Showing papers in "Journal of Thermal Stresses in 2003"
TL;DR: In this paper, the problem of reflection from the insulated and isothermal stress-free as well as rigidly fixed boundaries of homogeneous isotropic solid half-spaces in the context of various linear theories of thermoelasticity was investigated.
Abstract: We investigated the problem of thermoelastic wave reflection from the insulated and isothermal stress-free as well as rigidly fixed boundaries of homogeneous isotropic solid half-spaces in the context of various linear theories of thermoelasticity, namely, Lord-Shulman, Green-Lindsay, Green-Nagdhi, coupled thermoelasticity, and uncoupled thermoelasticity. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave incidence cases. The results for partition of the energy for various values of the angle of incidence are computed numerically and presented graphically for aluminum-epoxy composite material in case of incident P- and SV-waves from the stress-free and rigidly fixed thermally insulated boundaries. The results obtained are discussed and compared in various models of thermoelasticity.
180 citations
TL;DR: In this paper, the thermal buckling loads of cylindrical shells of functionally graded material are considered and derived equations are based on the first-order shell theory and the Sanders kinematic equations.
Abstract: In this article, the thermal buckling loads of cylindrical shells of functionally graded material are considered. Derivation of equations are based on the first-order shell theory and the Sanders kinematic equations. The derived equilibrium and stability equations for the functionally graded cylindrical shell are identical with the equations for homogeneous shells expressed in the form of forces and moments per unit length. Assuming that the material properties vary linearly through the thickness direction, the system of fundamental partial differential equations in terms of the displacement components is established. Buckling analysis of functionally graded cylindrical shells under two types of thermal loads with simply supported boundary conditions are carried out. Results are obtained in the analytical form. The results are validated with the known data in the literature.
160 citations
TL;DR: In this article, an efficient reformulation of HOTFGM is presented based on the local/global conductivity and stiffness matrix formulations, which eliminates redundant continuity equations and, therefore, decreases the size of the overall systems of equations for the thermal and mechanical prob...
Abstract: The majority of techniques employed in the analysis of functionally graded materials (FGMs) use the so-called uncoupled approach, based on homogenized material property variations, which ignores the effect of local microstructural interaction. The higher-order theory for FGMs (HOTFGM) is a coupled approach that explicitly takes the effect of microstructural gradation and, thus, the local interaction of the spatially variable inclusion phase(s), into account. Despite its demonstrated utility, however, the original formulation of HOTFGM is computationally intensive. Herein, an efficient reformulation of HOTFGM is presented based on the local/global conductivity and stiffness matrix formulations. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation eliminates redundant continuity equations and, therefore, decreases the size of the overall systems of equations for the thermal and mechanical prob...
66 citations
TL;DR: In this article, a dynamical problem for an infinite thermoelastic solid with an internal penny-shaped crack, which is subjected to prescribed temperature and stress distributions, is solved using the Laplace and Hankel transforms.
Abstract: In this work, we solve a dynamical problem for an infinite thermoelastic solid with an internal penny-shaped crack, which is subjected to prescribed temperature and stress distributions. The problem is solved using the Laplace and Hankel transforms. The boundary conditions of the problem give a set of four dual integral equations. The operators of fractional calculus are used to transform the dual integral equations into a Fredholm integral equation of the second kind, which is solved numerically. The inverse Hankel and Laplace transforms are obtained using a numerical technique. Numerical results for the temperature, stress, and displacement distributions, as well as for the stress intensity factor, are shown graphically.
65 citations
TL;DR: In this paper, the authors explain the damage mechanisms of disc brakes leading to macroscopic cracks on the friction surface and discuss the failure of disc brake failure, giving indications of how to improve the design of this type of friction system in order to enhance its performances.
Abstract: The aim of this article is to explain the damage mechanisms of disc brakes leading to macroscopic cracks on the friction surface. The work combines microanalysis of cracks and a thermomechanical modeling describing the thermal fatigue solicitation. The failure of disc brakes is discussed, giving indications of how to improve the design of this type of friction system in order to enhance its performances
63 citations
TL;DR: Several optical methods for in-situ displacement measurement are presented as a tool to characterize thermomechanical behavior of microelectronics subassemblies as mentioned in this paper, and applications to diverse problems are illustrated to demonstrate wide applicability.
