Showing papers on "Thermoelastic damping published in 1995"
TL;DR: In this article, the damping characteristics of beam-shaped microactuators that oscillate in the transverse direction are analyzed to establish a design method that minimizes energy consumption and increases dynamic performance.
Abstract: The damping characteristics of beam-shaped microactuators that oscillate in the transverse direction are analytically evaluated to establish a design method that minimizes energy consumption and increases dynamic performance. The damping force due to airflow is calculated using the Navier-Stokes equation, the accuracy of which is verified by comparing the calculated damping with experimental results. The contributions to the damping due to squeeze force, internal friction, and support loss are calculated by using the Reynolds equation, structural damping theory, and a two-dimensional theory of elasticity, respectively. The final formulae, obtained in simple and closed forms for easy use in the actual design process, are then used to evaluate the relationships between the beam size and the damping ratio of silicon cantilevers, Permalloy cantilevers, and Permalloy spiral springs. Finally, the step response of a Permalloy cantilever is calculated and the relationship between beam size and settling time is determined.
402 citations
TL;DR: In this paper, the authors focus on the method of analytical development of thermoelastic problems for nonhomogeneous materials, such as functionally gradient materials (FGM), for which both the thermal and mechanical material constants are described by the function of the variable of the coordinate system.
Abstract: The focus of this review is on the method of analytical development of thermoelastic problems for nonhomogeneous materials, such as functionally gradient materials (FGM). For such nonhomogeneous materials, both the thermal and mechanical material constants are described by the function of the variable of the coordinate system. Then, the governing equations for the temperature field and the associated thermoelastic field become of nonlinear form in general cases. Therefore, the theoretical treatment is very difficult and the exact solution for the temperature and the thermoelastic field is almost impossible to obtain. This nonlinear equation system is usually treated by introducing some linearization technique with appropriate theoretical approximation. In this review, the method of some analytical developments for the heat conduction problem and the associated thermal stress problem of a body with nonhomogeneous material properties is explained briefly, and some boundary value problems of technical interest, such as optimization problems for material nonhomogeneity and the problems of thermal stress intensity factor for a body with a crack, are discussed.
257 citations
TL;DR: In this article, the cyclic thermal response in multi-layered materials which comprise layers of fixed compositions of a metal and a ceramic, and a compositionally graded interface is analyzed.
Abstract: Elastopllastic analyses are presented for the cyclic thermal response in multi-layered materials which comprise layers of fixed compositions of a metal and a ceramic, and a compositionally graded interface. Analytical solutions for the characteristic temperature at which the onset of thermally induced plastic deformation occurs are derived for the layered composite. Solutions for the evolution of curvature and thermal strains, and for the initiation of plastic yielding are also obtained for different combinations of the geometry, physical properties and compositional gradation for both thermoelastic and thermoplastic deformation. Finite-element formulations incorporating continuous and smooth spatial variations in the composition and properties of the graded layer are used to simulate the evolution of thermal stresses, the accumulation of plastic strains, and the development of monotonic and cyclic plastic zones at the interfaces, edges and free surfaces of different layers during thermal cycling. Engineering diagrams detailing the effects of compositional gradients are also presented for optimizing thermal residual stresses, layer geometry, and plastic strain accumulation.
176 citations
TL;DR: In this paper, high macroscopic residual stresses in PVD hard coatings up to about −10 GPa are caused by both the thermoelastic effects and grown-in defects, generated by fast particles during deposition.
Abstract: High macroscopic residual stresses in PVD hard coatings up to about −10 GPa are caused by both the thermoelastic effects and grown-in defects, generated by fast particles during deposition. Defect recovery, relaxation by plastic deformation or cracking limit the residual stresses. The mechanical behaviour of coated materials can be explained by the combination of the residual stresses and the exterior stresses (bending, hardness, critical load, erosion, abrasive wear). Owing to the lack of generalized knowledge about these relations a prediction of the performance of tools or components has to be sketchy.
175 citations
TL;DR: In this paper, a formulation of isotropic finite strain thermoelasticity is presented, based on the Finger tensor as a strain measure, and a rigorous decomposition of the thermo-elastic response functions into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts.
147 citations
TL;DR: In this article, the authors studied the general stress-strain behaviors due to the thermoelastic martensitic transformation induced by a combination of external forces of axial load and torque.
