Showing papers in "Journal of Thermal Stresses in 2009"

Residual Stresses in Orthogonal Cutting of Metals: The Effect of Thermomechanical Coupling Parameters and of Friction

Abstract: The generation of residual stresses in orthogonal machining is analysed by using an Arbitrary Lagrangian Eulerian (ALE) finite element approach. It is shown that a substantial level of tensile residual stresses can be obtained in the vicinity of the machined surface without any contribution of thermal effects. This motivates the development of a parametric study to analyse the effects of the thermomechanical coupling parameters on residual stresses. The roles of thermal expansion, of thermal softening and of the Taylor–Quinney coefficient (controlling the heat generated by plastic flow) are considered separately. The influence of friction is also analysed by assuming dry cutting conditions and a Coulomb friction law. The friction coefficient has a complex effect by controlling heat generation (frictional heating) along the tool rake and clearance faces and the propensity for the chip to stick to the tool. Geometrical effects such as the tool rake angle and the tool edge radius are also discussed.

Thermoelastic Interactions on Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity

Abstract: The present work is aimed at the study of thermoelastic interactions in an infinite medium with a cylindrical cavity in the context of a theory of generalized thermoelasticity in which the theory of heat conduction in deformable bodies depends on two different temperatures—conductive temperature and dynamic temperature. The cavity surface is assumed to be stress free and is subjected to a thermal shock. In order to make a comparison between the two-temperature generalized thermoelastic model and one-temperature generalized thermoelastic model the problem is formulated on the basis of two different models of thermoelasticity: namely, the Lord–Shulman model and the two temperature Lord–Shulman model in a unified way. Laplace transform technique and decoupling of coupled differential equations are used to derive the solution in transform domain which is then followed by the inversion of Laplace transform by a numerical method to obtain the solutions for field variables in the physical domain. Short-time appr...

Generalized Thermoelastic Infinite Layer Subjected to Ramp-Type Thermal and Mechanical Loading under Three Theories—State Space Approach

Abstract: A problem of thermoelastic interactions in an elastic infinite layer 0 ≤ x ≤ h with an elevated temperature field arising from ramp-type heating and loading has been constructed. The governing equations are written in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite rise times of temperature and stress. The problem has been solved analytically by using a state-space approach. Solutions from the derived analytical expressions have been computed for a specific situation. The solution for the half-space when (h → ∞) has been found also. Numerical results for the temperature distribution and thermal stress are represented graphically. A comparison was made among the results predicted by the theories.

Theory of Generalized Micropolar Thermoelastic Diffusion Under Lord–Shulman Model

Abstract: The general equations of motion and constitutive equations, based on the theory of Lord–Shulman with one relaxation time, are derived for a general homogeneous anisotropic medium with a microstructure, taking into account the effects of heat and diffusion. A variational principle for the governing equations is obtained. Then we show that the variational principle can be used to obtain a uniqueness theorem under suitable conditions. A reciprocity theorem for these equations is given. The obtained results are valid for some special cases which can be deduced from our generalized model.

Characterization of the Thermo-Viscoelastic Property of Glass and Numerical Simulation of the Press Molding of Glass Lens

Abstract: A measurement technique for obtaining the thermo-viscoelastic properties of glass with high accuracy is discussed. An unidirectional compression creep test was employed to measure the relaxation modulus of the glass specimens. The creep function derived from the experimental creep test is approximated by a generalized Voigt model, and then converted into a relaxation modulus expressed by a generalized Maxwell model using the Laplace transform and its inversion. Relaxation moduli and shift factors of the glass specimens BK-7 and TaF-3 were estimated according to the presented procedure, and the accuracy of the relaxation modulus was verified by a numerical demonstration using finite element analysis. A fundamental numerical simulation of the press molding of glass lenses was carried out to illustrate the validity of the thermo-viscoelastic properties obtained by the presented approach. Residual stresses under processing conditions were estimated, and the optimal conditions for residual stress minimization ...

