Two Cases of Rapid Contact on a Coupled Thermoelastic Half-Space: Sliding Ellipsoidal Die,Rolling Sphere

In one case, a rigid ellipsoidal die translates over the surface of a coupled thermoelastic half-space under compression, and because of sliding friction, shear. In the other, a rigid sphere rolls on the surface under a compressive force. Both motions occur along a straight path at constant sub-critical speed. A dynamic steady state is treated, i.e., the contact zone and its traction remain constant in the frame of the die or sphere. Robust asymptotic expressions in analytic form for contact zone traction, temperature and geometry are derived. Axial symmetry is not required in the solution process. Instead Cartesian coordinate formulations are used, but a system of quasi-polar coordinates is introduced that allow problem reduction to integral equations similar in form to those found in 2D contact.     

Field Equations and Surface Convection with Thermal Relaxation: Illustration for Rapid Sliding Contact

A rigid cylinder slides without friction at constant speed on a thermoelastic half-space. Surface convection occurs, and both it and half-space exhibit thermal relaxation. An analytical solution valid near the contact zone center and for high sub-critical speeds is obtained. Its form resembles that for a half-space with surface friction but no convection. Calculations show that contact zone temperature is sensitive to sliding speed, the relaxation model for the half-space and a dimensionless convection layer constant. In particular, a half-space with one relaxation time predicts decreases in temperature; a double-relaxation time model can give increases as well.     

SLIDING CONTACT WITH FRICTION OF A THERMOELASTIC SOLID AT SUBSONIC,TRANSONIC, AND SUPERSONIC SPEEDS

The steady-state two-dimensional sliding contact of a half-space by a rigid indentor subject to Coulomb friction is considered. Coupled thermoelasticity governs, and the indentor translates at any constant speed. Results show the existence of three distinctive sliding speeds in addition to those found for frictionless isothermal sliding and speed ranges for physically acceptable solutions that differ from their frictionless isothermal counterparts. Results also show that friction defines surface temperature change outside the contact zone for subsonic sliding but that such change occurs in the transonic case whether friction exists or not. Transonic sliding also exhibits a speed at which no temperature change occurs anywhere in the half-space, while surface temperature change for supersonic sliding occurs only on the contact zone and is always positive.     

Rapid Sliding on a Thermoelastic Half-Space: Rigid Die with Two Contact Surfaces

A rigid die with two spherical contact surfaces translates, at constant speed, into a thermoelastic half-space. The spherical surfaces are frictionless and have identical radii, and translation is parallel to the line connecting their centers. Sliding speed is subcritical but may be rapid, and a 3D (dynamic) steady state is assumed. An asymptotic approximation gives integral transform inversions in analytic form. The process of imposing the auxiliary conditions for sliding contact is then presented in some detail. Formulas, calculations and plots illustrate the sensitivity of contact zone geometry and temperature change to sliding speed and proximity of the two spheres.     

COUPLED THERMOELASTIC ANALYSIS OF PERFECT ROLLING CONTACT: SOLUTION BEHAVIOR NEAR YIELD INITIATION

An insulated rigid cylinder of infinite length rolls without slip on a half-space at constant rolling speed. The equations of coupled thermoelasticity in the dynamic steady state hold. The analytical solution for the mixed boundary-value problem is extracted from robust asymptotic versions of exact integral transforms. The solution, in turn, gives contact zone size and location, and temperature change and von Mises yield function on the contact zone. The function exhibits a maximum at the contact zone center, which is above the location of its maximum in the half-space. For some insight into behavior near yield initiation, therefore, contact zone center yield is used to derive expressions for the corresponding contact zone size, compressive load on the cylinder, and zone temperature increase. Calculations for 4340 steel indicate that initiation is multi-axial and that mild temperature increases occur. In addition, the contact zone center, which corresponds to the contact point in the rigid–rigid limit, is found to have a small tangential speed. The rolling speed is allowed to take any value between zero and the thermoelastic Rayleigh speed. This range perhaps exceeds that required in applications, but allows a clearer view of variation with rolling speed.     

Normal Mode Analysis to a Two-Dimensional Generalized Electromagnetothermoelastic Problem with Diffusion

A two-dimensional generalized electromagnetothermoelastic problem for a half-space with diffusion is investigated in the present work. The problem is formulated in the context of the generalized thermoelastic diffusion theory. The half-space is initially placed in an external magnetic field with constant intensity, and its bounding surface in contact with a permeating substance is taken to be traction free and subjected to a time-dependent thermal load. The chemical potential is also assumed to be known function of time on the bounding surface. The half-space deforms because of the thermal load, and due to the application of magnetic field, there results in an induced magnetic field and an induced electric field in the half-space. The system of Maxwell's equations is given and the generalized electromagnetothermoelastic diffusive coupled governing equations are established. To solve the formulated equations, normal mode analysis is adopted and the exact expressions for the non-dimensional temperature, displacement, stress, induced magnetic field, induced electric field, and chemical potential and concentration are obtained and represented graphically.     

