Transient thermoelectroelastic response of a piezoelectric material strip with two parallel cracks in arbitrary positions

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks in arbitrary positions of a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time-dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. The temperature, stress and electric displacement distributions in a transient state are also included.     

Transient Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations, respectively, which are solved numerically. A numerical method is employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. Temperature change, the stress and electric displacement distributions in a transient state are also included.     

Infinite Row of Parallel Cracks in a Functionally Graded Piezoelectric Material Strip Under Mechanical and Transient Thermal Loading Conditions

In this paper, the problem of an infinite row of parallel cracks in a functionally graded piezoelectric material strip (FGPM strip) is analyzed under static mechanical and transient thermal loading conditions. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the bottom surface. By using the Laplace and Fourier transforms, the thermoelectromechanical problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors for both the embedded and edge cracks are computed. The results for the crack contact problem are also included.     

Transient Thermal Stress Analysis of Orthotropic Functionally Graded Materials with a Crack

The transient thermal fracture problem of a crack (perpendicular to the gradient direction) in a graded orthotropic strip is investigated. Most of the materials properties are assumed to vary as an exponential function of thickness direction. The transient two-dimensional temperature problem is analyzed by the methods of Laplace and Fourier transformations. A system of singular integral equations are obtained and solved numerically. Numerical results are figured out to show the variation of the temperature on the crack faces and extended line and stress intensity factors for different material parameters with dimensionless time.     

Transient Intensity Factors for a Parallel Crack in a Plate of a Functionally Graded Piezoelectric Material Under Thermal Shock Loading Conditions

A crack in a plate of a functionally graded piezoelectric material is studied under thermal shock loading conditions. The crack faces are supposed to be completely insulated. All material properties are assumed to be exponentially dependent on the distance from the crack line parallel to the boundaries of the plate. By using both the Laplace transform and Fourier transform, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations that are solved numerically. The stress and electric displacement intensity factors vs. time for various material constants and geometric parameters are calculated.     

Thermoelectromechanical Response of a Center Crack in a Symmetrical Functionally Graded Piezoelectric Strip

The thermoelectromechanical fracture problem for a symmetrical functionally graded piezoelectric strip containing a center crack parallel to the free boundaries is considered in this study. It is assumed that the thermoelectroelastic properties of the medium vary continuously in the thickness direction, and that the strip is under thermomechanical loadings. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to singular integral equations, respectively, which are solved numerically. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the crack length and the material nonhomogeneity on the temperature-stress distributions and the stress intensity factor.     

Transient Response of a Cracked Piezoelectric Strip Under Thermoelectric Loading

In this study, the theoretical analysis of a transient piezothermoelastic problem is developed for a piezoelectric strip with a parallel crack under static electric loading and thermal shock loading conditions. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Some numerical results for the temperature change, the stress and electric displacement distributions, and the energy density factor as well as the stress and electric displacement intensity factors in a transient state are shown in figures.     

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.     

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.     

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 Influence of Graded Coatings on the Thermal Stress Intensity Factors of an Oblique Crack in a Semi-Infinite Substrate Subjected to Local Heating on the Boundary

Thermally induced singular behavior of an arbitrarily oriented crack in a homogeneous substrate overlaid with a functionally graded coating is considered, within the framework of linear plane thermoelasticity. It is assumed that the graded coating/substrate system is subjected to steady-state thermal loading applied over a finite region at the coating surface and the crack in the substrate is thermally insulated, disturbing the prescribed heat flow. Based on the method of Fourier integral transform and the coordinate transformations of basic field variables in thermoelasticity equations, formulation of the crack problem is reduced to two sets of Cauchy-type singular integral equations for temperature and thermal stresses in the coated medium. In the numerical results, the main emphasis is placed on the investigation of influences of loading, geometric, and material parameters of the coated system on the variations of mixed-mode thermal stress intensity factors. Further addressed are the probable cleavage angles for the incipient growth of the original crack and the corresponding values of effective tensile-mode stress intensity factors.     

Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal loading. The crack faces are assumed to be insulated thermally and electrically. Fourier transform techniques are used to reduce the mixed boundary value problems to two systems of singular integral equations. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the geometric parameters on the thermal stress and electric displacement intensity factors.     

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.     

An Annular Crack in a Functionally Graded Piezoelectric Strip Under Thermoelectric Loadings

A thermoelectroelastic problem of a functionally graded piezoelectric material (FGPM) strip containing an annular crack is solved. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under the thermoelectric loadings. The crack faces are supposed to be insulated thermally and electrically. Using integral transform techniques, the problem is reduced to that of solving a singular integral equation and a system of singular integral equations. Numerical calculations are carried out, and the variations of the stress and electric displacement intensity factors are plotted against the geometric parameters for some values of the material non-homogeneity parameters.     

Thermal Intensity Factors for a Parallel Crack in a Functionally Graded Piezoelectric Strip

In this paper, the mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under the thermoelectric loadings. The crack faces are supposed to be insulated thermally and electrically. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

Effects of Crack Surface Conductance on Intensity Factors for a Functionally Graded Piezoelectric Material Under Thermal Load

Effects of crack surface conductance on intensity factors for a functionally graded piezoelectric material under thermal load are investigated. The heat flux through the crack is assumed to be proportional to the local temperature difference. Moreover, two models for more realistic crack face electric boundary conditions are proposed. By using the Fourier transform, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations, respectively, which are solved numerically. Detailed results are presented to illustrate the influence of the thermal and electric conductance on the stress and electric displacement intensity factors.     

Thermal Stress Intensity Factors for a Normal Crack in a Piezoelectric Material Strip

This paper investigates the electromechanical fracture behavior of a normal crack in a piezoelectric material strip subjected to a uniform heat flow far away from the crack region. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to singular integral equations, respectively, which are solved numerically. Both the cases of an internal crack and an edge crack are studied. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the crack location and length on the temperature distribution and the stress intensity factors.     

IMPORTANCE OF INERTIA TERM IN DYNAMIC CRACK PROBLEMS CONSIDERING LORD–SHULMAN THEORY OF THERMOELASTICITY

A numerical technique is presented for the accurate calculation of stress intensity factors as a function of time for generalized coupled thermoelastic problems. In this task, the effect of the inertia term is investigated, considering different theories of thermoelasticity, and its importance is shown.

A boundary element method using the Laplace transform in time domain is developed for the analysis of fracture mechanics; dynamic coupled thermoelasticity problems with relaxation time are considered in the two-dimensional finite domain. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. Actual physical quantities in the time domain are obtained using the numerical inversion of the Laplace transform method.

The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. The thermal dynamic stress intensity factor for mode I is evaluated using the J-integral method. The accuracy of the method is investigated through comparison of the results with the data available in literature.

The J integral, which represents the dynamic energy release rate for propagating cracks, contains a boundary integral and a domain integral. The boundary integral contains strain energy, tractions, and strains whereas the domain integral contains inertia and strains. The J-integral method allows these two terms to be calculated separately. In this way, the importance of each term may be investigated by considering different theories of dynamic thermoelasticity.     

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.     

EDGE-CRACKED PLATE WITH ONE FREE AND ONE CONSTRAINED BOUNDARY SUBJECTED TO SUDDEN CONVECTIVE COOLING

The transient thermal stress edge crack problem for an elastic strip with free and fully constrained boundaries is considered. The plate is suddenly subjected to convective cooling on the face containing the edge crack while the other face is insulated. The solution of the problem is obtained by using the superposition technique results in a singular integral equation that is solved numerically. The results of the transient temperature and thermal stress distributions in the uncracked strip are presented. Also, numerical results are obtained for the stress-intensity factor in terms of the Fourier number, crack length, and different values of the Biot number.