A Unified Generalized Thermoelasticity Formulation: Application to Penny-Shaped Crack Analysis

Abstract: This paper is concerned with an internal penny-shaped crack subjected to prescribed temperature and stress distribution in an infinite thermoelastic solid which obeys classical coupled thermoelasticity theory (CCTE), the Lord–Shulman (L-S) and Green–Naghdi (G-N) models of thermoelasticity. The generalized coupled thermoelasticity theories are combined into a unified formulation introducing the unified parameters. The Laplace and Hankel transforms are used to solve the problem. The boundary conditions of the problem give a set of four dual integral equations. The operators of fractional calculus are used to transform the dual integral equations into a Fredholm integral equation of second kind, which is then solved numerically. The infersions of double transforms have been done numerically and for numerical inversion of Laplace transform Bellman method is used. Numerical results for temperature, displacements, stress near the crack and stress intensity factor are shown graphically for classical coupled ther...

Effects of three-phase-lags on generalized thermoelsticity for an infinite medium with a cylindrical cavity

Abstract: The present work is concerned with the effects of three-phase lags on thermoelastic interactions due to step input in temperature on the stress free boundary of a cylindrical cavity in an unbounded medium. The problem is studied in the context of theory of generalized thermoelasticity with three phase lags (Roychoudhuri, [24]) and the theory of thermoelasticity with energy dissipation (Green and Naghdi, [4]) in a unified way. Solution of the problem is obtained by using the Laplace transform technique. Significant dissimilarities between two models showing the effects of phase lags are pointed out on the basis of analytical as well as numerical results of the problem. A numerical method for the inversion of Laplace transform is employed.

Transient solution of the unperturbed thermoelastic contact problem

Abstract: Automotive brake and clutch systems experience temperature and contact pressure variation due to frictional heat generation. Due to geometrical complexity and the coupled thermo-mechanical nature of this class of problems, direct finite element simulation is found to be computer-intensive. This paper explores a more time-efficient method that can be used to obtain the transient solution for the unperturbed clutch and brake system based on an eigenfunction expansion and a particular solution. An approximate solution can also be sought based on the same method in which only a subset of the eigenfunctions are used.

Potential Method in the Linear Theory of Thermoelasticity with Microtemperatures

Abstract: In the present paper the linear theory of thermoelasticity with microtemperatures is considered. The basic boundary value problems of steady vibrations are investigated using the potential method. Sommerfeld–Kupradze type radiation conditions and the basic properties of thermoelastopotentials are established. The uniqueness and existence theorems of classical solutions of the external (with respect to an unbounded domain) boundary value problems are proved.

State Space Approach of Two-Temperature Magneto-Viscoelasticity Theory with Thermal Relaxation in a Medium of Perfect Conductivity

Abstract: The model of one-dimensional equations of the two-temperature generalized magneto-viscoelasticity theory with one relaxation time in a perfect conducting medium is established. The state space approach developed in [Bahar and Hetnarski, J. Thermal Stresses, vol. 1, pp. 135–145, 1978; M. Ezzat, Int. J. Engng. Sci., vol. 35, pp. 741–752, 1997] is adopted for the solution of one-dimensional problems for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Some comparisons have been shown in figures to estimate the effects of the temperature discrepancy and the applied magnetic field.

On Inconstant Poisson's Ratios in Non-Homogeneous Elastic Media

Abstract: For non-homogeneous linear elastic materials, it is demonstrated that even for the simplest loading case, i.e. quasi-static uniaxial, the Poisson's ratio (PR) is space dependent and not a constant. Furthermore, the assumption of constant PR values or of separable temporal and spatial PR functions leads to ill-posed overdetermined problems. Additionally, elastic PRs become space and time dependent under time dependent stresses in non-homogeneous elastic media. Under these and more general circumstances, PRs cannot be considered material property descriptors since they now become functions of the spatially changing moduli and stresses, and vary accordingly. The same conclusions are also drawn for nonlinear elastic media with small or large deformations.

