Constant Thermal Expansion Coefficient Research Articles

The Effect of Thermal Residual Stress on the Stress State in a Short-Fiber Reinforced Thermoplastic

Upon their cooling and solidification, significant thermal residual stresses can develop in short-fiber reinforced thermoplastics due to the mismatch in coefficient of thermal expansion between fiber and matrix. In this study we set out to investigate this effect numerically. The build-up of thermal residual stresses is modeled by expanding a well-established constitutive model, the Eindhoven glassy polymer (EGP) model, with thermal expansion. The experimentally measured thermal residual stresses can be described using an effective glass-transition temperature and a constant coefficient of thermal expansion without the need for complex equilibrium kinetics associated with the glass transition itself. Subsequently, the influence of thermal residual stress on the deformation behavior for a short-fiber reinforced thermoplastic is studied employing multi-fiber representative volume elements (RVEs) for different fiber-weight fractions. The micromechanical models are evaluated on the importance of thermal residual stresses on the local and nominal stress state. From these analyses it can be concluded that the thermal residual stresses should be accounted for when assessing the quantitative local stress state and are therefore essential when local mechanisms are studied. In contrast, thermal residual stresses are not required to capture the nominal transient stress–strain response.

Influence of temperature on the elastic properties of graphene and graphene-like nanosheets based on the asymptotic homogenization method

In this paper, the effective elastic properties of hexagonal monolayers such as graphene, boron nitride, silicon carbide, and aluminum nitride are evaluated using the asymptotic homogenization method taking into account temperature changes. The effective properties are determined analytically by considering temperature, force constants, bond lengths, and thickness, using atomic interactions within the context of the unit cell problem. The relationship between environmental temperature and the coefficient of thermal expansion is established by considering changes in the values ​​of bond stretching, bond angle bending, and torsion resistance constants at different temperatures from 0 to 1800 K. The results provided by the proposed homogeneous model are consistent with the valid findings of other researchers in the literature. It is found that these different hexagonal nanosheets exhibit isotropic temperature-dependent properties and their Young's and shear modulus decrease almost linearly as the temperature rises, considering a constant coefficient of thermal expansion. However, Poisson's ratio is found to be independent of temperature. Furthermore, the temperature-dependent elastic properties of these nanosheets become nonlinear when the variation of the coefficient of thermal expansion with temperature is taken into account. The Young and shear moduli of the nanosheets increase as the coefficient of thermal expansion decreases and vice versa. The highest elastic modulus values are obtained when the thermal expansion is close to its minimum threshold. However, it is recognized that the elastic modulus of graphene and boron nitride nanosheets is higher than that of silicon carbide and aluminum nitride at any temperature. As an alternative to lengthy computer modeling or rigorous testing, the homogeneous models provided can be used to simulate nanosheets.

Thermal Conductivity and Thermal Diffusivity of Tremolite at High Temperature and Pressure and Implications for the Thermal Structure of the Venusian Lithosphere

AbstractThermal conductivity (κ) and thermal diffusivity (D) of tremolite were measured at up to 2.5 GPa and 1,373 K using the transient plane‐source method in a multi‐anvil apparatus. Thermal conductivity and thermal diffusivity of tremolite decrease monotonically before dehydration (<1,173 K) and increase significantly after dehydration. Tremolite exhibits positive pressure dependence before dehydration. Heat capacity (C) of tremolite calculated fromκandDshows a positive pressure dependence and is controlled by an almost constant thermal expansion coefficient (α) with temperature. Conductive heat transport and radiative heat transport dominate the heat transport process before dehydration, and the significant increase in thermal conductivity after dehydration is attributed to convective heat transport. A compositional model of the Venusian lithosphere composed of a basaltic crust and peridotite mantle with or without tremolite was established. The thickness of the Venusian lithosphere with or without tremolite for Venus was calculated by combining the heat flow (from 20 to 80 mW/m2) at a certain depth (from 5 to 25 km) of crust, ranging from 24.4 to 184.6 km.

Transverse electric-thermal-fluid instabilities in an electromagnetic heat exchanger

Electromagnetic (EM) heat exchangers (HX) are critical components in power beaming applications where EM waves are radiated towards an EM HX, which then converts incident energy into heat or mechanical work. An EM HX consists of a lossy ceramic and a fluid flow that maintains thermal contact with and transfers heat from the ceramic. These materials have loss factors which increase with temperature, so that beyond a critical temperature thermal runaway can take place. Stable characteristic temperatures, which depend on the rate of energy removal from the system, during high-power EM heating of ceramic materials suggest that coolants would be in the gaseous phase. As a first step, we consider a model EM HX system consisting of a horizontal channel containing a viscous, dielectric fluid with a constant coefficient of thermal expansion, bounded from below by a grounded ceramic receiver of finite thickness. The system is subject to plane EM waves, propagating normally to the channel from above, and polarized in the same direction as a plane Poiseuille flow of the coolant. With the Boussinesq approximation, we calculate the base state solution of the system and then investigate the linear stability of this base-state. We find three modes of instability: thermal runaway, Rayleigh-Bénard convection, and a novel instability which we call the fringe-field instability, that takes place in the plane normal to base-state flow direction.

