Thermoelastic deformation of three-layer combined die under steady-state temperature field

Multiple forging cycles are required to reach a steady-state temperature distribution in forging dies, which can lead to thermoelastic deformation and impact on the dimensional accuracy of the final forging components. The steady-state temperature fields of a three-layer combined die with constant, convection, conduction and convection thermal boundary conditions were determined in the present study. Thermoelastic deformation and the contact stresses between layers were directly related to geometric and material properties, external stresses and the temperature distribution. Warm/hot and cold forging case studies were studied using finite-element analysis. In warm/hot forging, the contact stress of the steady-state temperature distribution was smaller than the hypothetical non-uniform temperature distribution. During cold forging, the difference in total deformation between steady-state and uniform temperature distributions at the same temperature was 0.025 mm, which may reduce the geometrical accuracy of cold forging parts.     

TRANSIENT ANALYSIS OF THERMOELASTIC CONTACT BEHAVIORS IN COMPOSITE MULTIDISK BRAKES

The transient analyses of the thermoelastic contact problem are performed for carbon–carbon composite multidisk brakes subject to mechanical and frictionally excited thermal loads. The finite element method, based on the coupled theory in which displacement and temperature fields are mutually affected, is applied for the numerical simulations. In the present study, to improve the accuracy of computations and stabilize the algorithm, the implicit transient scheme is used for the thermoelastic analysis. The law of action and reaction, Signorini's law of contact, Coulomb's law of friction, and Archard's law of wear are applied to be valid locally at each point for friction surfaces. The computation results are obtained for the antiskid brake conditions and presented for the transient evolution of contact pressure, temperature on each friction surface between the bodies, and thermoelastic deformations. It is also found that the high thermal stresses due to considerable temperature difference during the landing process occur in multidisk brakes.     

FROZEN DEFORMATIONS,FROZEN STRESSES,AND STRUCTURE-INDUCED Na DISTRIBUTIONS IN SODIUM-SILICATE GLASSES

Sodium-silicate glass consists of a SiO₂ network and Na ions, which can diffuse through the network. The network structure freezes, whenever the local temperature decreases below the glass transition temperature T_g. Depending on the cooling process, different nonuniform network structures can be frozen in, this being the reason for frozen deformations, stresses, and structurally induced Na distributions. These are calculated adopting the following constitutive model in which it is assumed, that glass behaves like a thermoelastic material for temperatures above T_g and like a (structurally) rigid one below T_g. For spherical symmetric cooling of glass spheres we calculate under the classical boundary conditions and certain smoothness assumptions at the moving interface between the thermoelastic and the frozen glass analytical expressions for the frozen deformations, stresses, and Na distributions, ft turns out that these distributions depend strongly on the cooling history, such that the frozen network density increases from the center to the surface, the Na density decreases and the stress distributions decrease from strongly tensile at the center to slightly compressive at the surface of the sphere. Comparison of calculated and measured distributions show good agreement. The theoretically predicted and experimentally proven structurally induced Na diffusion might be of technical importance.     

The Rigid Die on a Half-Space with Thermal Relaxation and Convection: Influence of Sliding Speed,Die Temperature,and Geometry

A rigid die slides without friction on the surface of a coupled thermoelastic half-space at a constant sub-critical speed. A 3D dynamic steady state is treated, i.e., contact zone and its traction are invariant in the frame of the die. The die is maintained at a temperature that differs from the uniform ambient temperature prior to sliding, and die/half-space thermal convection occurs. The half-space exhibits thermal relaxation governed by the Lord–Shulman model. Three cases are treated: The die is a sphere in Case I and a cone in Case II. Case III involves a wedgelike die, formed by joining the bases of two cones. Asymptotic expressions in analytic form are derived for contact zone traction. Expressions and calculations for contact zone geometry are also given. These show that unstable behavior occurs when die ambient temperature exceeds that of the half-space by a critical value that itself may depend on die shape and speed.     

Thermoelastic analysis of laminated composite and sandwich shells considering the effects of transverse shear and normal deformations

Abstract

In the present study, thermoelastic analysis of laminated composite and sandwich shells (cylindrical/spherical) is presented using fifth-order shear and normal deformation theory. The significant characteristic of the present theory is that it includes the effects of both transverse shear and normal deformations. The mathematical formulation uses the principle of virtual work to derive the variationally consistent governing equations and traction free boundary conditions. To obtain the static solution, these governing equations are solved by employing Navier’s solution technique. The shell is subjected to a mechanical/thermal load sinusoidally distributed over the top surface of the shell. The thermal load linearly varies across the thickness of the shell. The present results are compared with other higher-order models and 3D elasticity solution wherever possible. Thermal stresses presented in this study will act as a benchmark for the future work.     

