Stick Contact Condition Research Articles

The Effect of Surface Roughness on Static Friction and Junction Growth of an Elastic-Plastic Spherical Contact

A model for elastic-plastic spherical contact of rough surfaces under combined normal and tangential loadings, with full stick contact condition, is presented. The model allows evaluation of the effect of surface roughness on the real contact area, static friction and junction growth under small normal loads. It is shown that as the normal load approaches a certain threshold value, which depends on the plasticity index, the results of the present rough surface model approach these of previous corresponding models for smooth sphere and a rigid flat. At normal load values below the threshold load, the correlation of the present results and published experimental results is much better in comparison with the results of the smooth surface models.

A Model for Contact and Static Friction of Nominally Flat Rough Surfaces Under Full Stick Contact Condition

A model for elastic-plastic nominally flat contacting rough surfaces under combined normal and tangential loading with full stick contact condition is presented. The model incorporates an accurate finite element analysis for contact and sliding inception of a single elastic-plastic asperity in a statistical representation of surface roughness. It includes the effect of junction growth and treats the sliding inception as a failure mechanism, which is characterized by loss of tangential stiffness. A comparison between the present model and a previously published friction model shows that the latter severely underestimates the maximum friction force by up to three orders of magnitude. Strong effects of the normal load, nominal contact area, mechanical properties, and surface roughness on the static friction coefficient are found, in breach of the classical laws of friction. Empirical equations for the maximum friction force, static friction coefficient, real contact area due to the normal load alone and at sliding inception as functions of the normal load, material properties, and surface roughness are presented and compared with some limited available experimental results.

Discussion: “A Greenwood–Williamson Model of Small-Scale Friction” (Jones, R. E., 2007, ASME J. Appl. Mech., 74, pp. 31–40)

The author is to be commended for his attempt to cope analytically with the complex problem of friction. A few comments regarding the present paper are in place. The present simplified friction model is essentially based on the 1949 Mindlin approach (see Ref. 1). According to this concept, it is assumed that the contact area of an elastic spherical asperity is given by the frictionless Hertz solution (see Eq. (2)) and that slip of such an asperity will ensue when the average shear stress at its contact area reaches a critical value (see Eq. (6)). These simplifying assumptions may lead to some unrealistic situations where the local equivalent von Mises stress in the contact interface can exceed the yield strength of the sphere material. Additional shortcomings of the Mindlin concept is that an increase of the contact area due to the tangential load is completely excluded, and that sliding inception always occurs in the contact interface of each asperity regardless of its level of normal loading. This would contradict the well known phenomena of junction growth and material transfer, where the latter requires slip below the contact interface. In this regard, it is worthwhile mentioning a different approach to sliding inception of a single spherical asperity (2) and to modeling of static friction of contacting rough surfaces 3. These papers are not limited to elastically deformed asperities, and in Ref. 3 adhesion effect was also considered. However, these two models still assume, like in the present paper, that the contact area resulting from a frictionless normal loading is unaffected by the additional tangential load. A more realistic model was recently presented in two papers by Brizmer et al. assuming full stick contact condition for both normal and tangential loadings (see Refs. 45). The full stick contact condition captures very well the concept of an adhesive joint formed in the contact interface. It does not require simplifying assumptions regarding the size of the contact area and the location of slip at the contact interface; therefore, it never violates the von Mises yield criterion. Furthermore, it utilizes first principles to predict the sliding inception at the instant of vanishing tangential stiffness (as shown in Fig. 1 of the present paper) and to obtain the resulting corresponding static friction and junction growth. Since the full stick contact condition does not impose slip at the contact interface, it allows for the possibility of material transfer under severe normal loads. Additionally, the results of Refs. 45 correlate well with some preliminary experimental results obtained by Ovcharenko et al. (6).

In situ investigation of the contact area in elastic–plastic spherical contact during loading–unloading

The real contact area between a sphere and a flat during loading, unloading, and cyclic loading–unloading in the elastic–plastic regime of deformations was investigated experimentally. A direct optical technique was used to observe in situ the evolution of the contact area. The experimental results obtained with copper and stainless steel spheres of different diameters that were pressed against a sapphire flat were compared with existing theoretical models, and whenever possible, with previous experimental works. These models are based on the assumption of either perfect slip (i.e., frictionless) or full stick contact condition. Good agreement was found between the experimental and theoretical results for the contact area and mean contact pressure. The existing models for the unloading process fail to accurately predict the residual radius of curvature of fully unloaded spheres, and the irreversibility of multiple loading unloading cycles at least for the several initial cycles. Some recommendations to improve the models are provided.

Elastic–plastic spherical contact under combined normal and tangential loading in full stick

The behavior of an elastic–plastic contact between a deformable sphere and a rigid flat under combined normal and tangential loading with full stick contact condition is investigated theoretically. Sliding inception is treated as a plastic yield failure mechanism, which allows static friction modeling under highly adhesive conditions. Several contact parameters such as: junction tangential stiffness, static friction force and static friction coefficient are extensively investigated. The phenomenon of junction growth and the evolution of the plastic zone in the contact region are briefly described. It is found that at low normal dimensionless loads the static friction coefficient decreases sharply with increasing normal load, in breach with the classical laws of friction. As the normal load further increases the static friction coefficient approaches a constant value that is about 0.3 for many material properties combinations.

Contact conditions and surface degradation mechanisms in low amplitude fretting

The characteristic contact conditions and mechanisms of surface degradation in low amplitude (1–16 μm) fretting have been investigated. A crossed cylinder geometry set-up was used with pure niobium as test material. Fretting experiments, varying displacement amplitude, normal force, frequency of vibration and number of cycles, have been performed. Dynamic tangential force measurements and metallographic examination revealed the existence of three different fretting regimes: stick, mixed stick and slip, and gross slip. In the study, the influence of normal force and frequency on the regime boundaries was determined. Niobium was selected as test material since it is a pure metal with strongly strain-rate-dependent mechanical properties and, therefore, is expected to be sensitive to frequency-related effects in fretting. The size of the fretting wear scar was found to increase rapidly with increasing amplitude. The wear rates were significantly higher in the gross slip regime in which material removal predominantly occurred by delamination and crushing of surface oxides. Surface degradation and wear were also observed under partial stick contact conditions. In this case, wear was mainly due to the generation and intersection of surface cracks. The extensive crack formation is caused by the cyclic shearing of material in the near-surface region during fretting. The frequency of vibration is found to influence both the contact conditions and the rate of surface damage. The limiting displacement amplitude to yield partial stick conditions is reduced and the size of the wear scar is increased with increasing frequency (in the range 10–20 000 Hz). This is an effect of the increase in both the interfacial strain rate and the temperature with increasing frequency.