Sergiu Spinu | Stefan cel Mare University of Suceava (original) (raw)
Papers by Sergiu Spinu
International Journal of Modern Manufacturing Technologies, Dec 20, 2022
International Journal of Modern Manufacturing Technologies, Jun 20, 2023
Finding the distributions of eigenstresses induced by eigenstrains regardless of their type is a ... more Finding the distributions of eigenstresses induced by eigenstrains regardless of their type is a fundamental problem in mechanical engineering, described by complex mathematical models. Analytical solutions exist only for a small number of particular distributions of eigenstrains. This paper advances a numerical solution for the eigenstresses due to arbitrary distributions of eigenstrains in an infinite space. The imposed discretization transforms the continuous problem space into a set of adjacent cuboids, each characterized by a single value calculated analytically in a chosen point, usually the cuboid centre. In this manner, continuous functions are replaced in the mathematical model by sets of values calculated in discrete points, which, if the discretization is fine enough, replicate well the continuous distributions. The contribution of the uniform eigenstrains from a specific cuboid, to the eigenstresses in the calculation point, expressed analytically in the literature, is used as a starting point. To reduce the high computational requirements for superposition, state-of-the-art spectral methods for the acceleration of convolution products are applied. A Matlab computer program was developed to implement the newly advanced method. The case of a cuboid containing uniform dilatational eigenstrains was first simulated for validation purposes. Small deviations from the analytical solution can be observed near the inclusion boundary, but their magnitude decreases with finer meshes, suggesting it’s a discretization related error. The results were then extended by considering radially decreasing eigenstrains inside an ellipsoid.
IOP conference series, Sep 11, 2020
Minute relative motions along the interface of contacting machine elements, brought about by cycl... more Minute relative motions along the interface of contacting machine elements, brought about by cyclic tangential loading, lead to failure of many mechanical components from fretting fatigue. From the point of view of applied mechanics, the understanding of the fretting fatigue rely on the modelling of contact problems with partial slip. The experimental simulation of fretting fatigue often implies cylindrical pads in contact with a flat specimen, leading to a plane strain contact scenario requiring the solution of the two-dimensional contact problem. The numerical solution for the latter problem is achieved in this paper for similar elastic materials by employing the technique of influence functions, derived from fundamental half-plane solutions of point forces acting on the boundary. The contact model is first divided into two parts with solutions more easily to obtain. The linear systems with the normal and shear tractions as unknowns are solved with the conjugate gradient method, which can be applied for symmetric and positive definite system matrices. The most time-consuming operations are the convolutions products assessing the displacements induced by the contact tractions. A method based on the fast Fourier transform is applied for increased computational speed without sacrificing accuracy. The proposed algorithm was benchmarked by reproducing the solution of the classic two-dimensional Cattaneo-Mindlin problem. In practical situations, other loadings besides the contact itself may induce bulk stresses within one or both of the contacting bodies. New results are obtained by introducing a bulk stress, thus replicating the conditions from fretting fatigue experiments. The advanced numerical program for the two-dimensional contact with partial slip proves itself as an efficient tool for the understanding of the fretting fatigue by numerical modelling and simulation.
Tribology in industry, Jun 15, 2019
Competent design decisions for the optimum configuration of a coated contact require the predicti... more Competent design decisions for the optimum configuration of a coated contact require the prediction of the stress state developing in the coated body under contact load. Conventional methods of superposition of effects applied in the elasticity of homogenous bodies fail in case of multilayered materials as the response of the latters to point load has only been derived in the frequency domain. A technique for assessment of the elastic response of coated bodies to arbitrary loadings is advanced in this paper, by employing the convolution theorem in the calculation of the stresses and displacements resulting in a sliding contact process. The solution of the elastic frictional contact in full sliding is achieved iteratively, using a state-of-the-art method originally developed for the contact of rough homogenous bodies. Results presented in the literature for the sliding contact of coated bodied are replicated using the newly proposed algorithm. A parametric study is subsequently performed to assess the combined influence of the frictional coefficient, the coating thickness and the elastic modulus mismatch between the coating and the substrate, on the locations and intensity of the maximum von Mises equivalent stress.