ANALYSIS OF TRANSIENT THERMAL BENDING MOMENTS AND STRESSES OF THE WORKPIECE DURING SURFACE GRINDING

Geometrical inaccuracy is often induced by heat generated during grinding. Furthermore, the transient thermal process is the main cause for the residual stresses on theground surface. The objective of this article is to investigate the three-dimensional transient temperature distribution of the workpiece using the finite difference method,and based on the acquired temperature and beam theory, the thermal moment and thermoelastic stress as calculated using Simpson's multiple numerical integral method. The energypartition is the key factor in accurately predicting the temperature distribution, on which the solution of the thermal moment and stress rely. As the heat conductivity of the workpiece decreases, the stress and moment increase near the wheel-workpiece contact zone and the peaks move closer to the contact position. A smaller thickness results in higher thermal stress and lower thermal moment. Enhancing cooling in grinding effectively reduces temperature and the induced stress.     

TRANSIENT THERMOELASTIC ANALYSIS OF DISK BRAKES IN FRICTIONAL CONTACT

The transient analysis of the thermoelastic contact problem of automotive disk brakes with frictional heat generation is performed using the finite element method. To analyze the thermoelastic phenomenon occurring in disk brakes, the coupled heat conduction and elastic equations are solved with contact problems. In the present work, the fully implicit transient scheme for the thermoelastic analysis is used to improve the accuracy of computations at every time step. The numerical simulation for the thermoelastic behavior of disk brakes is obtained in drag brake condition. The computational results are presented for the distributions of pressure and temperature on each friction surface between the contacting bodies. Also, the thermoelastic instability (TEI) phenomenon (the unstable growth of contact pressure and temperature) is investigated in the present study. The effects of the rotating speed of the disk on thermoelastic behaviors, such as the temperature distribution and contact ratio of the friction surfaces, are investigated.     

Transient Thermal Stresses of a Cross-Ply Laminated Cylindrical Shell Using a Higher-Order Shear Deformation Theory

This paper is concerned with the theoretical treatment of transient thermoelastic problem of a cross-ply laminated cylindrical shell due to axisymmetrical heat supply. We analyze the transient thermoelastic problem of a cross-ply laminated cylindrical shell under a simply supported condition using a higher-order shear deformation theory. Some numerical results for the temperature change, the displacements and the stresses are shown in figures. Furthermore, numerical results from this formulation are compared with those obtained using classical and first-order shear deformation theories.     

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.     

Propagation of waves in transversely isotropic micropolar generalized thermoelastic half space

The propagation of waves in a transversely isotropic micropolar medium possessing thermoelastic properties based on Lord and Shulaman (L–S), Green and Lindsay (G–L) and Coupled thermoelasticity (C-T) theories are discussed. After developing the solution, the phase velocities and attenuation quality factor have been obtained. The expressions for amplitudes of stresses, displacements, microrotation and temperature distribution have been derived and computed numerically. The numerical results have been plotted graphically.     

The Temperature Distribution of a Two‐Dimensional Thermoelastic Material with Voids

In this paper, an attempt has been made to investigate the temperature field in a two‐dimensional thermoelastic medium with voids. This takes place when it is subjected to a time‐dependent temperature source under the conditions of conduction heat transfer and interaction between the thermoelastic medium and its surroundings. Analytical expressions of displacements, stresses, temperature increment, and change in the volume fraction field for a layer of thermoelastic medium and a half‐space thermoelastic problem are derived by using the Laplace and Fourier transformation techniques. Two scalar potential functions of the displacement are introduced in the solution process. Then, the integral transform is inverted by using a numerical technique, and numerical results are illustrated graphically to analyze the distribution of the fields. Furthermore, the influence of the thermo‐void coefficient for two kinds of temperature boundaries is discussed. A comparison is also presented with the corresponding half‐space thermoelastic model without voids to ascertain the validity and the difference between these models. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 507–522, 2010; Published online in Wiley Online Library ( wileyOnlinelibrary.com ). DOI 10.1002/htj.20313     

Steady-state Green's functions for thermal stresses within rectangular region under point heat source

This article presents new steady-state Green's functions for displacements and thermal stresses for plane problem within a rectangular region. These results were derived on the basis of structural formulas for thermoelastic Green's functions which are expressed in terms of Green's functions for Poisson's equation. Structural formulas are formulated in a special theorem, which is proved using the author's developed harmonic integral representation method. Green's functions for thermal stresses within rectangle are obtained in the form of a sum of elementary functions and ordinary series. In the particular cases for a half-strip and strip, ordinary series vanish and Green's functions are presented by elementary functions. These concrete results for Green's functions and respective integration formulas for thermoelastic rectangle, half-strip and strip are presented in another theorem, which is proved on the basis of derived structural formulas. New analytical expressions for thermal stresses to a particular plane problem for a thermoelastic rectangle under a boundary constant temperature gradient also are derived. Analytical solutions were presented in the form of graphics. The fast convergence of the infinite series is demonstrated on a particular thermoelastic boundary value problem (BVP). The proposed technique of constructing thermal stresses Green's functions for a rectangle could be extended to many 3D BVPs for unbounded, semibounded, and bounded parallelepipeds.     

