Axisymmetric Asperities Research Articles

Numerical analysis on the adhesive contact between a rigid power-law shaped axisymmetric asperity and an elastic half-space

There exist many well-known analytical models for adhesive contact for spherical asperities. However, in many situations, the asperities are not spherical and may be better described by a power-law function. Thus, these well-known analytical models were extended to power-law-shaped axisymmetric asperities in the past decades. In this paper, numerical simulation is employed for the adhesive contact between a rigid power-law axisymmetric asperity and an elastic half-space. The realistic Lennard-Jones potential and the Derjaguin approximation are used for the surface traction. Numerical simulations are performed with different shape indexes and different Tabor parameters. The whole solution is obtained. Semi-empirical formulas for the pull-off forces, the contact radius at zero loads, the jump-in distance, and the pull-off distance are proposed. All these equations are both simple and as accurate as of the numerical simulations.

Surface initiation of rolling contact fatigue at asperities considering slip, shear limit and thermal elastohydrodynamic lubrication

Abstract A numerical investigation was performed, with single axisymmetric asperities passing through lubricated rolling contacts at different slip. Two explanatory and cooperating phenomena were found as to why the damage develops more frequently at negative than positive slip. Metal contact occurred in the inlet, where tractive asperity contacts at negative slip provided a large tensile surface stress outside the contact. As the asperity moved through the contact, sliding supplied it with lubricant and heated the lubricant along the contact. The shear tractions were thus higher near the inlet than the outlet, making them more detrimental for negative than positive slip.

A dynamic friction model for the pre‐sliding behavior of a tangentially loaded single asperity contact

AbstractWe introduce a dynamic friction model for the pre‐sliding behavior of a single asperity subjected to a constant normal and a varying tangential load based on Cattaneo‐Mindlin's theory. The geometry of an arbitrary, axisymmetric asperity is included in the formulation of the governing differential equation. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computational modelling of constrained sintering in EB-PVD thermal barrier coatings

A micromechanical model is developed to simulate the evolution of microstructure during in-service sintering and eventual inter-columnar cracking in coatings made using electron beam vapour deposition (EB-PVD) route. The coating is idealized with a discrete distribution of axisymmetric asperities across interfaces between columnar grains. The model assumes that inter-columnar sintering is driven by changes in interface free energy of columns and the potential energy of the applied stress. Much faster diffusion that occurs over the free surfaces of the asperities is neglected. It is further assumed that the rate of sintering of the contacting asperities is determined by diffusion along the interface between the contacting asperities. Time evolution of contact modulus of the coating is accounted for as a function of sintering strain. The developed macroscopic constitutive model is employed to evaluate the sensitivity of the sintering response to imperfections and examine the conditions under which inter-columnar cracks can develop within the coating.

Adhesive Elastic Contact of Rough Surfaces with Power-Law Axisymmetric Asperities

The contact model for rough surfaces with power-law axisymmetric asperities in the presence of adhesion is developed. The extended JKR adhesive contact model for power-law axisymmetric asperities, denoted as JKR-n, developed by Zheng and Yu (2007,“Using the Dugdale Approximation to Match a Specific Interaction in the Adhesive Contact of Elastic Objects,” J. Colloid Interface Sci., 310, pp. 27–34) is utilized to investigate the adhesive contact of rough surfaces. The JKR-n adhesive contact model generalizes the most adopted JKR model for spherical objects of n = 2. This work compares the effect of surface roughness on the adhesion force for rough surfaces with various power-law axisymmetric asperities. It is found that shapes of the asperities influence the pull-off forces greatly during the separation of rough surfaces. A general adhesion parameter that includes the shape index of asperities is proposed, and it can be used to characterize the adhesion performance of rough surfaces.

Stress Transfer During Pressure Solution Compression of Rigidly Coupled Axisymmetric Asperities Pressed Against a Flat Semi-Infinite Solid

In a previous work, we developed a numerical model of compression by pressure solution (PS) of a single axisymmetric asperity pressed against a flat semi-infinite solid. The dissolution rate at any point along the contact and at any time t was determined by (1) computing the normal stress distribution from the current shape of the asperity, and (2) solving the diffusion equation inside the fluid-saturated solid-solid interface, including local dissolution source terms corresponding to the stress field previously determined. The change in shape of the asperity during an infinitesimal time interval δt can then be calculated and the entire procedure repeated as many times as desired. Our results showed that, as the contact flattens and grows during PS, the initial elastic deformation is partially relaxed and the stress transferred from the contact center to the edge. Our goal in the present paper is to demonstrate that, among a population of asperities, stress can also be transferred from one contact to another and that the overall compaction rate can be significantly affected by this process. For this purpose we extended our previous numerical model to simulate PS of two rigidly coupled spherical asperities simultaneously pressed against a flat semi-infinite solid. We considered two end-member cases: 1) transfer of stress to a newly created, not initially present contact, 2) transfer of stress between asperities with different sizes. In both cases, stress was transferred from the most stressed asperity to the least, and, the overall PS displacement rate was reduced. Thus, formation of new contacts and heterogeneous distribution of asperity sizes, which are both expected to exist in rough fractures with self-affine aperture or in heterogeneous granular materials with variable grain-packing geometry, may significantly slow down PS creep compaction.

