Search

Abstract This paper proposes a new damage index for the crack identification of beams made of functionally graded materials (FGMs) by using the wavelet analysis. The damage index is defined based on the position of the wavelet coefficient modulus maxima in the scale space. The crack is assumed to be an open edge crack and is modeled by a massless rotational spring. It is assumed that the material properties follow exponential distributions along the beam thickness direction. The Timoshenko beam theory is employed to derive the governing equations which are solved analytically to obtain the frequency and mode shape of cracked FGM beams. Then, we apply the continuous wavelet transform (CWT) to the mode shapes of the cracked FGM beams. The locations of the cracks are determined from the sudden changes in the spatial variation of the damage index. An intensity factor, which relates to the size of the crack and the coefficient of the wavelet transform, is employed to estimate the crack depth. The effects of the crack size, the crack location and the Young's modulus ratio on the crack depth detection are investigated. [ABSTRACT FROM AUTHOR]

Both of the frictional heat and thermal contact resistance have a grave responsibility for the localized high temperature (hot spots) at the contact region, which is known as one of the most dangerous appearances in the brakes systems. In this paper, we study the thermoelastic instability (TEI) of a functionally graded material (FGM) half-plane sliding against a homogeneous half-plane at the in-plane direction. The interaction of the frictional heat and thermal contact resistance is taken into account in the TEI analysis. The material properties of the FGM half-plane are supposed to follow the exponential function along the thickness direction. The coupled TEI problem of FGMs is solved by using the perturbation method. The frictionally excited TEI of FGMs is also considered by neglecting the effect of the thermal contact resistance. The results show that the thermal contact resistance, sliding speed and gradient index have significant influence on the TEI. It is found that the variation of the gradient index of FGMs can increase the critical sliding speed and critical heat flux, and therefore improve the TEI of the sliding system. [ABSTRACT FROM AUTHOR]

Using the homogeneous multi-layered model, this paper studies the thermoelastic instability (TEI) of the functionally graded material (FGM) coating with arbitrary varying properties considering the frictional heat and thermal contact resistance. A homogeneous half-plane slides on an FGM coated half-plane at the out-of-plane direction under a uniform pressure. The perturbation method and transfer matrix method are used to deduce the characteristic equation of the TEI problem, which is then solved to obtain the relationship between the critical sliding speed and critical heat flux. The effects of the gradient index and varying form of material properties of the FGM coating on the stability boundaries are examined. The results show that FGM coating can adjust the thermoelastic contact stability of sliding systems. [ABSTRACT FROM AUTHOR]

The interaction between the thermoelastic distortion and pressure-dependent thermal contact resistance can cause the themoelastic instability when the conductive heat transfers between two elastic bodies in the static frictionless contact. Using the perturbation method, this paper investigates the thermoelastic instability of a system consisting of a functionally graded material (FGM) layer and a homogeneous layer under the plane strain state. The two layers are pressed together by a uniform pressure, and transmit a uniform heat flux at their interface. The material properties of the FGM layer are assumed to be of exponential variation along the thickness direction. The thermoelastic stability behavior of five types of material combinations depending on the ratio of their material properties are discussed in details. The results imply that the FGMs can be used to improve the thermoelastic contact stability of the systems. [ABSTRACT FROM AUTHOR]

The conductive heat transfer between two elastic bodies in the static contact can cause the system to be unstable due to the interaction between the thermoelastic distortion and pressure-dependent thermal contact resistance. This paper investigates the thermoelastic contact instability of a functionally graded material (FGM) layer and a homogeneous half-plane using the perturbation method. The FGM layer and half-plane are exposed to a uniform heat flux and are pressed together by a uniform pressure. The material properties of the FGM layer vary exponentially along the thickness direction. The characteristic equation governing the thermoelastic stability behavior is obtained to determine the stability boundary. The effects of the gradient index, layer thickness and material combination on the critical heat flux are discussed in detail through a parametric study. Results indicate that the thermoelastic stability behavior can be modified by adjusting the gradient index of the FGM layer. [ABSTRACT FROM AUTHOR]

