Showing papers on "Thermoelastic damping published in 1990"

One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials

Abstract: The use of the thermoelastic martensitic transformation and its reverse transformation has recently been proposed and demonstrated for several active control ap plications. However, the present constitutive models have lacked several important funda mental concepts that are essential for many of the proposed intelligent material system ap plications such as shape memory hybrid composites.A complete, unified, one-dimensional constitutive model of shape memory materials is developed and presented in this paper. The thermomechanical model formulation herein will investigate important material characteristics involved with the internal phase transformation of shape memory alloys. These characteristics include energy dissipation in the material that governs the damping behavior, stress-strain-temperature relations for pseudoelasticity, and the shape memory effect. Some numerical examples using the model are also presented.

On the driving traction acting on a surface of strain discontinuity in a continuum

Abstract: The notion of the driving traction on a surface of strain discontinuity in a continuum undergoing a general thermomechanical process is defined and discussed. In addition, the associated constitutive notion of a kinetic relation, in which the normal velocity of propagation of the surface of discontinuity may be a given function of the driving traction and temperature, is introduced for the special case of a thermoelastic material.

The effect of thermoelastic internal friction on the Q of micromachined silicon resonators

Abstract: Resonator damping measurements made on flexural beams micromachined from single-crystal silicon are described. A theoretical analysis of thermoelastic internal friction that accurately predicts the measurements that were taken is described. The results of these tests show that thermoelastic internal friction is a fundamental damping mechanism that can determine the quality of high-Q resonators over a range of operating conditions. Single-crystal silicon beams were tested under vacuum conditions over a range of frequencies from 80 kHz to 1.6 MHz and over a range of temperatures from 300 K to 400 K. measured values of Q varied from 10000 to more than 70000 and showed good agreement with theoretical estimates of thermoelastic internal friction. It is concluded that thermoelastic internal friction is a measurable phenomenon in micromachined flexures and should be considered when designing, testing, and evaluating miniature resonators for solid-state sensors. >

Residual stresses and stored elastic energy of composites and polycrystals

Abstract: R esidual Stresses in heterogeneous materials may arise because of differential or anisotropic thermal expansion of constituents. The paper is concerned with thermoelastic solids whose material properties fluctuate on the microscopic scale. Rigorous general relations between stored elastic energy and statistical averages (mean values and fluctuations) of residual stresses are derived. These results are applied to two-phase composites and to materials where the fluctuations of elastic constants can be neglected. One obtains exactly the stored energy, certain conditional mean values and the covariance matrix of the residual stresses. Under the assumptions of statistical homogeneity and isotropy, the results hold for any type of heterogeneous microstructure.

Calculated elastic and thermal properties of MGO at high pressures and temperatures

Abstract: Using the potential-induced breathing model, we calculate the pressure and temperature dependence of the thermoelastic properties of MgO. These calculations represent the first attempt to obtain a consistent set of thermodynamic elastic moduli for an oxide from an ab initio model over a wide range of pressure and temperature. By assuming the quasi-harmonic approximation for the free energies, we find excellent agreement between the temperature dependence of calculated elastic moduli and those obtained from experiments. Comparison of the calculated athermal and isothermal elastic moduli shows approximations using athermal values to be unreliable at high temperature. The elastic moduli for MgO are presented for pressures and temperatures appropriate for the lower mantle, a regime in which elastic moduli cannot be obtained by direct measurement.

On the precursor in laser‐generated ultrasound waveforms in metals

Abstract: A laser pulse, when focused on a metal sample, produces characteristic elastic waveforms, which depend on whether thermoelastic or ablative/evaporative mechanisms dominate the generation process. In the thermoelastic regime, with an unconstrained surface, the predominant axial displacement is opposite to the direction of propagation (negative), but there is typically a small transient positive displacement. This precursor is not predicted by elastic point source models, but is predicted by models including thermal diffusion. A recent formulation of pulsed photoacoustic generation is used to show how the precursor arises from interaction of the thermal and elastic modes at the illuminated surface.

