Nonuniform Thermal Field Research Articles

Free vibration and buckling behavior of porous P-type FGM and S-type FGM circular plates on elastic foundation under non-uniform thermal field

In this paper, in order to satisfied the design and manufacturing requirements of functional materials, an investigation is carried out to study the free vibration and thermal buckling characteristics of porous P- and S-type functionally graded materials (FGM) circular plates in non-uniform thermal fields in the context of first-order shear deformation theory. FGM is formed by gradient changes in metals and ceramics, the thermomechanical properties were characterized by a gradient along the thickness direction of the circular plate by a power-law function containing porosity correction. The differential equations of motion control are derived using the Hamiltonian variational principle, and the dimensionless equations of motion and boundary conditions are solved analytically by the DTM transformation procedure. The problem has been degraded and compared with the results of the existing literature to confirm its validity. In conclusion, the influence of each parameter on the dimensionless natural frequency of the porous FGM circular plate and the influence of relevant parameters on the critical temperature rise are calculated and evaluated. The porosity weakens the overall stiffness and equivalent mass of the structure, and the foundation enhances the stiffness. The DTM calculation iteration speed is fast, and the results are highly consistent. The results can be used to provide model guidance and data support for future studies of porous FGM circular plates as well as follow-up studies.

Free vibrations of axially loaded thin-walled shaft-disk rotors subjected to non-uniform temperature field

Research on vibrations of shaft-disk rotors in non-uniform thermal field is essential for the design of rotating machinery. In this paper, the dynamic model of axially loaded thin-walled shaft-disk rotors in axial non-uniform temperature field is developed, considering three-dimensional displacement fields of the shaft and disk. This model introduces the temperature-dependent properties of materials, and gyroscopic and centrifugal effects. Based on the Euler-Bernoulli beam theory and the Kirchhoff plate theory, Lagrange's equation is used to derive the differential equations of motion. By comparing with the results of the existing reference and finite element results, the accuracy of the present model is verified. The effects of the axial displacement of shaft, temperature-dependent material property, temperature difference, temperature distribution, disk position and axial preload on the free vibration of shaft-disk rotors are discussed. Results show that the present model can effectively predict free vibrations of shaft-disk rotors in axial non-uniform temperature field. The effect of thermal field on vibrations of shaft-disk rotors is affected by the rotational speed and disk location as well.

Mechanical behavior of thermally-induced shape memory polymer composites thin-wall tube in non-uniform thermal field: Experiments and simulations

Thermally-induced shape memory polymer composites (SMPCs) have the capability to self-deploy when stimulated by a specific temperature. As a basic component of deployable truss structure, SMPCs thin-wall circular tubes will undergo complex non-linear deformation and changing thermal boundary conditions during application. This article aims to research the mechanical behavior of thermally-induced SMPCs thin-wall circular tubes in a non-uniform thermal field. Thermal properties of SMPCs including thermal conductivities and coefficients of thermal expansion are tested as fundamental temperature-dependent parameters. A 500 mm-long SMPCs thin-wall tube is conducted in the flattening-folding-cooling-reheating experiments through a specially manufactured loading apparatus. Combining phase transition theory and Fourier heat conduction, a coupling algorithm is proposed to describe the thermo-mechanical behavior of SMPCs, which is implemented by the user subroutines VUMAT by commercial finite element analysis packages ABAQUS. By comparing the results from the simulation of the non-uniform thermal field, the simulation of the uniform thermal field and experiments, the coupling algorithm is verified, and the effect on SMPCs from the non-uniform thermal field is given.

Nonlinear vibration responses of lattice sandwich beams with FGM facesheets based on an improved thermo-mechanical equivalent model

An investigation on the nonlinear vibration behaviors of a lattice sandwich beam with pyramidal truss core and functionally graded material (FGM) facesheets under thermo-mechanical loads is performed with consideration of the temperature-dependency of material properties. In present work, an improved equivalent methodology is proposed to determine the transverse shear modulus of pyramidal core subjected to a non-uniform thermal field across thickness direction and makes lattice truss core transformed to a continuous layer. Finally, the lattice sandwich beam is modeled as a three-layered sandwich structure. The facesheets are made of FGMs with mixture of ceramics and metals in a pow-law form. The outer surfaces of facesheets are ceramic-rich, while the inner surfaces are metal-rich. The nonlinear strain–displacement relations are established based on the von Kármán large deflection and classical beam theory. The Lagrange method are implemented to yield equations governing the free and forced vibration behaviors. With the help of Newton-Raphson iteration technique as well as the Newmark-β method, the nonlinear time-independent responses of the sandwich beam under thermal environment are solved. A comprehensive parameter study is directed to address the effects of non-uniform thermal environment, FMG facesheets, external load, and lattice core on the nonlinear vibrations of the beams.