Remote Propulsion of Miniaturized Mechanical Devices via Infrared‐Irradiated Reversible Shape Memory Polymers

Remote propulsion of miniature mechanical devices possesses a great challenge to the scientific community. Herein, a lightweight two‐way shape memory polymer (2WSMP)‐based motor is presented, which operates a demo vehicle via a novel infrared‐irradiated 2WSMP actuator. Most of the polymers that possess 2WSMP properties suffer from inadequate mechanical properties and low durability in harsh environments. Herein, the 2WSMP bilayer actuator, based on Kapton and polyPOSS (PP), possesses superior 2WSMP and mechanical properties, high lifting abilities, and durability in harsh environments. Kapton is well known for its outstanding physical properties. PP, a polyhedral oligomeric silsesquioxane (POSS)‐based epoxy‐like thermoset, possesses unique properties. Its advanced ability to maintain mechanical properties over a range of temperatures, while presenting a constant coefficient of thermal expansion, is essential for its 2WSMP actuation properties. The effects of the Kapton and PP layers’ thickness on the force and deflection, generated by the 2WSMP actuators during heating, are studied. A theoretical model is used to predict the actuator's deflection, based on the layers’ thickness. These actuators present excellent thermal stability at temperatures as high as 150 °C, while maintaining outstanding motion repeatability and extremely high lifting capacity of up to 6500 times of their own weight.

Influence of thermo-mechanical material properties on the structural response of a welded butt-joint by FEM simulation and experimental tests

This paper deals with the development of a Finite Element (FE) model for the simulation of a two-passes V-groove butt weld joint. Specifically, in order to reduce the computational costs and the efforts aimed to the numerical evaluation of residual stresses distribution in welded joints, a sensitivity analysis has been performed to quantify the level of accuracy provided by the model when the strict dependence of some material properties on the temperature is neglected. Before proceeding with the sensitivity analysis, the reliability of the proposed FE model was assessed against an experimental test; a good agreement between numerical and experiment results has been achieved.In detail, the material properties involved in this sensitivity analysis are: thermal conductivity, specific heat, Young's modulus and thermal expansion coefficient; the investigated outputs are: temperatures, residual stresses, displacements and angular distortion. Several test cases have been simulated by considering all of these material properties as constant, one at a time or all together. The results analysis showed that the levels of accuracy provided by the different simplifications depend on the selected output. Among the most relevant results, it has been found out that the predicted temperatures distributions are not significantly influenced by the considered material simplifications. The effects on the residual stresses in considering the thermal conductivity and the specific heat as constant are negligible. The hypothesis of a constant thermal expansion coefficient provides an acceptable level of accuracy only in proximity of the weld seam. Finally, concerning the displacements field and the angular distortion of the welded plates, by considering the thermal conductivity and Young's modulus as constant, the effectiveness of the model appears to be compromised.

Experimental Determination of Aluminum Burning Velocity During Flame Propagation in a Tube

Modeling the consequences of dust explosions is a challenging research topic. A key parameter of these models is the burning velocity, which represents the consumption rate of the reactants by the flame front. Especially, a relation between burning velocity and RMS (root-mean square) air velocity fluctuations has to be implemented in such models; RMS velocity fluctuations representing the turbulence of the fresh air flow in front of the flame front.This paper focuses on the experimental determination of this relation in the case of dust flames propagating in a tube. The most commonly used method is the “open-tube method”, which assumes a constant thermal expansion coefficient and the estimation of a 3D flame surface. These assumptions are discussed, and a new method is proposed, based on the measurement of the fresh flow velocity in front of the flame front. The corresponding optical setup implemented for analyzing aluminum burning velocity is then exposed. Analysis method for obtaining burning velocity and RMS velocity fluctuations is detailed. Finally, first results obtained are presented and commented.

