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The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.

For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.

An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.

This law is only valid as long as the creep is of the size of the surface roughness. The modified model admits an analytical solution for the case when the behavior is linear viscoelastic. The proposed model shows a good agreement when compared with experimental results available in the literature.

The objective of this paper is to construct a continuous model for the viscoelastic contact of a nominal flat punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied load. The proposed model assumes the punch surface material to behave according to Kelvin‐Voigt viscoelastic material. The punch surface, which is known to be fractal in nature, is modelled in this work using a deterministic Cantor structure. An asymptotic power law, deduced using iterative relations, is used to express the punch surface approach as a function of the remote force when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

The objective of this paper is to construct a continuous model for the thermo‐visco‐elastic contact of a nominal flat, non‐smooth, punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied loads and temperatures. The proposed model assumes the punch surface material to behave according to the linear Kelvin‐Voigt visco‐elastic material. The punch surface, which is known to be fractal in nature, is modeled in this work using a deterministic Cantor structure. An asymptotic power low, deduced using approximate iterative relations, is used to express the punch surface approach as a function of the remote forces and bulk temperatures when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact.

The rough surfaces, known to be physical fractal, are modelled using a deterministic Cantor structure. Such structure shows several levels of imperfections and including, therefore, several scales in the constriction of the flux lines. The proposed model will study the effect of the deformation (approach) of the two rough surfaces on the TCC as a function of the remotely applied load.

An asymptotic power law, derived using approximate iterative relations, is used to express the area of contact and, consequently, the thermal conductance as a function of the applied load. The model is valid only when the approach of the two surface in contact is of the order of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results both in trend and the numerical values.

The model obtained provides further insight into the effect that surface texture has on the heat conductance process. The proposed model could be used to conduct an analytical investigation of the thermal conductance of rough surfaces in contact. This model, although simple (composed of springs), nevertheless works well.