Coupled Dynamical Thermoelasticity of a Functionally Graded Cracked Layer

Abstract: The effect of thermal shock on a cracked FGM layer is analized using the Galerkin finite element method. The thermoelasticity equations are assumed in the classical form and the effect of thermal-mechanical coupling in the energy equation is included in the calculations. The eight node rectangular element is used and the nodes near the crack tip are replaced to introduce the crack tip singularity. The coupled dynamical system of equations obtained from the finite element discretization are solved by the Newmark method in the time domain. The domain form of the J integral is then employed to calculate the dynamical thermal stress intensity factors at each instance of time. A computer program in C+ + environment is developed to do the different stages of calculations from mesh generation to numerical calculation of the J integral. Some numerical examples are implemented to investigate the validity and accuracy of the written computer program to simulate the shock phenomena on a functionally graded cracked body.

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

Abstract: 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.

Analyticity of Semigroups Associated with Thermoviscoelastic Mixtures of Solids

Abstract: In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one-dimensional theory of mixtures of thermoviscoelastic solids. Our main goal is to present conditions which insure the analyticity and the lack of analyticity of the corresponding semigroup.

Transient Thermoelastic and Piezothermoelastic Problems of Functionally Graded Materials

Abstract: This paper is concerned with the theoretical treatment of transient thermoelastic problems involving functionally graded thick plate, laminated composite strip with an interlayer of functionally graded material, and functionally graded hollow cylinder, and transient piezothermoelastic problems involving functionally graded piezoelectric cylindrical panel. The thermal, thermoelastic and piezoelectric constants of the functionally graded materials are expressed as power functions of the radial coordinate variable or exponential functions of the thickness coordinate variable. The exact solutions for the two-dimensional temperature change in a transient state, and thermoelastic or piezothermoelastic response under the state of plane strain are presented herein. Some numerical results are shown in figures.

Simulation of Laminated Thermoelastic Membranes

Abstract: A model of thermoelasticity in laminated thin films is derived from three-dimensional considerations. Its modification to accommodate wrinkling and slackening is described and a procedure for numerical solution is developed. This is used to solve a number of equilibrium problems that exhibit the effects of heating and mechanical loading on the stress field and consequent wrinkling pattern.

Analyses of Thermal Conduction and Stress Induced by Electric Current in an Infinite Thin Plate with an Elliptical Hole

Abstract: Uniform electric current at infinity is applied to a thin infinite conductor with an elliptical hole disturbing the electric current, which gives rise to Joule heat, temperature increase and heat flux. Joule heat produces uniform and uneven temperature fields which in turn initiate thermal stress. These electrical current, Joule heat, temperature, heat flux and thermal stress analyses are carried out and their closed form solutions are obtained. The heat conduction problem is solved as a temperature boundary value problem. Figures of distribution of Joule heat, temperature, heat flux and stress are shown. A dislocation and a rotation terms for thermal stress analysis appear, which makes problem complex. Solutions of Joule heat, temperature, heat flux and thermal stress are nonlinear for the direction of electric current. For an infinite plate with a circular hole, stress components do not occur on the whole plate. As a special case, a crack problem is analyzed and intensities at the crack tip of each prob...

Computation of Thermal Fracture Parameters for Inclined Cracks in Functionally Graded Materials Using J k -Integral

Abstract: This article describes the formulation and implementation of the J k -integral for the analysis of inclined cracks located in functionally graded materials (FGMs) that are subjected to thermal stresses The generalized definition of the J k -integral over a vanishingly small curve at the tip of an inclined crack is converted to a domain independent form that consists of area and line integrals defined over finite domains A numerical procedure based on the finite element method is then developed, which allows the evaluation of the components of the J k -integral, the modes I and II stress intensity factors and the T-stresses at the crack tips The developed procedure is validated and the domain independence is demonstrated by providing comparisons to the results obtained by means of the displacement correlation technique (DCT) Detailed parametric analyses are conducted by considering an inclined crack in an FGM layer that is subjected to steady-state thermal stresses Numerical results show the influence

Three-Dimensional Fundamental Solution for Transversely Isotropic Electro-Magneto-Thermo-Elastic Materials

Abstract: Fundamental solutions play an important role in the analyses of coupled fields in electro-magneto-thermo-elastic material. However, most works available on this topic address the case of uniform temperature. Based on the compact general solution of transversely isotropic electro-magneto-thermo-elastic material, which is expressed in harmonic functions, and employing the trial-and-error method, the three-dimensional fundamental solution for a steady point heat source in an infinite transversely isotropic electro-magneto-thermo-elastic material is presented by five newly induced harmonic functions. Numerical results are given graphically by contours.