One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials

Abstract: The use of the thermoelastic martensitic transformation and its reverse transformation has recently been proposed and demonstrated for several active control ap plications. However, the present constitutive models have lacked several important funda mental concepts that are essential for many of the proposed intelligent material system ap plications such as shape memory hybrid composites.A complete, unified, one-dimensional constitutive model of shape memory materials is developed and presented in this paper. The thermomechanical model formulation herein will investigate important material characteristics involved with the internal phase transformation of shape memory alloys. These characteristics include energy dissipation in the material that governs the damping behavior, stress-strain-temperature relations for pseudoelasticity, and the shape memory effect. Some numerical examples using the model are also presented.

Flow to a heated borehole in porous, thermoelastic rock: Analysis

Abstract: Exact solutions are obtained for fluid flow induced by the heating of a borehole. The rock is modeled as a fluid-saturated, porous, thermoelastic medium. The temperature and pore pressure fields are governed by a pair of diffusion equations, which are coupled through a source term in the pressure equation proportional to the temperature rate. The pressure profile exhibits a maximum that grows in magnitude and propagates away from the borehole. For a constant heat flux applied as an instantaneous step, the fluid flux to the borehole takes a finite initial value, and decays monotonically. When the heat flux exhibits a finite rise time, the fluid flux is initially zero, rises to a maximum, and then decays. At late time, the inverse of the fluid flux is linear in ln t; this observation can be exploited to estimate the permeability and fluid diffusivity of low-permeability rock. Sample calculations are shown for Westerly granite.

Thermal pressure in the laser‐heated diamond anvil cell

Abstract: Estimation of the thermal elastic effect is necessary for the calibration of the pressure and temperature conditions during laser-heated diamond anvil cell experiments, since above 800K, the standard technique of using ruby florescence to measure pressure fails. Continuum calculations based upon the thermoelastic equations for an elastic medium were used to estimate the thermal pressure resulting from a radially symmetric temperature gradient in an elastic sphere with zero displacement on its surface. This calculation corresponds to the thermal pressure generated in a laser-heated diamond anvil cell sample that is compressed without a pressure medium. This solution must fall between circumstances where the sample is held at constant pressure and where the sample is held at constant volume. It is shown here that the thermal pressure in an elastic medium with a Gaussian temperature gradient is approximately 40–60% of the thermodynamic value of the thermal pressure in a material raised to some constant temperature with the volume constrained to be constant. Even though the thermal pressure correction can be significant in terms of the total pressure that the sample experiences, these calculations indicate that the correction can be estimated to approximately 10%.

Mechanics of damping for fiber composite laminates including hygrothermal effects

Abstract: An integrated mechanics theory was developed for the modeling of composite damping from the micromechanics to the laminate level. Simplified, design oriented equations based on hysteretic damping are presented for on-axis plies, off-axis plies, and laminates including the effect of temperature, moisture, and interply hysteretic damping. The temperature rise within vibrating composite laminates resulting from strain energy dissipation is also modeled, and their coupled hygro-thermo-mechanical response is predicted. The method correlates well with reported damping measurements. Application examples illustrate the effect of various ply, laminate, and hygro-thermal parameters on the overall damping performance of composite laminates.

On Formation of Singularities in One-Dimensional Nonlinear Thermoelasticity

Abstract: It is well known that smooth motions of nonlinear elastic bodies generally will break down in finite time due to the formation of shock waves. On the other hand, for thermoelastic materials, the conduction of heat provides dissipation that competes with the destabilizing effects of nonlinearity in the elastic response. The work of Coleman & Gurtin [2] on the growth and decay of acceleration waves provides a great deal of insight concerning the interplay between dissipation and nonlinearity in one-dimensional nonlinear thermoelastic bodies. Assuming that the elastic modulus, specific heat, and thermal conductivity are strictly positive, the stress-temperature modulus is nonzero, and that the elastic response is genuinely nonlinear they show that acceleration waves of small initial amplitude decay but waves of large initial amplitude can explode in finite time. In other words, thermal diffusion manages to restrain waves of small amplitudes but nonlinearity in the elastic response is dominant for waves of large amplitudes.

