Sliding Contact Problem Research Articles

Adding friction to Third Medium Contact: A crystal plasticity inspired approach

This paper presents the first method to enable friction in the Third Medium Contact (TMC) method. TMC embeds a solid in a highly compliant medium, which becomes infinitely stiff under ultimate compression, thus allowing forces to be transferred between the solids when the medium between the solids is compressed. This approach is increasingly adopted for integrating internal contact in structural design processes, owing to its continuous, fully implicit characteristics, simplicity, and its stability when applying regularisation to the third medium regions. The lack of friction has previously restricted the use of the TMC method in simulating real-world contact conditions. Here, we address this issue by (1) integrating an anisotropic term into a Neo-Hookean material model to provide shear resistance, and (2) employing a framework inspired by crystal plasticity that includes a yield criterion specifically designed to replicate the effects of Coulomb friction.The effectiveness of the method is demonstrated through two examples: (1) a smooth sliding contact problem and (2) a non-smooth C-shaped structure. Results demonstrate a close agreement with reference solutions obtained by a conventional Lagrange multiplier approach. While the method, for now, requires user-defined slip directions, it represents a significant advancement by enabling the integration of friction into TMC, thereby broadening its applicability to problems involving realistic frictional contact. Future research should focus on restoring the fully implicit nature of TMC in the presence of friction, and on developing automated slip direction definitions to enhance usability and expand the method’s versatility.

On the time-dependent sliding contact behavior of three-phase polymer matrix smart composites

Abstract Three-phase smart composites consisting of magnetostrictive and piezoelectric reinforcements embedded with a polymer matrix can achieve specific multifunctional properties in response to external stimuli, which are well-suited for the application of sensors, actuators, and electronic devices. The materials exhibit complex behaviors characterized by electro-magneto-viscoelasticity coupling during the contact of these smart structures. This paper proposes a novel hybrid element method (HEM) for numerically analyzing the frictionless sliding contact problem stemming from the viscoelastic behavior and multiphase interactions of polymer matrix smart composites. The study aims to fully investigate the effects of material properties, sliding velocities, and action time on the contact behavior of materials via the integration of the conjugate gradient method (CGM) with the discrete convolution-fast Fourier transform (DC-FFT) algorithm. The analytical viscoelastic frequency response functions (FRFs) are derived by substituting elastic solutions with the time-dependent relaxation modulus. Numerical results show that three-phase polymer matrix smart composites exhibit lower contact pressure and higher surface electric/magnetic potential than three-phase magneto-electro-elastic composites. Sliding velocity and action time strongly influence the distribution of pressure/stress and electric/magnetic potential.

A numerical model to simulate the transient frictional viscoelastic sliding contact

Sliding motion has always been one of the major concerns when it comes to the analysis of viscoelastic contact problems. A new model simulating the transient sliding contact of smooth viscoelastic surfaces is developed in this paper. By taking the dry contact friction and the coupling between shear tractions and normal pressure into account, the effect of the early partial slip period, which is often neglected in the study of viscoelastic sliding contact problems, is investigated numerically. Compared with solutions based on the frictionless assumption, the steady-state pressure profile is found to be slightly different under the effect of the partial slip regime, including a lower peak pressure and the shift of the contacting region in the direction opposite to the sliding motion. Furthermore, the time required for the viscoelastic contact to reach its steady state is delayed owing to the partial slip period preceding the global sliding motion.