Abstract: Several optical methods for in-situ displacement measurement are presented as a tool to characterize thermomechanical behavior of microelectronics subassemblies. Features and recent developments of the methods are reviewed and applications to diverse problems are illustrated to demonstrate wide applicability of the methods. The whole-field displacement information, with various sensitivity and resolution scales, is ideally suited for the deformation study of a broad range of problems in microelectronics packaging. The methods are mature and they can be practiced routinely. More applications are anticipated.
60 citations
TL;DR: In this paper, the authors considered the thermally induced fracture problem for a piezoelectric laminate having a crack under uniform electric and temperature fields, where the crack is oriented normal to the interfaces of the laminate.
Abstract: The thermally induced fracture problem for a piezoelectric laminate having a crack under uniform electric and temperature fields is considered. The crack is oriented normal to the interfaces of the laminate. For the case of a crack that ends at the interface between the piezoelectric layer and the elastic layer, the order of the stress singularity around the tip of the crack is obtained. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and the main results presented are the variation of the the energy density factors as functions of the geometric parameters and the electrical boundary conditions of the layered composites.
58 citations
TL;DR: In this article, a one-dimensional problem of the Chandrasekharaiah-Tzou thermoelastic theory with two delay parameters θ and q was studied.
Abstract: In this article we study a one-dimensional problem of the Chandrasekharaiah-Tzou thermoelastic theory. In this theory two delay parameters θ and q are considered. We prove that when \tau_{\theta} > {{\tau_q} \over 2} the solutions decay exponentially and when \tau_{\theta} {{\tau_q} \over 2} holds.
52 citations
TL;DR: In this paper, a transient analysis of the thermoelastic contact problem of automotive disk brakes with frictional heat generation is performed using the finite element method, and the results are presented for the distributions of pressure and temperature on each friction surface between the contacting bodies.
Abstract: The transient analysis of the thermoelastic contact problem of automotive disk brakes with frictional heat generation is performed using the finite element method. To analyze the thermoelastic phenomenon occurring in disk brakes, the coupled heat conduction and elastic equations are solved with contact problems. In the present work, the fully implicit transient scheme for the thermoelastic analysis is used to improve the accuracy of computations at every time step. The numerical simulation for the thermoelastic behavior of disk brakes is obtained in drag brake condition. The computational results are presented for the distributions of pressure and temperature on each friction surface between the contacting bodies. Also, the thermoelastic instability (TEI) phenomenon (the unstable growth of contact pressure and temperature) is investigated in the present study. The effects of the rotating speed of the disk on thermoelastic behaviors, such as the temperature distribution and contact ratio of the friction su...
51 citations
TL;DR: In this article, the thermal stress induced by skin cryopreservation is analyzed and the most important issues are to prevent the loss of viability in the tissue and to understand the effects of thermal stress on the tissue.
Abstract: To prevent loss of viability in cryopreserved skin tissue, one of the most important issues is to understand the thermal stress induced by cryopreservation. During skin cryopreservation, which invo...
39 citations
TL;DR: In this article, geometrically nonlinear governing equations for static deformations of Timoshenko beams subjected to thermal as well as mechanical loadings are formulated, and the thermal postbuckled configurations and the equilibrium paths of the beam are presented.
Abstract: Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for static deformations of Timoshenko beams subjected to thermal as well as mechanical loadings are formulated. As an example, on the basis of the governing equations, thermal postbuckling response of an immovably pinned-fixed Timoshenko beam subjected to a static transversely nonuniform temperature rise is numerically analyzed by using a shooting method. Characteristic curves showing the relationships between the beam deformation and temperature rise are presented. The thermal postbuckled configurations and the equilibrium paths of the beam are presented. In particular, the effects of shear deformation on the buckling response are quantitatively investigated. The numerical results show, as we know, that shear deformation effects become significant with decrease of the slenderness and with increase of the shear flexibility.
TL;DR: In this article, the generalized plane strain thermopiezoelectric deformations of laminated thick plates are analyzed using the Eshelby-Stroh formalism, and results are presented for plates with edges either rigidly clamped, simply supported, or traction-free.