Effect of rotation on plane waves of generalized electromagnetothermoelastics with diffusion for a half-space

This article is aimed at studying the effects of rotation on the model of generalized thermoelastic diffusion for a thermally, isotropic and electrically conducting half-space with rotation at the uniform angular velocity. The rotating half-space is initially placed in an external magnetic field with constant intensity and its bounding surface in contact with a permeating substance is taken to be traction free and subjected to a time-dependent thermal load and chemical potential. The system of Maxwell's equations is given and the generalized electromagnetothermoelastic diffusion coupled governing equations are established. The normal mode analysis is adopted to solve the problems and the exact expressions for the non-dimensional temperature, displacement, stress, induced magnetic field, induced electric field, chemical potential and concentration are gained and represented graphically. The effects of rotation are evaluated by comparing the results obtained in the presence and absence of rotation.     

A pilot solar water disinfecting system: performance analysis and testing

In most countries, contaminated water is the major cause of most water-borne diseases. Disinfection of water may be accomplished by a number of different physical–chemical treatments including direct application of thermal energy, chemical and filtration techniques. Solar energy also can be used effectively in this field because inactivation of microorganisms is done either by heating water to a disinfecting temperature or by exposing to ultraviolet solar radiation. A pilot solar system for disinfecting contaminated water is designed, constructed and tested. Investigations are carried out to evaluate the performance of a wooden hot box solar facility as a solar disinfectant. Experimental data show that solar energy is viable for the disinfection process. A solar radiation model is presented and compared with the experimental data. A mathematical model of the solar disinfectant is also presented. The governing equations are solved numerically via the fourth-order Runge–Kutta method. The effects of environmental conditions (ambient temperature, wind speed, solar radiation, etc.) on the performance of the solar disinfectant are examined. Results showed that the system is affected by ambient temperature, wind speed, ultraviolet solar radiation intensity, the turbidity of the water, the quantity of water exposed, the contact area between the transparent water container in the solar disinfectant and the absorber plate as well as the geometrical parameters of the system. It is pointed out that for partially cloudy conditions with a low ambient temperature and high wind speeds, the thermal efficiency of the solar disinfectant is at a minimum. The use of solar energy for the disinfection process will increase the productivity of the system while completely eliminating the coliform group bacteria at the same time.     

Thermoelastic Deformation of Three-Layer Combined Die with Non-Uniform Temperature Distribution

During precision forging processes, the elastic and thermal deformations always take place simultaneously on the forging dies, which will affect the dimension accuracy of the final forging components. According to the classic Lamé formulas and thermoelastic mechanics theories, the thermoelastic deformation of a combined die was investigated. Directly related to geometric parameters, material properties, external stresses, and temperature distribution, the expressions of die deformation and contact normal stresses were derived. A three-layer combined die with three different temperature distributions was studied as a specific example. The thermoelastic deformations of each layer, as well as the contact normal stresses between them, were both calculated by the derived expressions and by finite element simulation. There was good agreement between the calculated values and simulated results, which demonstrated the effectiveness and accuracy of the theoretical derivation. Based on this, the total deformation on the inner surface of the combined die and the contact stress between contact layers under non-uniform temperature distribution that would influence the practical die initial design were discussed further.     

Effect of air velocity on thermal insulation systems

A thermal comfort model has been developed to relate skin surface temperature to ambient air temperature and windspeed. Relatively low wind assaults on clothing appreciably reduce the air boundary layer effective thermal resistance, whereas further equal increases in wind speed have decreasingly less effect in reducing the thermal resistance. Conclusions reached are extended to other insulation systems. The analysis assumes that no wind penetration through the insulant occurs.     