Analytical thermoelastic solutions for additive manufacturing processes

This work is motivated by the need to determine residual thermo-structural fields in a computationally efficient manner relative to the finite element method for solving the balance of energy and momentum partial differential equations. The present paper describes an analytical model that computes the time-dependent three-dimensional distributions of the thermo-mechanical fields for heat deposition problems in general, and additive manufacturing problems in particular. This corresponds to the determination of the displacement, strain, and stress fields generated by a moving heat flux in thermally conducting and mechanically deforming structures. The problem is solved by a one-way coupled approach where temperature fields determined analytically by the solution of the heat transfer problem are used as inputs for solving the analytical solution of the solid mechanics problem. The heat transfer problem is solved first using the recently developed Enriched Analytical Solution Method (EASM) for evaluating the spatio-temporal distribution of temperature fields generated during additive manufacturing (AM) processes. Because the EASM provides the temperature over the entire domain at any time, a non-uniform thermal eigenstrain field can be used in conjunction with Green’s function for the half-space to determine the corresponding elastic fields. The analytical predictions of the elastic fields are compared with those obtained by the finite element analysis for the case of a single track laser powder bed fusion application. The results indicate that the proposed analytical model accurately matches the finite element calculated structural response.

Marangoni flow of thin liquid film underneath a topographical plate

Marangoni flow occurs when a fluid-fluid free surface is exposed to a non-uniform thermal field. Recently, Marangoni flow has been used to fabricate micro/nano-structures in thin films, which is referred to as thermocapillary patterning. A thin liquid-air film is confined between a hot plate and a topographic cold plate. Marangoni flow thus takes place, and the film evolves into micro/nano-structures that comply with the geometry of the template. In this paper, a numerical model based on the moving mesh method is proposed to study the dynamic process of thermocapillary patterning. Liquid and air are calculated simultaneously with proper boundary conditions imposed at the interface. The numerical model enables characterization of the thermal field and the fluid flow, and thus the deformation of the liquid film. The effect of some key parameters, including temperature difference, template geometry, and liquid film viscosity, on thermocapillary patterning is investigated. The numerical model and the obtained results serve as a useful and representative guide for practical experiments.

Effect of material characteristics on thermal, tribological and mechanical properties of high temperature cast iron coatings

Coating is a desideratum part of material science and effort must be entailed for obtaining desired high temperature properties. Properties of high temperature cast iron coatings depend on various factors and each of them must be precisely tailored for meeting the huge industrial demand. The unlimited architecture of novel materials has led to growth of various coating with tailored properties. Single/multi layered structure offers remarkable possibilities to improve coating properties. Cast iron has been increasingly used in gas turbine, internal combustion engine manufacturing industries due to its low cost and structural strength. Numerous researches have been done on cast iron coatings to study the thermal, tribological plus mechanical properties. Novel material for improving the thermal, mechanical and tribological properties of Thermal barrier coatings (TBCs) required an extensive property-characteristics connection realization. Yttria Stabilized Zirconia (YSZ) is the most established coating material for thermal barrier application. YSZ alone cannot withstand the huge industrial demand. YSZ in engine application suffers failure due to non-uniform thermal field, thermal stress and sintering during the cycle of operation. YSZ cannot withstand engine thermal properties including thermal cycle life and thermal durability. Wear rate gets affected as a result of brittle fracture, speed of operation and abrasion. High temperature exposure leads to microcracks and this affects the mechanical properties. TBCs are usually made of ceramic top coat and it suffers failure. Few material characteristics and factors include thermal aging, fracture toughness of the material. This paper summarizes confirmed experimental results by researchers concerning different factors including thermal conductivity, thermal shock resistance, thermal cycle life, wear resistance, coefficient of friction, hardness and material characteristics in regard with cast iron coatings for high temperature applications. This paper also recommends feasible materials and material combinations to overcome certain limitations and failures.