Abstract: Combined tension and torsion experiments with thin wall specimens of Cu-Al-Zn-Mn polycrystalline shape memory alloy (SMA) were performed at temperatureT =A
f
+ 25 K. The general stress-strain behaviors due to the thermoelastic martensitic transformation, induced by a combination of external forces of axial load and torque, were studied. It is shown that the progress of martensitic transformation (MT) at general stress conditions can be well considered as triggered and controlled by the supplied mechanical work (a kind of equivalent stress) in the first approximation. Pseudoelastic strains in proportional as well as nonproportional combined tension-torsion loadings were found fully reversible, provided that uniaxial strains were reversible. The axial strain can be controlled by the change of torque andvice versa due to the coupling among tension and torsion under stress, not only in forward transformation, but also in reverse transformation on unloading. The pseudoelastic strains of SMA polycrystal are path dependent but well reproducible along the same stress path. The evolution of macroscopic strain response of SMA polycrystal, subjected to the nonproportional pseudoelastic loading cycles with imposed stress path, was systematically investigated. The results bring qualitatively new information about the progress of the MT in SMA polycrystal, subjected to the general variations of external stress.
134 citations
TL;DR: Transient thermal gratings (TTGs) at surfaces of absorbing materials have been utilized for investigating heat diffusion in bulk materials and thin films as mentioned in this paper, where TTGs were excited in the surface plane by interference of two pulsed laser beams and monitored by a cw probe beam, either via temperature dependence of the reflectivity or by deflection from the displacement pattern.
Abstract: Transient Thermal Gratings (TTGs) at surfaces of absorbing materials have been utilized for investigating heat diffusion in bulk materials and thin films. In this report, we describe the theoretical background of the technique and present experimental data. TTGs were excited in the surface plane by interference of two pulsed laser beams and monitored by a cw probe beam, either via temperature dependence of the reflectivity or by deflection from the displacement pattern. A theoretical model describing the thermal and thermoelastic surface response was developed, both for a homogeneous material and a multilayer structure. The potential of the technique will be demonstrated by experimental results on (i) thermal diffusivities of bulk materials, (ii) anisotropic lateral heat transport, and (iii) thermal diffusivities of metal and diamond films. Furthermore, we will show that TTGs allow thermal depth profiling of inhomogeneous materials whenever there is a vertical gradient in thermal conductivity.
127 citations
TL;DR: In this paper, it was proved that the equations of a linear thermoelastic plate are associated with an analytic semigroup, and it was shown that the equation of a non-asymptotic plate is associated with a semigroup.
125 citations
01 Mar 1995
TL;DR: In this article, a micromechanical theory for the thermoelastic response of functionally graded composites with non-uniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fibre spacing in two directions.
Abstract: A recently developed micromechanical theory for the thermoelastic response of functionally graded composites with nonuniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fiber spacing in two directions. In contrast to currently employed micromechanical approaches applied to functionally graded materials, which decouple the local and global effects by assuming the existence of a representative volume element at every point within the composite, the new theory explicitly couples the local and global effects. The analytical development is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense. Results are presented that illustrate the capability of the derived theory to capture local stress gradients at the free edge of a laminated composite plate due to the application of a uniform temperature change. It is further shown that it is possible to reduce the magnitude of these stress concentrations by a proper management of the microstructure of the composite plies near the free edge. Thus by an appropriate tailoring of the microstructure it is possible to reduce or prevent the likelihood of delamination at free edges of standard composite laminates.
124 citations
TL;DR: In this article, a boundary element method is developed for transient and time harmonic analysis of problems in dynamic poroelasticity and generalized thermoelasticy, involving both two-and three-dimensional geometries.
118 citations
TL;DR: In this article, the authors consider a nonlinear coupled system of evolution equations, the simplest of which models a thermoelastic plate, and investigate the local well-posedness and the global existence of solutions.
Abstract: We consider a nonlinear coupled system of evolution equations, the simplest of which models a thermoelastic plate. Smoothing and decay properties of solutions are investigated as well as the local well-posedness and the global existence of solutions. For the system of standard thermoelasticity it is proved that there is no similar smoothing effect.
TL;DR: In this paper, a two-dimensional closed-form analytical method has been developed for the thermoelastic analysis of 2D orthogonal plain weave fabric laminae.
