Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading

The transient thermal stress crack problem for a half-space with a multilayer coating under thermal surface loading containing an undercoat crack, perpendicular to the interface, is considered. The problem is solved using the principle of superposition and uncoupled quasi-static thermoelasticity. Transient temperature distribution and corresponding thermal stresses for the uncracked multilayer assembly are obtained in a closed analytical form using the model with generalized thermal boundary conditions of heat exchange of a half-space with ambient media via the coating. The crack problem is formulated as a perturbation mixed boundary value problem, in which the crack surface loading should be equal and opposite to the thermal stresses obtained for the uncracked medium, and is reduced to a singular integral equation and solved numerically. Numerical computations are performed for the analysis of influence of the coating upon thermal stresses and thermal stress intensity factor.     

Inhibition of a curvilinear bridged crack by induced thermoelastic stress field

Temperature changes near the end of a curvilinear crack in the presence of end areas with cohesive forces of the material are considered. It is assumed that these areas adjoin to the crack tip and their sizes are comparable with the crack size. The goal of local changes of temperature is to delay or inhibit the growth of a curvilinear crack. A boundary value problem on equilibrium of a bridged curvilinear crack under the action of external tensile loads, induced thermoelastic temperature field, and tractions in the bonds preventing its disclosure is reduced to the system of nonlinear singular differential equations with a Cauchy-type kernel. Normal and tangential tractions in the bonds are found from the solution of this system. The stress intensity factors are calculated. The condition of limit equilibrium of a curvilinear crack with an end area is formed based on two-parameter fracture criterion.     

A simplified approach for the thermoelastic large deflection in the thin clamped annular sector plate

The present article is concerned with analysis of large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution using Berger’s approximate methods. The prescribed surface temperature is at the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the Laplace transform as well as the classical method have been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length. The calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the numerical results for temperature, deflection, resultant bending moments, and thermal stresses have been illustrated by graphs.     

A generalized thermoelastic problem due to nonlocal effect in presence of mode I crack

Abstract

This article constructs a new model of nonlocal thermoelasticity which resolves a dynamical problem of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is being subjected to a prescribed temperature distribution and stress. In the context of three-phase lag model of generalized thermoelasticity, the governing equations have been solved employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm’s integral equation of the first kind. These integral equations have been solved employing the Maple software package, while the numerical inversion of the Laplace transform is carried out with the help of Bellman method. Numerical computations for a copper material are performed and demonstrated graphically. The results provide a motivation to further investigate the problem and draw concluding remarks due to the influence of nonlocality also.     

Effect of thermal stress on crack growth in inhomogeneous cylindrical superconductor

The effect of thermal stress on the growth of central cracks in inhomogeneous cylindrical superconductors is investigated assuming that the material properties vary linearly with the radial coordinate and temperature differences. General expressions for the temperature distribution and thermal stress in terms of a Bessel equation and the plane strain approach are derived. The results indicate that the distributions and variations in the radial and hoop thermal stresses in an inhomogeneous superconductor differ from those in homogeneous superconductors. However, thermal stress affects the crack growth similarly in both superconductor types. The thermal-stress analysis should be useful for the crack growth prediction regarding inhomogeneous superconductors.     

An axisymmetric crack in a functionally graded thermal barrier coating bonded to a homogeneous elastic substrate under transient thermal loading

Abstract

In this paper, the fracture problem of an axisymmetric crack in a functionally graded thermal barrier coating (FGTBC) bonded to a homogeneous substrate is considered. The problem is solved for the laminate that is suddenly heated from the upper surface of the FGTBC. The bottom surface of the homogeneous substrate is maintained at the initial temperature. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. By using both the Laplace and Hankel transforms, the thermo-mechanical fracture problem is reduced to a singular integral equation and a system of singular integral equations which are solved numerically. The stress intensity factors of the crack are computed and presented as functions of the normalized time for various values of the nonhomogeneous and geometric parameters.     

Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model

In this article, the size-dependent behavior of micro-beams with the thermoelastic damping (TED) phenomenon is studied. The coupled thermoelasticity equations are derived on the basis of the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model. By solving these coupled equations simultaneously, a closed-form expression for the TED parameter in micro-beams is presented which considers the small-scale effects incorporation. Then, the effect of various parameters on TED in micro-beams, such as micro-beam height, the type of material, boundary conditions, and aspect ratio is investigated. The results show that the influence of utilizing non-classical continuum and thermoelasticity theories on the amount of TED and the critical thickness is significant in small scales.     