Effect of iron content on thermal conductivity of olivine with implications for cooling history of rocky planets

The influence of Fe concentration on heat transport properties of olivine was investigated to understand the cooling history of rocky planets such as Mercury, Mars and asteroids. Thermal conductivity (λ) and thermal diffusivity (κ) were measured simultaneously for olivine polycrystal with different Fe contents (Fo, Fo90, Fo70, Fo50, Fo31 and Fo0) up to 10 GPa and 1100 K by a pulse heating method. With increasing Fe in olivine, thermal conductivity of olivine first decreases and then slightly increases. The minimum λ was found to be at composition near Fo31; the absolute λ value of Fo31 is about 65% lower than that of Fo. Small amounts of Fe in olivine can strongly reduce the thermal conductivity at low temperature; λ value of Fo90 is about 50% of Fo at room temperature. Thermal conductivities of polycrystalline olivine have smaller absolute values and weaker pressure and temperature dependences, compared with those of natural single crystal olivine determined by previous studies. Heat capacity of Fo70 and Fo50 calculated from λ and κ is independent of pressure and is controlled by nearly constant thermal expansion coefficient with increasing temperature. Smaller λ of olivine aggregate with high Fe content would produce a warmer mantle and, in turn, possibly a thicker crust in the Fe-rich Mars, while heat in the Fe-poor Mercury can escape faster than the other terrestrial planets. Olivine-dominant asteroids with high Fe concentration could have longer cooling history and lower thermal inertia on the surface.

Pressureless sintering behavior and properties of Ag–SnO2

In this study, the results of measurements on pressureless sintering behavior of Ag–SnO2 (88%wt Ag, 12%wt SnO2) pellets were reported. Dilatometric measurements, relative densities, hardness values, rupture transverse strength and electrical conductivities function of sintering temperatures were presented. A constant thermal expansion coefficient was determined, and a threshold temperature of densification (Td) was exhibited. Sintering kinetics were reported for different temperatures. Hardness values were measured, and no increase in hardness is found under Td. Three-points bending tests were used to determine the transverse rupture strength whose evolution appears importantly well under Td. In the same manner, the increase in initial electrical conductivities begins well under Td. Under the threshold temperature, the relative increase in electrical conductivity is found to be independent of initial density of green compact pellets. This work highlights different evolutions in function of sintering temperature for the electrical conductivity and transverse rupture strength on the one hand, and for the densification and hardness on the other hand.

The Temperature-Dependent Thermal Expansion of 2,6-Diamino-3,5-dinitropyrazine-1-oxide Effected by Hydrogen Bond Network Relaxation

The temperature-dependent thermal expansion of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) was investigated by using powder X-ray diffraction (PXRD) together with Rietveld refinement to estimate the dimension at a crystal lattice level. In the temperature range of 30–200°C, the coefficient of thermal expansion (CTE) of LLM-105 is temperature dependent, which is different from other explosives, such as hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), 2,2′,4,4′,6,6′-hexanitrostilbene (HNS) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), with constant CTEs. The results of temperature-dependent infrared (IR) spectra indicated that the intermolecular hydrogen bond network relaxes with increasing temperature, which results in temperature-dependent thermal expansion. In this work, more accurate CTEs for LLM-105 crystals are obtained and the effects of the hydrogen bond network on the thermal expansion are further clarified. These results are beneficial to the design of materials with structural peculiarities and as-expected thermal expansion to satisfy different application requirements.

Crystal and electronic structure of high temperature superconducting compound Y1−xCaxBa2Cu3Oy in the temperature interval 80–300 K

For Y1−хСахBa2Cu3Oy with varying oxygen and calcium content, the change of crystal structure at cooling from room temperature to 80 K has been investigated. The main change is associated with a shift of apical oxygen atoms. Using determined unit cell parameters as function of temperature, the coefficients of linear thermal expansion have been calculated as αX = 1/X·(dX/dT), where Х = a, b, c – unit cell dimensions. For the compound without calcium all αX values demonstrate anomalous behavior such as growing at cooling in temperature interval T1 ÷ T2 ∼ 150 ÷ 225 K. The calculation of electronic structure at temperatures above, below and within this interval shows the appearance of the electronic states density peak for Ba and O4 atoms. It is explained by the localization of charge carriers with the participation of the lattice distortion in a form of apical Cu–O bond compression. As the material Y0.9Са0.1Ba2Cu3Oy regardless of the oxygen content possess low and constant coefficient of thermal expansion along all crystallographic directions, that makes this material suitable for superconducting films and other composites.

Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition: new results

In a recent paper by Makinde and Olanrewaju (J Fluids Eng 132:044502, 2010) the effect of thermal buoyancy along a stationary vertical plate with a uniform free stream flow was considered. The plate’s wall thermal boundary condition and the fluid thermal expansion coefficient were variable along the plate in order that the problem accepts a similarity solution. In the present work, the problem has been changed to have a constant heat transfer coefficient and a constant thermal expansion coefficient which is considered to be more realistic and has much more practical applications. The present problem is non-similar and results are obtained by numerical solution of the governing equations. The problem is governed by the Prandtl number, the non-dimensional distance along the plate and the convective Grashof number. It is found that the wall shear stress, the wall heat transfer and the wall temperature all increases with increasing distance and the wall temperature tends to 1. The influence of the convective Grashof number is to increase the wall shear stress and the wall heat transfer and to reduce the wall temperature.

Temperature lapse rates at restricted thermodynamic equilibrium in the Earth system

Equilibrium temperature profiles obtained by maximizing the entropy of a column of fluid with a given height and volume under the influence of gravity are discussed by using numerical experiments. Calculations are made both for the case of an ideal gas and for a liquid with constant isobaric heat capacity, constant compressibility and constant thermal expansion coefficient representing idealized conditions corresponding to atmosphere and ocean. Calculations confirm the classical equilibrium condition by Gibbs that an isothermal temperature profile gives a maximum in entropy constrained by a constant mass and a constant sum of internal and potential energy. However, it was also found that an isentropic profile gives a maximum in entropy constrained by a constant mass and a constant internal energy of the fluid column. On the basis of this result a hypothesis is suggested that the adiabatic lapse rate represents a restricted or transitory and metastable equilibrium state, which has a maximum in entropy with lower value than the maximum in the state with an isothermal lapse rate. This transitory equilibrium state is maintained by passive forces, preventing or slowing down the transition of the system to the final or ultimate equilibrium state.

A self-consistent Gibbs excess mixing rule for cubic equations of state

The extension of the applicability of cubic equations of state (EoS) with Gibbs excess models to the prediction of high-pressure/high-temperature vapor–liquid equilibria of polar and/or asymmetric is well known. Despite the success of this category of mixing rules (EoS/GE), the combined model is often less accurate than the Gibbs excess model alone at low pressure. In this work a new Gibbs excess mixing rule for cubic equations of state is developed. The proposed method was derived solely based on the assumption of a zero excess volume liquid-like phase. Tests with substances dissimilar in size, shape and chemical nature have shown that any cubic equation of state coupled with the proposed mixing rule can reproduce the underlying liquid activity model at low pressures, showing that the method is self-consistent. Further, the method was extended for high pressures/temperatures by assuming a constant thermal expansion coefficient liquid-like phase as the reference state. Very good results were obtained when the proposed method was coupled with Wilson, UNIQUAC, UNIFAC and a COSMO-based model in liquid–liquid and vapor–liquid equilibrium examples.

Thermal expansion and lattice parameters of shaped metal deposited Ti–6Al–4V

Thermal expansion and lattice parameters are investigated up to 1100 °C for Ti–6Al–4V components, fabricated by shaped metal deposition. This is a novel additive layer manufacturing technique where near net-shape components are built by tungsten inert gas welding. The as-fabricated SMD Ti–6Al–4V components exhibit a constant coefficient of thermal expansion of 1.17 × 10 −5 K −1 during heating up to 1100 °C, not reflecting the α to β phase transformation. During cooling a stalling of the contraction is observed starting at the β transus temperature. These high temperature experiments denude the α phase of V and enrich the β phase. The development of the lattice parameters in dependence on temperature are observed with high temperature X-ray diffraction. The unit cell volumes derived from these parameters are at room temperature larger for the α than for the β phase. With increasing temperature the unit cell volume of the β phase increases stronger than the one of the α phase resulting in a similar unit cell volume at the β transus temperature. These observations are interpreted as an indication for as-fabricated the SMD components being in a non-equilibrium state and reaching equilibrium during the slow heating and cooling during of the two different high temperature experiments.

Thermal expansion of GaSb measured by temperature dependent x-ray diffraction

X-ray diffraction measurements were performed using a modified zone technique on Te-doped GaSb wafers, commonly used for molecular beam epitaxial growth, at temperatures between 32 and 546 °C to determine the thermal expansion. The authors found the thermal expansion to be very close to the data published by Bublik et al. [Phys. Status Solidi A 73, K271 (1982)]. Control measurements of the lattice constant of Si were found to agree with the results published by Okada and Tokumaru [J. Appl. Phys. 56, 314 (1984)] within our measurement error of ±2×10−4 Å. A fourth order polynomial, a(GaSb)(T)=6.0959+3.37×10−5T+5.63×10−8T2−1.29×10−10T3+1.05×10−13T4 (Å) (T in °C), was found to be a good fit to our data, while a linear fit with a constant thermal expansion coefficient of 7.17×10−6 K−1 was found to be a poorer fit.