This article presents a dynamic stability analysis of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to vary in the thickness direction and are estimated through the rule of mixture. The differential quadrature method is employed to convert the governing differential equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and elastic buckling are also discussed as subset problems. A parametric study is conducted to investigate the influences of nanotube volume fraction, slenderness ratio, and end supports on the dynamic stability characteristics of FG-CNTRC beams. Numerical results for composite beams reinforced by uniformly distributed carbon nanotube are also provided for comparison. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the thermoelastic frictional contact of functionally graded materials (FGMs) with arbitrarily varying thermoelastic properties. The homogeneous multi-layered model is used to approximate the arbitrarily varying material properties of the FGM coating which is divided into several sub-layers whose material properties is assumed to be constant. It is assumed that a rigid insulated punch is sliding over the surface of an FGM coated half-plane with a constant velocity, which generates frictional heating at the contact interface with its value proportional to the contact pressure, frictional coefficient and sliding velocity. The transfer matrix method and the Fourier integral transform technique are employed to convert the problem into Cauchy singular integral equations which are then numerically solved to obtain the contact stress, in-plane stress and surface temperature. The effects of the gradient index, Peclet number and friction coefficient on the thermoelastic contact characteristics are discussed in detail. Different gradient types of FGMs are considered in numerical examples to compare and identify effective gradient type in suppressing the maximum tensile stress and lowering the maximum surface temperature. Numerical results indicate that thermoelastic contact damage behavior can be changed by adjusting the Peclet number, friction coefficient and their gradient indices or gradient type. [Copyright &y& Elsevier]

Abstract: The two-dimensional thermoelastic sliding frictional contact of functionally graded material (FGM) coated half-plane under the plane strain deformation is investigated in this paper. A rigid punch is sliding over the surface of the FGM coating with a constant velocity. Frictional heating, with its value proportional to contact pressure, friction coefficient and sliding velocity, is generated at the interface between the punch and the FGM coating. The material properties of the coating vary exponentially along the thickness direction. In order to solve the heat conduction equation analytically, the homogeneous multi-layered model is adopted for treating the graded thermal diffusivity coefficient with other thermomechanical properties being kept as the given exponential forms. The transfer matrix method and Fourier integral transform technique are employed to convert the problem into a Cauchy singular integral equation which is then solved numerically to obtain the unknown contact pressure and the in-plane component of the surface stresses. The effects of the gradient index, Peclet number and friction coefficient on the thermoelastic contact characteristics are discussed in detail. Numerical results show that the distribution of the contact stress can be altered and therefore the thermoelastic contact damage can be modified by adjusting the gradient index, Peclet number and friction coefficient. [Copyright &y& Elsevier]

Abstract: Dynamic stability of microbeams made of functionally graded materials (FGMs) is investigated in this paper based on the modified couple stress theory and Timoshenko beam theory. This non-classical Timoshenko beam model contains a material length scale parameter and can interpret the size effect. The material properties of FGM microbeams are assumed to vary in the thickness direction and are estimated though Mori–Tanaka homogenization technique. The higher-order governing equations and boundary conditions are derived by using the Hamilton’s principle. The differential quadrature (DQ) method is employed to convert the governing differential equations into a linear system of Mathieu–Hill equations from which the boundary points on the unstable regions are determined by Bolotin’s method. Free vibration and static buckling are also discussed as subset problems. A parametric study is conducted to investigate the influences of the length scale parameter, gradient index and length-to-thickness ratio on the dynamic stability characteristics of FGM microbeams with hinged–hinged and clamped–clamped end supports. Results show that the size effect on the dynamic stability characteristics is significant only when the thickness of beam has a similar value to the material length scale parameter. [Copyright &y& Elsevier]

A two-dimensional fretting contact problem involving normal and tangential loading of two dissimilar elastic bodies with functionally graded coatings is analyzed. The bodies are first brought into contact by a monotonically increasing normal load and then a cycled tangential load is applied with the normal load held constant. Friction with a finite coefficient is assumed between the contact surfaces. The linear multi-layered model is used to model functionally graded coating with arbitrarily varying shear modulus and constant Poisson's ratio under plane strain deformation. With the use of the transfer matrix method and Fourier integral transform technique, the problem is reduced to a set of Cauchy singular integral equations which are solved numerically. An iterative method is developed to determine the stick/slip region and contact tractions. The numerical results show that the functionally graded coating on the harder body can lower the fretting contact stresses and thus improve the resistance to the fretting contact damage, and that in comparison with a homogeneous coating, a functionally graded coating can eliminate the interfacial stress concentration induced by material property mismatch. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory and von Kármán geometric nonlinearity. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and estimated though the rule of mixture. The Ritz method is employed to derive the governing eigenvalue equation which is then solved by a direct iterative method to obtain the nonlinear vibration frequencies of FG-CNTRC beams with different end supports. A detailed parametric study is conducted to study the influences of nanotube volume fraction, vibration amplitude, slenderness ratio and end supports on the nonlinear free vibration characteristics of FG-CNTRC beams. The results for uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) beams are also provided for comparison. Numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fraction, vibration amplitude, slenderness ratio, end supports and CNT distribution on the nonlinear free vibration characteristics of FG-CNTRC beams. [Copyright &y& Elsevier]

