Showing papers on "Thermoelastic damping published in 2001"

High-frequency ultrasound array element using thermoelastic expansion in an elastomeric film

Abstract: The thermoelastic effect was used to produce high-frequency, broadband ultrasound in water. A pulsed diode laser, followed by an erbium-doped fiber amplifier, was focused onto a light-absorbing film deposited on a glass substrate. Conversion efficiency was improved by over 20 dB using an elastomeric film instead of a more commonly used metallic one. Radiation pattern measurements show that considerable energy is radiated at +/−45° for frequencies beyond 50 MHz. These results show that the thermoelastic effect can be used to produce phased arrays for high-frequency ultrasound imaging.

Thermoelastic wave induced by pulsed laser heating

Abstract: In this work, a generalized solution for the thermoelastic plane wave in a semi-infinite solid induced by pulsed laser heating is developed. The solution takes into account the non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, which play significant roles in ultrashort pulsed laser heating. Based on this solution, calculations are conducted to study stress waves induced by nano-, pico-, and femtosecond laser pulses. It is found that with the same maximum surface temperature increase, a shorter pulsed laser induces a much stronger stress wave. The non-Fourier effect causes a higher surface temperature increase, but a weaker stress wave. Also, for the first time, it is found that a second stress wave is formed and propagates with the same speed as the thermal wave. The surface displacement accompanying thermal expansion shows a substantial time delay to the femtosecond laser pulse. On the contrary, surface displacement and heating occur simultaneously in nano- and picosecond laser heating. In femtosecond laser heating, results show that the coupling effect strongly attenuates the stress wave and extends the duration of the stress wave. This may explain the minimal damage in ultrashort laser materials processing.

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

Abstract: A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model's predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.

Mechanistic aspects and atomic-level consequences of elastic instabilities in homogeneous crystals

Abstract: Elastic stability criteria, derived for a homogenous lattice under arbitrary external load, provide an upper bound on the critical stress or strain which a crystalline solid can withstand. Since the onset of a structural instability is load dependent, the corresponding theoretical strength can be given similar interpretation. When combined with molecular dynamics simulation, such results allow a systematic discussion of competing structural transitions, as illustrated here in a case study of pressure-induced polymorphic and crystal-to-amorphous transitions and in some remarks on the thermoelastic mechanism for homogeneous (mechanical) melting, a process which defines an upper limit of metastability.

Averaging and finite-element discretization approaches in the numerical analysis of functionally graded materials

Abstract: Thermomechanical properties and responses of dual-phase functionally graded materials have been estimated by conventional averaging approaches, such as rules of mixtures, mean-field micromechanics and so on. However, the appropriateness of such models has been recently reported to be questionable. In this paper, we numerically investigated three representative averaging estimation methods, the linear and modified rules of mixtures and the Wakashima–Tsukamoto estimate, by comparing with the finite-element discretization approach utilizing rectangular cells. Through numerical experiments for the elastic and thermoelastic response of Ni–Al 2 O 3 functionally graded materials (FGMs), we presented comparative results together with introduction of a suggestive approach.

Thermoelastic effects at low temperatures and quantum limits in displacement measurements

Abstract: The displacement fluctuations of mirrors in optomechanical devices, induced via thermal expansion by temperature fluctuations due either to thermodynamic fluctuations or to fluctuations in the photon absorption, can be made smaller than quantum fluctuations, at the low temperatures, high reflectivities, and high light powers needed to readout displacements at the standard quantum limit. The result is relevant for the design of quantum-limited gravitational-wave detectors, both ``interferometers'' and ``bars,'' and for experiments to study directly mechanical motion in the quantum regime.

A three-dimensional thermomechanical model of contact between non-conforming rough surfaces

Abstract: A necessary step in understanding failure problems of tribological elements is to investigate the contact performance of rough surfaces subjected to frictional heating. It is essential that the interfacial variables are obtained through solving the interactive thermomechanical contact problem. This paper studies the three dimensional thermomechanical contact of non-conforming rough surfaces, the model of which includes the normal surface displacements caused by the contact pressure, frictional shear, and frictional heating. Influence coefficients and frequency response functions for elastic and thermoelastic displacements, as well as those for temperature rises, are investigated for model construction. In order to develop an accurate and efficient solver, the numerical algorithms with the discrete convolution and fast Fourier transform techniques and the single-loop conjugated gradient method are used. The model modules are numerically verified and the thermomechanical performance of the rough surfaces in a point contact is studied.