International Journal of Modern Manufacturing Technologies
"For the solution of the elastic contact problem, it is generally assumed that the contactin... more "For the solution of the elastic contact problem, it is generally assumed that the contacting solids can be assimilated to elastic half-spaces. This assumption is reasonable when the contact area is small compared to the dimensions of the contacting solids, and when the contact stresses are restricted to a small vicinity of the initial point of contact, without reaching the boundaries of the solids. These conditions are not met when a thin strip is bilaterally and symmetrically compressed between two punches, as the dimensions of the contact area might be of the same order of magnitude as the strip thickness. Moreover, the stresses induced in the strip will reach the boundary without a significant decay in intensity. Consequently, in this contact scenario, the classical solutions for a point force acting on the boundary of the half-space cannot be directly applied. The starting point for the problem solution is a modified Boussinesq-type solution for the thin elastic layer, expressing the displacement and stress fields induced in an elastic strip by two opposed normal forces perpendicular to the layer boundaries. To this end, supplementary displacements are added to the half-space solution to satisfy both geometric and loading symmetry, as well as the linear elasticity equations. Superposition principle is then applied, resulting in a contact model for an elastic strip compressed between two identical indenters with aligned axes. An algorithm for the contact of solids that can be assimilated to elastic half-spaces is modified and applied to the contact involving a thin strip. To this end, the required influence coefficients for displacements are derived. A calculation example involving a thin strip compressed between two spheres is presented, and a comparison with the half-space solution is performed. "
International Journal of Modern Manufacturing Technologies
The contacts of mechanical components transmit loads that lead to subsurface stresses developing ... more The contacts of mechanical components transmit loads that lead to subsurface stresses developing in the contacting bodies. In an efficient tribological design, these stresses are expected to remain under the yield strength of the softer contacting material. When this condition is not met, plastic flow occurs in the softer body. Under the assumption of isotropic hardening, the yield strength increases with the development of additional plastic strains. As plastic flow processes are dissipative and therefore path dependent, the elastic-plastic problem is unsolvable through analytical endeavours, but can be approached with a numerical algorithm capable of simulating the loading history. The Betti’s reciprocal theorem provides the theoretical framework for the application of superposition principle to elastic-plastic stresses and displacement. An algorithm consisting in three nested loops is assembled from the solutions of simpler problems: (1) the purely elastic rough contact problem, ...
IOP Conference Series: Materials Science and Engineering, 2020
Minute relative motions along the interface of contacting machine elements, brought about by cycl... more Minute relative motions along the interface of contacting machine elements, brought about by cyclic tangential loading, lead to failure of many mechanical components from fretting fatigue. From the point of view of applied mechanics, the understanding of the fretting fatigue rely on the modelling of contact problems with partial slip. The experimental simulation of fretting fatigue often implies cylindrical pads in contact with a flat specimen, leading to a plane strain contact scenario requiring the solution of the two-dimensional contact problem. The numerical solution for the latter problem is achieved in this paper for similar elastic materials by employing the technique of influence functions, derived from fundamental half-plane solutions of point forces acting on the boundary. The contact model is first divided into two parts with solutions more easily to obtain. The linear systems with the normal and shear tractions as unknowns are solved with the conjugate gradient method, w...
IOP Conference Series: Materials Science and Engineering, 2019
Hard coatings provide low friction, high wear resistance and corrosion protection that improve th... more Hard coatings provide low friction, high wear resistance and corrosion protection that improve the tribological performances of the machine elements undergoing contact load. In lack of analytical solutions, a numerical study is performed in this paper for a better understanding of the engineering applications of hard coatings with consideration of friction. A previous study on the frictionless contact of bi-layered materials is extended by considering the effect of friction on the contact stress state. The assumption of a sliding contact in which the shear tractions do not affect the pressure distribution is adopted. This simplification, often present in the literature, decouples the contact problems in the normal and in the tangential direction and allows for a pressure distribution solution that is independent of the frictional regime. The shear tractions are subsequently obtained from a kinetic Coulomb-type friction law, under the assumption that the normal load is kept constant....
IOP Conference Series: Materials Science and Engineering, 2015
IOP Conference Series: Materials Science and Engineering, 2015
The failure of the mechanical contact due to plastic yielding is generally predicted employing st... more The failure of the mechanical contact due to plastic yielding is generally predicted employing stress analysis coupled with the von Mises yield criterion, which uses the maximum of the second deviatoric stress invariant as a threshold value. This paper aims to establish the relation between the frictional regime and the normal and tangential loading components which lead to yield inception in the slip-stick spherical contact between similarly elastic materials. The Boussinesq and Cerruti fundamental solutions for the elastic half-space are used in a robust semi-analytical method based on the superposition principle applicable in the frame of linear elasticity, and enhanced with an acceleration technique derived from the convolution theorem. A rapid algorithm for accurate computation of elastic stresses induced in subsurface by a known but arbitrary distribution of surface tractions, normal or shear, is advanced. The obtained data is normalized to allow model extension to any elastic constants or contact curvature, and curve fitting is employed to derive simple empirical formulas pertinent to practical engineering applications.