Mantle convection models with temperature‐ and depth‐dependent thermal expansivity

We investigate the effects of temperature‐ and depth‐dependent thermal expansivity in two‐dimensional mantle convection models in cylindrical shell and plane layer geometries. Most previous models of mantle convection have employed either a constant coefficient of thermal expansion, α, or a depth‐dependent α = α(r), where r is the radial coordinate antiparallel to gravity. We consider α to have the form α(r,T) = αr (r)αT (T), where αr(r) increases with radius, r (or decreases with depth), and αT (T) increases with temperature, T. We find that the depth dependence and temperature dependence of α each have a significant, but opposite, effect on the mean surface heat flux (or Nusselt number) and the mean surface velocity of the convecting system. For α = αr (r), a decrease of α with depth by a factor of 4 across the mantle causes a decrease of surface heat flux by about 20% and a decrease in mean surface velocity by about 30%, relative to the constant α case, in either cylindrical or plane layer geometry. However, when the temperature dependence of α is also included, αT (T) effectively compensates for the effects of αr(r) such that the predicted decreases in heat flow and surface velocity are either eliminated or, in some cases, become increases. Consequently, previous studies that include only the effects of depth dependence of α may underestimate surface heat flow and plate velocities by as much as 20% and 50%, respectively.

Thermal expansion behaviour of barium and strontium zirconium phosphates

Ba1.5-xSrxZr4P5SiO24 compounds withx = 0, 0.25, 0.5, 0.75, 1.0, 1.25 and 1.5, belonging to the low thermal expansion NZP family were synthesized by the solid state reaction method. The XRD pattern could be completely indexed with respect to\(R\bar 3\) space group indicating the ordering of vacancy at the divalent cation octahedral sites. The microstructure and bulk thermal expansion coefficient from room temperature to 800°C of the sintered samples have been studied. All the samples show very low coefficient of thermal expansion (CTE), withx = 0 samples showing negative expansion. A small substitution of strontium in the pure barium compound changes the sign of CTE. Similarly,x = 1.5 sample (pure strontium) shows a positive CTE and a small substitution of barium changes its sign.X = 1.0 and 1.25 samples have almost constant CTE over the entire temperature range. The low thermal expansion of these samples can be attributed to the ordering of the ions in the crystal structure of these materials

Preparation and properties of binary oxide bioceramics

Candidate inert bioceramics based on Al2O3 and ZrO2 and on SiO2-TiO2 were prepared via slip casting and sol-gel/hot-pressing techniques, respectively. Their properties relevant to applicability in biomedicine-microstructure, microhardness and coefficient of thermal expansion-were determined. The affinity of the oxides with body-liquids was evaluated by wetting experiments at 37°C. High-quality materials were achieved due to the advantages offered by the preparation techniques employed. The Al2O3 and ZrO2 based ceramics have high hardness, a constant coefficient of thermal expansion within a wide temperature range and low adhesion with biological liquids. The SiO2-TiO2 samples, the crystallinity of which depends on the preparation conditions, have lower hardness and lower coefficient of thermal expansion, which in the case of crystalline samples considerably changes at low temperatures, and display good affinity with biological liquids, strongly affected by the presence of glassy phase in the oxide.

Numerical studies of open ocean deep convection

Open ocean deep convection is examined with a nonhydrostatic model based on primitive equations. Strong cooling on the surface of the ocean enforces vertical motion which takes place in the narrow regions of convective cells. Different equations of state are considered, and it is shown that a linear equation of state with a constant thermal expansion coefficient cannot represent the buoyancy field and fluxes properly. The inclusion of thermobaric effects leads to additional vertical acceleration in the whole water column. The parametrization of the convective fluxes by a convective adjustment algorithm represents the horizontal mean temperature quite well but suppresses the entire vertical mass transport within the convective cells. This mass transport may be important for the transport of other tracers. Investigation of an energy cycle of the convective motion sorts out sources and sinks and reveals the conversion between different forms of energy during convective events. Both the vertical and the horizontal component of the Earth rotation vector contribute to the time mean energy balance with the same order of magnitude, but the instantaneous amplitudes of the distinct terms may differ substantially. A sensitivity study with respect to eddy and thermal diffusion coefficients distinguishes two regions; at high values of the diffusivities the velocities and tracer distributions show that a strong dependence on this values occurs, while for sufficiently small coefficients, only a weak dependence is observed.