Abstract: The generalized plane strain thermopiezoelectric deformations of laminated thick plates are analyzed using the Eshelby–Stroh formalism. The laminated plate consists of homogeneous laminae of arbitrary thicknesses. The three-dimensional equations of linear anisotropic thermopiezoelectricity simplified to the case of generalized plane strain deformations are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series. The continuity conditions at the interfaces and boundary conditions at the top and bottom surfaces and edges are used to determine coefficients in the series. The formulation admits different thermal, electrical, and mechanical boundary conditions at the edges of each lamina and is applicable to thick and thin laminated plates. Laminated plates containing piezoelectric laminae poled either in the thickness direction or in the axial direction are analyzed, and results are presented for plates with edges either rigidly clamped, simply supported, or traction-free. Smart structures, consisting of piezoelectric materials integrated with structural systems, have found widespread use in engineering applications. Piezoelectric materials are capable of altering the structure’s response through sensing, actuation, and control. They exhibit two basic electromechanical phenomena that have led to their use as sensors and actuators in the control of structural systems. In sensor applications, an applied mechanical strain induces an electric potential in the material due to the direct piezoelectric effect; whereas in actuator applications, an applied electric field causes the material to deform. Of the 21 crystal classes that
TL;DR: In this paper, the postbuckling behavior of slender rods subjected to uniform temperature variations and constrained by double-hinged nonmovable boundary condition is studied, where the material is assumed linear elastic and its thermal strain-temperature relationship is nonlinear.
Abstract: Formulation and analytical solution for the postbuckling behavior of slender rods subjected to uniform temperature variations and constrained by double-hinged nonmovable boundary condition are presented. The material is assumed linear elastic and its thermal strain-temperature relationship is nonlinear. Large displacements are considered, hence the formulation is geometrically nonlinear. The governing equations are derived from geometrical compatibility, equilibrium of forces and moments, constitutive equations, and strain-displacement relation, yielding a set of six first-order nonlinear ordinary differential equations with boundary conditions specified at both ends, which constitute a complex boundary value problem. A closed-form analytical solution found via complete elliptic integral is derived from the governing equations defining the shape of the postbuckled rod (elastica). The results are presented in nondimensional graphs for a range of temperature gradients and different values of slenderness ratios.
TL;DR: In this paper, a geometrically nonlinear theory of magnetothermoelasticity of electroconductive anisotropic plates in a magnetic field is developed, where the Kirchhoff hypothesis is adopted for the plate modeling and the geometrical nonlinearities are considered in the von Karman sense.
Abstract: A geometrically nonlinear theory of magnetothermoelasticity of electroconductive anisotropic plates in a magnetic field is developed. In this context, the Kirchhoff hypothesis is adopted for the plate modeling and the geometrical nonlinearities are considered in the von Karman sense. In addition, the assumptions related to the distribution of electric and magnetic field disturbances through the plate thickness as proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e., the ones by Faraday, Ampere, Ohm, Maxwell, and Lorentz), on the modified Fourier law of heat conduction, and elastokinetic field equations, the three-dimensional coupled problem is reduced to an equivalent two-dimensional one appropriate to the theory of plates. The theory developed herein enables one to investigate the interacting effects among the magnetic, thermal, and elastic fields in orthotropic thin plates. As a special case, the problem of the free vibration of simply supported plate ...
TL;DR: In this article, a pyroelectric hollow cylinder is transformed to a second kind of Volterra integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method.
Abstract: By virtue of the separation of variables technique, the piezothermoelastic axisymmetric dynamic problem of a pyroelectric hollow cylinder is transformed to a second kind of Volterra integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a pyroelectric hollow cylinder with an arbitrary thickness subjected to arbitrary thermal loads. Numerical results are presented.
TL;DR: In this paper, the authors studied a transmission problem in thermoelasticity and showed that the linear system is well posed and that the solution decays exponentially to zero as time goes to infinity.
Abstract: In this article we study a transmission problem in thermoelasticity. We show that the linear system is well posed and that the solution decays exponentially to zero as time goes to infinity. That is, denoting by E(t) the first-order energy associated to the thermoelastic system, there exists positive constants c and n such that E(t) h cE (0) e m n t .
