Receding Contact Problem Research Articles

Frictional receding contact problem of a functionally graded orthotropic layer / orthotropic interlayer / isotropic half plane system

Frictional receding contact problem of a functionally graded orthotropic layer / orthotropic interlayer / isotropic half plane system

A Receding Contact Problem of Two Layers one of Functionally Graded, Loaded by Circular Rigid Block and Resting on a Pasternak Foundation

In this study, frictionless receding contact problem of two elastic layers which one is functionally graded material (FGM) resting on a Pasternak foundation is considered. The external load is applied to the homogeneous elastic layer by means of a circular rigid block and the functionally graded layer rests on a Pasternak foundation. The effect of gravity forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. Displacement and stress expressions for the layers are obtained using the theory of elasticity and integral transformation technique. By applying the boundary conditions for the problem, reduced to two integral equations in which the contact stresses and contact lengths are unknown. The system of integral equations is numerically solved by making use of appropriate Gauss Chebyshev integration formulas. The equilibrium conditions are satisfied in the solution and the contact stresses and contact distances related to the problem are obtained for various dimensionless quantities.

Effects of a tilted flat-ended punch on the receding contact between a graded and a homogeneous layer

This paper considers the receding contact problem between an exponentially graded layer and a homogeneous layer under the indentation of a tilted rigid flat-ended punch. In the presence of an offset load deviated from the symmetry axis of the rigid punch, the contact pressures both under the rigid punch and along the receding contact interface between the layers lose symmetry. Depending on the magnitude of eccentricity, either complete or incomplete contact may take place under the rigid flat-ended punch, whereas a receding type of contact always occurs along the interface separating the graded and the homogeneous layers. Fourier integral transforms help to convert the governing equations and mixed boundary conditions of the double-contact problem into dual Fredholm integral equations of the second kind with Cauchy-type singular kernels. Gauss–Chebyshev and Gauss–Jacobi numerical quadratures are subsequently employed to discretize and collocate the dual singular integral equations, together with the four force and moment equilibrium equations, for the complete and incomplete contact, as well as the transitional status corresponding to the critical load eccentricity. Extensive parametric studies indicate that the critical load eccentricity depends on the property gradation of the graded layer and the layer-thickness ratio, but not on the magnitude of the indentation load. The extent of contact both under the rigid flat-ended punch and along the receding contact interface is also independent of the magnitude of the indentation load. The results suggest reasonable departures from the contact properties of a homogeneous half-plane under a tilted rigid flat-ended punch, indicating the valuable information on optimizing the double-contact properties in terms of the property gradation and layer-thickness ratio under a given eccentricity.

Receding contact between an inclusion of generalized shape and a remotely-stressed plate

This paper examines the problem of frictionless contact and separation of a rigid inclusion from an infinite elastic plate. The inclusion initially fits perfectly into a hole in the plate, and separates from it upon remote stressing. In a significant generalization of the classical work of Wilson and Goree on receding contacts of elliptical inclusions, the present formulation allows the inclusion to be of quite general shape. In particular, superellipses provide a convenient way to describe a family of such generalized inclusion shapes by varying two parameters. A highly accurate conformal mapping scheme based on rational functions and the Adaptive Antoulas–Anderson (AAA) algorithm is used to map the interior of a unit circle to the exterior of these generalized inclusions. Notably, a rational function representation is far more efficient than a polynomial representation. The governing Singular Integro-Differential Equation (SIDE) of the contact is then derived using the conformal map and analytic continuation, and solved using standard orthogonal polynomial techniques. The contact size and transmitted pressure traction are obtained for a wide range of shapes, including superelliptical, curvilinear hexagonal, and hypotrochoidal square inclusions. The role of the remote stress ratio on the contact response is studied, and a phase diagram demarcating various contact regimes is obtained. A comparison of the pressures for selected inclusion shapes using finite element analysis (FEA) shows good agreement with the present (semi-analytical) SIDE results. For shapes like hypotrochoidal squares, subtle changes in the inclusion geometry can cause significantly different peak contact pressures, pointing to the importance of accurate modeling of geometry in conforming–receding contact problems.

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by an exponential function which varies along the thickness direction. Both the governing equations and the boundary conditions of the receding contact problem are converted into a pair of singular integral equations using the Fourier integral transforms, which are numerically integrated by the Chebyshev–Gauss quadrature. The contact pressure and the contact size at both contact interfaces are eventually obtained iteratively, as developed from the steepest descent algorithm. Extensive parametric studies suggest that it is possible to regulate the contact pressure and contact size by constructing the top layer from a soft functionally graded material.

