Effect of rotation and relaxation time on a thermal shock problem for a half-space in generalized thermo-viscoelasticity

Summary. In this article, we propose a model of generalized thermo-viscoelastic plane waves for a half-space whose surface is subjected to a thermal shock under the effect of rotation with one relaxation time. The normal mode analysis is used to obtain the exact expressions for the considered variables. The resulting formulation is applied to two kinds of boundary conditions. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermo-elasticity with one relaxation time in the absence of rotation.     

A two-dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation

In this work we study a two-dimensional problem in electromagneto-thermoelasticity for a half-space whose surface is subjected to a non-uniform thermal shock and is stress free in the presence of a transverse magnetic field. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. Laplace and exponential Fourier transform techniques are used to obtain the solution by a direct approach. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The distributions of the temperature, the displacement, the stress and the induced magnetic and electric fields are obtained. The numerical values of these functions are represented graphically.     

Analysis of three-dimensional wave motions in a cubically anisotropic thermoelastic medium with allowance for the relaxation time of thermal disturbances

Formulas for the coordinates of points of a cubically anisotropic thermoelectric medium, which determine the geometry of wave fronts excited by a lumped disturbance source, have been obtained. The three-dimensional fronts of a quasilongitudinal modified elastic wave, a modified thermal wave, and quasitransverse elastic waves propagating in lead have been constructed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 4, pp. 808–813, July–August, 2008.     

Electromagneto-hydrodynamic instability in a horizontal viscoelastic fluid layer with one relaxation time

Summary The stability of viscoelastic conducting liquid (Walters's liquid B) heated from below in the presence of a magnetic field is considered. Linear stability theory is used to derive an eigenvalue system of sixth order, and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh number and wavenumber for the onset of instability are presented graphically as functions of the Chandrasekhar number at a Prandtl numberP _r=100 and for various values of the one relaxation time and the elastic parameters.     

Propagation of a planar shock thermal wave in a nonlinear medium

Conditions are analyzed for a strong discontinuity of a thermal field in a nonlinear medium, possessing thermal relaxation. The solution of the heattransfer equations is obtained in the region between the mobile boundaries and the front of the strong discontinuity.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 436–443, September, 1985.     

A finite element study of thermal relaxation of residual stress in laser shock peened IN718 superalloy

The residual stresses in laser shock peened (LSP) Inconel 718 Ni-base superalloy and their thermal relaxation behavior were investigated based on three-dimensional nonlinear finite element analysis. To account for the nonlinear constitutive behavior, the Johnson-Cook model has been employed and the model parameters for high strain rate response of IN718 are calibrated by comparison with recent experimental results. Based on the LSP simulation, the thermal relaxation behavior was studied through coupled thermal-structure analysis in LS-DYNA. More specifically, the effects of test temperature, exposure time and degree of initial plastic deformation are analyzed and discussed. It is observed that stress relaxation mainly occurs during the initial period of exposure, and the relaxation amplitude increases with the increase of applied temperature and as-peened plastic deformation. Based on the simulation results, an analytical model based on Zener-Wert-Avrami function is proposed to model the thermal residual stress relaxation.     

State space approach of two-temperature magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity

A one-dimensional model of the two-temperature generalized magneto-thermoelasticity theory with one relaxation time in a perfect conducting medium is established. The state space approach developed in [1]; [M. Ezzat, Int. J. Eng. Sci. 35 (1997) 741] 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 two-temperature parameter and the applied magnetic field.     

Measurement of thermal relaxation and temperature damping time in a solid

Differential equations of heat conductance of solid body are presented, a result of Fourier, Cattaneo–Vernotte, and two-phase delay hypotheses. The experimental set-up and automated measuring system is described for the study of transient thermal processes in solid. The solution of the boundary problem of the third kind is given with differential equations of heat conductance of parabolic and hyperbolic types. The results of experimental and theoretical study of transient thermal processes in the plate center are given in the sudden immersion into a hot environment. Based on the comparison of theoretical transient processes with recorded automated measuring system, the adequacy of hypotheses and corresponding differential equations of heat conductance are concluded with respect to short-term transient processes. Thermal relaxation and temperature damping constants for polymethyl methacrylate are measured.     