TL;DR: In this paper, the von Karman nonlinear displacement-strain relationships based on layerwise theory are applied to evaluate the postbuckling and panel flutter behavior of cylindrical laminated panels subject to thermal stresses.
Abstract: The thermal postbuckling and aerodynamic-thermal load analysis of cylindrical laminated panels has been performed using the finite element method. To consider large deflections due to thermomechanical loads, the von Karman nonlinear displacement-strain relationships based on layerwise theory are applied. The cylindrical arc-length method is used to take account of the snapping phenomena. The panel flutter analysis of cylindrical panels subject to thermal stresses is carried out using Hans Krumhaar's supersonic piston theory. For the enhancement of the postbuckling and panel flutter behavior subjected to thermal load, the shape memory alloy hybrid composite (SMAHC) panel is investigated.
TL;DR: In this paper, a plate theory for thermoelastic materials with voids is presented, where the authors establish the field equations for the bending of thin plates made from an isotropic and homogeneous material in the context of dynamic linear theory.
Abstract: This article is concerned with a plate theory for thermoelastic materials with voids. We establish the field equations for the bending of thermoelastic thin plates made from an isotropic and homogeneous material in the context of the dynamic linear theory. Then, we present a uniqueness theorem with no definiteness assumptions on the constitutive coefficients. Finally, by means of the logarithmic convexity method, we obtain continuous dependence results and study the instability of the solutions.
TL;DR: In this article, the thermal and mechanical buckling loads of a cap of a shallow spherical shell of isotropic material and geometrically imperfect shell are considered and the equilibrium and stability equations are based on Donnell-Mushtari-Velasov (DMV) theory.
Abstract: In this article, the thermal and mechanical buckling loads of a cap of a shallow spherical shell of isotropic material and geometrically imperfect shell are considered The equilibrium and stability equations are based on Donnell-Mushtari-Velasov (DMV) theory and are derived using the variational method The Sander's nonlinear strain-displacement relations are used The shell is under external pressure for mechanical loading and uniform temperature rise and radial temperature difference for thermal loadings A simply supported boundary condition is assumed The solutions for thermal and mechanical buckling loads are obtained using the stability equations and the Galerkin method One-term approximation for the middle-plane shell displacement is considered The expressions for the thermal and mechanical buckling loads are obtained analytically and are given by closed-form solutions
TL;DR: In this paper, a computational analysis of the nonlinear vibration and thermal postbuckling of a heated orthotropic annular plate with immovably hinged edges was presented, based on von Karman's plate theory and Hamilton's principle.
Abstract: A computational analysis of the nonlinear vibration and thermal buckling of a heated orthotropic annular plate with immovably hinged edges was presented. First, based on von Karman's plate theory and Hamilton's principle, the governing equations, in terms of the displacements of the middle plane, of the problem are derived. Then, upon assuming that harmonic responses of the system exist, the nonlinear dynamic equations in the von Karman version were converted into the corresponding nonlinear ordinary differential equations through elimination of the time variable using the Kantorovich time-averaging method. Finally, by applying a shooting method, the fundamental responses of the linear as well as nonlinear vibration and thermal postbuckling of the heated plate were numerically obtained.
TL;DR: In this paper, an exact thermal stress solution for a piecewise piecewise functionally graded plate with a circular hole is presented. But the exact series expressions for the two unknown functions are presented only for a pair of first-order ordinary differential equations.
Abstract: An exact thermal stress solution is provided for a functionally graded plate that has a circular hole, with the material properties and applied temperature varying arbitrarily in the radial direction. Building on an existing solution for homogeneous materials, an exact formulation for the functionally graded plate is established by generalizing the material constants and the two integration constants as variables and unknown functions of r, the radial coordinate. By solving a pair of first-order ordinary differential equations, the exact series expressions for the two unknown functions are presented. Numerical results are furnished to demonstrate the numerical effectiveness and application potential of the formulation and the solution. Further extension is established to present an exact thermal stress solution for a composite, piecewise functionally graded plate with a circular hole.
TL;DR: In this article, an investigation was carried out to understand the thermal buckling behavior of local delamination near the surface of fiber-reinforced laminated cylindrical shells and the delaminated growth.