TL;DR: In this article, the effect of interstitial mobile hydrogen on the linear elastic behavior of metals and alloys has been investigated in the case of a dislocation and a line force in an infinite medium under plane strain conditions by using analytic function theory.
Abstract: The general principles of the mechanics of materials are used to describe the effect of interstitial mobile hydrogen on the linear elastic behavior of metals and alloys. The linear field equations reveal that during transient hydrogen diffusion the Laplacian of the hydrostatic stress is related to the Laplacian of the hydrogen concentration in the lattice, and it is not zero, as has often been assumed in calculations involving stress-driven diffusion of hydrogen under plane strain conditions. When the hydrogen reaches equilibrium with the local stress and diffusion terminates, the linear elastic constitutive response of the solid accounting for the hydrogen effect can be described by the standard Hooke's law of infinitesimal elasticity in which the stiffness moduli are termed moduli at fixed solute chemical potential and are calculated in terms of the moduli at fixed solute composition, the nominal hydrogen concentration, and the material parameters of the system. These moduli at fixed solute chemical potential can be viewed as the counterparts of those characterizing the drained deformation at constant pressure of fluid-infiltrated porous geomaterials, or the adiabatic deformation of thermoelastic materials. Next the linear transient field equations are solved in the case of a dislocation and a line force in an infinite medium under plane strain conditions by using analytic function theory. The range of validity of the solution to the linear field equations for an isolated edge dislocation is investigated for specific materials. Lastly, the implications of the constitutive behavior of the hydrogen-metal binary system on the fracture and dislocation behavior are discussed when the hydrogen is in equilibrium with local stress.
TL;DR: Strong evidence that short-pulse laser ablation of biological tissues is a photomechanical process is presented and a full three-dimensional, time-dependent solution to the thermoelastic wave equation is compared to the results of experiments using an interferometric surface monitor to measure thermoalastic expansion.
Abstract: Strong evidence that short-pulse laser ablation of biological tissues is a photomechanical process is presented A full three-dimensional, time-dependent solution to the thermoelastic wave equation is compared to the results of experiments using an interferometric surface monitor to measure thermoelastic expansion Agreement is excellent for calibrations performed on glass and on acrylic at low laser fluences For cortical bone, the measurements agree well with the theoretical predictions once optical scattering is included The theory predicts the presence of the tensile stresses necessary to rupture the tissue during photomechanical ablation The technique is also used to monitor the ablation event both before and after material is ejected
TL;DR: In this article, a theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction from the inner and /or outer surfaces.
Abstract: In this paper, a theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction from the inner and /or outer surfaces. Assuming that the hollow circular cylinder has nonhomogeneous thermal and mechanical material properties in the radial direction, the heat conduction problem and the associated thermoelastic behaviors for such nonhomogeneous medium are developed by introducing the theory of laminated composites as one of theoretical approximation. The transient heat conduction problem is treated with the help of the methods of Fourier cosine transformation and Laplace transformation, and the associated thermoelastic field is analyzed making use of the thermoelastic displacement potential, Michell's function, and the Boussinesq's function. Some numerical results for the temperature change and the stress distributions are shown in figures, and the effect of relaxing the thermal stress ...
TL;DR: In this article, a Voronoi cell finite element model is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials.
Abstract: In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.
TL;DR: In this article, the authors describe a number of calibration techniques commonly used for stress analysis of a steel and an experimental calibration study of a “steel” is also included, and discuss the factors which affect the accuracy of each technique.
Abstract: In recent years thermoelastic stress analysis has been established as an important experimental technique. The SPATE (Stress Pattern Analysis by Thermal Emissions) system, marketed by Ometron Ltd., is the standard equipment for thermoelastic stress analysis. The signal obtained from the SPATE equipment is directly proportional to the sum of the principal stress on the surface of the structure under evaluation. For quantitative stress analysis accurate calibration constants must be obtained; these are dependent on the radiometric properties of the SPATE system detector and the material properties and condition of the surface in question. This paper describes a number of calibration techniques commonly in use. The factors which affect the accuracy of each technique are discussed in detail. An experimental calibration study of a “steel” is also included.
TL;DR: In this article, a fiber optic delivery system was employed with the laser based ultrasonic transducer 600 and a thermoelastic medium to rapidly and accurately access the radii of complex structures in the field without the need for liquid or gel couplants.