Analytical model for three-dimensional non-uniform temperature field and welding stress of thick plates via friction stir weld

The non-uniform thermal field for thick plates jointed by friction stir welding (FSW) easily causes the complex stress state and affects the mechanical behaviour of welded components. The transient non-uniform temperature field for thick plates by FSW is analytically studied based on the heat conduction problem solved by three-dimensional Green’s function. The asymmetric volumetric heat source model is developed by considering the flux distributions in the thickness direction, which is used to obtain the semi-analytical temperature field for welded plates with nonhomogeneous boundary conditions. Then, the analytical model for welding stress is proposed for thick plates by FSW according to the non-uniform temperature field in the weld. The elastic-plastic boundary and the variations of welding stress in the thickness direction are discussed based on the temperature gradient in the welding process. The non-uniform stress distribution in the weld may be analytically predicted in the welding process. The residual stress in the weld is numerically calculated in the cooling process and compared with experiment data to verify the models for the non-uniform temperature field and stress distribution of thick plates. The results show that the three-dimensional temperature field may be used effectively to provide insights into the mechanical response by FSW.

Modular-Pouring Furnace with the Local Granular Media Flow Rates Distributed Between Thermal Zones

The paper presents the results of analytical and experimental studies of the thermal zones in the working space of the modules of an electric pouring furnace. To increase the production rate and reduce the energy content of the work process, the local granular media flows were distributed between such zones depending on their heating. The modular-pouring furnace, equipped with plate accelerators located inside the modules to accelerate the local granular media flows, has been upgraded by adapting a drum dispenser provided with the longitudinal stepped slots having variable depth. Based on the analysis of the incident, effective, and resulting flows in the working spaces of the modules, performed by the methods of algebra of radiant fluxes, the causes of the formation of a non-uniform thermal field on the refractory surfaces of the firing modules were established. The analysis of experimental data, confirming the conclusions of the analytical study, was carried out, and the width of each thermal zone was determined. By comparing the heat quantities absorbed by vermiculite, used as an example, the minimum amount of time required for its particles to travel through each thermal zone and the average local velocities of the particles within such zones were determined. It was shown that the nature of the distribution of the average local velocities of vermiculite flows between the thermal zones is nonlinear. The local and overall production rates of the furnace were determined with the latter (equal to 0.95 m3/sec) being 27% higher compared to a prototype pilot furnace under equal power consumption.

Composition and electrical properties characterization of a 5” diameter PIN-PMN-PT single crystal by the modified Bridgman method

A Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 relaxor ferroelectric single crystal with a 5” diameter and 145 mm length was grown by the modified Bridgman method. The composition distribution of the crystal boule was investigated. The result showed that the PbTiO3 contents increased along the growth direction, which means that compositional segregation existed, and the effective segregation coefficient was simulated to be 0.84, which is close to that of 3” single crystal. The horizontal composition distribution in the crystal demonstrated that the solid-melt interface of the 5” single crystal was serious convex during crystal growth and was caused by the nonuniform radial thermal field of the large melt. The dielectric, piezoelectric, ferroelectric properties and domain structures were measured to investigate the effect of the composition change along the crystal growth direction. Based on the domain structure and electrical performance, the crystal boule was divided into rhombohedral, morphotropic phase boundary and tetragonal regions. It was found that the optimal piezoelectric coefficient d33 of the 5” single crystal was more than 2000 pC/N. This work provided positive information for large sized single crystal growth of a relaxor ferroelectric single crystal.

Nonlinear Dynamics of Composite Microsheet with Graphene Skins in Non-uniform Thermal Field

The effects of different parameters on the nonlinear dynamic characteristics of macrofiber composite (MFC) microsheet with graphene (GP) skin under non-uniform thermal field are investigated. Firstly, the physical parameters of the MFC–GP structure are calculated by the mixing rule, and the constitutive equations of the structure are set up by employing the Eringen theory. The nonlinear dynamic equations of the microsheet are obtained by using Hamilton’s principle. Then, the heat conduction equations of the microsheet are considered, adopting Green and Naghdi’s generalized thermoelasticity theory. According to the Galerkin weighted residual method, the thermoelasticity coupling equations of the structure are obtained. Meanwhile, the influence of the positive piezoelectric effect of GP and MFC on the vibration response of the structure is also investigated. The nonlinear dynamic governing equations including displacement, coupled thermoelasticity, and electricity field are discretized by the Galerkin method. The effects of non-local parameter, volume fraction of GP, and thermal and electricity coupling coefficients on structural dynamic behavior are discussed in the numerical simulation.