Abstract: An investigation is carried out to understand the thermal buckling behavior of local delamination near the surface of fiber-reinforced laminated cylindrical shells and the delaminated growth. The shape of the delaminated region considered is elliptic and triangular. The direction of the fiber material's axis is arbitrary. The relationships between the critical thermal load and the geometrical and physical parameters of base laminated shells and sublaminated shells are described and some valuable conclusions are obtained. Finally, the possible expanding direction of the elliptic and triangular delaminated shape under thermal load is discussed.
TL;DR: In this paper, a review of the literature on sensing and controlling thermally induced transient structural deformations by means of piezoelectric elements is presented, and a solution procedure for determining the thermal, elastic, and electric fields in composite structures constructed of thermo-elastic and piezothermoelastic layers is discussed.
Abstract: Investigations on sensing and controlling thermally induced transient structural deformations by means of piezoelectric elements are reviewed in this article. Past research in the field of thermopiezoelasticity having relevance to smart structures is discussed briefly. Equations governing the linear response of piezothermoelastic media are outlined; and solution procedures for determining the thermal, elastic, and electric fields in composite structures constructed of thermoelastic and piezothermoelastic layers are discussed. Applications of the solution techniques to direct problems (prescribed transient thermal loadings), control problems (applied electric potentials), inverse problems (determination of thermal loadings from knowledge of induced electric potentials), and intelligent problems (piezoelectric layers serve both to sense thermal loadings and suppress deformations) are addressed.
TL;DR: In this paper, a homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space on both sides is investigated in the context of coupled thermoelasticity.
Abstract: The propagation of thermoelastic waves in a homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides is investigated in the context of coupled thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases. The different regions of secular equations are obtained; and special cases, such as Lame modes, thin plate waves, and short wavelength waves, of the secular equations are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. Finally, the numerical solution is carried out for an aluminum-epoxy composite material plate bordered with water. The dispersion curves for symmetric and antisymmetric wave modes are presented in order to illustrate and compare the theoretic...
TL;DR: In this paper, the thermal buckling analysis of an isotropic inhomogeneous rectangular plate subjected to the arbitrary thermal loads is studied. But the authors consider the case where the material properties such as the coefficient of linear thermal expansion α, the thermal conductivity λ and Young's modulus of elasticity, E, are changed in the thickness direction with the power law of the coordinate variable, whereas Poisson's ratio ν is assumed to be constant.
Abstract: This paper is concerned with the thermal buckling analysis of an isotropic inhomogeneous rectangular plate subjected to the arbitrary thermal loads. The fundamental equations system is derived by introducing the technique of the newly defined position of the reference plane, which allows us to analyze the problem using an elementary plate theory. It is assumed that the material properties such as the coefficient of linear thermal expansion α, the thermal conductivity λ, and Young's modulus of elasticity, E, are changed in the thickness direction with the power law of the coordinate variable, whereas Poisson's ratio ν is assumed to be constant. As an illustrative example, we consider the thermal buckling problem of a simply supported inhomogeneous rectangular plate due to uniform heat supply. Numerical calculations are carried out for several cases taking into account the variations of the inhomogeneous material properties, aspect ratio, and width-to-thickness ratio.
TL;DR: In this paper, the fundamental field equations of coupled thermoelasticity for general microperiodic composite materials are derived and a one-dimensional layered composite model is obtained using a modeling procedure proposed in papers by Wo et al.
Abstract: The aim of this article is to present (i) a formulation of the field equations characterizing a "refined averaged model" describing the dynamical thermoelastic processes in microperiodic composite materials, (ii) an analysis of particular models, and (iii) an application of an "effective modulus model" to solve a boundary initial value problem for a microperiodic layered semispace. Using a modeling procedure proposed in papers by Wo niak et al. [1,2], the fundamental field equations of coupled thermoelasticity for general microperiodic composite materials are derived and a one-dimensional layered composite model is obtained. The fundamental field equations involve the functions \eqalign{{\bf u}({\bf x}, t) = {\bf U} ({\bf x}, t)+h^a({\bf x}){\bf V}^a({\bf x}, t)\cr \vartheta({\bf x}, t) =\Theta({\bf x}, t)+h^a({\bf x})\Phi^a({\bf x}, t)\qquad a=1,\ldots ,n} where h a are the microshape functions; u and are the displacement and temperature fields, respectively; U , V a , , and | a are the basic unkno...