On the origin of the intrinsic thermoelasticity associated with a single-interface transformation in Cu-Zn-Al shape-memory alloys

Abstract: Thermoelasticity is one of the important characteristics of the martensitic transformation in shape-memory alloys, that is the need for continuous undercooling (overheating) in order to force the transformation (reversion) to proceed. In this work the thermoelastic behaviour of a single-interface L21-to-18R transformation has been studied. It was found that the slope of curves of interface position against temperature varied from 0.05 to 0.004 K μm−1 depending on the thermal treatment to which the sample had been subjected. The smallest hysteresis width in a carefully polished material was found to be about 0.06 K. A simple model suggests that the thermoelasticity is ultimately related to the interaction of the martensite with pre-existent dislocations in the matrix.

Viscous damping approximation of laminated anisotropic composite plates using the finite element method

Abstract: The main source of mechanical damping in laminated composite materials arises from the inelastic nature of the matrix and the relative slipping at the fiber/matrix interfaces. Damping in laminated composite materials is usually a function of many parameters including the volume fraction of the fibers, fiber diameter and fiber orientation relative to the axis of loading. Also the magnitude and frequency of the applied load and many environmental factors should be mentioned. Since the complex phenomenon of damping is difficult to incorporate into the structural dynamic analysis of laminated plates, a viscous damping approximation is employed here. Experimental data on specific damping capacity (SDC) of unidirectional composite beams is used to define an average modal loss factor associated with each mode of vibration of a laminated plate. These loss factors are then employed with a finite element analysis and a multidimensional definition of critical damping to form a Rayleigh damping matrix [ C ] as a linear combination of the stiffness and mass matrices. Realistic examples illustrate the importance of several parameters in the vibration of laminated composite plates with damping. Such an analysis can be useful in the development of new composite materials where high damping is one of the primary objectives.

Joint damping and nonlinearity in dynamics of space structures

Abstract: Analysis of the effect of linear joint characteristics on the vibration of a free-free, three-joint beam model shows that increasing joint damping increases resonant frequencies and modal damping, but only to the point at which the joint gets «locked up» by damping. The maximum amount of passive modal damping obtainable from the joints is greater for low-stiffness joints and for modal vibrations where large numbers of joints are actively participating. A joint participation factor is defined to study this phenomenon. Analysis of the nonlinear three-joint model, with cubic spring at the joints, shows classical single-degree-of-freedom nonlinear response behavior at each resonance of the multiple-degree-of-freedom

Creep of sensor's elastic elements: Metals versus non-metals

Abstract: Sensors for the dynamometrical quantities force, pressure, acceleration, torque etc. usually are based on the ‘spring balance principle’, where an Upon application of an abrupt change of the load, one observes a steplike immediate elastic response—plus some time-dependent aftereffect. This highl (a) The thermoelastic effect, i.e. the change of temperature of an adiabatically deformed body, in turn causing a dimensional change of the spring—ev (b) The pure anelastic effect which is caused by a redistribution of certain atoms in the deformed lattice. This anelasticity is a diffusion-dominated This gradient enhancement of creep may increase the aftereffect of the homogeneously strained material by a factor of ten or more. Thus the creep of a

Uniqueness and stability of the solution to a thermoelastic contact problem

Abstract: Uniqueness and continuous dependence on the initial temperature are proved for a onedimensional, quasistatic and frictionless contact problem in linear thermoelasticity. First the problem is reformulated in such a way that it decouples. The resulting problem for the temperature is a nonlinear integro-differential equation. Once the temperature is known the displacement is recovered from an appropriate variational inequality. Uniqueness is proved by considering an integral transform of the temperature. The steady solution is obtained and the asymptotic stability is shown. It turns out that the asymptotic behaviour and the steady state are determined by a relation between the coupling constant a and the initial gap.

Three‐dimensional theory of pulsed photothermal deformation

Abstract: In this paper, the three‐dimensional theory of pulsed photothermal deformation is presented; by taking two appropriate assumptions, the rigorous solutions of three‐dimensional thermal conduction and thermoelastic equations are given for the first time. The theoretical shape of the signal of two different samples is calculated, and the effects of pulse width, radius of pump beam, and sample thickness are discussed. As an example, the potential application of pulsed photothermal deformation for thin‐film thickness measurement is analyzed.

Simultaneous stress separation, smoothing of measured thermoelastic isopachic information and enhanced boundary data

Abstract: A new thermoelastic hybrid method of stress analysis is demonstrated experimentally which simultaneously smooths the measured isopachic data, enhances the boundary information, and separates the stresses at nonboundary locations using only the isopachics. The technique is illustrated by application to a tensile plate containing a hole.

