Stick Zone Research Articles

Effect of plastic deformation on the evolution of wear and local stress fields in fretting

During fretting, the removal of material by wear leads to an increase of contact stress in the stick zone. If elastic behavior is assumed, the boundary between stick and slip zones does not move, wear eventually ceases, and a mode-I singularity of contact pressure is predicted after infinitely many cycles. For real materials, the development of singular stresses must be limited by plastic deformation. Here we investigate the effect of plasticity on fretting wear, using a finite-element model. We find that the principal effect of plasticity is to allow the wear scar to extend continuously into the contact region. Thus, wear continues indefinitely, and extensive damage or catastrophic failure is to be anticipated, given a sufficient number of fretting cycles. In the elastic régime, the results can be cast in dimensionless terms, permitting application to any material or loading condition. Plasticity introduces an additional dimensionless parameter into the analysis, but results of considerable generality can still be obtained. In particular, the contact pressure distribution exhibits a stable maximum related to the yield strength of the material, and the maximum accumulated plastic strain increases approximately linearly with the number of loading cycles and occurs close to the instantaneous slip-stick boundary.

Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo–Mindlin problem revisited

Classically, the transition from stick to slip is modelled with Amonton–Coulomb law, leading to the Cattaneo–Mindlin problem, which is amenable to quite general solutions using the idea of superposing normal contact pressure distributions – in particular superposing the full sliding component of shear with a corrective distribution in the stick region. However, faults model in geophysics and recent high-speed measurements of the real contact area and the strain fields in dry (nominally flat) rough interfaces at macroscopic but laboratory scale, all suggest that the transition from ‘static’ to ‘dynamic’ friction can be described, rather than by Coulomb law, by classical fracture mechanics singular solutions of shear cracks. Here, we introduce an ‘adhesive’ model for friction in a Hertzian spherical contact, maintaining the Hertzian solution for the normal pressures, but where the inception of slip is given by a Griffith condition. In the slip region, the standard Coulomb law continues to hold. This leads to a very simple solution for the Cattaneo–Mindlin problem, in which the “corrective” solution in the stick area is in fact similar to the mode II equivalent of a JKR singular solution for adhesive contact. The model departs from the standard Cattaneo–Mindlin solution, showing an increased size of the stick zone relative to the contact area, and a sudden transition to slip when the stick region reaches a critical size (the equivalent of the pull-off contact size of the JKR solution). The apparent static friction coefficient before sliding can be much higher than the sliding friction coefficient and, for a given friction fracture “energy”, the process results in size and normal load dependence of the apparent static friction coefficient. Some qualitative agreement with Fineberg's group experiments for friction exists, namely the stick–slip boundary quasi-static prediction may correspond to the arrest of their slip “precursors”, and the rapid collapse to global sliding when the precursors arrest front has reached about half the interface may correspond to the reach of the “critical” size for the stick zone.

FINITE ELEMENT SIMULATION OF HOT ROLLING PROCESS FOR SiCp/Al COMPOSITES

In this work, the hot rolling process of SiCp/2009 Al composites is simulated using the fully coupled thermal-stress analysis in Abaqus/Explicit. By the investigation of formation process for rolling along with different fields of temperature, strain rate, strain and stress and their evolutionary history, the hot rolling mechanisms under complicated stress states is achieved. The results show that the maximum principal stress changes from compressive stress to tensile stress at the stage of rolling entrance and a reverse trend replaces it at the exit, and that the compressive stress is dominant in the deformation zone at the steady rolling stage. The temperature drop effect due to heat transfer is far greater than the temperature rise effect due to friction on the plate surface while the temperature rise is embodied in the center due to plastic deformation. Besides, the effect of strain rate on flow stress plays a leading role at the entrance and exit stage, and the flow stress on the plate surface in the deformation region is mainly determined by strain and temperature except the stick zone which is controlled by strain rate, however, the center flow stress in deformation is mainly affected by temperature.

Experimental simulation of rolling–sliding contact for application to planetary roller screw mechanism