Numerical and experimental investigations on the influence of preheating and dilution on transition of laminar coflow diffusion flames to Mild combustion regime

A numerical and experimental study has been carried out to acquire knowledge about the structure and stabilization mechanism of coflow flames in their transition to the Mild combustion regime. In total, three CH₄/N₂/oxidizer coflow flames have been studied with a systematic dilution and preheating of the fuel and coflow streams. These flames comprise the non-preheated case (Case NP), preheated case (Case P) and Mild case (Case M), diluted and preheated from ambient temperature up to 1530 K. Radial profiles of temperature and species concentrations have been measured using spontaneous Raman scattering. Detailed computations have been performed by steady-state simulations of these cases using detailed chemistry with the GRI 3.0 mechanism, multi-component mixture-averaged transport and an optically thin approximation for radiative heat losses. An overall good agreement has been found between results of the detailed computations and experiments for Case NP, Case P and at lower axial distances for Case M. The importance of using multicomponent transport and radiative heat losses in the computations has been investigated by performing additional computations with more simplified models for Case NP. A comparison of computed temperature distributions indicates that the progressive preheating and dilution of the oxidizer and fuel leads to a reduction of the temperature rise in the reaction zone with respect to a non-reacting case; this rise in Case M is less than 200 K. Comparison of computed heat release and CH₂O distributions reveals that stabilization of Case NP and P occurs by an edge flame, while for Case M, it takes place by autoignition. Further investigations on the structure of Case M has been done by flamelet analyses in mixture fraction space. It is found that igniting flamelets, in contrast to steady flamelets, represent very well the structure of Case M at lower axial distances. This observation further emphasizes the stabilization of the Mild case by the autoignition phenomena.     

THE COUPLED THERMOELASTICITY PROBLEM OF THE TRANSIENT MOTION OF A LINE HEAT/MECHANICAL SOURCE OVER A HALF-SPACE

Abstract

A procedure is developed for obtaining fundamental thermoelastic two-dimensional solutions for thermal and/or mechanical loadings moving unsteadily over the surface of a half-space. These solutions are within the bounds of the transient coupled thermoelastodynamic theory of M. A. Biot. The concentrated line loadings (sources) are suddenly applied on the surface of the half-space and then move in a fixed direction with nonuniform speed. The problem is of basic interest in contact mechanics and tribology, and it is especially related to the well-known heat checking problem (thermo-mechanical cracking in an unflawed half-space material from high-speed asperity excitations). Here, an exact and general formulation is considered and explicit results are given for some special cases. These results are obtained by generating asymptotic expressions from one- and two-sided Laplace transforms and then performing the inversions in an exact manner.     

State Space Approach for Conducting Magneto-Thermoelastic Medium with Variable Electrical and Thermal Conductivity Subjected to Ramp-Type Heating

The equations of magneto-thermoelasticity with one relaxation time with variable electrical and thermal conductivity for one-dimensional problems are cast into matrix form using the state-space and Laplace transform techniques. The resulting formulation is applied to a half-space subjected to ramp-type heating and traction free. The inversion of the Laplace transform is carried out using a numerical approach. Numerical results for the temperature, the displacement and the stress distributions are given and illustrated graphically.     

Transient response for a half-space with variable thermal conductivity and diffusivity under thermal and chemical shock

The present work aims to investigate the transient thermoelastic diffusive response for a half-space with variable thermal conductivity and diffusivity in the context of the generalized thermoelastic diffusion theory. The boundary plane of the half-space is assumed to be traction free and subjected to a time-dependent thermal and chemical shock. The governing equations of the problem are formulated by using Kirchhoff’s transformation. Due to the complexity of the equations, Laplace transformation method is applied to solve them. Numerical results are obtained and illustrated graphically. Parameter studies are performed to evaluate the effects of variable thermal conductivity and diffusivity on the response. The present investigation could be helpful for better understanding the multifield coupling effect of mechanical and thermal fields in real materials.     

Effects of thermal load on wheel–rail contacts: A review

This article presents a technical review on the effects of thermal loads evolved at the wheel–rail–brake contact interfaces. These dynamic contact interfaces develop heat transfer conditions of widely varied thermal level. Their modeling to identify the sources for a variety of defect formation, observable on wheel tread or rail surface, is very important. The railway system, in general, has to bear axle load, friction load, and thermal load arising from their contact conditions in addition to traction and dynamic loads. The defects arising from the interaction of thermal load and other loadings may be identified as hot spots, shelling, spalling, rolling contact fatigue (RCF), and corrugation. The mechanisms for the formation of such defects are pivoted over the existing thermal environment of dynamic interacting surfaces. This review summarizes the works of early investigations and recent advances in modeling the heat transfer conditions required to estimate the temperature distribution at the contact zone. The heat partitioning method for both drag and stop braking conditions, in the presence of rail chill effect, is emphasized. Thermal gradient, introduced by localized temperature rise in the contact zone, in the presence of variable friction coefficient, promotes the RCF process. These alter the residual stresses in the contact region to cause a structural shakedown, aggravate plastic flow and activates ratchetting phenomenon in rails. The evolution of thermomechanical surface and subsurface fatigue cracks are also discussed for the completeness of this article. The effect of all such defect formation, emerging from thermal loading condition, and their countermeasures for defect mitigation are presented in this review. This abridged technical documentation envisions attracting more research in the area to improve wheel–rail set design and performance standards to extend enhanced safety and comfort to rail transport operation. It is opined that the thermomechanical loading, their effects on promoting defect formation and propagation should be studied in combination instead of the current practice of treating them separately.     

Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading

The transient thermal stress crack problem for a half-space with a multilayer coating under thermal surface loading containing an undercoat crack, perpendicular to the interface, is considered. The problem is solved using the principle of superposition and uncoupled quasi-static thermoelasticity. Transient temperature distribution and corresponding thermal stresses for the uncracked multilayer assembly are obtained in a closed analytical form using the model with generalized thermal boundary conditions of heat exchange of a half-space with ambient media via the coating. The crack problem is formulated as a perturbation mixed boundary value problem, in which the crack surface loading should be equal and opposite to the thermal stresses obtained for the uncracked medium, and is reduced to a singular integral equation and solved numerically. Numerical computations are performed for the analysis of influence of the coating upon thermal stresses and thermal stress intensity factor.     

Linear stability analysis of the solidification of a supercooled liquid in a half-space

The instability of the solidifying front of a supercooled liquid in a half-space is investigated by introducing a small disturbance at the solid-liquid interface. A relationship between the thermal properties of the material and the disturbance growth rate is obtained using the heat balance equation at the interface, including the effects of surface curvature on the equilibrium temperature. The heat balance equation is solved numerically and compared to the analytical solution obtained by neglecting the effects of surface curvature. The results show that the thermal gradients increase the growth rates of disturbances at the solid-liquid interface and that the effect of surface curvature results in a decrease in the disturbance growth rates. Further analysis shows that marginal stability occurs in both the longer wavelength and capillary regions.     

Parabolic modeling of the pultrusion process with thermal property variation

Pultrusion is a manufacturing method for fiber-reinforced composite with constant cross-section. In this process, a fiber creel is impregnated in a resin bath and passes through a heated die with a constant pulling force and the elevated die temperature induces the curing-resin process. At the present work the effect of variable properties (thermal conductivity and volumetric heat capacity) during the pultrusion process of thermosetting composite materials is numerically studied. The thermal properties are considered as a function of both temperature and degree of cure distributions inside the carbon/epoxy matrix composites. A two-dimensional parabolic model using the finite element method to solve the energy and degree of cure transport equations was used. These two equations are coupled by a source term from resin curing exothermic reaction. The resin cure kinetics and the properties that are temperature-dependent are both modeled by expressions obtained from the literature. The computational domain is discretized using an unstructured mesh with triangular elements and an adaptive refinement. Iterative algorithms are used to solve the algebraic equation system. Results showed that as the temperature and degree of cure along the die extension increase the volumetric heat capacity and the thermal conductivity also elevate. The influence of the pulling speed and the die temperature in the thermal property variation is also analyzed. It is verified that the temperature profile at the pultruded bar centerline for the variable property case is smoother than the constant one, similarly when the pulling speed is increased. The degree of cure development is delayed for the variable property simulation, requiring a larger die length to reach a suitable degree of cure design value. Moreover, the proper knowledge of these characteristics allows a better pultrusion process design.     

Fracture caused by wedging in a thermoelastic solid

Dynamic steady-state fracture in 3D of an unbounded, coupled thermoelastic solid is considered. Fracture is brittle and results from the wedging effect of a rigid die that slides between surfaces of an initially closed, semi-infinite slit. Friction is neglected, and the possibility that slit surfaces resume contact in the wake of the die is considered. For subcritical rate of sliding and resultant slit extension, an asymptotic solution is obtained in analytic form. A dynamic energy release rate criterion, with kinetic energy included, is imposed. The result is a relation between parameters for locations of slit edge, slit closure, and contact zone, in the form of a nonlinear differential equation. The mathematical norm of temperature change is also developed and indicates that thermal response near the slit edge is highly dependent on the relative distances of slit edge and closure contour from the die.     

A Two-Dimensional Problem for Two Media in the Generalized Theory of Thermoelasticity

The two-dimensional problem for an elastic half-space with a thick layer on its top is considered with the context of the theory of generalized thermoelasticity with one relaxation time. The half-space and the thick layer are composed of different elastic materials. The surface of the upper layer is traction free and subjected to the effect of a thermal shock. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transform.