Thermoelastic stress intensity factors for a cracked layer between two different anisotropic solids

Steady-state anisotropic thermoelasticity equations are used to obtain the stress intensity factors for a cracked layer sandwiched between two different anisotropic elastic solids. The anisotropy is assumed to arise from discrete fibers whose orientation could alter with reference to the crack edges. A generalized plane deformation prevails in the dissimilar media domain with a line of discontinuity disturbing a uniform heat flow. The flexibility/stiffness matrix approach is used such that the crack problem reduces to solving two sets of singular integral equations. Numerical values of the crack tip stress-intensity factors are obtained for various crack size, crack location, crack surface insulation, fiber volume fraction and orientation angles. The results are displayed graphically.     

On some crack problems in anisotropic thermoelasticity

Some basic equations recently derived by Clements are used to consider crack problems in anisotropic thermoelasticity. The problems concern a single crack in an anisotropic material in which the displacement and stress are independent of one Cartesian coordinate. No symmetry elements of the material are assumed and the temperature, displacement and stress fields are determined for an arbitrary distribution of temperature or heat flux over the crack faces.     

Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat

In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.     

Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells

The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of yon Ktirrntin and the theory of thermoelusticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin ‘ s technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors us well us boundary conditions on thermoelustically coupled nonlinear vibration behaviors are discussed.     

Comparative asymptotic analysis of coupled and uncoupled thermoelasticity

The asymptotic solution of the three-dimensional dynamic of coupled thermoelasticity problem (with the mutual influence of the strain and temperature fields taken into account) for an isotropic rectangular plate is used to perform a comparative analysis of the results obtained according to this theory and the theory of temperature stresses. The parameters whose values affect the applicability of these theories and of the applied theory used to solve quasistatic problems of thermoelasticity are obtained.     

Nonlocal coupled thermoelastic wave propagation band structures of nano-scale phononic crystal beams based on GN theory with energy dissipation: An analytical solution

This paper deals with the band structures of thermoelastic waves in nano-scale phononic crystal or metamaterial beams considering nano-size effects. The nonlocal coupled thermoelastic governing equations are derived using the Green–Naghdi theory of the generalized coupled thermoelasticity with energy dissipation and Eringen’s nonlocal theory. The derived governing equations are analytically solved and the field quantities including the temperature and the deflection are obtained in the closed forms. Using the proposed analytical solution, the transfer matrix between two unit-cells are obtained using the thermal and mechanical continuity conditions on the interfaces between the unit-cells and between the two sections of each unit-cell. The band structures of the phononic crystals are obtained using the Bloch–Floquet theorem. The detailed discussions are presented for the band structures of nonlocal thermoelastic waves in nano-scale aluminum/epoxy phononic crystal or metamaterial beams. Also, the effects of the small-scale parameter and the thickness of the epoxy layers on the band structures are studied and discussed by using the derived analytical solution.     

On the finite deformation and heating of thermoelastic spherical sectors

The possibility of holding certain non-uniform temperature fields in finitely deformed spherical sectors is considered. An exact solution in spherical coordinates to the coupled equations of thermoelasticity for Fourier-like materials is given.     

2-D problem of a Mode-I crack for a generalized thermoelasticity under Green-Naghdi theory

A general model of the equations of the generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solved. The crack is subjected to prescribed temperature and stress distribution in the context of Green-Naghdi theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature and the couple stresses. Comparisons are made with the results predicted in the both type II, III of Green-Naghdi theory. It is found that a Mode-I crack has great effects on the distribution of field quantities with energy dissipation.     

On problem of transient coupled thermoelasticity of an annular fin

In this paper, the radial deformation and the corresponding stresses in a homogeneous annular fin for an isotropic material has been investigated. A numerical technique is proposed to obtain the solution of the transient coupled thermoelasticity in an annular fin cylinder with it’s base suddenly subject to a heat flux of a decayed exponential function of time. The system of fundamental equations is solved by using an implicit finite-difference method. The present method is a second-order accurate in time and space and unconditionally stable. A numerical method is used to calculate the temperature, displacement and the components of stresses with time t and through the radial of the annular fin cylinder. The results indicate that the effect of coupled thermoelasticity on temperature, stresses and displacement is very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of coupled thermoelasticity.     