Tribology in Industry, 2020
International Journal of Modern Manufacturing Technologies, Dec 20, 2022
The starting point in the calculation of normal displacement due to transient heating is the Gree... more The starting point in the calculation of normal displacement due to transient heating is the Green's function for the elastic half-space. Superposition principle leads to a triple integral (double integral over surface and simple integral over time) that can be formally rewritten as a threedimensional convolution product. Given the singularities of the Green's function in the time/space domain, it is more convenient to employ its spectral counterpart, i.e. the frequency response function (FRF), in the convolution calculation. A special technique for the calculation of the 3D convolution product based on the FRF is advanced in this paper. The resulting algorithm is very efficient from a computational point of view, as the transfers to and from the time/space domain to the frequency domain are handled by the fast Fourier transform. A simulation example is presented, involving the transient thermoelastic displacement due to a uniform heat source that vanishes everywhere except for a square surface domain, and which is applied continuously only in a limited time window. The numerical results predict that the displacement increases with time as long as heat is supplied, and is gradually recovered once the heat is removed. The loaded half-space patch undergoes a growth-release process that is accurately captured by the simulation method. The developed framework anticipates the solution of the contact process with transient heating.
International Journal of Modern Manufacturing Technologies
Due to model complexity, classical contact mechanics theory assumes isothermal contact processes,... more Due to model complexity, classical contact mechanics theory assumes isothermal contact processes, involving bodies with uniform temperatures and no heat transmitted or generated through or near the contact interface. This paper addresses the problem of frictional heating in non-conforming or rough contacts by investigating the thermoelastic behaviour of asperities. The heat generated in a sliding contact by interfacial friction leads to thermoelastic distortion of the contact surface, further modifying contact parameters such as pressure, gap or temperature. The thermal expansion of the contacting bodies must therefore be accounted for when solving the contact problem. The thermoelastic displacement is computed with the aid of the half-space theory and of fundamental solutions for point sources of heat located at the free surface, derived in the literature of heat conduction in solids. The linearity of conduction equations encourages the use of superposition principle in the same wa...
IOP Conference Series: Materials Science and Engineering, 2020
The service life of contacting coated machine elements is ultimately determined by the distributi... more The service life of contacting coated machine elements is ultimately determined by the distribution of stresses in the coating and in the substrate. By assuming the elastic bodies as elastic half-spaces, the contact stress computation entails the calculation of convolutions expressing the superposition of effects of unit point loads acting on the boundary. The fundamental solutions of stresses and displacements in multilayered materials have only been calculated in the frequency domain, and are known as the frequency response functions. An additional difficulty arises in the stress calculation, related to frequency response function valuation in the origin of the frequency domain, where a singularity is usually encountered. This case of un-determination is circumvented in this paper by substituting the required value with the mean value of the frequency response function over a vicinity centered in origin. The latter approach is endorsed by the fact that the frequency response funct...
IOP Conference Series: Materials Science and Engineering, 2020
This paper advances an algorithm for the simulation of the elastic contact undergoing a constant ... more This paper advances an algorithm for the simulation of the elastic contact undergoing a constant normal force and an oscillating torsional moment, under the assumption of partial slip. The solution of this type of contact can be achieved with a numerical formulation based on influence coefficients that express the contribution of elementary rectangular patches of uniform surface tractions, normal or tangential, to the displacement field induced in the elastic half-space. Summation of these elementary contributions allows for the calculation of the displacement field for arbitrary distributions of tractions, thus allowing for an iterative problem resolution that can handle arbitrary contact geometry, various frictional regimes and consideration of coated materials. The displacement response of multi-layered bodies is calculated based on the frequency response functions, and a previously advanced technique for calculation of convolution products in the Fourier transform domain is impl...
IOP Conference Series: Materials Science and Engineering, 2018
In a tribological system containing protective coatings, the knowledge of stresses generated in b... more In a tribological system containing protective coatings, the knowledge of stresses generated in both the hard layer and the substrate are essential to the design of the tribological elements. The stress field due to the contact load is required to assess the coating performance and to guide the coating design. Rough contact analyses can only be performed numerically, but conventional techniques applied to layered solids may lead to very time-consuming simulations. The semi-analytical method for the analyses of contact stresses in a bilayered medium advanced in the companion paper is enhanced and applied to stress analyses in the layered body. The main difficulty in applying FFT-based spectral analysis to the study of subsurface stresses consists in the treatment of the frequency response function (FRF) at the origin of the frequency domain, where the FRF may be singular. As the FRF is integrable in the neighbourhood of the origin, the discrete sample corresponding to the patch centred in origin is substituted by the average value over the latter patch. The conditions of stress continuity at the interface between the protective layer and the substrate are verified. The influence of both coating thickness and dissimilarity in the elastic properties between the coating and the substrate, on the intensity of the maximum von Mises equivalent stress, is assessed. The numerical examples prove the method ability to tackle contact scenarios involving protective coatings and to assist the design of competent tribological elements.