The planetary roller screw mechanism is used in the aeronautics industry for electro-mechanical actuators application. It transforms a rotational movement into a translation movement, and it is designed for heavy loads. The main components are made of martensitic stainless steel, and lubricated with grease. Like most usual rolling mechanisms, smearing and jamming can occur before the theoretical fatigue lifetime, especially in defective lubrication conditions.The actuated load is carried by small contacts between the threads of the screw, the rollers and the nut. The static single contact can be described as an ellipsoid on flat contact; motion consists of rolling with sliding perpendicular to the rolling direction. A calculation method based on elastic theories (Hertz, Carter, Johnson) has been implemented. It calculates the normal and tangential stresses distributions, generated in the micro-slip and stick zones of the contact area, using several input parameters such as material properties, normal force, and creep ratio.A specific apparatus has been developed to support these calculations and to experimentally study the damage of the contacts in this mechanism. It consists of a freely rolling wheel loaded on a rotating disc with a component of sliding that simulates the roller screw contact. The tribometer inputs are the normal load, the speed, the creep ratio, and the lubrication. The wheel rolling speed and the tangential force generated in the direction perpendicular to rolling are measured.The experiments reveal a quick adhesive wear in dry or bad lubricated conditions, while a low friction coefficient remains if the contact is well lubricated. The influence of the input parameters concurs with the theoretical calculation. The evolution of grease lubrication during duty lifetime and the influence of the tribo-chemical films on this lifetime are also studied.

Two-dimensional symmetric double contacts of elastically similar materials

The two-dimensional contact problem for an elastic body indenting an elastically similar half plane resulting in double contacts is important for various applications. In this paper, a generic quasi-static two-dimensional symmetric double contact problem with nonsingular end points between two elastically similar half planes, under the constant normal and oscillatory tangential loading, is analyzed. The classical singular integral equations approach is utilized to extract the pressure and shear functions in the contact zones; subsequently boundary conditions at end points are applied and a new side condition is derived and titled “the consistency condition” for symmetric double contacts. This condition is necessary for determining the extent of the contact and stick zones. Next, this analytical approach is applied to the symmetric indentation of a flat surface by two rigidly interconnected wedge-shaped punches.

A numerical and effective method for the contact stress calculation of elliptical partial slip

A general elliptical Hertzian contact, such as a ball rolling in a non-conforming groove or two non-orthogonal cylinders, is a universal phenomenon in engineering. A partial elliptical contact is formed by contact bodies under a normal force and a transverse force that is insufficient to cause complete sliding. A computational model based on the semi-analytical method is established to calculate the von Mises stress distribution. Furthermore, a parametric study on factors influencing the location of the maximum von Mises stress point, such as the coefficient of friction and stick zone ratio, is conducted. Results show that the location of the maximum von Mises stress point depends on the coefficient of friction f and stick zone ratio c. The von Mises stress increases significantly with the increasing coefficient of friction f. Moreover, the maximum von Mises stress point tends to occur at a subsurface when the stick ratio c increases.

Investigation on the Interaction between Plasticity Response and Fretting Wear under Partial Slip Condition

The fretting wear behavior of Ti-6Al-4V is studied with the focus on cyclic plasticity effect under partial slip condition. The analysis is simulated using finite element based method with a new worn surface profile model represent a given number of cycles using a cylinder-on-flat geometry. The effect of surface modification on the stresses and plastic strain distribution is studied. As the profiles become deeper and wider, the contact pressure and shear stress increase at the stick zone. Due to this increment, the accumulation of plastic strain will become more significant. This may lead to material’s ductility exhaustion that could initiate the nucleation of crack. Plastic deformation is predicted to occur in the 6000th cycle model and onwards. Overall the relationship of fretting wear and plasticity has been defined qualitatively.

Stick, partial slip and sliding in the plane strain micro contact of two elastic bodies.

The plane strain problem of a curved elastic body pressed against an elastic half-space is considered. The effect of adhesion is included through the use of surface energy in a manner similar to the well-known JKR theory for spherical contacts. The compressive normal force is held constant while a tangential force is gradually increased from zero. The contact is characterized by complete stick up to a critical value of the tangential force when there is a transition either directly to complete sliding or to a partial slip state in which a central stick region is surrounded by two slip regions. In the latter case, at a finite value of the stick zone width, a second critical condition exists at which there is a transition from partial slip to complete sliding. This behaviour is determined for a range of dimensionless values of the work of adhesion, the assumed constant shear stress during slip/sliding and the initial compressive load.

Shear traction and sticking scope of frictional contact between two elastic cylinders

In this study, the frictional contact with partial slide between two dissimilar elastic cylinders is considered. According to the Spence׳s self-similarity condition, a system of singular integral equations is constructed with respect to the normal pressure and the shear traction in the contacting area. Based on the Goodman׳s hypothesis, the preceding system is uncoupled. From this, the tangential load in the central sticking zone is possible to be obtained analytically by means of the theory on the singular integral equation. Besides, a nonlinear equation in regard to the ratio of the adhesive and slip zone sizes is derived on the basis of the continuity of the tangential load. The sticking zone size can thus be determined by solving the nonlinear equation mentioned above iteratively. The problem in question is additionally solved by utilizing numerical method to make verification and validation of the theory and the related prevision found in the present paper. Numerical examples are provided to instantiate the theroy and method proposed.

Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions

We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a ‘friction cone’, but the exact position of any ‘stuck’ node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle.Here we prove that if the elastic system is ‘uncoupled’, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique ‘permanent stick zone’ T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions.Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs’ mismatch parameter β=0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

Analysis of corner filling behavior during tube hydro-forming of rectangular section based on Gurson–Tvergaard–Needleman ductile damage model

Friction plays an important role in the corner filling behavior during hydro-forming of rectangular section. In order to study the variation in corner filling behavior with internal pressure under the condition of different coefficients of friction, Gurson–Tvergaard–Needleman ductile damage model was used to describe material deformation involving damage evolution. First, an experimental–numerical hybrid method was applied to determine the parameters of critical porosity and failure porosity in Gurson–Tvergaard–Needleman ductile damage model. Second, a model describing the deformation behavior was established, in which the deformation zone was divided into three parts: sticking zone, sliding zone and corner zone. Third, the effect of coefficient of friction on the corner filling process was studied through simulation and experiments. The results show that as the internal pressure increases, the sticking zone starts at certain pressure and increases rapidly until taking over the whole contact length. Sticking friction will lead to greater thinning, and bursting occurs rapidly at the transition zone. Furthermore, the increase in the coefficient of friction will lead to greater variation in thinning and corner radius. For µ = 0.05 in experiments, corner filling is acceptable without bursting, correspondingly the final internal pressure is 67 MPa.

Numerical Analysis of the Effect of Slip Ratio on the Fatigue Crack Initiation Life in Rolling Contact

This paper presents a numerical analysis of the effect of slip ratio on the fatigue crack initiation life, considering the tangential traction on the rolling contact surface. The distribution of tangential traction and contact stresses on the contact surface, when rolling contact occurs between two cylindrical test specimens, are obtained using three-dimensional finite element analysis. The effect of slip ratio on the fatigue crack initiation life was evaluated by applying multiaxial fatigue criteria based on critical plane approaches. As a result, the 3D-FE model developed well represent the distribution of tangential traction and contact stresses on the contact surface at stick-slip condition, which is differ from the static or full sliding contact condition. As the slip ratio increases, the maximum tangential traction also increases in slip zone and the location of maximum stress closer to the contact surface in stick zone. The fatigue strength decreased with the increase in the slip ratio. Therefore, it is clear that the slip ratio has an important role in prediction of fatigue crack initiation life on the rolling contact surface.

Frictional contact FE analysis in a railway wheel-rail contact

Our investigation aimed to analyse the contact pressure distribution, the contact area and the sliding procedure in a railway wheel-rail contact by using finite element method. The analysis were created with linear elastic material model. The elaborated model provides opportunity to analyse the initial sticking zone within the contact zone that disappears and transforms into full sliding contact due to the tangential displacement of the contact zone. In that state we examined the equivalent stress distribution under the surface in full sliding condition as well.

Interference assembly and fretting wear analysis of hollow shaft.

Fretting damage phenomenon often appears in the interference fit assembly. The finite element model of hollow shaft and shaft sleeve was established, and the equivalent stress and contact stress were computed after interference assembly. The assembly body of hollow shaft and shaft sleeve was in whirling bending load, and the contact status (sticking, sliding, and opening) and the distribution of stress along one typical contact line were computed under different loads, interferences, hollow degrees, friction coefficient, and wear quantity. Judgment formula of contact state was fixed by introducing the corrected coefficient k. The computation results showed that the “edge effect” appears in the contact surface after interference fit. The size of slip zone is unchanged along with the increase of bending load. The greater the interference value, the bigger the wear range. The hollow degree does not influence the size of stick zone but controls the position of the junction point of slip-open. Tangential contact stress increases with the friction coefficient, which has a little effect on normal contact stress. The relationship between open size and wear capacity is approximately linear.

Third body modeling in fretting using the combined finite-discrete element method

A new approach was developed for modeling the effect of the third body on fretting. This was accomplished using the combined finite-discrete element method (FDEM) in which the third body is analyzed as discrete elements while the first bodies are modeled using finite elements. This approach provides a link between large scale models which treat the mass of wear debris as a single or small number of bodies and small scale models which only study a control volume. The FDEM was used to analyze the behavior of third body particles between flat sliding surfaces. When the third body mass is composed of unconnected particles, it behaves as a Newtonian fluid, but this behavior ceases when the particles are connected into platelets. The FDEM was also used to study the behavior of third body particles inside a Hertzian line contact. As the number of particles and platelet size increase the load carried by the worn slip zone grows larger in relationship to the unworn stick zone.

