THERMAL SHOCK FRACTURE IN AN EDGE-CRACKED PLATE

In this paper the transient thermal stress problem for an elastic strip with an edge crack is investigated. The elastic medium is assumed to be insulated on one face and cooled by surface convection on the face contaning the edge crack. Using the principle of superposition, the formulation results in a mixed boundary value problem, with the thermal stresses calculated from the thermoelasticity solution for an uncracked strip utilized as the necessary crack surface tractions. The resulting singular integral equation is of a well-known type and is solved numerically. In this paper, inertia effects are assumed negligible and possible temperature dependence of thermoelastic constants is not considered. The numerical results presented, include the stress intensity factor as a function of nondimensional time (Fourier number) and crack length, for various values of the dimensionless Biot number. The temperature distribution and the thermal stresses in the uncracked strip are also included. The time lag, which occurs between the time at which the stress on the surface of the strip is a maximum and the time when a maximum occurs in the stress intensity factor, is clearly shown to be a function of the Biot number for any given ratio of crack length to strip thickness. A result of particular interest is the degree with which the maximum stress intensity factor decreases, as a function of crack length, for decreasing values of the Biot number.     

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.     

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 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.     

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.     

THERMAL SHOCK PROBLEMS OF ELASTIC BODIES WITH A CRACK

This paper deals with thermal shock, problems of elastic bodies with a crack. The case considered is that of an infinitely long circular cylinder with an edge crack, and a homogeneous flat plate with an edge crack initially at uniform temperature and suddenly immersed into a medium of lower temperature. The thermal disturbance near the crack tip is assumed to be neglible in the analysis of the temperature field because thermal shocks occur very quickly. We analyze the transient thermal stress problems of elastic solids with a crack and determine the stress intensity factor at the crack tip. The nondimensional maximum transient stress intensity factor is expressed as a function of the Biot number and the nondimensional crack length. Then we propose simplified formulations of the nondimensional maximum transient stress intensity factor as a function of the Biot number and the nondimensional crack length.     

MULTIPLE SURFACE CRACKING IN GLASS-FIBER-REINFORCED PLASTICS DUE TO A THERMAL SHOCK AT A LOW TEMPERATURE

We consider the transient thermal singular stress problem of multiple surface cracking in glass-fiber-reinforced plastics due to a thermal shock at a low temperature. The layered composite is made of a layer bonded between two layers of different physical properties, and it is suddenly cooled on the surfaces. The surface layers contain parallel arrays of the embedded or edge cracks perpendicular to the boundaries. The thermal and elastic properties of the material are dependent on the temperature. For the case of the crack that ends at the interface between orthotropic elastic materials, the order of stress singularity around the tip of the crack is obtained. Finite element calculations are carried out, and the transient thermal stress intensity factors are shown graphically.     

FRACTURE OF THICK-WALLED CYLINDERS SUBJECTED TO TRANSIENT THERMAL STRESSES

In this paper, the fracture problem of a thick cylinder subjected to transient thermal stresses is considered. The problem has practical significance in the conventional and nuclear power industries where the structural integrity of components may be damaged due to sudden temperature changes. Neglecting the inertia effects, the thermal fracture problem is uncoupled. First the thermal stresses in a thick cylinder due to a sudden change in temperature are computed separately as a function of time. Then, these stresses are used as external loads in analyzing the fracture of a thick cylinder. The assumed crack, may be an inner edge crack, outer edge crack or an embedded crack. Extensive results are obtained by varying the parameters of the problems. The main parameters affecting fracture are identified and the results are discussed in some detail.     

TRANSIENT STRESS INTENSITY FACTORS FOR PERIODIC ARRAY OF CRACKS IN A HALF-PLANE DUE TO CONVECTIVE COOLING

The problem of periodic cracks perpendicular to the boundary of a half-plane under transient thermal loading is investigated. The thermal stresses are generated as a result of convective cooling on the boundary of the plane. The problem is solved using the superposition technique. The perturbation problem is formulated using the thermal stresses obtained from the uncracked problem with the opposite sign as the only external load. The formulation results in a singular integral equation of Cauchy type that is solved numerically. Numerical results are obtained for the stress intensity factors as a function of time, crack length, location of the crack, and periodic crack spacing.     