IOP Conference Series: Materials Science and Engineering, 2017
The classic approach to the slip-stick contact is based on the framework advanced by Mindlin, in ... more The classic approach to the slip-stick contact is based on the framework advanced by Mindlin, in which localized slip occurs on the contact area when the local shear traction exceeds the product between the local pressure and the static friction coefficient. This assumption may be too conservative in the case of high tractions arising at the asperities tips in the contact of rough surfaces, because the shear traction may be allowed to exceed the shear strength of the softer material. Consequently, the classic frictional contact model is modified in this paper so that gross sliding occurs when the junctions formed between all contacting asperities are independently sheared. In this framework, when the contact tractions, normal and shear, exceed the hardness of the softer material on the entire contact area, the material of the asperities yields and the junction growth process ends in all contact regions, leading to gross sliding inception. This friction mechanism is implemented in a previously proposed numerical model for the Cattaneo-Mindlin slip-stick contact problem, which is modified to accommodate the junction growth theory. The frictionless normal contact problem is solved first, then the tangential force is gradually increased, until gross sliding inception. The contact problems in the normal and in the tangential direction are successively solved, until one is stabilized in relation to the other. The maximum tangential force leading to a non-vanishing stick area is the static friction force that can be sustained by the rough contact. The static friction coefficient is eventually derived as the ratio between the latter friction force and the normal force.
IOP Conference Series: Materials Science and Engineering, 2016
Existing solutions for the contact problem involving viscoelastic materials often require numeric... more Existing solutions for the contact problem involving viscoelastic materials often require numerical differentiation and integration, as well as resolution of transcendental equations, which can raise convergence issues. The algorithm advanced in this paper can tackle the contact behaviour of the viscoelastic materials without any convergence problems, for arbitrary contact geometry, arbitrary loading programs and complex constitutive models of linear viscoelasticity. An updated algorithm for the elastic frictionless contact, coupled with a semi-analytical method for the computation of viscoelastic displacement, is employed to solve the viscoelastic contact problem at a series of small time increments. The number of equations in the linear system resulting from the geometrical condition of deformation is set by the number of cells in the contact area, which is a priori unknown. A trial-and-error approach is implemented, resulting in a series of linear systems which are solved on evolving contact areas, until static equilibrium equations and complementarity conditions are fully satisfied for every cell in the computational domain. At any iteration, cells with negative pressure are excluded from the contact area, while cells with negative gap (i.e. cells where the contacting bodies are predicted to overlap) are reincluded. The solution is found when pressure is stabilized in relation to the imposed normal load. This robust algorithm is expected to solve a large variety of contact problems involving viscoelastic materials.
International Journal of Modern Manufacturing Technologies, 2021
Various biomedical components, such as dental crowns and hip prostheses, data processing devices,... more Various biomedical components, such as dental crowns and hip prostheses, data processing devices, and other numerous mechanical components that transmit load through a mechanical contact, may benefit from a tri-layer design. The coating may be optimized for wear protection and corrosion prevention, whereas the intermediate layer provides increased adhesion between the outer layer and the substrate, and confines the crack propagation. The solution to the contact problem involving tri-layered materials can be pursued numerically with the finite element or the boundary element methods, but semi-analytical techniques benefitting from the efficiency of the fast Fourier transform (FFT) technique have also been successfully applied. At the heart of the FFT-assisted approach lie the frequency response functions (FRFs), which are analytical solutions for fundamental problems of elasticity such as the Boussinesq and Cerruti problems, but expressed in the frequency domain. Considering recent e...
International Journal of Modern Manufacturing Technologies, 2021
The line-contact is a particular type of contact with a contact length much greater than its widt... more The line-contact is a particular type of contact with a contact length much greater than its width. Such contact scenarios can be treated in the frame of a two-dimensional plane-strain problem if the contacting surfaces can be considered nominally smooth. However, surface irregularities inherent to any manufacturing technique lead to a discontinuous contact area that differs from the one derived on the basis of the smooth profile assumption. It is therefore tantalizing to pursue the solution of a line-contact problem using an intrinsically three-dimensional (3D) model, which can only be numerical due to lack of general analytical solutions in contact mechanics. Considering the geometry of the line-contact, a major challenge in its numerical modelling is that the expected contact area is orders of magnitude larger in one direction compared to the other. This may lead to an unreasonably large number of grids in the contact length direction, which translates to a prohibitive computatio...