Two-Dimensional Thermoelasticity Problem for a Thick Plate Under the Action of a Body Force in Two Relaxation Times

Abstract: The two-dimensional problem for a thick plate whose upper surface is subjected to a known temperature distribution, while the lower surface is laid on a rigid foundation and thermally insulated is considered within the context of the theory of thermoelasticity with two relaxation times under the action of a body force. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

Quasi-Static Thermal Deflection of a Thin Clamped Circular Plate Due to Heat Generation

Abstract: This paper deals with the determination of thermal deflection in a thin clamped circular plate defined as 0 ≤r ≤ b; 0 ≤z ≤ h due to internal heat generation within it. A thin clamped circular plate is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary (r = b). The lower surface (z = 0) is at zero temperature whereas upper surface (z = h) is thermally insulated. The governing heat conduction equation has been solved by using integral transform technique. The edge of the circular plate is fixed and clamped at r = b. The results are obtained in series form in terms of Bessel's functions. As a special case different metallic plates have been considered and the results for thermal deflection have been computed numerically and are illustrated graphically.

Heterogeneous Solids and the Micro/Macro Connection: Structure and Elasticity in Architecturally Complex Media as Emergent Collective Phenomena

Abstract: Launched before the atomic hypothesis took hold, elasticity theory is a spectacular achievement. A continuum-level description, it provides a powerful toolkit for determining how architecturally simple solids such as crystals respond macroscopically to stress, whilst encoding microscopic, atomic-realm details parsimoniously, via a few parameters. Solids that are architecturally complex at the atomic level—such as vulcanized rubber, gels and glasses—are commonly addressed using elasticity theory, too. However, their microscopic-level irregularity raises new issues, not only of elasticity but also of structure: How do the elastic ‘constants’ of such media fluctuate across a sample? Do such media strain non-affinely in response to stresses? Are there regional variations in the position-fluctuations of the atoms? More generally, can the structure and elasticity of architecturally complex solids be viewed as emergent collective phenomena, determinable from their underlying microscopic thermal motion and charac...

Basic Problems of Coupled Thermoelasticity with Thermal Relaxation and Pre-Stress: Aspects Observed in Exact and Asymptotic Solutions

Abstract: Some 1- and 2-D dynamic problems of coupled thermoelasticity in an unbounded solid, half-space and slab are treated. The problems are basic, and have been addressed in the literature. This treatment considers (possibly finite) pre-stress and both Fourier and thermal relaxation models, and generates analytical results from exact solutions or inversions of asymptotic expressions for exact transform solutions. The results illustrate the role of wave speeds in solution behavior, how pre-stress affects these speeds, and how the models themselves define solution behavior, especially near wave fronts.

Transient Thermoelastic Problem of a Functionally Graded Hollow Cylinder Due to Asymmetrical Surface Heating

Abstract: This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to asymmetrical heating from its surfaces. The thermal and thermoelastic constants of the hollow cylinder are expressed as power functions of the radial coordinate variable. The exact solution for the two-dimensional temperature change in a transient state, and thermal stresses of a hollow cylinder under the state of plane strain is obtained herein. Some numerical results are shown in figures. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change and stresses is investigated.

