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.     

CRACK ARREST ANALYSIS UNDER CYCLIC THERMAL SHOCK FOR AN INNER-SURFACE CIRCUMFERENTIAL CRACK IN A FINITE-LENGTH THICK-WALLED CYLINDER

This article presents a crack arrest depth analysis under cyclic thermal shock for an inner-surface circumferential crack in a finite-length thick-walled cylinder with rotation-restrained edges. The inside of the cylinder is cooled from a uniform temperature distribution. The effects of heat transfer conditions on the maximum transient stress intensity factor for the problem were investigated with systematical evaluation methods formerly developed. Then, under an assumption of a tentative threshold stress intensity range j K th together with the Paris law, the crack arrest depth under cyclic thermal stress was evaluated. The results suggested the existence of an upper limit for the normalized crack arrest depth, independent of the cylinder material in an engineering sense. Finally, the validity of applying j K max h j K th as a crack arrest criterion under cyclic thermal shock was confirmed by fatigue tests under mechanical loads equivalent to those induced by cyclic thermal shock.     

GENERALIZED THERMOELASTICITY OF AN INFINITE BODY WITH A CYLINDRICAL CAVITY AND VARIABLE MATERIAL PROPERTIES

ABSTRACT

The equations of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with temperature-dependent mechanical and thermal properties are established. The modulus of elasticity and the thermal conductivity are taken as linear function of temperature. A problem of an infinite body with a cylindrical cavity has been solved by using Laplace transform techniques. The interior surface of the cavity is subjected to thermal and mechanical shocks. The inverse of the Laplace transform is done numerically using a method based on Fourier expansion techniques. The temperature, the displacement, and the stress distributions are represented graphically. A comparison was made with the results obtained in the case of temperature-independent mechanical and thermal properties.     

THEORY OF GENERALIZED MICROPOLAR THERMOELASTICITY AND AN AXISYMMETRIC HALF-SPACE PROBLEM

ABSTRACT

The general equations of motion and constitutive equations are derived for a general homogeneous anisotropic medium with a microstructure, taking into account the effects of heat and allowing for second sound effects. A uniqueness theorem is also derived. As an illustration of the obtained equations, we solve a problem for a half-space whose boundary is rigidly fixed and subjected to an axisymmetric thermal shock. There are no body forces, body couples, or heat sources affecting the medium. Laplace and Hankel transform techniques are used. Numerical results are obtained and graphically illustrated.     

GENERALIZED THERMOELASTICITY IN AN INFINITE SOLID WITH A HOLE

This paper deals with one-dimensional generalized thermoelasticity based on the theories of Lord and Shulman and of Green and Lindsay. A formulation of generalized thermoelasticity that combines both generalized theories is derived. The generalized thermoelastic problems for an infinite solid with a cylindrical hole and an infinite solid with a spherical hole are analyzed by means of the Laplace transform technique. Numerical calculations for temperature, displacement, and stresses under the generalized formulation are carried out and compared with those of classical dynamic coupled theory.     

A SHORT TIME SOLUTION FOR A PROBLEM IN THERMOELASTICITY OF AN INFINITE MEDIUM WITH A SPHERICAL CAVITY

The problem of a thermoelastic infinite medium with a spherical cavity is considered within the context of the theory of thermoelasticity with two relaxation times. The surface of the cavity is stress free and suddenly subjected to a time-dependent thermal shock. Laplace transform techniques are used. The inverse Laplace transforms are obtained analytically using asymptotic expansions valid for small values of time. Numerical computations for the temperature, the displacement, and stress distribution are carried out and represented graphically.     

A PROBLEM IN GENERALIZED THERMOELASTICITY FOR AN INFINITELY LONG ANNULAR CYLINDER COMPOSED OF TWO DIFFERENT MATERIALS

The problem of heat conduction of a thermoelaslic cylindrical medium composed of two different materials is considered. The problem is solved in the framework of the generalized thermoelasticity theory with one relaxation time. The solution is obtained in the Laplace transform domain by using the potential function approach. Numerical inversion formula is used to obtain the corresponding solutions in the physical domain     

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.     

TWO-DIMENSIONAL PROBLEM IN GENERALIZED THERMOELASTICITY WITH HEAT SOURCES

In this work, a two-dimensional problem for a half-space is solved. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. The surface of the half-space is taken to be traction free and the temperature on it is specified. Heat sources permeate the medium. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.     

TWO-DIMENSIONAL PROBLEM OF A MOVING HEATED PUNCH IN GENERALIZED THERMOELASTICITY

The two-dimensional equations of generalized thermoelasticity are solved for the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions. The exponential Fourier transform with respect to one space variable in a coordinate system moving with the punch is applied. The resulting equations are solved and numerical results are given. The results are compared with those obtained by Roberts for the coupled thermoelastic case.     

THE DISTURBANCE OF A UNIFORM HEAT FLOW BY TWO LINE CRACKS IN AN INFINITE ANISOTROPIC THERMOELASTIC SOLID

Integral transform techniques are used to determine the stress intensity factors of a pair of colinear line cracks that disturb a uniform heat flow in an anisotropic thermoelastic solid that is under uniaxial tension. A solution is given for the case in which the tension is large enough to ensure that the cracks open fully.     