International Journal of Modern Manufacturing Technologies, Dec 20, 2022
International Journal of Modern Manufacturing Technologies, Jun 20, 2023
Finding the distributions of eigenstresses induced by eigenstrains regardless of their type is a ... more Finding the distributions of eigenstresses induced by eigenstrains regardless of their type is a fundamental problem in mechanical engineering, described by complex mathematical models. Analytical solutions exist only for a small number of particular distributions of eigenstrains. This paper advances a numerical solution for the eigenstresses due to arbitrary distributions of eigenstrains in an infinite space. The imposed discretization transforms the continuous problem space into a set of adjacent cuboids, each characterized by a single value calculated analytically in a chosen point, usually the cuboid centre. In this manner, continuous functions are replaced in the mathematical model by sets of values calculated in discrete points, which, if the discretization is fine enough, replicate well the continuous distributions. The contribution of the uniform eigenstrains from a specific cuboid, to the eigenstresses in the calculation point, expressed analytically in the literature, is used as a starting point. To reduce the high computational requirements for superposition, state-of-the-art spectral methods for the acceleration of convolution products are applied. A Matlab computer program was developed to implement the newly advanced method. The case of a cuboid containing uniform dilatational eigenstrains was first simulated for validation purposes. Small deviations from the analytical solution can be observed near the inclusion boundary, but their magnitude decreases with finer meshes, suggesting it’s a discretization related error. The results were then extended by considering radially decreasing eigenstrains inside an ellipsoid.
IOP conference series, Sep 11, 2020
Minute relative motions along the interface of contacting machine elements, brought about by cycl... more Minute relative motions along the interface of contacting machine elements, brought about by cyclic tangential loading, lead to failure of many mechanical components from fretting fatigue. From the point of view of applied mechanics, the understanding of the fretting fatigue rely on the modelling of contact problems with partial slip. The experimental simulation of fretting fatigue often implies cylindrical pads in contact with a flat specimen, leading to a plane strain contact scenario requiring the solution of the two-dimensional contact problem. The numerical solution for the latter problem is achieved in this paper for similar elastic materials by employing the technique of influence functions, derived from fundamental half-plane solutions of point forces acting on the boundary. The contact model is first divided into two parts with solutions more easily to obtain. The linear systems with the normal and shear tractions as unknowns are solved with the conjugate gradient method, which can be applied for symmetric and positive definite system matrices. The most time-consuming operations are the convolutions products assessing the displacements induced by the contact tractions. A method based on the fast Fourier transform is applied for increased computational speed without sacrificing accuracy. The proposed algorithm was benchmarked by reproducing the solution of the classic two-dimensional Cattaneo-Mindlin problem. In practical situations, other loadings besides the contact itself may induce bulk stresses within one or both of the contacting bodies. New results are obtained by introducing a bulk stress, thus replicating the conditions from fretting fatigue experiments. The advanced numerical program for the two-dimensional contact with partial slip proves itself as an efficient tool for the understanding of the fretting fatigue by numerical modelling and simulation.
Tribology in industry, Jun 15, 2019
Competent design decisions for the optimum configuration of a coated contact require the predicti... more Competent design decisions for the optimum configuration of a coated contact require the prediction of the stress state developing in the coated body under contact load. Conventional methods of superposition of effects applied in the elasticity of homogenous bodies fail in case of multilayered materials as the response of the latters to point load has only been derived in the frequency domain. A technique for assessment of the elastic response of coated bodies to arbitrary loadings is advanced in this paper, by employing the convolution theorem in the calculation of the stresses and displacements resulting in a sliding contact process. The solution of the elastic frictional contact in full sliding is achieved iteratively, using a state-of-the-art method originally developed for the contact of rough homogenous bodies. Results presented in the literature for the sliding contact of coated bodied are replicated using the newly proposed algorithm. A parametric study is subsequently performed to assess the combined influence of the frictional coefficient, the coating thickness and the elastic modulus mismatch between the coating and the substrate, on the locations and intensity of the maximum von Mises equivalent stress.