Mechanical Integrity Analysis of a Printed Circuit Heat Exchanger with Channel Misalignment

Printed circuit heat exchangers (PCHEs), which are used for thermal heat storage and power generation, are often subject to severe pressure and temperature differences between primary and secondary channels, which causes mechanical integrity problems. PCHE operation may result in discontinuity, such as channel misalignment, due to non-uniform thermal fields in the diffusion bonding process. The present paper analyzes the mechanical integrity, including the utilization factors of stress and deformation under various channel misalignment conditions. The pressure difference of the target PCHE is 19.5 MPa due to the high pressure (19.7 MPa) of the steam channel in the Rankine cycle and the low pressure (0.5 MPa) of molten salt or liquid metal in the primary channel. Additionally, the temperature difference between channels is around 25 °C, however the average temperature is around 500 °C. The PCHE has a relatively large primary channel measuring approximately 3 x 3 mm, and a steam channel measuring 2 x 1.5 mm. The finite element method (FEM) is applied to determine the stress by changing the misalignment to below 30% of the primary channel width. It was found that the current PCHE is operable up to 700 °C in terms of the ASME code under these design conditions. Additionally, the change of utilization factor due to the misalignment increases, but is still under the ASME acceptance criteria of 700 °C; however, it violates the criteria at 725 °C, which is the allowable temperature condition. Therefore, the mechanical integrity of the PCHE with low-pressure molten salt or liquid metal and a high-pressure steam channel is acceptable in terms of utilization factor.

Structural investigation of the snow-melting heated bridge deck based on the thermal field distribution

This paper aims to improve the energy utilization of the snow-melting heated bridge deck system with a thermally conductive layer (SHBD-TCL) and reduce its deformation caused by the non-uniform thermal field distribution. Therefore, three structures of the SHBD-TCL were proposed, and there are thermally conductive layers and heating cables embedded in different layers. Then, the finite element models corresponding to the above structures were developed. The energy utilization and the deformation caused by the thermal gradient were analyzed, and the embedded spacing and embedded depth were set as input factors. Also, the effective energy ratio and the maximal deformation were set as the optimization targets, and their prediction models were established based on the above input factors. Finally, to obtain greater effective energy ratio and less deformation, the multi-objective optimization was applied to achieve the optimum structure and rational parameters. The optimum structure was selected to conduct the laboratory experiments, which verified the reasonability of the finite element model of SHBD-TCL. The research enriches the thermodynamic structure design theory of the snow-melting bridge system.

Joule heating-induced particle manipulation on a microfluidic chip.

We develop an electrokinetic technique that continuously manipulates colloidal particles to concentrate into patterned particulate groups in an energy efficient way, by exclusive harnessing of the intrinsic Joule heating effects. Our technique exploits the alternating current electrothermal flow phenomenon which is generated due to the interaction between non-uniform electric and thermal fields. Highly non-uniform electric field generates sharp temperature gradients by generating spatially-varying Joule heat that varies along the radial direction from a concentrated point hotspot. Sharp temperature gradients induce a local variation in electric properties which, in turn, generate a strong electrothermal vortex. The imposed fluid flow brings the colloidal particles at the centre of the hotspot and enables particle aggregation. Furthermore, maneuvering structures of the Joule heating spots, different patterns of particle clustering may be formed in a low power budget, thus opening up a new realm of on-chip particle manipulation process without necessitating a highly focused laser beam which is much complicated and demands higher power budget. This technique can find its use in Lab-on-a-chip devices to manipulate particle groups, including biological cells.

The Structure of Iron Powder Aggregation Obtained by Selective Laser Melting

A powder of different fractional composition was obtained from the iron ingot using the melt atomization method, from which samples for further studies were grown on the EOSint M270 unit using the selective laser melting (SLM) method. When considering the thin sections of the samples, we observed equiaxed recrystallized grains up to 20 μm in size, randomly distributed particles in the form of fragments up to 5 μm in size and equally oriented non-axial crystallites, forming groups in the form of arcuate layers with a front width of 800 μm and depth from 10 to 30 microns. Between them, narrow zones of increased chemical content were found, which are interpreted as probable traces of the stoppages of thermal fronts. We recorded traces of mass localized microplastic flow in the form of extended (up to 350x40 µm) and curved microregions with unequal-sized grains bordering microregions filled with equiaxial recrystallized grains due to the action of non-uniform thermal fields. Thus, in metal objects produced by the SLM, the complex morphology of the structure indicates a combination of different-scale mechanisms of structural changes. It has been established that in non-stationary temperature conditions of structure formation, the role of kinetic processes increases.