Surface stresses at an axisymmetric asperity in a rolling contact with traction

Rolling contact between a smooth cylinder and a cylinder with an axisymmetric surface asperity was modelled numerically. The influence of tangential slip and friction was investigated through relative contact movement between the cylinders. As the asperity entered the rolling contact it acted as a point type contact force, which gave a tensile surface stress in the forward rolling direction. The tensile stress maximum was greatly influenced by slip and coefficient of friction. Data for the simulations were captured from a gear example with surface initiated rolling contact fatigue or spalling. The cylindrical contact load and geometry corresponded to that at the roll-circle of the gear. The geometrical properties of the asperity were based on surface profiles of the gear flank. The combined isotropic and non-linear kinematic Chaboche material model was used with parameters determined from cyclic compression–tension tests on the gear material. The residual stress profile due to heat-treatment of the gear was included into the model. Two different frictional set-ups were investigated. One contained a non-zero coefficient of friction throughout the rolling contact. This was believed to compare to dry contacts. The other set-up was supposed to model lubricated rolling with asperity break-through to metal contact. Here friction was non-zero on the asperity and zero elsewhere in the contact. With traction throughout the cylindrical contact a sufficiently long start distance had to be travelled before the asperity interaction. Thus, the transient rolling distance was determined together with the slip limit for sliding in the cylindrical contact. Numerical predictions of residual stresses and surface distress angles suggested that the asperity friction model agreed with gear conditions. Evaluation of elastic–plastic asperity indentation suggested that the asperity deformation was approximately as severe as repeated macro-scale experiments with fatigue cracks. Since the stresses at the asperities were of the same size as those at the repeated indentations and since the Findley multi-axial fatigue criteria predicted fatigue damage, it was concluded that the stresses in front of the asperity could be sufficient to initiate rolling contact fatigue cracks in applications. The influences of some parameters on the stress maximum were also evaluated.

Numerical modelling of pressure solution deformation at axisymmetric asperities under normal load

Abstract We developed a numerical model of compression of asperities by pressure solution (PS). The dissolution rate along the contact was determined by (1) computing the normal stress distribution from the present shape of the asperities, and (2) solving the diffusion equation inside the fluid-saturated solid–solid interface, including local dissolution source terms corresponding to the stress field previously determined. The change in shape of the asperities during an infinitesimal time interval can then be calculated and the entire procedure repeated as many times as desired. We simulated PS compaction of axisymmetric asperities with different sizes and shapes under various temperatures and loads, and using different values of the interface diffusion coefficient. Our results show that as the contact flattens and grows during PS, the initial elastic deformation is partially relaxed and the stress transferred from the contact centre to the edge. Transient stress release remains significant during an extended period and could strongly influence the interpretation of laboratory experiments. In our model, dissolution and interface diffusion are not sequentially combined as is usually assumed, making it impossible to identify a single rate-limiting process. The convergence rate of the asperities was approximately proportional to the mean effective stress at the contact, and depended in a complex way on the contact radius, but was not sensitive to the asperity size. We also estimated the conditions under which undercutting at the contact edge is triggered.

Influence of a single axisymmetric asperity on surface stresses during dry rolling contact

The effect from contact loading of some single axisymmetric asperities as a potential mechanism for surface initiated rolling contact fatigue was investigated numerically using FEM. Computational results were compared to properties of some rolling contact fatigue craters, or spalls, in the teeth surfaces of four driving gear wheels. The gears were geometrically identical but had experienced slightly varying load conditions. The residual surface stresses of a used teeth with spalls were measured using the hole drilling technique. The combined cylinder asperity contact was first modelled with a stationary model in which an asperity was introduced at the contact rim. By varying asperity height, width, position and contact load dangerous asperity configurations were sought for. The gear contact close to the rolling circle was modelled as two rolling cylinders. A single asperity was introduced into the contact surface of one of them. Due to the presence of the asperity a three-dimensional contact model was required. The simulation included residual stresses from heat treatment and plastic deformation due to the first roll cycle. Thus, the stress results were computed from the second roll cycle. The important overall conclusion was that a single asperity may serve as a stress raiser in the contact surfaces. Furthermore, the computed values of the increased surface stresses were comparable to those that are reported in the literature to give cracks. Example of dangerous asperity dimensions were noted and changes in residual stresses from moderate plastic deformation during rolling were estimated. The asperity deformed plastically during over-roll but remained sufficiently high. The trajectory of the largest principal stress was computed, starting from the position in front of a loaded asperity with maximum tensile stress. The trajectory was compared to the spalling entry angle of a representative spall. For some asperity-cylinder configurations a convex region with large stress was found in the surface. The presence of such a convex stress region was compared to the convex shaped of the spalling tip that sometimes could be found.

Adhesion of elastic spheres

Bradley (1932) showed that if two rigid spheres of radii R 1 and R 2 are placed in contact, they will adhere with a force 2πΔ R γ, where R is the equivalent radius R 1 R 1 /( R 1 + R 2 ) and Δγ is the surface energy or ‘work of adhesion’ (equal to γ1+γ2-γ12). Subsequently Johnson et al. (1971) (JKR theory) showed by a Griffith energy argument (assuming that contact over a circle of radius a introduces a surface energy -π a 2 Δγ) how the Hertz equations for the contact of elastic spheres are modifed by surface energy, and showed that the force needed to separate the spheres is equal to (3/2)πΔ R γ, which is independent of the elastic modulus and so appears to be universally applicable and therefore to conflict with Bradley9s answer. The discrepancy was explained by Tabor (1977), who identified a parameter 3 Δγ 2 / 3 / E * 2 / 3 \e governing the transition from the Bradley pull-off force 2π R Δ|γ to the JKR value (3/2)π R Δγ. Subsequently Muller et al. (1980) performed a complete numerical solution in terms of surface forces rather than surface energy, (combining the Lennard–Jones law of force between surfaces with the elastic equations for a half-space), and confirmed that Tabor9s parameter does indeed govern the transition. The numerical solution is repeated more accurately and in greater detail, confirming the results, but showing also that the load–;approach curves become S-shaped for values of μ greater than one, leading to jumps into and out of contact. The JKR equations describe the behaviour well for values of μ of 3 or more, but for low values of μ the simple Bradley equation better describes the behaviour under negative loads.