A finite element analysis of thermal relaxation of residual stress in laser shock processing Ni-based alloy GH4169

The residual stress induced by laser shock processing and the thermal relaxation behaviors of residual stress in Ni-based alloy GH4169 were investigated by means of three-dimensional nonlinear finite element analysis. To study the effect of different given exposure time and different temperatures on residual stress in laser shock processing Ni-based alloy GH4169, Johnson–Cook material model was used in order to account for the nonlinear constitutive behavior. The influence of heating temperature and exposure time on the stress thermal relaxation was studied. It was concluded that stress relaxation mainly occured during the initial period of exposure, and the degree of relaxation increased as the temperature risen. The results would provide a theoretical basis for controlling the laser shock processing and guiding subsequent experiments.     

Temperature shock waves in a moving medium with allowance for the relaxation of the heat flux

The solution of the gasdynamic equation with allowance for the heat transfer in the relaxation of the heat flux is analyzed. The relations expressing the laws of conservation on the front of strong discontinuity of the quantities sought, including the discontinuity of the temperature and the heat-flux density, are discussed. The possibility of existence of two shock waves with fixed initial data is shown using the self-similar solution of the problem on gas motion ahead of the piston. The occurrence of two strong discontinuities is due to the presence of different velocities of propagation of gasdynamic and thermal disturbances — the velocity of sound and the finite rate of heat transfer at a nonzero time of relaxation of the heat flux. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 57–68, July–August, 2006.     

Propagation of a shock wave in a locally anisotropic medium containing channels with elevated thermal diffusivity

We consider the interaction between a shock wave and thin extended channels with elevated a thermal diffusivity. It is shown that a thermal perturbation ahead of the shock wave front leads to the effect of a warm layer, i.e., to the formation of a large-scale self-similarly growing precursor.Notation T temperature - p pressure - density - velocity - e specific internal energy - thermal conductivity coefficient - effective specific heat ratio - q heat flux density - t time - x, y Cartesian coordinates Institute of the Dynamics of the Geospheres, Russian Academy of Sciences, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 643–650, June, 1994.     

Problem in electromagneto thermoelasticity for an infinitely long solid conducting circular cylinder with thermal relaxation

The problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis is considered. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. The solution is obtained by a direct approach without the customary use of potential functions. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions.Numerical computations for the temperature, the displacement and stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically. Comparison is made with the results obtained when using the coupled equation of heat conduction.     

Stabilized finite element approximations for heat conduction in a 3-D plate with dominant thermal source

The present work studies the finite element approximation for the heat transfer process in an opaque three-dimensional plate with a temperature-dependent source dominating the conductive operator. The adopted mechanical model assumes the existence of a heat transfer from/to the plate following Newton's law of cooling. The numerical simulations performed have attested the instability of the classical Galerkin method when subjected to very high source-dominated regimen. Usual strategies in the Engineering practice of dealing with this shortcoming proved to be inefficient. A Gradient-Galerkin/Least-Squares formulation was adopted in the numerical simulations as a remedy for the Galerkin's instability when subjected to those regimen. Received 25 May 1998     

The thermal inertia of materials heated with a laser pulse faster than relaxation time

The nonlocal hyperbolic heat conduction equation is used to describe the thermal inertia of thin metal films (TMF) heated with femtosecond laser pulses. It is shown that for TMF the signatures of thermal inertia are (i) the delay of the heating process and (ii) the strong localization of the thermal energy in TMF.Paper presented at the Fourth International Workshop on Subsecond Thermophysics, June 27–29, 1995, Köln, Germany.     

Analytical study of the thermal shock problem of a half-space with various thermoelastic models

Summary The thermal shock problem of a half-space is frequently used as a test example for checking computer programs which are suitable for solving thermoelastic problems. As there are no exact solutions for the problem formulated on the basis of complicated models, authors have compared their own results to previous numerical results in their publications so far. In the present paper six thermoelastic models are investigated. Curves of temperature, displacement and stress fields arising as a result of sudden and ramp-type surface heating are given in a very handy form for program testing. A thorough analysis of elastic and thermal waves is also included.     

One case of strengthening a shock wave in loading of a condensed medium with an explosion

An analysis is made of the wave configurations in a layer system with surface loading by a sliding detonation wave. The relationship of the threshold thickness of a steel plate at which the material fails to the thickness and properties of the intermediate layer is determined experimentally.Translated from Problemy Prochnosti, No. 8, pp. 3–6, August, 1992.