Transient thermal fracture analysis of a penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder

The problem of penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder is investigated under thermal shock load. The problem is reduced to solve three coupled Fredholm integral equations. The field intensity factors are derived. Numerical results of crack opening displacement intensity factors are presented, and the effects of thermal shock time, crack configuration, and magnetoelectrical crack surface conditions on crack propagation and growth are evaluated. Among others, the larger cylinder's radius, the easier to propagate the crack is. For a fixed crack configuration, magnetoelectrical crack surface conditions have different effects on crack propagation as well.     

A Surface Crack in a Graded Coating Bonded to a Homogeneous Substrate under Transient Thermal Loading

The elastodynamic problem of a surface crack in a graded coating bonded to a homogeneous substrate under transient heat flux is considered. The coating is graded along the thickness direction and modelled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The resulting crack problem is of mode I because the orientations of the crack axis, the material gradient and the heat-flux are all parallel. The equivalent crack surface tractions are first obtained and substituted in the plane elasticity equations which are then converted analytically using appropriate integral transforms into a singular integral equation. The resulting equation is solved numerically using orthogonal Jacobi polynomials to yield the Mode I stress intensity factor. The main objective of the research is to study the effect of the layer thickness and nonhomogeneity parameters on the dynamic crack tip stress intensity factor for the purpose of gaining better understanding on the behavior of graded coatings under transient thermal loading.     

Solution of steady-state thermoelastic problems using a scaled boundary representation based on nonuniform rational B-splines

This work explores the application of isogeometric scaled boundary method in the two-dimensional thermoelastic problems of irregular geometry. The proposed method inherits the advantages of both isogeometric analysis and scaled boundary finite element method and overcomes their respective disadvantages. In the proposed approach, the boundaries of the problem domain are discretized with nonuniform rational B-splines (NURBS) basis functions, while the temperature distributions inside the domain are represented by a sequence of power functions in terms of radial coordinate within the framework of scaled boundary finite element method. The resulting solution of the stress in radial direction can be computed analytically for the temperature changes. The construction of tensor product structure is circumvented for the two-dimensional problems as only the boundary information of the problem domain is required. Hence, the flexibility to represent the complex geometry can be significantly improved in the proposed method. Numerical examples are presented to validate the performance of the proposed method where it is seen that superior accuracy, e?ciency, and convergence behavior can be achieved over the conventional scaled boundary finite element method.     

Thermo-Elastic Analysis of a Cracked Half-Plane Under a Thermal Shock Impact Using the Hyperbolic Heat Conduction Theory

The transient thermal stresses around a crack in a thermo-elastic half-plane are obtained under a thermal shock using the hyperbolic heat conduction theory. Fourier, Laplace transforms and singular integral equations are applied to solve the temperature and thermal stress fields consecutively. The integral equations are solved numerically and the asymptotic fields around the crack tip are obtained. Numerical results show that the hyperbolic heat conduction have significant influence on the dynamic temperature and stress field. It is suggested that to design materials and structures against fracture under thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

Different from previous two-dimensional thermal weight function (TWF) method, a three-dimensional (3D) TWF method is proposed for solving elliptical interface crack problems in bimaterial structures under a transient thermal loading. The present 3D TWF method based on the Betti's reciprocal theorem is a powerful tool for dealing with the transient thermal loading due to the stress intensity factors (SIFs) of whole transient process obtained through the static finite element computation. Several representative examples demonstrate that the 3D TWF method can be used to predict the SIFs of elliptical interface crack subjected to transient thermal loading with high accuracy. Moreover, numerical results indicate that the computing efficiency can be enhanced when dealing with transient problems, especially for large amount of time instants.     

Effect of point heat source on growth of subsurface crack induced in brittle material machining

Based on the indentation fracture mechanics, a thermal-assisted grinding model is established to investigate the effect of heat source on subsurface crack propagation. Combining the complex function method with the continuous distribution technique of dislocations, the stress intensity factors (SIFs) near the crack tip under various thermal and mechanical loads are calculated numerically. Results show that whether the median crack propagation is inhibited or promoted by the heat source mainly depends on the relative positions between thermal loading and mechanical loading. The stronger heat source in front of the abrasive grain can inhibit the growth of subsurface crack. When the heat source is located behind the abrasive grain, a minimum value of SIF can be obtained if the grinding parameters are well controlled. Especially, with the increase in heat source intensity, the maximum and minimum SIFs occur when the heat source is located at 1.5 times the distance of half crack length behind and in front of the abrasive grain, respectively.     

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.     

Transient thermal response of a functionally graded piezoelectric laminate with a crack normal to the bimaterial interface

In this article, the problem of a functionally graded piezoelectric material strip (FGPM strip) containing a crack perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Laplace and Fourier transforms, the thermoelectromechanical problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors of embedded and edge cracks are computed. The results for the crack contact problem are also included.     