Time-domain simulation of damped impacted plates. I. Theory and experiments

Abstract: A time-domain formulation for the flexural vibrations in damped rectangular isotropic and orthotropic plates is developed, in order to investigate transient excitation of plates by means of sound synthesis. The model includes three basic mechanisms of damping (thermoelasticity, viscoelasticity and radiation) using a general differential operator. The four rigidity factors of the plate are modified by perturbation terms, each term corresponding to one specific damping mechanism. The first damping term is derived from the coupling between the thermoelastic stress - Strain relations and the heat diffusion equation. The second term is obtained from the general differential formulation of viscoelasticity. The third term is obtained through a Pade approximation of the damping factor which governs the coupling of the plate with the surrounding air. The decay factors predicted by the model reproduce adequately the dependence on both dimensions and frequency of the decay factors measured on rectangular plates of various sizes and thicknesses made of four different materials (aluminum, glass, carbon fiber, and wood). The numerical resolution of the complete problem, including initial and boundary conditions, and the comparison between real and simulated sounds are presented in a companion paper © 2001 Acoustical Society of America.

High Temperature Elastic Constant Prediction of Some Group III-Nitrides

Abstract: Thermoelastic properties are important for modeling thermal residual stresses and for optimizing the growth conditions of semiconductor thin films. Thermal expansions of AlN and GaN have been evaluated and predicted by us earlier. Here, high temperature elastic constants are estimated empirically from corresponding state relationships and data from other hexagonal Grimm-Sommerfeld compounds. This information together with our earlier thermal expansion data will further improve capabilities for calculating thermal residual stresses in various semiconductor thin films.

Nonlinear Transient Behavior of a Sliding System With Frictionally Excited Thermoelastic Instability

Abstract: A transient finite element simulation is developed for the two-dimensional thermoelastic contact problem of a stationary layer between two sliding layers, with frictional heat generation. The petrov-Galerkin algorithm is used to discretize the sliding layers because of the high Peclet numbers involved. The results in the linear, full contact regime were validated by comparison with the analytical predictions of Lee and Barber (1993). After separation occurs, there is a non-monotonic transition to a steady state with the contact regions separated by the same wavelength. During the transition, the migration speed exhibits values lower than those in either the linear regime or the final steady state. When several wavelengths are unstable, the final steady state is generally that corresponding to the longest unstable wavelength, even though other modes have more rapid growth rates in the linear regime.

Diffuse martensitic transitions and the plasticity of crystals with a shape memory effect

Abstract: The mechanism of diffusion-free (thermoelastic) martensitic transitions in solids is theoretically examined using a thermodynamic approach together with a self-consistent-field order parameter model. Based on the resulting equations, a theory of smeared martensitic transitions is constructed as a kinetic equilibrium theory of heterophase structures which takes into account heterogeneous martensite nucleation and the interaction of interphase boundaries with various types of structural defects in real materials. An extensive comparison is made between the theoretical predictions and the experimental data on thermoelastic martensitic transformations in alloys with shape memory. The universal nature of the theory of diffuse first-order phase transitions is illustrated by applying it to ferroelectric and ferroelastic transitions in some classical ferroelectric and high-temperature superconductors.

Electromagneto-thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity

Abstract: The model of the two-dimensional equations of generalized magneto-thermoelasticity with one relaxation time in a perfectly conducting medium is established. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses, and the displacement components. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate of perfect conductivity subjected to a time-dependent heat source on each face; the second concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space of perfect conductivity subject to appropriate boundary conditions; and the third problem deals with a plate with thermo-isolated surfaces subjected to time-dependent compression. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermoelasticity with one relaxation time.

Thermoelastic topology optimization for problems with varying temperature fields

Abstract: Elastic structures that exist in a thermal environment usually experience complex steady-state or transient heat conduction, whereby operational temperatures and stresses may change with time, heat sources, and thermal or kinematic boundary conditions. This article proposes an evolutionary optimization procedure for topology design involving thermoelasticity in which finite element heat analysis, finite element thermoelastic analysis, and subsequently design modification are iteratively carried out. To achieve as efficacious a material usage as possible, the relative efficiency of an element is defined in terms of its thermal stress level. In this article, design cases with uniform temperature fields, nonuniform temperature fields subjected to single or multiple heat load cases, and transient temperature fields are studied. The examples presented show the capabilities of the proposed procedure to solve various thermoelastic problems under varying temperature fields.