Stress-intensity factors for 3-D dynamic loading of a cracked half-space

A half-space containing a surface-breaking crack of uniform depth is subjected to three-dimensional dynamic loading. The elastodynamic stress-analysis problem has been decomposed into two problems, which are symmetric and antisymmetric, respectively, relative to the plane of the crack. The formulation of each problem has been reduced to a system of singular integral equations of the first kind. The symmetric problem is governed by a single integral equation for the opening-mode dislocation density. A pair of coupled integral equations for the two sliding-mode dislocation densities govern the antisymmetric problem. The systems of integral equations are solved numerically. The stress-intensity factors are obtained directly from the dislocation densities. The formulation is valid for arbitrary 3-D loading of the half-space. As an example, an applied stress field corresponding to an incident Rayleigh surface wave has been considered. The dependence of the stress-intensity factors on the frequency, and on the angle of incidence, is displayed in a set of figures.     

Dynamic compactness of coupled thermoelastic waves in continuously nonuniform anisotropic media

In the present work, the dynamic problem of coupled thermoelasticity with the most general type of nonuniformity and anisotropy is analyzed. The hyperbolic nature of the system of equations of coupled thermoelasticity is demonstrated, effects of extinction of separate waves by superposition of elastic and thermoelastic wave fronts are investigated, and the interrelationship of different orders of discontinuity of stresses, displacements, and temperature is determined. The case of the uncoupled problem of thermoelasticity is especially analyzed. Sufficient conditions are obtained for the dynamic density for wave processes in thermoelasticity, previously investigated for boundary value problems of hyperbolic systems of second order differential equations [1], andelastic stress waves [2] are obtained. The generally accepted system of tensor notation for the theory of thermoelasticity is used [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 154–163, May–June, 1981.     

THE EFFECT OF DUAL-PHASE-LAG MODEL ON REFLECTION OF THERMOELASTIC WAVES IN A SOLID HALF SPACE WITH VARIABLE MATERIAL PROPERTIES

The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.     

Wave diffraction by a line of finite crack in a saturated two-phase medium

An application of the Biot’s theory to the diffraction problem of plane harmonic dilatational waves (P-waves) of the first kind and the second kind by a line crack or geometric discontinuity of finite width embedded in a saturated two-phase medium is presented in this paper. The crack surfaces are assumed impermeable, and the integral transform method is utilized to reduce the mixed boundary-value problem to a single Fredholm integral equation. The magnitudes of the intensity of the stress fields near the crack tips measured by Mode I dynamic stress-intensity factor (dimensionless) are computed and displayed graphically against dimensionless circular frequency (ω) for several dimensionless material property values, namely, viscosity-to-permeability and mass density ratios. In the case of the normally incident P-waves of the first kind, the results in terms of stress-intensity factor are also compared with the corresponding values of dry elastic material. All the stress-intensity factor curves are shown to exhibit a similar character in that they rise to the peaks at certain frequency values and then decay with increasing frequencies. At certain frequency ranges and material property values, amplification in the dynamic stress-intensity factor can be substantially larger than those encountered in dry elastic materials. The stress-intensity factor is found to be more affected by the changes in the ratio of viscosity-to-permeability at lower mass density ratio. With fluid mass density 10% of the bulk mass density, the viscosity-to-permeability ratio of 0.01 gives the highest increase of about 32% in the magnitude of stress-intensity factor compared to the dry material counterpart value, while a decrease of about 9% is observed for the viscosity-to-permeability ratio of 100. It is also found that change in mass density ratio has significant effect upon the magnitude of stress-intensity factor at lower ratio of viscosity-to-permeability. As for the normally incident P-waves of the second kind, the presence of the pore fluid affects both the magnitude and character of the stress-intensity factor. Large variations in the magnitude of stress-intensity factor are observed as viscosity-to-permeability ratio changes from 1 to 100. At the ratio of viscosity-to-permeability of 1.0, the stress-intensity factor curves increase gradually with frequency and exhibit the peaks in curves for mass density ratio of 0.3 and higher. As the viscosity-to-permeability ratio is raised to 100, the stress-intensity factor curves increase monotonically with frequency at a much faster rate throughout the frequency range of interest (ω = 0–2), and the change in mass density ratio is shown to have little effect on the stress-intensity factor, especially within the low frequency ranges. The results obtained in this study are useful in the mechanics of fracture initiation of saturated porous materials under the fluctuating mechanical and/or pore fluid loadings that are periodic with time.     

Heat propagation in a nonuniform rod of variable cross section

An integral formula is used to average a coupled problem of thermoelasticity for a nonuniform rod of variable cross section. Effective characteristics are found. It is shown that, in addition to the expected effective coefficients, there appear five independent coefficients characterizing the temperature change rate effect on the stresses in the rod, on the longitudinal heat flux, and on the entropy distribution along the length of the rod. A feature of these new coefficients is that they become equal to zero in the case of a uniform rod. The homogenization of the thermoelasticity equations for nonuniform rods allows one to propose a new theory of heat conduction in rods. This new theory differs from the classical one by the fact that some new terms are added to the Duhamel–Neumann law, to the Fourier heat conduction law, and to the entropy expression. These new terms are proportional to the temperature change rate with time. It is also shown that, in the new theory of heat conduction, the propagation velocity of harmonic heat perturbations is dependent on the oscillation frequency and is finite when the frequency tends to infinity.     