CRITICAL STRESS INTENSITY FACTORS FOR CRACKED HOLLOW PIPES UNDER TRANSIENT THERMAL LOADS

Finite element analyses of a long hollow cylinder having an axisymmetric circumferential internal edge crack, subjected to convective cooling on the inner surface are performed. The transient thermal stress intensity factor is estimated using a domain version of the J-integral method. The effect of the thickness of the cylinder, crack length, and heat transfer coefficient on the stress intensity factor history are studied. The variations of critical normalized stress intensity factor with crack length-to-thickness ratio for different parameters are presented. The results show that if a small inner surface crack begins to grow, its stress intensity factor will increase with increase in crack length, reach a maximum, and then begin to drop. Based on the results, a fracture-based design methodology for cracked hollow pipes under transient thermal loads is discussed.     

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.     

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.     

THERMAL STRESS ANALYSIS IN THERMOPIEZOELASTIC STRIP WITH AN EDGE CRACK

The analysis of thermal stresses becomes important when the piezoelectric material has to be operated in either extremely cold or hot temperature environments. Hence, it is essential to know the interaction of mechanical defects with temperature changes. This investigation is concerned with a strip problem of transversely isotropic thermopiezoelastic material containing an edge crack under partial thermal and electric loading conditions. Thermopiezoelastic stresses are analyzed by introducing potential functions and Fourier transforms. The problem reduces to solving a singular integral equation, and the singular integral equation is solved. Numerical calculations of the thermal stress intensity factors are carried out for a cadmium selenide material.     

THERMAL STRESS PROBLEM FOR MIXED HEAT CONDUCTION BOUNDARY AROUND AN ARBITRARILY SHAPED HOLE WITH CRACK UNDER UNIFORM HEAT FLUX

This article deals with a thermal stress problem for thermal conduction around an arbitrarily shaped hole with a crack under uniform heat flux. Two cases for the hole edge and the crack faces are assumed: adiabatic and isothermal conditions or vice versa (isothermal and adiabatic). A closed-form solution is obtained using conformal mapping, dislocation functions, and the complex variable method. Results of temperature, heat flux, stress, and stress intensity factor are illustrated.     

Transient Thermoelastic Analysis for a Laminated Composite Strip with an Interlayer of Functionally Graded Material

This paper is concerned with the theoretical treatment of transient thermal stress problem involving a laminated composite thick strip with an interlayer of functionally graded material due to nonuniform heat supply in the width direction. The thermal and thermoelastic constants of the interlayer of functionally graded material are assumed to vary exponentially in the thickness direction. We obtain the exact solution for the two-dimensional temperature change in a transient state, and thermal stresses of a simple supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement and the stress distributions are shown in figures. Furthermore, the influence of the thickness and position of the interlayer is investigated.     

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.     

TRANSIENT THERMOELASTIC PROBLEM FOR AN INFINITE PLATE CONTAINING A PENNY-SHAPED CRACK AT AN ARBITRARY POSITION

This article deals with the transient thermoelastic problem for an infinite plate containing a penny-shaped crack that is parallel to the surfaces of the plate but at an arbitrary position of the plate. The transient thermal stresses are set up by the heat generation on the surfaces and the sudden heat exchange on the surfaces. By using the finite difference method for the time variable, the analytical solution for spatial variables can be obtained. The numerical results for the temperature and stress intensity factor are obtained, and results are shown in graphs.     

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.     

Pressurized thermal shock analyses of a reactor pressure vessel using critical crack depth diagrams

Evaluated in this study is the pressure vessel integrity under a pressurized thermal shock. Using transient histories such as temperature, pressure and heat transfer coefficient, the stress distribution is calculated and then stress intensity factors are obtained for a wide range of crack sizes. The stress intensity factors are compared with the fracture toughness to check if cracking is expected to occur during the transient. Critical crack depth diagrams are prepared for each transient which is expected to initiate a pressurized thermal shock accident. Plant-specific analyses of the most limiting plant in Korea are performed to assure the structural integrity of the reactor vessel and the results are discussed.