Consideration of spatial variation of the friction coefficient in contact mechanics analysis of laterally graded materials

Dağ, Serkan

doi:10.1002/zamm.201400116

Cited by 17 publications

(15 citation statements)

References 32 publications

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“…Therefore, instead of assigning constant coefficient of friction and the friction force for all the motion of the punch, friction force applied to punch is calculated as function of C ,X, 0 l∕N , D . Dag [52] studied the spatial variation of the coefficient of friction due to the utilization of graded material in horizontal direction. However, the spatial variation of the friction force beneath the flat punch is ignored in the present study.…”

Section: Equations Of Motion In Planar Theory Of Elastodynamics Readsmentioning

confidence: 99%

Implementation of Dahl’s dynamic friction model to contact mechanics of elastic solids

Balcı

2021

SN Appl. Sci.

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This study presents an analytical method for the solution of dynamic frictional contact problem between a rigid punch and an isotropic elastic solid. Rigid flat punch moves over the isotropic elastic solid at a constant subsonic speed and friction force develops based on Dahl’s friction law instead of Coulomb’s dry friction law. Dahl’s dynamic friction model is adopted since this model is one of the well-known dynamic friction models in the literature. According to this model, friction force depends only on a displacement rather than the speed of the punch since viscous effects are ignored. Influences of the parameters describing Dahl’s friction model on contact stress at slow and high speed sliding cases are examined. Analytical solution is conducted by means of Galilean and Fourier transformations. Friction force is computed numerically by the use of 4th order Runge–Kutta method for various displacements of the punch. Formulation for the contact problem is reduced to a singular integral equation and normal stress over the surface of elastic half-plane is determined. Obtained contact stresses are compared with those generated through finite element method and results display a high degree of accuracy. The influences of direction of motion, Coulomb’s coefficient of friction, pre-sliding displacement, asperity stiffness and shape factor of hysteresis loop upon contact stresses and stress intensity factors are revealed.

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Section: Equations Of Motion In Planar Theory Of Elastodynamics Readsmentioning

confidence: 99%

Implementation of Dahl’s dynamic friction model to contact mechanics of elastic solids

Balcı

2021

SN Appl. Sci.

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“…The finite element analysis of the plane contact problem between an orthotropic laterally graded half-plane and a rigid flat stamp was also executed. 28 The spatial variations of the friction coefficient through the contact interface were taken into account in the sliding frictional contact problems of a laterally graded half-plane 29 and a half-plane graded through an arbitrary direction. 30 Note that the laterally graded materials are practically employed in the form of finite-thickness strips, 21–23 and the deposited materials substantially exhibit anisotropic material behavior.…”

Section: Introductionmentioning

confidence: 99%

Frictional contact problem of an anisotropic laterally graded layer loaded by a sliding rigid stamp

Arslan

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study proposes analytical and computational methods for the solution of the sliding frictional contact problem of an anisotropic laterally graded layer loaded by an arbitrarily shaped rigid stamp. The plane-strain orthotropy prevails in the layer which is bonded to a rigid foundation. Each of four orthotropic stiffness coefficients is exponentially varied through the lateral direction of the elastic layer. The Fourier transformations of the field variables are employed in the formulation. The gradient of a displacement component on the surface is then converted to a singular integral equation of the second kind. The singular integral equation is solved by means of the Gauss–Jacobi quadrature integration techniques, a collocation method, and a recursive integration method for the Cauchy integral considering the flat and triangular stamp profiles. The finite element method solutions of the same contact problems are performed using the augmented Lagrange method which is implemented in virtue of ANSYS design parametric language. An iterative algorithm is additionally utilized for the (incomplete) triangular stamp problem to conveniently reach the solutions for predetermined contact lengths. The convergence and comparative analyses are carried out to elucidate the trustworthiness of the analytical and computational methods proposed. Moreover, the parametric analyses infer that the contact-induced damage risks can be effectively alleviated upon tuning the degree of orthotropy and the lateral heterogeneity of the elastic layer.

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“…FE analyses were performed using ANSYS, in which the effective value of shear modulus was specified at the centroid of each finite element. Their analytical model was extended by Dag 32 to account for the spatial variation in the coefficient of friction along the indentation interface between a laterally FGM elastic medium and a rigid flat punch. Considering the receding contact problems, El-Borgi and Çömez 33 studied analytically the receding frictional contact between an FGM layer and a homogeneous half-plane, which were pressed against each other by a rigid stamp.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

Attia

El-Shafei

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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In tribological and thermo-electro-mechanical applications with an appropriate gradation of properties, functionally graded materials provide superior performance for damage and wear resistance of contact systems and thermal and mechanical responses for other mechanical devices. This paper presents a nonlinear mixed variational-based computational model for the analysis of nonlinear plane indentation problems of elastic functionally graded layered elastic solids. The functionally graded elastic layer is perfectly bonded to the elastic substrate and is normally loaded by a cylindrical rigid punch. In addition to nonlinearity inherent to the contact problem, the developed model accounts for the geometric nonlinearity in the sense of larger displacements and rotations, but smaller strains. The modulus of elasticity as well as Poisson's ratio of the graded layer are varying along the thickness of the layer according to both exponential and power laws. On the contrary, in the conventional homogeneous finite element formulation the isoparametric graded finite element formulation is adopted on the level of Gaussian integration points to realize the gradation in material properties. The friction at the contact interface is modeled using Coulomb's friction law. Moreover, the inequality contact constraints are exactly satisfied throughout the contact interface by employing the Lagrange multiplier method, where the indentation force and the displacement fields are treated as independent variables. The obtained results of contact pressure, tangential contact stress, stress distribution, and indentation force show a significant influence of the material distribution, gradation law, gradient index, and thickness of the functionally graded layer.

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Consideration of spatial variation of the friction coefficient in contact mechanics analysis of laterally graded materials

Cited by 17 publications

References 32 publications

Implementation of Dahl’s dynamic friction model to contact mechanics of elastic solids

Implementation of Dahl’s dynamic friction model to contact mechanics of elastic solids

Frictional contact problem of an anisotropic laterally graded layer loaded by a sliding rigid stamp

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

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