to solve at the mesoscale that are used to compute homogenized material constants for use at the engineering scale.In this work, we employ AEH to explore the effect of evolving microstructural thermal conductivity and elastic constants on nuclear fuel performance. We show that the AEH approach fits cleanly into the BISON and MARMOT codes and provides a natural, multidimensional homogenization capability.