A Multiphase Rail Launcher With Circular Geometry and Modular Design: Development, Construction, and First Experiments

Electromagnetic railguns allow to accelerate payloads to extremely high muzzle speeds ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&gt;$</tex-math> </inline-formula> 2 km/s). Conventionally, the launcher design is based on two rails. The power supply consists of a capacitor bank and a pulse-forming network allowing unipolar operation. In this work, a different system setup is presented. The idea is to use multiphase alternating current instead of direct current to drive a rail launcher. The basic idea had been brought up in the past in connection with the use of compulsators as power supply. Here, it is suggested to connect the launcher to a (noncompensated) multiphase generator. An interesting but not obvious feature of such an approach is that a stationary acceleration force profile can be realized. However, the launcher becomes more complex as more than two rails are required and an appropriate power supply has to be developed. When considering this approach, an important finding is that if one aims at high speeds, several stages are required. It means that a modular or segmented setup is required. As the passage of the armature between the segments is expected to be a critical point, the idea came up to build a three-phase circular geometry, meaning that the armature leaves at the “muzzle” and re-enters at the “breech” of the launcher. This also allows using an electric motor for a preacceleration in order to minimize sliding contact problems during start. As power supply served a redesigned 100-kW high-current transformer, which can be connected directly to the local power grid. Experimental data including electrical parameters (e.g., an armature current of 20 kA) are presented and discussed. For the first time, it can be experimentally shown that stationary acceleration profiles can be realized, in principle.

Stability of thermoelastic sliding problem with contact pressure-dependent thermal contact resistance

The sliding contact problem of a rigid indenter over an elastic body with constant temperature difference was investigated using finite element method by considering a contact pressure-dependent thermal resistance. The stability boundary was identified by inspecting the transient contact behaviors, which showed a linear relationship between two nondimensional parameters at the log scale. This proportionality resulted in a nondimensional ratio, which depended on temperature, contact resistance, and sliding speed in the case of unit nondimensional material properties, suggesting “critical temperature difference”. Moreover, the inclusion of Poisson ratio prevented the indefinite bifurcation behavior and led to a finite length scale in the steady state.

On the Applicability of Approximate Rolling and Sliding Contact Algorithms in Anisothermal Problems with Thermal Softening

The residual stress approximation methods formulated by McDowell and Moyar, Jiang and Sehitoglu, and McDowell for rolling and sliding contact problems are reconsidered in the context of single anisothermal loading cycles and isotropic hardening. A consistent extention to incorporate thermal softening is developed and the generalized thermoelastoplastic algorithms are cast into a proper predictor–corrector formulation. Detailed explicit and implicit numerical integration strategies are presented and validated using specifically designed finite element models that conform to the underlying mechanical assumptions. Then, the applicability of the approximate algorithms to anisothermal problems with isotropic hardening and thermal softening is analyzed by assuming a rate-independent Johnson–Cook-type yield stress model and by comparing the obtained transient and residual stresses to results from full-scale finite element half-space models under varying loading and strain-hardening intensities. An in-depth, comparative discussion on the adequacy of the algorithms in conjunction with the justification of their respective mechanical simplifications follows. Sufficiently strong strain hardening is found to be a prerequisite for accurate predictions, and Jiang and Sehitoglu’s approach is deemed to be preferable for the considered type of problem. The conclusions drawn from the investigations are discussed in the context of common applications with particular emphasis on manufacturing process modeling and the corresponding guidelines are proposed for such use cases.

Analytical Model for Studying the Influence of Thickness on the Protective Effect

This paper presents an analytical model to study the influence of the thickness of the built-up layer (BUL) / built-up edge (BUE) on its protective effect during cutting. A new elastic-plastic contact model at the tool-chip interface is proposed to analyze the sliding contact problem with a layer of adhesion (including the BUL and BUE). The equivalent inclusion method (EIM) is utilized to analyze the stress disturbance caused by the adhesion and to evaluate the protective effect of the adhesion. In this method, the adhesion is considered as an equivalent elliptical inclusion at the tool-chip interface. The protective effect of the adhesion and the influence of the adhesion thickness on its protective effect can be evaluated. The proposed analytical model was verified based on experimental data obtained from dry cutting of SUS304 stainless steel. From the results, it can be confirmed that BUL/BUE can protect the cutting tool by affecting the stress distributions in the tool, the positions of yield initiation, and the tangential force acting on the tool. It can also be concluded that a greater thickness improves the protective effect of the BUL/BUE. Furthermore, the proposed model can also provide a clear understanding of the BUL/BUE formation phenomenon.

