Elastic–Plastic Spherical Contact Modeling Including Roughness Effects

Abstract

The effect of material properties and surface roughness on the contribution of asperities and sphere bulk displacements to the total displacement of a rough spherical contact is investigated. A dimensionless transition load, above which the contribution of the bulk displacement exceeds the contribution of the asperities displacement, is found as a function of the plasticity index and dimensionless critical interference of the sphere bulk. A criterion is proposed for evaluating the importance of surface roughness in calculating the displacement of a rough spherical contact. Some experimental results with a spherical micro-contact are presented to verify the model.

The Effect of Asperity Flattening During Cyclic Normal Loading of a Rough Spherical Contact

“…2 yields values of the shell parameter k about 1 for both dimple types. Therefore, the following analysis for the rough dimple contact behavior will be based on a rough solid sphere contact model presented in reference [31]. The critical load P c at yield inception can be obtained from Eq.…”

“…Hence, the bulk of the dimples under examination is elastically deformed and can be analyzed as a solid sphere in elastic contact. Figure 11 presents an equivalent rough spherical contact model that was studied theoretically by Li et al [31]. In reference [31], a model was developed for the effect of the dimensionless normal load P * , the dimensionless critical interference x à c and the plasticity index w, on the individual contributions of the sphere bulk and the asperities to the total displacement of a rough spherical contact.…”

“…Figure 11 presents an equivalent rough spherical contact model that was studied theoretically by Li et al [31]. In reference [31], a model was developed for the effect of the dimensionless normal load P * , the dimensionless critical interference x à c and the plasticity index w, on the individual contributions of the sphere bulk and the asperities to the total displacement of a rough spherical contact. In this model, the total dimensionless displacement c à ¼ c=r of the rough spherical contact is the sum of two displacement components: x à ¼ x=r (contributed by the sphere bulk alone), and h à 1 ¼ h 1 =r (contributed by the contacting asperities).…”

Finite Element Based Surface Roughness Study for Ohmic Contact of Microswitches

“…Since the roughness of the bridge is much inferior to that of the bump, only the roughness of the bump is taken into account; Which gives a contact between a spherical rough surface and a flat surface. Unlike contact between nominally flat surfaces, in a spherical rough contact, both contact asperities and the bulk deform under normal load [13]. Several works on spherical contact are found in the literature, while most of them deal with the contact between a rough flat and a smooth spherical [14][15], further the displacement is assumed to be elastic and/or purely plastic.…”

“…The work [16] studied the spherical rough contacts, with the deformation of asperities assumed to be purely plastic. More recently, references are given as, [13] and [17] analyzed the contact of a rough sphere and a rigid flat, with elastic, elastic-plastic and fully plastic regime considered for the deformation of the sphere and the asperities; however, the roughness of the sphere was transferred to the flat. Reference [18] found that the flatten models predict larger contact areas and higher loads than the indentation model at the same interference, and they cannot be replaced by each other.…”