A sub-interface thermal crack problem for bonded dissimilar plates with interfacial thermal resistance

The present work aims to investigate the effect of interfacial thermal resistance on thermal fracture behavior of bonded and composite materials. We consider a sub-interface crack parallel to the interface between two semi-infinite dissimilar plates subjected to remote heat flux thermal loading. A constant thermal resistance is assumed to exist along the interface. The temperature distribution along the crack, the thermal stress intensity factors (TSIFs), and the crack opening/sliding displacements (COD/CSD) are obtained using an integral transform/superposition method. The numerical results for Al₂O₃/Si₃N₄ bimaterial systems show that the magnitude of the mode I TSIF generally decreases with increasing thermal resistance of the interface but increases with increasing thermal resistance for cracks that are very close to the interface. On the other hand, the model II TSIF increases with increasing thermal resistance if the crack is in the Al₂O₃ semi-infinite plate, and decreases if the crack is in the Si₃N₄ semi-infinite plate. The COD/CSD are also significantly influenced by the thermal resistance of the interface.     

Transient Thermoelastic Analysis of a Solid Cylinder Containing a Circumferential Crack Using the C–V Heat Conduction Model

This article presents the transient thermoelastic analysis in a long solid cylinder with a circumferential crack using the C–V heat conduction theory. The outer surface of the cylinder is subjected to a sudden temperature change. The Laplace transform technique is adopted to solve the one-dimensional hyperbolic heat conduction equation, and the axial thermal stress is obtained for the un-cracked cylinder in the Laplace domain. Then this axial thermal stress with a minus sign is applied to the crack surface to form a mixed boundary value problem in the cylindrical coordinate system. A singular integral equation is derived by applying the Fourier and Hankel transforms to solve the mode I crack problem. The transient thermal stress intensity factors are obtained by solving the singular integral equation numerically. The influences of thermal relaxation time, crack geometry, and Biot's number upon transient temperature distributions, axial stress fields, and stress intensity factors are analyzed.     

The transient thermo-electro-elastic fields in a piezoelectric plate with a crack

This paper is concerned with a thin plate made by a piezoelectric ceramic material and containing a crack perpendicular to its surfaces. It is assumed that the transient thermal stress is set up by the application of a heat flux as a function of the time and position along the crack edge and the heat flow by convection from the plate surfaces. The plate is also subjected to mechanical and electric loadings. The exact analytical formulae are obtained for transient thermo-electro-elastic fields in the plate. The exact analytical solutions for the stress and electric displacement intensity factors and crack-opening displacement are obtained. Numerical examples show, among others, a dependence of the stress and electric displacement intensity factors on the thermal and elastic, piezoelectric and dielectric constants of the piezoelectric materials.     

Stress intensity factors for an axially oriented internal crack embedded in a buried pipe

In this paper, the finite element method has been used to study the effect of soil weight on the stress intensity factors of an axially oriented semi-elliptical crack located on the inner surface of a buried pipe. The Burns and Richard model has been utilized to take into account the interaction between the soil and the pipe. The finite element results revealed that the cracks in a buried pipe are subjected to mixed mode loading. The mode I and mode II stress intensity factors depend on the circumferential location of internal crack. K_I is always significantly larger than K_II and is maximum when the internal crack is along the vertical direction. A comparison between the results of two-dimensional and three-dimensional cracks also signified that the two-dimensional analysis always represents more conservative results. Depending on the crack aspect ratio (a/c), the discrepancy between the results of two and three-dimensional analyses can be significant.     

The Axisymmetric Problem of a Partially Insulated Mixed-Mode Crack Embedded in a Functionally Graded Pyro Magneto-Electro-Elastic Infinite Medium Subjected to Thermal Loading

This article describes our investigation of the influence of an axisymmetric partially insulated mixed-mode crack on the coupled response of a functionally graded magneto-electro-elastic material (FGMEEM) subjected to thermal loading. The crack is embedded at the center of an infinite medium, and the material is graded in the direction orthogonal to the crack plane and is modeled as a nonhomogeneous medium with anisotropic constitutive laws. The heat conduction equation is first solved using the Hankel transform to yield the temperature field in the medium. Using the same integral transform, the magneto-electro-elasticity equations are converted analytically into a system of four singular integral equations that are solved numerically to yield the crack-tip mode I and II stress intensity factors, the electric displacement intensity factor and the magnetic induction intensity factor. The main objective of this research is to study the influence of material nonhomogeneity on the fields’ intensity factors for the purpose of gaining better understanding on the behavior of graded pyro magneto-electro-elastic materials.