Thermal contact resistance at low contact pressure: Effect of elastic deformation

Existing models over-predict the thermal contact resistance of conforming rough joints at low contact pressures. However, the applicable pressure range in some applications such as microelectronics cooling is low. A new model is developed which is more suitable for low pressures. The effect of elastic deformations beneath the plastically deformed microcontacts is determined by superimposing normal deformations due to self and neighboring contact spots in an elastic half-space. A parametric study reveals that the elastic deformation effect is an important phenomenon at low contact pressures. The model is compared with data and good agreement is observed at low contact pressures.     

透平叶片在流-热-固耦合场下的变形研究

透平叶片在复杂耦合场下工作会产生形变,与设计流道曲面产生偏差,严重影响涡轮机的工作效率。基于流-热-固耦合有限元模型对复杂工况下叶片的变形进行了研究。采用RNGk-e湍流模型经FLUENT流场仿真实现叶片的三维温度场和压力场模拟,利用ANSYS分析得到叶片在温度、压力、离心力单独作用和耦合作用下对应的变形量,并运用灰色关联度理论分析变形之间的关系。通过分析发现,耦合场下的叶片变形并不是各载荷单独作用下变形的线性叠加,而是复杂地耦合;温度是影响叶片变形的优势子因素,压力和离心力的影响较小。分析结果对叶片形变控制策略、补偿及重构都具有重大指导价值。     

Stress Analysis of an Infinite Plate with a Coated Elliptic Hole Under a Remote Uniform Heat Flow

A thermoelastic solution to a coated elliptic hole embedded in an infinite matrix subjected to a remote uniform heat flow is provided in this article. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stresses in the coated layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. It is found that a coated layer has a strong effect on thermal stresses of the problem with an elliptic hole embedded in an infinite plate.     

Mathematical modelling of the transient response of pipeline

Steam pipelines applied in power units operate at high pressures and temperatures. In addition, to stress from the pipeline pressure also arise high thermal stresses in transient states such as start-up, shutdown or a load change of the power unit. Time-varying stresses are often the cause of the occurrence of fatigue cracks since the plastic deformations appear at the stress concentration regions. To determine the transient temperature of the steam along the steam flow path and axisymmetric temperature distribution in the pipeline wall, a numerical model of pipeline heating was proposed. To determine the transient temperature of the steam and pipeline wall the finite volume method (FVM) was used Writing the energy conservation equations for control areas around all the nodes gives a system of ordinary differential equations with respect to time. The system of ordinary differential equations of the first order was solved by the Runge-Kutta method of the fourth order to give the time-temperature changes at the nodes lying in the area of the wall and steam. The steam pressure distribution along pipeline was determined from the solution of the momentum conservation equation. Based on the calculated temperature distribution, thermal stresses were determined. The friction factor was calculated using the correlations of Churchill and Haaland, which were proposed for pipes with a rough inner surface. To assess the accuracy of the proposed model, numerical calculations were also performed for the thin-walled pipe, and the results were compared to the exact analytical solution. Comparison of the results shows that the accuracy of the proposed model of pipeline heating is very satisfactory. The paper presents examples of the determination of the transient temperature of the steam and the wall.     

Coupled heat equation in thermoelasticity with temperature dependent moduli

Abstract

New and consistent expressions for the coupled heat equation are developed within the framework of small-strain thermoelasticity for both Fourier and Cattaneo–Vernotte conduction models. These expressions place no restrictions on the changes in temperature, allow for the temperature dependence of the thermoelastic moduli, and include all the coupling terms as functions of the thermoelastic moduli and their derivatives. As applications, (i) an extended Lord–Shulman-type model is derived that takes into account the temperature dependence of the thermoelastic moduli, and (ii) the equations underpinning the experimental technique of thermoelastic stress analysis are revisited.     

The thermoelastic problem of a stretchable rigid line inhomogeneity at soft bimaterial interface

Abstract

The thermoelastic problem of a stretchable rigid line inhomogeneity at a bimaterial interface is considered. The closed-form solution is presented and the explicit expressions of the stress at the tip of the rigid line inhomogeneity are derived. The effects of thermal expansion of rigid line on the stress intensity factors are investigated. It is found that the singularity of stress maintains the same structure, and the stresses possess an apparent oscillatory character, as in the case of a rigid line without the effects of thermal expansion. However, there is a significant difference in the coefficient of the singular behavior of the stresses at the tip of rigid line, which is due to the temperature changes.     

Effect of heat-conductive filler of interface gap on thermoelastic contact of solids

The thermoelastic contact of two isotropic solids separated by an interface gap is considered. The gap is formed due to an initial sloping smooth groove on the boundary of one of solids and filled with heat-conductive substance (gas or liquid). The heat is supposed to flow from the material with the higher thermal distortivity into the material with the smaller one. The gap filler influence on heat transfer between two solids is modeled by thermal resistance linearly dependent on the height of the gap. The conditions of perfect thermal contact and nonfrictional mechanical contact are assumed to be satisfied at the interface outside the gap. The contact problem is reduced to a set of two nonlinear singular integrodifferential equations, which is solved numerically. The effect of the imposed heat flow and heat conduction of the gap filler on the length and height of the gap, temperature jump at the interface, distribution of heat flows along and through the interface and distribution of contact stresses is analyzed.