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.     

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.     

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.     

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.     

Thermal fatigue crack growth experiments on austenitic steel plates

A thermal cycling fatigue crack growth experiment has been performed on austenitic stainless steel plates in which a semi-elliptical surface crack grows through a surface layer experiencing cyclic plasticity. Linear elastic fracture mechanics crack growth assessments over-predict the surface growth and under-predict the through thickness growth. An alternative crack growth analysis has been performed using a pseudo stress intensity factor which is closely related to a strain intensity factor. The pseudo stress used to derive the pseudo stress intensity factor is calculated from uncracked body inelastic finite element analysis. It is demonstrated that a much improved prediction of fatigue crack shape can be made provided that the effects of crack closure are incorporated into the analysis. The method is relevant to leak-before-break and leak tightness arguments where the accurate prediction of through-thickness crack growth is particularly important.     

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.     

THERMAL STRESSES IN A CIRCULAR CYLINDER WITH A CIRCUMFERENTIAL EDGE CRACK UNDER UNIFORM HEAT FLOW

The linear thermoelastic problem of an infinitely long circular cylinder with a circumferential edge crack is solved. The thermal stresses are caused by a uniform heat flow disturbed by the presence of the crack. The crack surfaces and the cylindrical surface are assumed to be insulated. Integral transform techniques are used to reduce the problem to that of solving two singular integral equations of the first kind. The equations are solved numerically, and the variation of the stress intensity factor with the crack depth is shown graphically.     

CIRCUMFERENTIAL CRACK PROBLEM FOR AN FGM CYLINDER UNDER THERMAL STRESSES

The main objective of this study is to determine the stress intensity factors associated with a circumferential crack in a thin-walled cylinder subjected to quasi-static thermal loading. The cylinder is assumed to be a functionally graded material. In order to make the problem analytically tractable, the thin-walled cylinder is modeled as a layer on an elastic foundation whose thermal and mechanical properties are exponential functions of the thickness coordinate. Hence a plane strain crack problem is obtained. First temperature and thermal stress distributions for a crack-free layer are determined. Then using these solutions, the crack problem is reduced to a local perturbation problem where the only nonzero loads are the crack surface tractions. Both internal and edge cracks are considered. Stress intensity factors are computed as functions of crack geometry, material properties, and time.     

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.     

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 SINGULAR STRESSES NEAR A CIRCUMFERENTIAL EDGE CRACK IN A SPHERICAL CAVITY UNDER UNIFORM AXIAL HEAT FLOW

The linear thermoelastic problem of a spherical cavity with a circumferential edge crack is solved. The thermal stresses are caused by a uniform heat flow disturbed by the presence of the crack and the cavity. The surfaces of the crack and the cavity are assumed to be insulated. Integral transform techniques are used to reduce the problem concerning the temperature and thermoelastic fields to that of solving two singular integral equations of the first kind. The integral equations are solved numerically and the variation of the thermal stress intensity factor with the crack depth and the crack opening displacement are shown graphically.     

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 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.     

THERMAL STRESSES INTENSITY FACTOR FOR FUNCTIONALLY GRADIENT PLATE WITH AN EDGE CRACK

Thermal stress problems of a functionally gradient plate as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, with and without an edge crack, are discussed One of the most important problems of the thermal stress in the functionally gradient plate with the crack are how to decrease the thermal stress intensity factor and how to determine the optimally continuous profile of the composition of the plate. The functionally gradient plate is subjected to a cycle of heating and cooling on the ceramics surface of the plate. The material properties of the functionally gradient plate are dependent on the temperature and the position. The optimally continuous profile of the composition of the plate is discussed. The numerical results for thermal stresses and the thermal stress intensity factor are shown for many temperature conditions and for many continuous profiles of the composition of the plate.     

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.     

Effects of location,thermal stress and residual stress on corner cracks in nozzles with cladding

The stress intensity factors (K_I) for corner cracks in a boiling water reactor feedwater nozzle with stainless steel cladding are obtained for loading by internal pressure and a fluid quench in the nozzle. Conditions both with and without residual stress in the component are considered. The residual stress is simulated by means of a reference temperature change. The stress distribution for the uncracked structure is obtained from a three-dimensional finite element model.A three-dimensional influence function (IF) method, in conjunction with the boundary-integral equation method for structural analysis, is employed to compute K_I values from the uncracked stress distribution. For each type of loading K_I values are given for cracks at 15 nozzle locations and for six crack depths. Reasonable agreement is noted between calculated and previously published pressure-induced K_I values. Comparisons are made to determine the effect on K_I of crack location, thermal stress and residual stress, as compared with pressure stress. For the thermal transient it is shown that K_I for small crack depths is maximised early in the transient, while K_I for large cracks is maximised later under steady state conditions. Computations should, therefore, be made for several transient time points and the maximum K_I for a given crack depth should be used for design analysis. It is concluded that the effects on K_I of location, thermal stresses and residual stresses are significant and generally too complex to evaluate without advanced numerical procedures. The utilised combination of finite element analysis of the uncracked structure and three-dimensional influence function analysis of the cracked structure is demonstrated and endorsed.     

THERMAL STRESSES IN A LONG ELASTIC CYLINDER CONTAINING A PENNY-SHAPED CRACK AND EMBEDDED IN A THERMALLY CONDUCTIVE ELASTIC INFINITE MEDIUM

This paper is concerned with- the state of stress in a long circular elastic cylinder with a concentric penny-shaped crack whose surfaces are subjected to a prescribed temperature. The plane of the crack is assumed to be perpendicular to the axis of the cylinder. The cylinder is bonded to a thermally conductive elastic infinite medium. The thermal and elastic constants of the cylinder and infinite medium are assumed to be different. By assuming suitable representations for the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Similarly, the thermoelastic problem is also reduced to the solution of a Fredholm integral equation of the second kind. A closed-form expression is obtained for the stress-intensity factor. The integral equations are solved numerically, and the results are used to obtain numerical values for the stress intensity factor. These values are presented graphically.     

Thermal Stress Analysis in Magneto-Electro-Thermo-Elasticity with a Penny-Shaped Crack Under Uniform Heat Flow

ABSTRACT

The magnetoelectroelastic material possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. Piezoelectric-piezomagnetic materials exhibit magneto-electric effect. When magneto-electro-elastic materials are subjected to thermal flow, they can fracture prematurely due to their brittle behavior. Hence, it should be important to know the fracture behavior of magneto-electro- elastic materials. The penny-shaped crack problem in a medium possessing coupled electro-magneto-thermo-elastic is considered in this paper. It is assumed that the crack is isothermal. The analysis is an exact treatment of penny-shaped crack in a magneto-electroelastic solid subjected to uniform heat flow far away from the crack region. The governing equations of temperature, elastic displacements and electric potential as well as magnetic potential for an anisotropic magneto-electro-elastic medium are partial differential equations of second order, which are solved by means of the Hankel transform technique. Expressions for elastic displacements, thermal stresses, electric displacements and magnetic inductions are determined from the dual integral equation method. Exact thermal stress intensity factor of the problem is obtained, and the near crack tip solutions are provided.     

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.     

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.