Abstract: A method and apparatus for non-destructive inspection of complex structures employs a portable laser based ultrasonic transducer 600 output to rapidly detect and size flaws in such structures, including the radii of composites, laminates, and complex skin/substructure assemblies, such as airplane wings. A fiber optic delivery system 610A is employed with the laser based ultrasonic transducer 600 and a thermoelastic medium to rapidly and accurately access the radii of complex structures in the field without the need for liquid or gel couplants, with the thermoelastic expansion of the test piece 680 producing mechanical stresses that initiate detectable sound waves regardless of the angle of the laser based ultrasonic transducer 600 output with respect to the test piece 680. A MAUS III scanning device may be employed to detect these sound waves and provide accurate information as to the detected flaws.
TL;DR: In this article, the Helmholtz free energy and the stress associated with general constitutive equations of a simple continuum are proposed to model dispersive effects of an inherent material characteristic length.
Abstract: Modifications of the Helmholtz free energy and the stress associated with general constitutive equations of a simple continuum are proposed to model dispersive effects of an inherent material characteristic length. These modifications do not alter the usual restrictions on the unmodified constitutive equations imposed by the first and second laws of thermodynamics. The special case of a thermoelastic compressible Newtonian viscous fluid is considered with attention focused on uniaxial strain. Within this context, the linearized problems of wave propagation in an infinite media and free vibrations of a finite column are considered for the simple case of elastic response. It is shown that the proposed model predicts the dispersive effects observed in wave propagation through a chain of springs and masses as the wavelength decreases. Also, the nonlinear problems of steady wave propagation of a soliton in the absence of viscosity and of a shock wave in the presence of viscosity are discussed. In particular it is shown that the presence of the dispersive terms can cause the stress in a shock wave to overshoot the Hugoniot stress by as much as 50%. This phenomenon may cause an underprediction of the threshold level for failure determined by analysis of stress in shock experiments.
TL;DR: In this article, a femtosecond optical pump and probe technique was used to study the ultrafast generation of acoustic waves in copper lattice, where the authors used a nonlinear model to solve the nonequilibrium diffusion equations governing stress generation.
Abstract: The ultrafast generation of acoustic waves in copper films is investigated with a femtosecond optical pump and probe technique. By studying the generation at times before the electrons and the lattice come into equilibrium, the strength of their interaction can be measured and the dynamics of ultrafast electron diffusion can be studied. The acoustic strain pulses observed are bipolar in shape with exponential tails that are much broader than expected from simple thermoelastic stress generation. This can be explained by the supersonic diffusion of electrons over distances larger than the optical skin depth. The nonequilibrium diffusion equations governing stress generation are nonlinear, and are solved numerically. Using a linearized formulation, we also solve them analytically to a good approximation. The acoustic strain profile provides a 'snapshot' of the initial spatial temperature distribution of the lattice, thus allowing a sensitive probe of the nonequilibrium dynamics of the diffusion. The electron-phonon coupling constant can be estimated directly from the acoustic pulse duration, provided that the sound velocity and thermal conductivity are known. In general, the relaxation and diffusion of carriers is specific to the sample in question, whether metal or semiconductor, suggesting the use of this method for thin film characterization. >
TL;DR: In this paper, the authors have studied the elastic properties of the C15 compound NbCr{sub 2] in order to understand better the physical properties and deformation behavior of the compound, including load-deflection, thermoelastic stress, internal strain, sound velocities, dislocation core structure, and fracture toughness.
Abstract: Elastic properties of a solid are important because they relate to various fundamental solid-state phenomena such as interatomic potentials, equations of state, and phonon spectra. Elastic properties are also linked thermodynamically with specific heat, thermal expansion, Debye temperature, and Gruneisen parameter. Most important, knowledge of elastic constants is essential for many practical applications related to the mechanical properties of a solid as well: load-deflection, thermoelastic stress, internal strain (residual stress), sound velocities, dislocation core structure, and fracture toughness. In order to understand better the physical properties and deformation behavior of the C15 compound NbCr{sub 2}, the authors have studied its elastic properties in this paper. In Section 2, the experimental methods are described, including the preparation of the sample and the measurement of the elastic constants. In Section 3, the experimental results are presented and the implications of these experimental results are discussed. Conclusions are drawn in Section 4.