A Study on Coupled Thermo-Elasto-Plastic-Damage Dissipative Phenomena: Models and Application to Some Innovative Materials

Abstract: This is a review paper on some irreversible thermodynamics-based constitutive models capable of capturing complex dissipative physical bahaviour in multifunctional innovative materials. The thermomechanical response of such materials accounts for two basic sources of material nonlinearity, plasticity and damage, which may result in various failure mechanisms. A number of couplings, such as thermo-elastic-damage, elastic-plastic hardening, plastic-damage hardening, thermo-elastic-plastic-damage, etc., are discussed. Various material symmetry classes, including anisotropy, orthotropy, transverse isotropy, are referred to some innovative materials, such as composite materials, functionally graded structures, thermal or wear resistant coatings, etc. Examples of implementation of chosen models for simulation of some initial boundary problems are presented.

Ultrafast Laser-Induced Elastodynamics in Single Crystalline Silicon Part I: Model Formulation

Abstract: The various responses of a silicon wafer excited by a femtosecond pulsed laser are investigated. A multi-time scale axisymmetric model that governs the transport dynamics in silicon is presented based on the relaxation-time approximation of the Boltzmann equation. Temperature-dependent multi-phonons, free-carrier absorptions, and the recombination and impact ionization processes are considered using a set of balance equations. The mechanical response of the lattice is described by momentum equations. To solve the model of 17 coupled time-dependent partial differential equations without having to be concerned with non-physical oscillations in the solution, an implicit finite difference scheme on a staggered grid is developed. The staggered finite difference scheme allows velocities and first-order spatial derivative terms to be calculated at locations midway between two consecutive grid points, and shear stresses to be evaluated at the center of each element. A multi-time-scale approach involving the use o...

Closed Forms of Goursat Functions in Presence of Heat for Curvilinear Holes

Abstract: In this paper, we consider a general conformal mapping function with complex constant coefficients, to solve the elasticity problems for an infinite plate weakened by a curvilinear hole. Conformal was used outside and inside of a unit circle in the presence of an initial heat flowing perpendicular to the plate. The use of the complex variable method gives convenient expressions of Goursat functions in applications, it also achieves the objective rapidly. Several previous works are considered as special cases of this work. The hole takes different shapes that make this study applicable to many cases, like tunnels, caves, excavations in soil or rock, etc. Stress and strain components have been obtained and plotted to investigate their physical meanings. With the aid of a computer, shapes of holes were received, and distribution of stresses obtained.

On Spatial Behavior of the Harmonic Vibrations in Thermoviscoelastic Mixtures

Abstract: This paper concerns the study of time–harmonic vibrations for homogeneous and anisotropic thermoviscoelastic mixtures. The dissipative effects are used to introduce an appropriate measure associated with the amplitude of the steady–state vibrations and to establish an exponential decay estimate of Saint–Venant type, which holds for every value of the frequency of vibrations and for arbitrary values of the elastic coefficients.

Thermoelasticity of Thin Shells on the Basis of Asymmetrical Theory of Elasticity

Abstract: The boundary value problem of general three-dimensional asymmetrical (momental) theory of elasticity for a thin shell is considered. It is assumed that the general stress-deformed state has resulted from interior stress-deformed state and boundary layers. An asymptotic method of integration of three-dimensional boundary value problem of asymmetrical theory of elasticity is applied for approximate computation of the interior stress-deformed state and boundary layers. Depending on the values of dimensionless physical parameters of shell's material, three various asymptotics are constructed. Initial approximation, correspondingly, for the first asymptotics brings to the general theory of micropolar thermoelastic shells with independent rotation, for the second asymptotics—to the general theory of micropolar thermoelastic shells with constraint rotation, and for the third asymptotics—to so-called theory of micropolar thermoelastic shells with “small shift rigidity”. Corresponding micropolar thermoelastic boun...

Singular Surfaces in the Theory of Thermoelasticity with Microtemperatures

Abstract: This work concerns the behavior of shock waves and higher-order discontinuities which propagate in a thermoelastic body with inner structure and microtemperatures. The response of the material is assumed to be linear. The propagation conditions and growth equations that govern the propagation of singular surfaces of order r ≥ 1 are derived. The coupling between the discontinuities in the mechanical and thermal fields is discussed.