On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods

AbstractThe frictionless double receding contact problem for two functionally graded (FG) layers pressed by a uniformly distributed load is addressed in this paper. The gradation in the layers is assumed to follow an exponential variation through the height with constant Poisson's ratios. The lower layer rests on a homogeneous half‐plane (HP). There is no adhesion between the FG layers or between the lower layer and the HP. The body forces of the FG layers and HP are ignored. First, the governing equations are reduced to a system of two singular integral equations with contact pressures and contact lengths as unknowns using Fourier transform techniques and boundary conditions. The integral equations are solved numerically using the Gauss‐Chebyshev integration formula. Then, a parametric finite element analysis is performed using the augmented contact method. Finally, the problem was extended based on the multilayer perceptron (MLP), an artificial neural network used for different problem parameters. The effects of stiffness parameters, the normalized load length, the ratio of shear moduli, the ratio of FG layer heights to the normalized contact lengths, and normalized maximum contact pressures are explored. The results of finite element analysis and the MLP approach are used to validate the normalized maximum contact pressures and contact lengths obtained from an analytical method based on elasticity theory, and finally, good agreement between these three methods results is obtained. The obtained results could help in designing multibody indentation systems with FGMs.

A receding contact problem between a graded piezoelectric layer and a piezoelectric substrate

A receding contact problem between a graded piezoelectric layer and a piezoelectric substrate

On the receding contact between a graded and a homogeneous layer due to a flat-ended indenter

This paper solves the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter. Although its Poisson’s ratio is kept as a constant, the shear modulus in the graded layer is assumed to exponentially vary along the thickness direction. The primary goal of this study is to investigate the functional dependence of both contact pressures and the extent of receding contact on the mechanical and geometric properties. For verification and validation purposes, both theoretical analysis and finite element modelings are conducted. In the analytical formulation, governing equations and boundary conditions of the double contact problem are converted into dual singular integral equations of Cauchy type with the help of Fourier integral transforms. In view of the drastically different singularity behavior of the stationary and receding contact pressures, Gauss–Chebyshev quadratures and collocations of both the first and the second kinds have to be jointly used to transform the dual singular integral equations into an algebraic system. As the resultant algebraic equations are nonlinear with respect to the extent of receding contact, an iterative algorithm based on the method of steepest descent is further developed. The semianalytical results are extensively verified and validated with those obtained from the graded finite element method, whose implementation details are also given for easy reference. Results from both approaches reveal that the property gradation, indenter width, and thickness ratio all play significant roles in the determination of both contact pressures and the receding contact extent. An appropriate combination of these parameters is able to tailor the double contact properties as desired.

Frictionless contact mechanics of an orthotropic coating/isotropic substrate system

This study has been performed to investigate the receding contact problem of a homogeneous orthotropic coating that is not bonded to a homogeneous isotropic substrate without any interfacial defects. The isotropic substrate is supported on a Winkler foundation. The problem is solved assuming that the contact between the rigid punch and orthotropic coating, and that between the orthotropic coating and isotropic substrate, are frictionless. Additionally, the effect of the body forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. The contact analysis of the orthotropic coating, which is subjected to a contact load using a rigid cylindrical punch, is performed under plane strain conditions. The governing equations are analytically found using the theory of elasticity and Fourier integral transformation techniques. Subsequently, the governing equations are reduced to a system of two singular equations, wherein the unknowns are the contact stresses and contact widths. To numerically solve the resulting singular integral equations, Gauss-Chebyshev integration formulas are employed. It is analyzed the influence of the following parameters on the contact stresses and contact widths: orthotropicmaterial properties, punch radius, load ratio, Winkler foundation stiffness.

Plane frictional receding contact of a thin layer pressed onto a substrate by finite pressure distributions

A frictional receding contact problem of an infinitely long layer pressed by different finite pressure distributions onto a half-plane of the same linear elastic material is solved with the distributed dislocation technique. Solutions are obtained for when the layer is subject to three different pressure distributions: finite patch of constant pressure, square-root bounded (Hertzian) pressure and square-root singular pressure. The contact tractions, the locations of slip and separation, and the slope of the layer at remote points are found for different coefficients of friction and for different widths of pressure distribution. A universal relationship is deduced between the total slip, the remote slope of the layer and the shear traction.

Thermoelastic receding contact problem of a layer resting on a half plane with frictional heat generation

The plane steady-state thermoelastic receding double contact problem between a rigid cylindrical punch and a homogenous layer lying on a half plane is investigated in this paper. The frictional rigid insulated punch slides over the layer with a constant velocity and heat flux is generated due to the friction. The speed of the punch is taken so small that the inertia effects may be neglected. The general stress and displacement expressions for the thermoelastic contact problem are derived using the theory of thermoelasticity and Fourier integral transform technique. Applying the boundary conditions, the contact problem is reduced to Cauchy-type singular integral equations of the second kind in which the contact stresses and contact widths are unknown. The singular integral equations are solved numerically using the Gauss-Jacobi integration formula. The effect of thermoelastic parameters, friction coefficient, external load, punch radius on the contact stress, and contact widths are discussed in detail. This is the first study to investigate the thermal effect on the receding contact problem.