Self-Propulsion of Water-Supported Liquid Marbles Filled with Sulfuric Acid

Self-propulsion of liquid marbles filled with sulfuric acid and coated with hydrophobic fluorosilica powder on a water surface is reported. The prolonged self-propulsion of marbles occurs over a couple of minutes with a typical velocity of the center of mass of the marble being [Formula: see text]. The shell of the marble is not uniform, resulting in the asymmetric absorption of water by a marble, giving rise to the nonuniform thermal field within its volume. The maximum temperature reached at the liquid marble surface was 70 °C. The self-propelled marble increased its mass by one-third during the course of its motion. The increase in mass followed by the marbles' heating is due to the adsorption of water vapor by their surface, which is permeable to gases. This gives rise to an exothermic chemical reaction, which in turn gives rise to Marangoni thermo-capillary flow driving the marble. Thermo-physical analysis of the problem is presented. The role of soluto-capillary flow in self-propulsion is negligible.

Effect of initial variance of microstructures on grain growth under mean curvature

Surface Evolver was used to simulate grain growth under motion by mean curvature starting with non-uniform microstructures. The study was conducted for different microstructures that begin evolving with an identical mean grain area and a differing value of statistical variance of the grain areas. Correlation between a microstructure’s initial variance, a geometric property of the polycrystalline network, and its growth rate in the normal regime was studied. It was observed that the microstructures evolved at different growth rates. The microstructures with the largest and smallest variances evolved with highest and lowest growth rates. The analysis was performed in the normal grain growth regime. It is observed that a direct correlation can be made between the initial variance of the microstructure and its growth rate in the normal regime. These results highlight the importance of including the grain size variance when controlling microstructure using non-uniform thermal fields.

Thermomagnetic Convection of Magnetic Fluid in an Annular Space under a Non-Uniform Magnetic and Thermal Field

Two-dimensional thermomagnetic convection of magnetic fluid possessing internal spin and relaxation of magnetization with high thermal sensitivity is numerically analyzed under a non-uniform magnetic and thermal field, using a spectral difference scheme, magnetic fluid is assumed to be placed between concentric cylinders, an azimuthal magnetic field being produced by an electric current though the inner cylinder, which is an adiabatic wall, whereas a half of the outer cylinder is kept at a high constant temperature and the rest half is at a lower constant temperature. As a result, in case of ▽T × ▽|H| ≠ 0, thermomagnetic convection is found to be produced, the convection pattern depends on electric current distribution, depending on which multiple or single circulation is produced, thus, it shows that thermomagnetic convection pattern is controlled by changing relative direction of temperature gradient to that of a magnetic field.

Growing Solids and Thin-Walled Structures

The present paper provides a systematic treatment of modern differential-geometrical methods for modeling of incompatible finite deformations in solids and thin walled structures. The incompatibility of deformations may be caused by a variety of physical phenomena; among them are: growth, non-uniform thermal fields, shrinkage, etc. Incompatible deformations results in residual stresses and distortion of geometrical shape. These factors are associated with critical parameters in modern high-precision technologies, particularly, in additive manufacturing, and considered to be essential constituents in corresponding mathematical models. The methods in question are based on the representation of a body and physical space in terms of differentiable manifolds, namely material manifold and physical manifold. These manifolds are equipped with specific metrics and connections, non-Euclidian in general.

Modal Analysis of the Turbine Blade at Complex Thermomechanical Loads

The results of modal analysis of the turbine blade were presented. The turbine blade during the operation of the engine is subjected to complex thermomechanical loads induced by centrifugal forces of the rotating blade and a nonuniform thermal field. These loads have a great influence on the natural frequencies of the blade. In the first section of the study, modal analysis of the blade was performed using the vibration system. As a result, the resonant frequencies of the real blade were obtained. In order to check the effect of the rotational engine speed and the thermal field on the natural frequencies of the blade, the finite element method was employed. At the first stage of computations static analysis was conducted for the blade subjected to mechanical and thermal loads. Then modal analysis was used to isolate the natural frequencies and vibration modes of the blade. In modal analysis the stress state from the first stage was considered as preliminary conditions. Several results of numerical calculations and experimental analysis were compared to detect the relative error of natural frequency estimates.