English

This paper represents a continuation of a previous study on &ldquo;Analysis of a Sliding Frictional Contact Problem with Unilateral Constraint&rdquo;. This study considers a mathematical model which describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraints, associated to a sliding version of Coulomb&rsquo;s law of dry friction. After a description of the model, the variational formulation was presented. Then, the dependence of the solution was studied with respect to the data and a convergence result was proven. Regularization method was also used to study the existence and uniqueness of the contact problem for which a convergence result was presented. Finally, a semi-discrete scheme was introduced for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, an optimal order error estimate was derived. Key words: Elastic material, frictional contact, normal compliance, unilateral constraint, variational formulation, weak solution, regularization method, finite element, error estimate.

A Fractal Model of Elastic–Plastic Contact Between Rough Surfaces for a Low-Velocity Impact Process

Under the low-velocity impact conditions, in order to study the contact load variation law of the ellipsoid elastic bodies, an elastic–plastic contact analysis model of rough ellipsoid surfaces is provided based on elastic–plastic fractal theory. A spherical elastic–plastic fractal model considering friction factors is established, and the spherical diameter density distribution function and elastic contact mechanics are used as the solution methods. The two contact surfaces are taken as the research object, and the influence of relevant variables on the contact intensity is analyzed. The analysis results show that the fractal dimension and roughness have a greater effect on contact performance, the contact load is positively related to the surface roughness, and the lower friction coefficient has a weaker effect on the contact load, and the correctness of the present model is verified by comparing finite element simulation results and other studies. The modified spherical contact load function provides a theoretical basis for the friction and wear of the microscopic surface, it can be applied for solving the sliding contact problems with different impact velocities and the surface bearing capacity of the impact parts can be improved.

Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact

This paper represents a continuation of [1] and [2]. Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

A Finite Element Procedure for Sliding Contact Problems Involving Heterogeneous Coefficient of Friction

A new finite element procedure is developed for the analysis of sliding contact problems involving spatially varying coefficient of friction. The problem is implemented using APDL (ANSYS Parametric Design Language) considering the Augmented Lagrange method as the contact solver. Upon discretization of the contact interface into multiple contact pairs, a sequence of steps is followed to evaluate the resultant friction force required for the sliding contact. As a case study, heterogeneous-friction contact problem between an orthotropic laterally graded half-plane and a rigid flat stamp is investigated under plane strain assumption. The proposed iterative procedure is proved reliable by comparing the results to those generated by a SIE (Singular Integral Equation) approach for isotropic laterally graded half-planes. Extra results are presented to reveal the effects of problem parameters on the contact stresses and the friction force. The paper outlines a convenient numerical solution for an advance sliding contact problem, and the results can be used in validation purposes of experimental and analytical studies.

A nano-scale frictional contact problem incorporating the size dependency and the surface effects

In this paper, the nano-scale sliding contact problem of an isotropic semi-infinite medium is considered. The small scale effects are taken into account by means of the couple stresses and the surface energy theories. Employing the Fourier integral method, the plane elasticity problem is formulated in terms of the integral equations. The numerical results are provided for the plane strain state. The parametric study reveals that the surface material constants remarkably alter the surface stresses and the contact length. The results indicate that the stress singularity substantially decreases due to size effect compared with the classical theory predictions. For example, the in-plane stress tensile peak decreases by a %80 with respect to the Hertzian contact.

Sliding contact problem of an FGM coating/substrate system with two-dimensional material property grading

We consider the sliding contact problem of an FGM coating/substrate system with two-dimensional material property variations. The medium is pressed by a rigid flat stamp. It is assumed that the shear modulus varies exponentially within the coating both longitudinally and laterally. The governing integral equations associated with the mentioned contact problem are constructed using the Fourier transform technique. Finally, the numerical solution of the integral equations is obtained by applying the Gauss–Chebyshev integration method. The main objective of this study is to investigate the effect of different parameters such as the non-homogeneity parameter in two directions, the coefficient of friction, and the coating thickness on the surface contact tractions and the surface in-plane stress. The results indicate that the stress concentration factor near the contact edges can be reduced by appropriate material properties adjustments.