Assessment of different solution methods for receding contact problems in functionally graded layered mediums

This paper presents a comparative study of different methods, such as the analytical method, finite element method (FEM), and multilayer perceptron (MLP) for analyzing a frictionless receding contact problem. The problem consists of two layers resting on a Winkler foundation. The top layer is functionally graded (FG) along the depth and pressed using a rigid cylindrical stamp, whereas the bottom layer is homogeneous. We assumed that the contact between the two layers, and that between the FG layer and the rigid cylindrical stamp are frictionless; additionally, compressive normal tractions can be transmitted through the interface. First, the problem was solved analytically using the theory of elasticity and integral transform techniques. Second, the finite element solution of the problem was obtained using ANSYS software. Finally, the problem was extended based on the MLP, which an artificial neural network used for different problem parameters. The results of this study showed that the variations in the contact lengths at the interface between the rigid cylindrical stamp and the FG layer, those between the homogeneous layer and the FG layer, and the maximum contact pressures at these interfaces depended on various dimensionless quantities such as the stamp radius, stiffness parameter, shear modulus ratio, and elastic spring constant ratio. We observed that the results obtained with the three different methods, namely the analytical method, FEM, and MLP, are extremely compatible with each other, thus proving the accuracy of these results.

Finite element modeling of contact between an elastic layer and two elastic quarter planes

In this study, a two dimensional model of receding contact problem has been analyzed using finite element method (FEM) based software ANSYS and ABAQUS. For this aim finite element modeling of elastic layer and two homogeneous, isotropic and symmetrical elastic quarter planes pressed by means of a rigid circular punch has been presented. Mass forces and friction are neglected in the solution. Since the problem is examined for the plane state, the thickness along the z-axis direction is taken as a unit. In order to check the accuracy of the present models, the obtained results are compared with the available results of the open literature as well as the results of two software are compared using Root Mean Square Error (RMSE) and good agreements are found. Numerical analyses are performed considering different values of the external load, rigid circular radius, quarter planes span length and material properties. The contact lengths and contact stresses of these values are examined, and their results are presented. Consequently, it is concluded that the considered non-dimensional quantities have noteworthy influence on the contact lengths and contact stress distributions, additionally if FEM analysis is used correctly, it can be an efficient alternative method to the analytical solutions that need time.

Frictional receding contact problem of a functionally graded layer resting on a homogeneous coated half-plane

This paper investigates the frictional receding contact problem between a functionally graded (FG) layer resting on a homogeneous coated half-plane when the system indented by a rigid cylindrical punch. The shear modulus of the upper graded layer is assumed to vary exponentially in the depth direction. Upon loading, the advancing contact and receding contact occur between the FG layer and rigid punch and between the FG layer and coating, respectively. Under the assumptions of sliding contact, the shear and normal contact stresses are related through Coulomb’s law of friction. The contact problem is converted analytically using Fourier integral transforms and the proper boundary conditions into a system of two singular integral equations. The unknowns of these integral equations consist of the contact stresses under the punch and between the FG layer and coating as well as the dimensions of the contact zones. The Gauss–Jacobi quadrature collocation method is then employed to transform the singular integral equations into a system of nonlinear equations which are solved using an appropriate iterative algorithm to compute the contact stresses and the dimensions of the contact areas. The main purpose of this paper is to examine the influence of several parameters on the upper and lower contact stresses, which include the material inhomogeneity parameter, friction coefficient, punch radius, applied load, thickness of homogeneous layer, shear modulus of homogeneous layer and shear modulus of homogeneous half-plane. One of the most important conclusions from this study is that the contact stresses and contact areas can be controlled with the addition of the homogeneous layer.

Artificial neural network calculations for a receding contact problem

This paper investigates the artificial neural network (ANN) to predict the dimensionless parameters for the maximum contact pressures and contact areas of a contact problem. Firstly, the problem is formulated and solved theoretically by using Theory of Elasticity and Integral Transform Technique. Secondly, the contact problem has been extended based on the ANN. The multilayer perceptron (MLP) with three-layer was used to calculate the contact distances. External load, distance between the two quarter planes, layer heights and material properties were created by giving examples of different values were used at the training and test stages of ANN. Program code was rewritten in C++. Different types of network structures were used in the training process. The accuracy of the trained neural networks for the case was tested using 173 new data which were generated via theoretical solutions so as to determine the best network model. As a result, minimum deviation value (difference between theoretical and C++ ANN results) of was obtained for the network model. Theoretical results were compared with artificial neural network results and well agreements between them were achieved.