Crack growth induced by thermal-mechanical loading

Advanced aerospace structures are often subjected to combined thermal and mechanical loads. The fracture-mechanics behavior of these structures may be altered by the thermal state existing around the crack. Hence, design of critical structural elements requires the knowledge of stress-intensity factors under both thermal and mechanical loads. This paper describes the development of an experimental technique to verity the thermal-stress-intensity factor generated by a temperature gradient around the crack. Thin plate specimens of a model material (AISI-SAE 1095 steel) were used for the heart transfer and thermal-mechanical fracture tests. Rapid thermal loading was achieved using high-intensity focussed infrared spot heaters. These heaters were also used to generate controlled temperature rates for heat-transfer vertification tests. The experimental results indicate that thermal loads can generate stress-intensity factors large enough to induce crack growth. The proposed thermal-stress-intensity factors appear to have the same effect as the conventional mechanical-stress-intensity factors with respect to fracture.     

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field variables. In addition, comparisons are presented with the corresponding four theories.     

Effect of rotation on generalized thermo-viscoelastic Rayleigh–Lamb waves

The present paper is aimed at studying the effects of rotation on the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate rotating about the normal to its faces with uniform angular velocity. This facilitates the decoupling of anti-plane/in-plane motion which is not possible, in general. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The formulation is applied according to three theories of the generalized thermoelasticity: Lord-Shulman with one relaxation time, Green–Lindsay with two relaxation times, as well as the coupled theory. Secular equations are derived for the plate in closed form isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. In the absence of mechanical relaxations (Rotation and viscous effects), the results for generalized and couple theories of thermoelasticity were obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. Finally the numerical solution is carried out for copper material. The function iteration numerical scheme is used to solve the complex secular equations, in order to obtain phase velocity and attenuation coefficients of propagating wave mode. The dispersion curves and attenuation coefficients profiles so obtained for symmetric and skew-symmetric wave modes are presented graphically to illustrate and compare the theoretical results in the presence and absence of rotation. The study may be useful in the construction and design of gyroscopes and rotation sensors as well as in the application in diverse fields.     

Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method

In this paper, we constructed the equations of generalized magneto-thermoelasticity in a perfectly conducting medium. The formulation is applied to generalizations, the Lord–Shulman theory with one relaxation time, and the Green–Lindsay theory with two relaxation times, as well as to the coupled theory. The material of the cylinder is supposed to be nonhomogeneous isotropic both mechanically and thermally. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. The results indicate that the effects of nonhomogeneity, magnetic field, and thermal relaxation times are very pronounced. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and/or classical dynamical thermoelasticity, respectively. Results carried out in this paper can be used to design various nonhomogeneous magneto-thermoelastic elements under magnetothermal load to meet special engineering requirements. An erratum to this article can be found at     

Analysis of the nonstationary spatial propagation of elastic waves from cavities subject to mechanical and thermal loads

A numerical analytic method is proposed to solve nonstationary coupled problems of thermoelasticity with regard to the finite velocity of thermal waves. The method is used to analyze the nonstationary spatial propagation of elastic waves from a cavity subjected on its surface to mechanical and thermal loads. The ray theory of propagation of wavefield discontinuities is used. To determine the time dependence of the field parameters behind the wavefront and to account for the relationship between the mechanical and thermal fields with prescribed accuracy, a numerical iterative procedure that employs the properties of characteristics is used. Plots are presented for the nonstationary stresses and temperature near a prolate spheroidal cavity subject to step mechanical loading and near an elliptical cylindrical cavity subject to thermal shock __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 79–88, August 2006.     

Crack kinking in a piezoelectric solid

The intrinsic coupling between the mechanical and the electric fields assigns a uniquefeature for the fracture in a piezoelectric solid. We model the kink of a crack by continuousdistribution of edge dislocations and electric dipoles. The problem admits an approach based onthe Stroh formalism. A set of coupled singular integral equations are derived for the dislocationand electric dipole density functions associated with a kinked crack. Numerical results indicatethat the crack tends to propagate in a straight line under a tensile stress and a positive electricfield. For a crack subjected to the mixed mode mechanical loading, a superimposed positiveelectric field tends to reduce the kink angle. The influence of the non-singular T-stress-chargeparallel to a crack is also investigated. It is shown that a transverse tensile stress or a positivetransverse electric field will lead to further deviation of the kinked crack from the crackextension line.