International Journal of Modern Manufacturing Technologies
"For the solution of the elastic contact problem, it is generally assumed that the contactin... more "For the solution of the elastic contact problem, it is generally assumed that the contacting solids can be assimilated to elastic half-spaces. This assumption is reasonable when the contact area is small compared to the dimensions of the contacting solids, and when the contact stresses are restricted to a small vicinity of the initial point of contact, without reaching the boundaries of the solids. These conditions are not met when a thin strip is bilaterally and symmetrically compressed between two punches, as the dimensions of the contact area might be of the same order of magnitude as the strip thickness. Moreover, the stresses induced in the strip will reach the boundary without a significant decay in intensity. Consequently, in this contact scenario, the classical solutions for a point force acting on the boundary of the half-space cannot be directly applied. The starting point for the problem solution is a modified Boussinesq-type solution for the thin elastic layer, expressing the displacement and stress fields induced in an elastic strip by two opposed normal forces perpendicular to the layer boundaries. To this end, supplementary displacements are added to the half-space solution to satisfy both geometric and loading symmetry, as well as the linear elasticity equations. Superposition principle is then applied, resulting in a contact model for an elastic strip compressed between two identical indenters with aligned axes. An algorithm for the contact of solids that can be assimilated to elastic half-spaces is modified and applied to the contact involving a thin strip. To this end, the required influence coefficients for displacements are derived. A calculation example involving a thin strip compressed between two spheres is presented, and a comparison with the half-space solution is performed. "
International Journal of Modern Manufacturing Technologies
The contacts of mechanical components transmit loads that lead to subsurface stresses developing ... more The contacts of mechanical components transmit loads that lead to subsurface stresses developing in the contacting bodies. In an efficient tribological design, these stresses are expected to remain under the yield strength of the softer contacting material. When this condition is not met, plastic flow occurs in the softer body. Under the assumption of isotropic hardening, the yield strength increases with the development of additional plastic strains. As plastic flow processes are dissipative and therefore path dependent, the elastic-plastic problem is unsolvable through analytical endeavours, but can be approached with a numerical algorithm capable of simulating the loading history. The Betti’s reciprocal theorem provides the theoretical framework for the application of superposition principle to elastic-plastic stresses and displacement. An algorithm consisting in three nested loops is assembled from the solutions of simpler problems: (1) the purely elastic rough contact problem, ...
IOP Conference Series: Materials Science and Engineering, 2020
Minute relative motions along the interface of contacting machine elements, brought about by cycl... more Minute relative motions along the interface of contacting machine elements, brought about by cyclic tangential loading, lead to failure of many mechanical components from fretting fatigue. From the point of view of applied mechanics, the understanding of the fretting fatigue rely on the modelling of contact problems with partial slip. The experimental simulation of fretting fatigue often implies cylindrical pads in contact with a flat specimen, leading to a plane strain contact scenario requiring the solution of the two-dimensional contact problem. The numerical solution for the latter problem is achieved in this paper for similar elastic materials by employing the technique of influence functions, derived from fundamental half-plane solutions of point forces acting on the boundary. The contact model is first divided into two parts with solutions more easily to obtain. The linear systems with the normal and shear tractions as unknowns are solved with the conjugate gradient method, w...
IOP Conference Series: Materials Science and Engineering, 2019
Hard coatings provide low friction, high wear resistance and corrosion protection that improve th... more Hard coatings provide low friction, high wear resistance and corrosion protection that improve the tribological performances of the machine elements undergoing contact load. In lack of analytical solutions, a numerical study is performed in this paper for a better understanding of the engineering applications of hard coatings with consideration of friction. A previous study on the frictionless contact of bi-layered materials is extended by considering the effect of friction on the contact stress state. The assumption of a sliding contact in which the shear tractions do not affect the pressure distribution is adopted. This simplification, often present in the literature, decouples the contact problems in the normal and in the tangential direction and allows for a pressure distribution solution that is independent of the frictional regime. The shear tractions are subsequently obtained from a kinetic Coulomb-type friction law, under the assumption that the normal load is kept constant....
IOP Conference Series: Materials Science and Engineering, 2015
IOP Conference Series: Materials Science and Engineering, 2015
The failure of the mechanical contact due to plastic yielding is generally predicted employing st... more The failure of the mechanical contact due to plastic yielding is generally predicted employing stress analysis coupled with the von Mises yield criterion, which uses the maximum of the second deviatoric stress invariant as a threshold value. This paper aims to establish the relation between the frictional regime and the normal and tangential loading components which lead to yield inception in the slip-stick spherical contact between similarly elastic materials. The Boussinesq and Cerruti fundamental solutions for the elastic half-space are used in a robust semi-analytical method based on the superposition principle applicable in the frame of linear elasticity, and enhanced with an acceleration technique derived from the convolution theorem. A rapid algorithm for accurate computation of elastic stresses induced in subsurface by a known but arbitrary distribution of surface tractions, normal or shear, is advanced. The obtained data is normalized to allow model extension to any elastic constants or contact curvature, and curve fitting is employed to derive simple empirical formulas pertinent to practical engineering applications.