TL;DR: In this paper, a numerical method of design optimization for structural thermal buckling is investigated, where the analysis of heat conduction and structural stress and buckling are considered at the same time in the design optimization procedure.
Abstract: In this article, the numerical method of design optimization for structural thermal buckling is investigated. The analysis of heat conduction and structural stress and buckling are considered at the same time in the design optimization procedure. Based on the finite element method, the research takes the heat conduction and the structural buckling analysis into account. The unified finite element model is applied for both the thermal analysis and structural analysis. The coupling sensitivity effects of heat conduction on the structural thermal buckling are studied. The direct method and the adjoint method are employed to derive the sensitivity equations of the thermal buckling. The adjoint method for thermal buckling sensitivity analysis is proposed first here, and the coupling effects of the problem are particularly addressed. In the sensitivity analysis, the semianalytical method, which is adaptive for various elements and many kinds of design variables, is employed. Based on the results of the coupling...
TL;DR: In this article, the flexural characteristics and layup optimization of laminated composite plates are examined in environmental conditions of temperature and moisture, and the deflection of composite plates is analyzed in the design space of 12 lamination parameters.
Abstract: The flexural characteristics and layup optimization of laminated composite plates are examined in environmental conditions of temperature and moisture. The deflection of laminated composite plates is analyzed in the design space of 12 lamination parameters. The layup optimization for minimizing the deflection of laminated composite plates is carried out using all 12 lamination parameters as design variables. Mathematical programming methods are used for optimization. In hygrothermal conditions, the maximum deflection of laminated composite plates with in-plane hygrothermal stresses can be reduced by optimized nonsymmetric laminate configurations.
TL;DR: In this article, the authors investigated the thermal induced bending vibration of spacecraft booms modeled as circular thin-walled beams of closed cross-section and subjected to thermal radiation, and derived the dynamic governing equations involving the temperature effects and the related boundary conditions via the application of the extended Hamilton principle.
Abstract: Thermally induced bending vibration of spacecraft booms modeled as circular thin-walled beams of closed cross section and subjected to thermal radiation is investigated One assumes that the boom is built up of composite material systems, and in this context, the constituent materials of the beam include nonclassical effects such as anisotropy and transverse shear In addition, in order to induce beneficial elasticcouplings, a special ply-angle distribution achieved via the usual helically wounding fiber-reinforced technology is implemented Both the dynamic governing equations involving the temperature effects and the related boundary conditions are obtained via the application of the extended Hamilton principle The case of the spacecraft boom equipped with a concentrated mass at its free end, fixed at the other end, and exposed to solar radiant heating is studied from both the induced-vibration and stability points of view The numerical simulations display deflection time history of bending displaceme
TL;DR: In this article, three kinds of cracks are considered for the tribological failure process: two-dimensional multiple surface cracks, planar surface cracks and curved cracks, and a two dimensional multiple kinked crack in a half-space.
Abstract: Three kinds of cracks are considered for the tribological failure process. First, two-dimensional multiple surface cracks are analyzed. The stress intensity factors of the multiple surface cracks are calculated, and the noticeable effects on the crack growth are investigated. Second, as a more realistic model, a three-dimensional analysis is considered for straight growth of the planar surface crack. On the basis of the stress intensity factors at the crack front, and using the fatigue crack growth law for cemented carbide, silicon nitride, and bearing steel, the three-dimensional fatigue crack growth contour and the fatigue crack propagation life are predicted. Finally, corresponding to the curved crack, a two-dimensional multiple kinked crack in a half-space is considered. On the basis of the stress intensity factors, and using the fatigue crack growth law for the bearing steel, the two-dimensional fatigue crack growth path and the fatigue crack propagation life are predicted. In addition, the thermomechanical effects such as the frictional coefficient, sliding/rolling ratio, and the crack-face fluid pressure on the fatigue crack propagation life and induced fatigue pitting failures are considered.