Effect of Material Properties on the Stability of Static Thermoelastic Contact

Abstract: It is found that most material combinations exhibit one or other of two kinds of stability behavior. In one of these, the stability criterion is closely related to that for uniqueness of the steady-state solution and instability is only possible for one direction of heat flow. In the other, instability can occur for either direction of heat flow and in one case is characterized by the oscillatory growth of a pressure perturbation

Analysis of thermoacoustic wave propagation in elastic media

Abstract: Wave propagation in a material continuum is a thermodynamic process that is governed, not only by the mechanical character of the propagation medium, but by the thermal character as well. The dispersion relation derived on the basis of linear thermoelastic theory shows that two distinct types of dilatational waves can propagate in an isotropic elastic medium. In each such wave, mechanical and thermal effects are coupled. The behavior of these thermoacoustic waves, in particular, their speeds and absorption coefficients as functions of frequency, is described. Three models of thermoacoustic wave propagation are considered. The classic model, which incorporates the Fourier description of heat conduction, is analyzed first. The shortcomings of this model are pointed out. Two models incorporating the Vernotte hypothesis of heat conduction are examined next—a ‘‘lattice’’ model, which is based upon an idea implicit in the Debye theory of specific heats, and a ‘‘phonon‐gas’’ model. Both models incorporating the Vernotte hypothesis are shown to describe linear thermoacoustic wave propagation in a more physically realistic fashion than does the classic model. Thermoacoustic wave propagation is considered from a general phenomenological (i.e., from a macroscopic) standpoint, and only the most general assumptions about the constitution of the propagation medium are made. In the analysis, only the dissipation of energy by heat conduction is considered; the medium is assumed to be elastic in that no purely mechanical mechanisms for energy dissipation (e.g., classic viscosity) are considered to be present.

A layered composite shell element for elastic and thermoelastic stress and stability analysis at large deformations

Abstract: A finite shell element for layered fibre reinforced composite shells has been developed. The degeneration principle is used in combination with specific kinematic assumptions. The thermo-elastic material is either described by the behaviour of the local components, i.e. fibre and matrix material laws and geometrical configuration in each layer, or by the overall orthotropic layer material laws. Thickness integration for obtaining the different contributions to the shell element's stiffness matrix is performed analytically and prior to the numerical in-plane integration. This leads to a considerable saving in computer time during the incremental-iterative analysis. Geometrical non-linearities in terms of large deformations and material non-linearities in terms of layer craccking are taken into account. Accompanying eigenvalue analyses allow the determination of the—sometimes rather complicated—buckling behaviour with non-linear prebuckling deformations.

Thermoelasticity and the formation of black smokers

Abstract: Darcy's Law flow in a permeable medium, consisting of uniform parallel evenly spaced fractures, is used to elucidate how thermoelastic effects may modify the permeability and flow in fracture-controlled hydrothermal systems. Some simple permeability models are then used to investigate whether black smoker venting can result from focussing of low velocity porous flow into fractures at shallow depths (≃ 100 m.). The models indicate that: (a) thermoelastic processes may be important in controlling the temporal evolution of hydrothermal upflow zones; (b) permeability structure, not just the bulk value of the permeability, may be critical for the formation of black smokers; (c) a small zone extending to a depth of ≃ 100 m containing a few fractures a factor of 2 or more wider than average may be sufficient to focus upflow into discrete vents provided thermoelastic and chemical effects seal parts of the upper crust.

Generalized Thermoelasticity for an Infinite Body with a Circular Cylindrical Hole

Abstract: A one-dimensional generalized thermoelasticity is presented based on Lord and Shulman's Theory which involves one relaxation time of the thermoelastic process. This theory has been developed in an attempt to eliminate the paradox of an infinite velocity of thermoelastic propagation inherent in the classical one. The analytical object of this paper is an infinite body with a circular cylindrical hole. The boundary condition is that a constant heat flux is flowing into the infinite body so that the displacement at a circular cylindrical hole is constrained. An approximate analysis for short times is carried out because it is very difficult to obtain an exact solution. The numerical results of the effect of the relaxation time on displacement, temperature and stress distributions are shown.