INVERSE TRANSIENT THERMOELASTIC PROBLEM FOR A COMPOSITE CIRCULAR DISK

The present article deals with the application of a piezoelectric material as a sensor of thermomechanical disturbance. We consider a composite circular disk constructed of a transversely isotropic layer onto which a piezoceramic layer of crystal class 6mm is perfectly bonded. An inverse transient thermoelastic problem is solved to determine the unknown transient heating temperature distribution on the surface of the transversely isotropic layer, when the distribution of the electric potential difference across the piezoceramic layer is known. A finite difference method with respect to the time variable is employed to solve this inverse problem. The thermoelastic fields in the transversely isotropic and piezoceramic layers are analyzed by means of a transversely isotropic potential function method and a piezothermoelastic potential function method, respectively. Numerical results are presented for the time variation of the inferred heating temperature distribution and the corresponding distributions of temperature, displacements, stresses, and electric displacements.     

CONTACT ZONE MODELS FOR AN INTERFACE CRACK IN A THERMOMECHANICALLY LOADED ANISOTROPIC BIMATERIAL

An interface crack between two anisotropic semi-infinite spaces under the action of remote mixed-mode mechanical loading and a temperature flux is considered. Assuming that all fields are independent of the x ₃ -coordinate co-directed with the crack front, the stresses and the temperature flux as well as the jumps of the displacements and the temperature at the interface are presented via a set of holomorphic functions in the whole (x ₁ , x ₂ )-plane with a cut along the crack area. By means of this representation a solution for an open crack model can be given in an analytical form, and further an inhomogeneous combined Dirichlet-Riemann boundary value problem could be formulated for a crack with an artificial contact zone. An exact analytical solution of this problem has been found, and the stress intensity factors are presented for different contact zone lengths with a special success in the case of a small length of the contact zone. Furthermore, it is shown that the obtained solution can be used for the numerical solution of interface crack problems for finite-sized bimaterials. Real contact zone lengths and the associated stress intensity factors are found from the obtained solution; in addition, their dependencies on the intensity of the temperature flux and the mechanical load mixity are demonstrated.     

ON THE EVALUATION OF THE FREE-EDGE STRESS INTENSITY FACTORS FOR A JOINT SUBJECTED TO A UNIFORM CHANGE IN TEMPERATURE

A contour integral is applied to the evaluation of the stress intensity factors at interface corners of bimaterial joints subjected to a uniform change in temperature. In order for the contour integral to work for the free-edge stress intensity factors, closed-form solutions for the stress and displacement fields near interface corners of bimaterial joints subjected to a uniform temperature change are derived. The derivation is based on the hypothesis that the two dissimilar materials, which are bonded along their common interface, experience identical rigid body displacements. Accordingly, the asymptotic displacements are continuous along the interface irrespective of the rigid body displace ments near the interface corner. A case study is carried out for a problem where the combination between the material properties and the geometry at the interface corner is such that the stresses at the interface corner are comprised of several stress fields of the form Hr     

GREEN'S FUNCTION FOR THERMAL STRESS MIXED BOUNDARY VALUE PROBLEM OF AN INFINITE PLANE WITH AN ARBITRARY HOLE UNDER A POINT HEAT SOURCE

Green's function of a point heat source is derived for a mechanical mixed boundary value problem of an infinite plane with an arbitrary hole, for which zero-displacement and traction-free boundary conditions are prescribed to its boundary. As the thermal boundary condition on the hole, either an adiabatic or isothermal condition is considered. By employing the mapping technique and complex variable method, an explicit solution including a hypergeometrical function is obtained. Stress distributions are shown in illustrative examples for a square hole.     

THERMOELASTIC PROBLEM OF UNIFORM HEAT FLOW DISTURBED BY A FLAT TOROIDAL CRACK IN A TRANSVERSELY ISOTROPIC MEDIUM

The thermoelastic problem of uniform heat flow disturbed by a flat toroidal crack in a transversely isotropic medium is investigated using the method of Hankel transforms. The three-part mixed thermoelastic boundary conditions are satisfied using the tech niques of triple integral equations and multiplying factors. The stress intensity factors at the inner and outer crack tips are obtained in exact expressions as the products of a dimensional quantity and nondimensional functions. The fracture transition of a flat toroidal crack to a penny-shaped crack and to a two-dimensional line crack is studied at different values of the ratio of the inner crack radius to the outer crack radius.     

STRESS INTENSITY FACTOR FOR TRANSIENT THERMAL STRESSES IN AN INFINITE ELASTIC BODY WITH AN EXTERNAL CRACK

Abstract

This paper deals with a transient thermal stress problem in an infinite body with an external crack. The elastic medium is cooled by time- and position-dependent temperature on the external crack. It is very difficult to obtain the analytical expression for the temperature, so the finite-difference method is used with respect to a time variable. Thus, the analytical expression for the temperature with respect to the spatial variables may be obtained. The temperature solution reduces to a dual-integral equation for spatial variables by use of the finite-difference method for a time variable. The numerical results for stress intensity factor are obtained.     

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.     

TWO CRACK GROWTHS IN A FUNCTIONALLY GRADED PLATE UNDER THERMAL SHOCK

This article examines the problem of two thermal cracks under a transient temperature field in a ceramic/metal functionally graded plate. When the functionally graded plate is subjected to thermal shock, multiple cracks often occur on the ceramic surface. It is shown that the crack paths are influenced by interaction between multiple cracks and a compositional profile of the functionally graded plate. Transient thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane strain state. The crack paths of two cracks are obtained using the finite element method with mode I and mode II stress intensity factors.