Abstract: In this paper, the postbuckling response of beams made of functionally graded materials (FGMs) containing an open edge crack is studied based on Timoshenko beam theory and von Kármán nonlinear kinematics. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through thickness direction. Ritz method is employed to derive the nonlinear governing equations, which are then solved by using Newton–Raphson method to obtain the postbuckling load-end shortening curves and postbuckling deflection-end shortening curves. A detailed parametric study is conducted to study the influences of crack depth, crack location, material property gradient, and slenderness ratio on the postbuckling behavior of cracked FGM beams. It is found that both intact and cracked FGM beams exhibit similar postbuckling behavior under end shortening. Unlike isotropic homogeneous beams, bifurcation buckling does not occur for both intact and cracked FGM beams due to the presence of bending–extension coupling effect. [Copyright &y& Elsevier]

Free vibration and elastic buckling of beams made of functionally graded materials (FGMs) containing open edge cracks are studied in this paper based on Timoshenko beam theory. The crack is modeled by a massless elastic rotational spring. It is assumed that the material properties follow exponential distributions along beam thickness direction. Analytical solutions of natural frequencies and critical buckling load are obtained for cracked FGM beams with clamped-free, hinged-hinged, and clamped-clamped end supports. A detailed parametric study is conducted to study the influences of crack depth, crack location, total number of cracks, material properties, beam slenderness ratio, and end supports on the free vibration and buckling characteristics of cracked FGM beams. [ABSTRACT FROM AUTHOR]

The surface temperature distribution and thermo-elastic stress fields of an inhomogeneous coating system subjected to mixed Hertz pressure, tangential traction, and frictional heating are studied in this paper. The coating system consists of a surface coating and an intermediate functionally graded layer perfectly bonded to a substrate. The surface coating and the substrate are homogeneous materials with distinct physical properties while the intermediate layer is inhomogeneous with material properties changing exponentially along the thickness direction. It is assumed that the friction is of Coulomb type. Solutions for the temperature field and interfacial stresses are obtained using Fourier transform technique. The effects of total thickness, the graded layer thickness, Peclet number, and friction coefficient on the surface temperature field and interfacial stresses are investigated in detail. Direct comparisons with the results of a homogeneous single-layer coating system show that the use of the double-layer coating system can significantly reduce the surface temperature and interfacial normal stress. [ABSTRACT FROM AUTHOR]

Abstract: The two-dimensional frictionless contact problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated in this paper. The coating and substrate are homogeneous materials with distinct physical properties, while the intermediate layer is inhomogeneous with its shear modulus changing arbitrarily along the thickness direction. To approximate the through-thickness variation, a piecewise linear multi-layer model is used and the graded layer is divided into a number of sub-layers whose shear modulus is assumed to vary linearly. Poisson''s ratio, however, is taken as a constant within the structure for simplicity. By using the transfer matrix method and Fourier integral transform technique, the governing equations are reduced to a Cauchy singular integral equation which is numerically solved to determine the normal contact pressure, contact region, the through-thickness stress fields and longitudinal stress distributions at interfaces. A parametric study is conducted, showing that both normal contact pressure and stress fields in the structure are significantly influenced by the shear modulus ratio and the thickness ratio of the exponentially graded layer but are less sensitive to the gradient index of the graded layer whose shear modulus follows a power law variation. [Copyright &y& Elsevier]

Abstract: A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying shear modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Poisson''s ratio is assumed to be a constant. In the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically. The results show that appropriate gradual variation of the shear modulus can significantly alter the stresses in the contact zone. [Copyright &y& Elsevier]

Abstract: A multi-layered model for frictionless contact analysis of functionally graded materials (FGMs) with arbitrarily varying elastic modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be linear function while the Poisson’s ratio is assumed to be a constant. With the model, the frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. [Copyright &y& Elsevier]