Prying action in an elastic T-stub tensile connection

We investigate a bolted T-stub joint in tensile loading as an elastic receding contact problem. In this configuration two flat flanges are fastened together by bolt tension and are subjected to central tension loading, possibly cyclic. Due to the bending flexibility of the flanges, large “prying” contact forces arise which can cause the bolt forces to exceed the applied load. Hence such joints may be prone to failure especially under repeated loading. This elastic analysis is suitable to determine the onset of plastic yield and to investigate fatigue failure.In many design procedures the analysis of a T-stub joint is based on the assumption of lift-off of the entire flange except its outer edges. We treat the T-stub joint as a compliant receding contact problem where the flexural deformation of the components induces variable-location prying forces. We show that the traditional approach can significantly underestimate the prying forces in cases where the prying forces act nearer to the bolt. Our analysis also demonstrates that, in cases in which the predicted lift-off distance is greater than the distance to the flange edge, the use of a longer flange would be protective of the bolt. We present results for the elastic T-stub bolt force based on two beam theories, as well as a sampling of results using three-dimensional finite element elasticity analysis. We also propose a formula for flange thickness that suppresses prying, and interpret our results via the Goodman fatigue criterion to define the required steel-bolt ultimate strength under cyclic loading.

Contact Mechanics of a Thin Layer Pressed Onto a Substrate by a Line Load

Abstract A fundamental plane frictional receding contact of a thin layer pressed onto a substrate is solved with the insertion of distributions of dislocations. The new formulation overcomes the restriction of standard contact analysis with the distributed dislocation technique, which requires the distributions to be square root bounded to zero or square root singular at the ends of the area of insertion. This new formulation opens up a range of plane frictional receding contacts to theoretical study. Solutions are obtained for the basic plane receding contact problem of a homogeneous linear elastic semi-infinite layer pressed by a line load onto a half-plane of the same material with a Coulomb friction interface. The frictional dependence of receding contact behavior is identified and discussed.

Double frictional receding contact problem for an orthotropic layer loaded by normal and tangential forces

With the increasing research in the field of contact mechanics, different types of contact models have been investigated by many researchers by employing various complex material models. To ascertain the orthotropy effect and modeling parameters on a receding contact model, the double frictional receding contact problem for an orthotropic bilayer loaded by a cylindrical punch is taken into account in this study. Assuming plane strain sliding conditions, the governing equations are found analytically using Fourier integral transformation technique. Then, the resulting singular integral equations are solved numerically using an iterative method. The weight function describing the asymptotic behavior of the stresses are investigated in detail and powers of the stress singularities are provided. To control the trustworthiness and correctness of the analytical formulation and to compare the resulting stress distributions and contact boundaries, a numerically efficient finite element method was employed using augmented Lagrange contact algorithm. The aim of this paper is to investigate the orthotropy effect, modeling parameters and coefficients of friction on the surface and interface stresses, surface and interface contact boundaries, powers of stress singularities, weight function and to provide highly parametric benchmark results for tribological community in designing wear resistant systems.

Shear–compression loaded interface crack between a rigid substrate and an FGM layer—frictional crack closure effects

A typical application of functionally graded materials (FGMs) is the coating of homogeneous or inhomogeneous substrates. This work investigates numerically an interfacial crack between an FGM coating and a rigid substrate that is subjected to shear–compression loading under the effect of friction. Two types of linearly graded coatings and one homogeneous coating exhibiting the same average Young’s modulus were examined. Two different numerical methods were applied for solving the singular receding contact problem: in-house finite difference software and a commercial finite element software. The effect of friction on the crack closure parameters such as tangential shifts and normal gaps of the crack face were studied with both methods and revealed an excellent agreement between the two. The effect of friction on the transition of the crack face from the slip to stick condition was studied as well. An extended J line formulation was used to extract the stress intensity factors (SIFs) for the crack tip for which the adjacent crack face experiences a large frictional contact. It was demonstrated that increasing the coefficient of friction causes a decrease in the tangential shifts and normal gaps until the whole crack face exhibits stick. The linear gradation in which the material is harder on the interface than on the top results in lower crack face displacement and SIFs.

Prying Action in a Bolted Cantilever Analyzed as a Receding Contact Problem

AbstractBolts are often used to hold flat components together while transmitting a tensile (separating) load. When the components are relatively rigid and the transmitted load exceeds the combined ...