TL;DR: In this paper, the analytical theory of thermal stresses is constructed under some natural simplifying assumptions, including the thermoelastic behavior of the bonded materials and the thermal-plastic behaviour of a bonding layer, after the latter is deposited and the composite system is cooled to an operational temperature.
Abstract: Thin bonding layers made of solders or metal‐filled adhesives are widely used in electronics They are mostly responsible for the integrity and reliability of computers and other electronic devices Major concerns are due to thermal stresses arising in the process of electronic packaging In this article, the analytical theory of thermal stresses is constructed under some natural simplifying assumptions The assumptions include the thermoelastic behavior of the bonded materials and thermoelastic–plastic behavior of a bonding layer, after the latter is deposited and the composite system is cooled to an operational temperature The closed system of governing partial differential equations for thermal stresses in a thin bonding layer is derived for any in‐plane shape of the layer Some particular problems are solved in an explicit form and the implication of the solutions for the prediction of planar voids and cracks formation are discussed
TL;DR: In this article, a new mechanical-mathematical model is developed wherein ablating composites are considered to be porous multiphase media with phase transformations and chemical reactions of components in heating, allowing description of the effect of physical-chemical transformations on a stress-strain state of the material.
TL;DR: In this paper, a general methodology for calculating the elasto-thermodynamic damping was presented, taking the second law of thermodynamics as a starting point, using this method, for two canonical problems concerning particle-reinforced metal-matrix composites: (1) a single spherical inclusion in an unbounded matrix and (2) an N layer finite concentric composite sphere.
Abstract: When a composite material is subjected to a homogeneous or inhomogeneous stress field, different phases undergo different temperature fluctuations due to the well-known thermoelastic effect. As a result, irreversible heat conduction occurs and entropy is produced. This entropy production is the genesis of elastothermodynamic damping. Recently, taking the second law of thermodynamics as a starting point, a general methodology for calculating the elasto-thermodynamic damping was presented by Kinra and Milligan. Using this method, we calculate the elastothermodynamic damping for two canonical problems concerning particle-reinforced metal-matrix composites: (1) a single spherical inclusion in an unbounded matrix and (2) anN layer finite concentric composite sphere. In both cases, a uniform radial time-harmonic loading is considered.
TL;DR: In this article, an effective method is presented to determine the individual stresses from measured thermoelastic data in a region adjacent to an arbitrarily shaped fraction-free boundary of loaded orthotropic composites.
Abstract: The temperature variation in a cyclically loaded orthotropic composite is proportional to a linear combination of the changes in the normal stresses in the directions of material symmetry. An effective method is presented here to determine the individual stresses from measured thermoelastic data in a region adjacent to an arbitrarily shaped fraction-free boundary of loaded orthotropic composites. The method, which is based on equilibrium and compatibility, uses complex-variable formulations involving conformal mappings, analytic continuation and numerical techniques.
TL;DR: In this article, the histories and distribution of the dynamic thermoelastic stress in a hollow cylinder subjected to rapid arbitrary heating were obtained by applying a finite Hankel transform, which can be used to obtain the exact solution for the transient waves caused by a sudden arbitrary heating shock.
Journal Article•
TL;DR: In this paper, an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions is established and continuous dependence of solutions upon the initial data and body forces is also established.
Abstract: In this paper we study the linear thermodynamical problem of mixtures of thermoelastic solids. We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of solutions upon the initial data and body forces is also established. We finish with a study of the asymptotic behavior of solutions of the homogeneous problem.
TL;DR: In this article, the important parameters causing energy dissipation in unidirectional glass fiber-reinforced epoxy laminae are investigated, and an energy balance approach is used to find closed-form relationships between material properties and design parameters.
TL;DR: In this paper, the pseudomomentum equation of material momentum for thermoelastic materials is obtained in the classic theory based on the heat conduction hypothesis, and also in the framework of a thermo-elasticity approach involving no dissipation of energy, as recently proposed by Green and Naghdi.
Abstract: The equation of material momentum, or pseudomomentum, is obtained for thermoelastic materials. This is done in the classic theory, based on the heat conduction hypothesis, and also in the framework of a thermoelasticity approach involving no dissipation of energy, as recently proposed by Green and Naghdi. The results are applied to the thermoelastic fracture problem. When the pseudomomentum equation is written in global form, for a fractured body, it provides path-domain invariant expressions for the thermoelastic energy-release rate.