Crack path instabilities in a quenched glass plate

Abstract: A crack driven by steadily quenching a hot glass plate into a water bath exhibits fascinating path instabilities that depend on the severity of the temperature jump involved in the quenching process. An experimental and analytical investigation of these crack path instabilities is presented in this paper. First, real-time observations of the growth of the crack at different temperature jumps are presented. With increasing temperature jump, the crack path changes from a straight path to a periodic oscillatory path, then to a chaotic oscillatory path, to an unstable (dynamic) straight crack path, and finally to multiple crack paths. The experimental observations show that the crack growth is not a steady process even though the quenching occurs at a constant speed. The experimental observations provide crucial insight and the basis for the analysis of the problem. The problem is then examined analytically by solving the underlying thermoelastic problem, within the framework of linear elastic fracture mechanics. The results of the numerical simulations in conjunction with the experimental observations are used to show that (i) the T-stress criterion commonly used for evaluating crack path instability is inapplicable to this problem, (ii) the crack path stability can be determined by using the maximum tangential stress criterion for crack advance and examining the divergence of adjacent crack paths, (iii) the initiation of a structurally unstable crack can be determined, and (iv) the complete oscillatory crack path can be obtained through an incremental solution of the thermoelastic problem.

On the spatial and temporal behavior in linear thermoelasticity of materials with voids

Abstract: The present article studies the spatial and temporal behavior of the solutions to the initial boundary value problems associated with the linear theory of thermoelastic materials with voids. The spatial behavior is described by spatial estimates of Saint-Venant type (for bounded bodies) and Phragmen-Lindelof type (for unbounded bodies) with time-dependent and time-independent rates. Some appropriate time-weighted integral measures are used. The temporal behavior is studied using the Cesaro means of various parts of the total energy. The relations describing the asymptotic behavior of the Cesaro means are established.

Thermoelastic buckling of thin spherical shells

Abstract: Thermoelastic stability of thin perfect spherical shells based on deep and shallow shell theories is presented. To derive the equilibrium and stability equations according to deep shell theory, Sanders's nonlinear kinematic relations are substituted into the total potential energy function of the shell and the results are extremized by the Euler equations in the calculus of variation. The same equations are also derived based on quasi-shallow shell theory. An improvement is obtained for equilibrium and stability equations related to the deep shell theory in comparison with the same equations related to shallow shell theory. Approximate one-term solutions that satisfy the boundary conditions are assumed for the displacement components. The Galerkin-Bubnov method is used to minimize the errors due to this approximation. The eigenvalue solution of the stability equations is obtained using computer programs. For several thermal loads it is found that the deep shell theory results are slightly more stable as c...

Energy decay for hyperbolic thermoelastic systems of memory type

Abstract: In this paper we study the hyperbolic thermoelastic system, which is obtained when, instead of Fourier's law for the heat flux relation, we follow the linearized model proposed by Gurtin and Pipkin concerning the memory theory of heat conduction. In this case the thermoelastic model is fully hyperbolic. We show that the linear system is well posed and that the solution decays exponentially to zero as time goes to infinity.

Structural stability and continuous dependence of solutions of thermoelasticity of type III

Abstract: We prove a structural stability result on the coupling coefficients and continuous dependence on the external data in the thermoelastic theory called of type III. The only condition we require on the elasticity tensor is the symmetry of the coefficients. We use logarithmic convexity arguments.

3. Laser-based surface acoustic waves in materials science

Abstract: Publisher Summary This chapter discusses the application of laser-based surface acoustic waves (SAWs) in materials science. Laser sources are widely used in investigations by means of SAWs of elastic properties of solids, various films, and coatings on surfaces. These sources are noncontact; they allow a SAW transmitter of desired shape to be created and thus an acoustic beam with predetermined properties to be formed. All laser-based methods of SAW generation in solids can be divided into two groups. The first group is connected with heating of the solid by the absorbed laser radiation and all consequences of this heating, such as thermal expansion, evaporation, and ablation. The second group combines the processes of interaction of the electromagnetic field with the lattice or electronic structure of the solid, including electrostriction, deformation because of carrier density modulation by laser radiation, and nonradiative recombination in semiconductors. The chapter considers thermal laser sources of SAWs, because they are universal and in general more effective. Among thermal methods, it is convenient to distinguish between two limiting cases according to the relation between the absorbed energy density and specific heat of fusion and evaporation of the solid. The low-energy limit is the linear thermoelastic regime of SAW generation. All thermal and elastic parameters are assumed constant. Local pulsed heating causes transient thermal expansion and elastic stresses, which subsequently lead to emission of bulk and surface waves. In the high-energy case, strong evaporation or ablation occurs in the irradiated area.

A Three-Dimensional Thermal-Mechanical Asperity Contact Model for Two Nominally Flat Surfaces in Contact

Abstract: The rough surface contact in a tribological process involves frictional heating and thermoelastic deformations. A three-dimensional thermal-mechanical asperity contact model has been developed, which takes into account steady-state heat transfer, asperity distortion due to thermal and elastic deformations, and material yield. The finite-element method (FEM), fast Fourier transform (FFT), and conjugate gradient method (CGM) are employed as the solution methods. The model is used to analyze the thermal-mechanical contact of typical rough surfaces and investigate the importance of thermal effects on the contact performance of surface asperities.