The effect of orthotropic material gradation on the plane sliding frictional contact mechanics problem

With the advent of new functional and intelligent non-conventional materials, understanding the behavior of these materials in different contact conditions over the conventional materials is one of the most crucial aspects in early design process for coated systems. Therefore, the sliding contact problem for a functionally graded orthotropic coating–substrate system and a rigid cylindrical punch is considered in this article to study the aforementioned aspects. The functionally graded orthotropic coating is modeled to be bonded to an isotropic substrate of finite thickness and is loaded by a sliding rigid cylindrical punch under plane strain conditions. For the material orthotropy, five different real orthotropic materials are utilized and the stiffness coefficients of each principal direction are graded separately. Navier’s equations are converted to ordinary differential equations using the Fourier integral transformation technique. Then, the algebraic equations are solved and the problem is cast into a singular integral equation. A parametric finite element analysis based on augmented contact method is also conducted. The normalized surface stress distributions and the normalized contact boundaries obtained from finite element analysis are validated with the results obtained from singular integral equation approach. The results of this study may be helpful for engineers in design and optimization of the characteristics of non-conventional coatings that are used as thermal or structural barriers and wear-resistant surfaces in engineering applications.

Mechanics of dynamic contact of coated substrate and rigid cylindrical ended punch

The dynamic contact mechanics of isotropic elastic coating bonded to homogeneous substrate was examined. The coating is indented by a sliding rigid punch of a cylindrical profile. The rigid punch moves over the coating at a steady subsonic speed. To determine contact stresses, an analytical method based on the singular integral equation technique is put forward. Governing partial differential equations are derived considering general theory of elastodynamics. The influences of dimensionless punch speed, mass density ratio, shear modulus, coefficient of friction, relative coating thickness and Poisson’s ratio on contact stresses and contact related parameters were found. Comparison of the contact stresses computed by elastodynamic and elastostatic theories clearly shows that the relative difference between these two results is quite remarkable. Hence, in sliding contact problems incorporating punches with relatively high speed, elastodynamic theory is required to find more realizable stress results.

Mesoscale Numerical Modeling for Predicting Wear Debris Generation

With the development of debris detection techniques, wear debris has become a powerful indicator for wear conditions monitoring of engineering machines. However, there is still a lack of effective method for predicting the generation of wear debris with given rough surfaces. Hence, a numerical model is developed based on atomic attrition mechanism. Boundary element method is used to solve the dry sliding contact problem. A discretized solution is used to calculate subsurface stress. From the quantity, size, and shape perspectives, wear debris is analyzed using the detailed information by a Monte Carlo simulation on 100 pairs of rough surfaces. The predictions are compared with results by the existing models quantitatively or qualitatively.

A Local Region Molecular Dynamics Simulation Method for Nanoscale Sliding Contacts

Computational efficiency and accuracy always conflict with each other in molecular dynamics (MD) simulations. How to enhance the computational efficiency and keep accuracy at the same time is concerned by each corresponding researcher. However, most of the current studies focus on MD algorithms, and if the scale of MD model could be reduced, the algorithms would be more meaningful. A local region molecular dynamics (LRMD) simulation method which can meet these two factors concurrently in nanoscale sliding contacts is developed in this paper. Full MD simulation is used to simulate indentation process before sliding. A criterion called contribution of displacement is presented, which is used to determine the effective local region in the MD model after indentation. By using the local region, nanoscale sliding contact between a rigid cylindrical tip and an elastic substrate is investigated. Two two-dimensional MD models are presented, and the friction forces from LRMD simulations agree well with that from full MD simulations, which testifies the effectiveness of the LRMD simulation method for two-dimensional cases. A three-dimensional MD model for sliding contacts is developed then to show the validity of the LRMD simulation method further. Finally, a discussion is carried out by the principles of tribology. In the discussion, two two-dimensional full MD models are used to simulate the nanoscale sliding contact problems. The results indicate that original smaller model will induce higher equivalent scratching depth, and then results in higher friction forces, which will help to explain the mechanism how the LRMD simulation method works. This method can be used to reduce the scale of MD model in large scale simulations, and it will enhance the computational efficiency without losing accuracy during the simulation of nanoscale sliding contacts.