Tribology in Industry, 2020
International Journal of Modern Manufacturing Technologies, Dec 20, 2022
The starting point in the calculation of normal displacement due to transient heating is the Gree... more The starting point in the calculation of normal displacement due to transient heating is the Green's function for the elastic half-space. Superposition principle leads to a triple integral (double integral over surface and simple integral over time) that can be formally rewritten as a threedimensional convolution product. Given the singularities of the Green's function in the time/space domain, it is more convenient to employ its spectral counterpart, i.e. the frequency response function (FRF), in the convolution calculation. A special technique for the calculation of the 3D convolution product based on the FRF is advanced in this paper. The resulting algorithm is very efficient from a computational point of view, as the transfers to and from the time/space domain to the frequency domain are handled by the fast Fourier transform. A simulation example is presented, involving the transient thermoelastic displacement due to a uniform heat source that vanishes everywhere except for a square surface domain, and which is applied continuously only in a limited time window. The numerical results predict that the displacement increases with time as long as heat is supplied, and is gradually recovered once the heat is removed. The loaded half-space patch undergoes a growth-release process that is accurately captured by the simulation method. The developed framework anticipates the solution of the contact process with transient heating.
International Journal of Modern Manufacturing Technologies
Due to model complexity, classical contact mechanics theory assumes isothermal contact processes,... more Due to model complexity, classical contact mechanics theory assumes isothermal contact processes, involving bodies with uniform temperatures and no heat transmitted or generated through or near the contact interface. This paper addresses the problem of frictional heating in non-conforming or rough contacts by investigating the thermoelastic behaviour of asperities. The heat generated in a sliding contact by interfacial friction leads to thermoelastic distortion of the contact surface, further modifying contact parameters such as pressure, gap or temperature. The thermal expansion of the contacting bodies must therefore be accounted for when solving the contact problem. The thermoelastic displacement is computed with the aid of the half-space theory and of fundamental solutions for point sources of heat located at the free surface, derived in the literature of heat conduction in solids. The linearity of conduction equations encourages the use of superposition principle in the same wa...
IOP Conference Series: Materials Science and Engineering, 2020
The service life of contacting coated machine elements is ultimately determined by the distributi... more The service life of contacting coated machine elements is ultimately determined by the distribution of stresses in the coating and in the substrate. By assuming the elastic bodies as elastic half-spaces, the contact stress computation entails the calculation of convolutions expressing the superposition of effects of unit point loads acting on the boundary. The fundamental solutions of stresses and displacements in multilayered materials have only been calculated in the frequency domain, and are known as the frequency response functions. An additional difficulty arises in the stress calculation, related to frequency response function valuation in the origin of the frequency domain, where a singularity is usually encountered. This case of un-determination is circumvented in this paper by substituting the required value with the mean value of the frequency response function over a vicinity centered in origin. The latter approach is endorsed by the fact that the frequency response funct...
IOP Conference Series: Materials Science and Engineering, 2020
This paper advances an algorithm for the simulation of the elastic contact undergoing a constant ... more This paper advances an algorithm for the simulation of the elastic contact undergoing a constant normal force and an oscillating torsional moment, under the assumption of partial slip. The solution of this type of contact can be achieved with a numerical formulation based on influence coefficients that express the contribution of elementary rectangular patches of uniform surface tractions, normal or tangential, to the displacement field induced in the elastic half-space. Summation of these elementary contributions allows for the calculation of the displacement field for arbitrary distributions of tractions, thus allowing for an iterative problem resolution that can handle arbitrary contact geometry, various frictional regimes and consideration of coated materials. The displacement response of multi-layered bodies is calculated based on the frequency response functions, and a previously advanced technique for calculation of convolution products in the Fourier transform domain is impl...
IOP Conference Series: Materials Science and Engineering, 2018
In a tribological system containing protective coatings, the knowledge of stresses generated in b... more In a tribological system containing protective coatings, the knowledge of stresses generated in both the hard layer and the substrate are essential to the design of the tribological elements. The stress field due to the contact load is required to assess the coating performance and to guide the coating design. Rough contact analyses can only be performed numerically, but conventional techniques applied to layered solids may lead to very time-consuming simulations. The semi-analytical method for the analyses of contact stresses in a bilayered medium advanced in the companion paper is enhanced and applied to stress analyses in the layered body. The main difficulty in applying FFT-based spectral analysis to the study of subsurface stresses consists in the treatment of the frequency response function (FRF) at the origin of the frequency domain, where the FRF may be singular. As the FRF is integrable in the neighbourhood of the origin, the discrete sample corresponding to the patch centred in origin is substituted by the average value over the latter patch. The conditions of stress continuity at the interface between the protective layer and the substrate are verified. The influence of both coating thickness and dissimilarity in the elastic properties between the coating and the substrate, on the intensity of the maximum von Mises equivalent stress, is assessed. The numerical examples prove the method ability to tackle contact scenarios involving protective coatings and to assist the design of competent tribological elements.