Finite Element Analysis of Fretting Wear for Nuclear Inconel 690 Alloy

Finite element method to analyze the fretting wear characteristics based on Hertz theory, Coulomb friction law and a modified Archard wear equation, has been applied to a cylinder-on-flat configuration for typical steam generator tube material Inconel 690 alloy and typical anti-vibration bar material Inconel 600 alloy (Cr plating) in the nuclear power plant, under gross slip and partial slip conditions. The evolutions of contact profile, surface contact variables with increase in wear cycles are predicted. The slip regime is predicted to have significant effects on the fretting wear behavior. Under the gross slip regime, it is found that the peak contact pressure occurs at the center of the contact scar, and the actual relative slip is slightly smaller than the applied value. The contact width increases, and the peak pressure decreases gradually with increase in wear cycles. Whereas under the partial slip regime, the peak contact pressure occurs at the stick-slip boundary, the actual relative slip is much smaller than the applied value, and no relative slip occurs in the stick zone. The contact width increases gradually, and the peak pressure increases rapidly with increase in wear cycles.

Analysis of stress states in compression stage of high pressure torsion using slab analysis method and finite element method

High pressure torsion (HPT) is useful for achieving substantial grain refinement to ultrafine grained/nanocrystalline states in bulk metallic solids. Most publications that analyzed the HPT process used experimental and numerical simulation approaches, whereas theoretical stress analyses for the HPT process are rare. Because of the key role of compression stage for the deformation of HPT, this paper aims to conduct a theoretical analysis and to establish a practical formula for stress and forming parameters of HPT process using the slab analysis method. Three equations were obtained via equations derivation to describe the normal stress states corresponding to the three zones of plastic deformation for HPT process as stick zone, drag zone and slip zone. As to the compression stage of HPT, the stress distribution results using the finite element method agree well with those using the slab analysis method. There are drag and stick zones on the contact surface of the HPT sample, as verified by the finite element method (FEM) and slab analysis method.

Shear Traction and Sticking Scope of Frictional Contact between Two Elastic Cylinders

In this study, the frictional contact with partial slide between two elastic cylinders is considered. According to the Spence’s self-similarity condition, a system of singular integral equations is constructed with respect to the normal pressure and the shear traction in the contacting area. Based on the Goodman’s hypothesis, the preceding system is uncoupled. Based on this, the tangential load in the central sticking zone is possible to be obtained analytically by means of the theory on the singular integral equation. Besides, a nonlinear equation with respect to the ratio of the slip and adhesive zone sizes is derived on the basis of the continuity of the tangential load. The stick zone size can thus be determined by solving the nonlinear equation mention above iteratively. A numerical example is provided to verify and validate the theory proposed in this work.

Location of the first yield point and wear mechanism in torsional fretting

Material wear in the contact area may lead to fatigue failure of a structural component under torsional fretting. It is necessary to investigate the wear mechanisms accompanying torsional fretting, especially during the unloading process. This paper intends to analyze the torsional stress field during loading and unloading processes and to explore the link between fretting wear and the location of material first yield, for which a parametric study on factors influencing this location, such as coefficient of friction and stick zone ratio, is committed. Because the surface shear traction is complex during the unloading process, the subsurface stress field is calculated by means of an efficient semi-analytical method. The relationship between the first yield location and wear mechanism is examined through observations of worn surfaces from a set of torsional fretting experiments.

Frictional dissipation in elastically dissimilar oscillating Hertzian contacts

We consider the problem of a cyclic Hertzian indentation between elastically dissimilar materials. In the case of loading, the problem was solved by Spence in a series of seminal papers, where he proved a relationship between the solution for a rigid square-shaped punch, to that for a power-law indenter. For example, the stick area is a constant ratio of the contact area, independently on the shape of the punch. “Unfortunately”, on unloading, many of the simple properties of the self-similar loading case are lost, there is a complicated development of an external region of slip which cycles in the two directions (forward and back-slip), and an inner region which continues to slip in the forward direction of the first loading cycle. However, this inner region gradually disappears, and further cyclic loading generates a convergence to a steady state solution which involves residual “locked-in” tangential slip displacements in a permanent stick zone, provided the contact is not fully unloaded. Dissipation in the steady state therefore occurs only in the external region of slip, and we provide some results for the energy dissipation per cycle, as a function of the governing parameters: coefficient of friction, Dundurs’ dissimilarity constant, normal load amplitude. We also show the likely independence of energy dissipation on initial conditions, limited to the possible scenario of overloading. It is seen that dependence of energy dissipation per cycle on load amplitude is closer to quadratic than to cubic, and this may explain some experimental findings which so far were not expected from oscillatory loading of elastically similar half-spaces.