The sliding contact problem for an orthotropic coating bonded to an isotropic substrate

We consider the sliding contact problem of an orthotropic coating/substrate system. The coating/substrate system is pressed by a rigid flat or cylindrical stamp. For the orthotropic coating, the principal material directions are assumed to be parallel and perpendicular to the contact surface. The governing integral equations corresponding to the mentioned contact problem are extracted by means of the Fourier transform technique. Later, the numerical solution of the singular integral equations is provided by applying the Gauss-Chebyshev integration method. The main goal of this study is to obtain analytical benchmark solutions in order to examine the effect of material orthotropy parameters, relative stiffness, the coefficient of friction and the coating thickness on the stress distribution at the surface of the orthotropic coating. The behavior of the surface in-plane stress intensity factor is analyzed as well. For a constant value of the applied load, the results indicate that the stiffness ratio and the shear parameter have a more pronounced effect on the surface stress components than the effective Poisson's ratio. Also, the stress intensity factor at sharp edges of the flat punch decreases as the coating softens with respect to the substrate and/or the coating thickness decreases.

Layer-substrate system with an imperfectly bonded interface: Spring-like condition

Materials having two or more constituents of different mechanical properties are often seen in engineering practice. These constituents are connected through their interfaces where the material displacements and tractions are most likely discontinuous, subjected to one, or more, of the five general interface conditions, i.e., perfectly bonded, dislocation-like, force-like, spring-like, and frictionless contact. This paper focus on the contact problem of a rigid sphere sliding on a layered half-space with a spring-like interface between the layer and the substrate. The frequency-domain analytical solutions for the elastic field caused by surface pressure and shear traction are derived. Three stiffness coefficients are introduced to reflect the relationship between tractions and the difference in displacements at both sides of the interface. Further, a sliding contact problem of a rigid sphere and a layered half-space with the spring-like interface is numerically investigated, and the effects of stiffness coefficients on the contact behaviors are explored. Finally, the two-layer model for a coated surface with an inner layer is compared to the spring-like model. When the inner layer is thin and soft, the pressures, as well as stresses, obtained by both models are similar to each other, and the two models are equivalent.

The Improvement of Incompatible Sliding Contact Problem Using Mesh Refinement And Its Application to Railway Skewed Culvert Problem

차량-궤도 구조물 동적 상호작용해석은 차량의 접촉점이 보요소로 모형화된 레일 위를 일정한 속도로 주행하는 미끄러지 는 접촉문제로 취급하였다. 하지만 Euler 보와 같은 고차 다항식의 형상함수가 적용된 유한요소를 사용할 경우 미끄러지는 접촉문제에서 적합조건을 만족하지 못한다. 이 연구에서는 유한요소해석프로그램이 미끄러지는 접촉문제에서의 적합조건을 만족시키지 못하는 것에 대한 해결법으로 주행로를 이루는 보요소를 보다 세분화하여 동적상호작용해석에서의 정확성을 확 보하고자 하였다. 이를 위해 간단한 예제들을 통해 주행로를 이루는 보요소의 세분화 정도에 따른 동적상호작용해석의 거동 을 분석하였으며, 해석 프로그램의 동적상호작용해석에의 적용성을 평가하였다. 마지막으로 사각을 갖는 철도 암거 접속부 의 뒷채움재 설치 형식에 따른 차량주행시의 거동을 평가하기 위하여 동적상호작용해석을 수행하고, 접속부 뒷채움재 형식 의 변경에 따른 지지강성의 변화에 의한 영향과 노반침하에 따른 궤도틀림의 영향을 비교분석하였다.