IOP Conference Series: Materials Science and Engineering, 2017
The classic approach to the slip-stick contact is based on the framework advanced by Mindlin, in ... more The classic approach to the slip-stick contact is based on the framework advanced by Mindlin, in which localized slip occurs on the contact area when the local shear traction exceeds the product between the local pressure and the static friction coefficient. This assumption may be too conservative in the case of high tractions arising at the asperities tips in the contact of rough surfaces, because the shear traction may be allowed to exceed the shear strength of the softer material. Consequently, the classic frictional contact model is modified in this paper so that gross sliding occurs when the junctions formed between all contacting asperities are independently sheared. In this framework, when the contact tractions, normal and shear, exceed the hardness of the softer material on the entire contact area, the material of the asperities yields and the junction growth process ends in all contact regions, leading to gross sliding inception. This friction mechanism is implemented in a previously proposed numerical model for the Cattaneo-Mindlin slip-stick contact problem, which is modified to accommodate the junction growth theory. The frictionless normal contact problem is solved first, then the tangential force is gradually increased, until gross sliding inception. The contact problems in the normal and in the tangential direction are successively solved, until one is stabilized in relation to the other. The maximum tangential force leading to a non-vanishing stick area is the static friction force that can be sustained by the rough contact. The static friction coefficient is eventually derived as the ratio between the latter friction force and the normal force.
IOP Conference Series: Materials Science and Engineering, 2016
Existing solutions for the contact problem involving viscoelastic materials often require numeric... more Existing solutions for the contact problem involving viscoelastic materials often require numerical differentiation and integration, as well as resolution of transcendental equations, which can raise convergence issues. The algorithm advanced in this paper can tackle the contact behaviour of the viscoelastic materials without any convergence problems, for arbitrary contact geometry, arbitrary loading programs and complex constitutive models of linear viscoelasticity. An updated algorithm for the elastic frictionless contact, coupled with a semi-analytical method for the computation of viscoelastic displacement, is employed to solve the viscoelastic contact problem at a series of small time increments. The number of equations in the linear system resulting from the geometrical condition of deformation is set by the number of cells in the contact area, which is a priori unknown. A trial-and-error approach is implemented, resulting in a series of linear systems which are solved on evolving contact areas, until static equilibrium equations and complementarity conditions are fully satisfied for every cell in the computational domain. At any iteration, cells with negative pressure are excluded from the contact area, while cells with negative gap (i.e. cells where the contacting bodies are predicted to overlap) are reincluded. The solution is found when pressure is stabilized in relation to the imposed normal load. This robust algorithm is expected to solve a large variety of contact problems involving viscoelastic materials.
International Journal of Modern Manufacturing Technologies, 2021
Various biomedical components, such as dental crowns and hip prostheses, data processing devices,... more Various biomedical components, such as dental crowns and hip prostheses, data processing devices, and other numerous mechanical components that transmit load through a mechanical contact, may benefit from a tri-layer design. The coating may be optimized for wear protection and corrosion prevention, whereas the intermediate layer provides increased adhesion between the outer layer and the substrate, and confines the crack propagation. The solution to the contact problem involving tri-layered materials can be pursued numerically with the finite element or the boundary element methods, but semi-analytical techniques benefitting from the efficiency of the fast Fourier transform (FFT) technique have also been successfully applied. At the heart of the FFT-assisted approach lie the frequency response functions (FRFs), which are analytical solutions for fundamental problems of elasticity such as the Boussinesq and Cerruti problems, but expressed in the frequency domain. Considering recent e...
International Journal of Modern Manufacturing Technologies, 2021
The line-contact is a particular type of contact with a contact length much greater than its widt... more The line-contact is a particular type of contact with a contact length much greater than its width. Such contact scenarios can be treated in the frame of a two-dimensional plane-strain problem if the contacting surfaces can be considered nominally smooth. However, surface irregularities inherent to any manufacturing technique lead to a discontinuous contact area that differs from the one derived on the basis of the smooth profile assumption. It is therefore tantalizing to pursue the solution of a line-contact problem using an intrinsically three-dimensional (3D) model, which can only be numerical due to lack of general analytical solutions in contact mechanics. Considering the geometry of the line-contact, a major challenge in its numerical modelling is that the expected contact area is orders of magnitude larger in one direction compared to the other. This may lead to an unreasonably large number of grids in the contact length direction, which translates to a prohibitive computatio...