Terms Of Fractal Parameters Research Articles

Fabrication and characterization of multiscale, fractal textured solar selective coatings

Photothermal conversion efficiency depends significantly on the selectivity of the thermal receiver surface through which a heat transfer fluid flows in a concentrated solar power system. This paper presents studies on novel multiscale, fractal textured solar selective coatings for solar thermal applications. The fractal surfaces are fabricated integrally on the substrate material using electrodeposition. The coatings are described in terms of fractal parameters that are uniquely determined from surface measurements, and the optical properties of the coatings are experimentally characterized in detail in terms of the fractal parameters. The effects of heat treatment on the optical properties of coatings over a range of fractal parameters are also described. The study is presented considering coatings on copper to demonstrate that fractal texturing of the surface provides a nearly three-fold performance improvement compared to coatings with no texturing or heat treatment. The findings equally apply to other materials used in higher temperature solar thermal applications.

An adhesion model for elastic-plastic fractal surfaces

The strong adherence (stiction) of adjacent surfaces is a major design concern in microelectromechanical system. The present research concerns the elastic-plastic adhesion of a rough surface contacting with a rigid flat. Rough surface is characterized by fractal geometry using a two-variable Weierstrass-Mandelbrot function [The Fractal Geometry of Nature (Freeman, New York, 1982)]. The microcontact model of single asperity is established in terms of fractal parameters, and the plastic adhesion model is also developed with the Dugdale approximation to consider the adhesive interaction within and outside the contact area. Then according to the plastic flow criterion, the Maguis-Dugdale transition theory [Adhesion of Adhesion and Rapture of Elastic Solids (Springer-Verlag, New York, 2005)] and the plastic adhesion model are used to solve the elastic-plastic adhesive interaction for the two approaching surfaces by incorporating the fractal surface model. Simulations of the adherence force versus the approaching distance of surfaces are performed. The necessity of considering the plastic deformation in microsized interface adhesion is also validated by comparing the result of the presented model with that of the Morrow model [J. Tribol 127, 206 (2005)]. The influence of fractal parameters on adherence force shows that controlling the surface topography is a readily means to control the adherence force for the elastic-plastic adhesion of rough surfaces, which is due to the intermolecular adhesive interactions.

A Mechanics Approach to Static Friction of Elastic–Plastic Fractal Surfaces

A contact mechanics theory of static friction is presented for isotropic rough surfaces exhibiting fractal behavior. The analysis is based on a piecewise power-law size distribution and a normal slope distribution of the asperity contacts and elastic–fully plastic deformation models. Numerical integration yields solutions for the normal and friction forces in terms of fractal parameters, elastic–plastic material properties, and interfacial shear strength. The variation of the static coefficient of friction with normal load is related to the effect of the surface topography on the dominant deformation mode at the asperity contacts. Plastic deformation of the smaller asperity contacts dominates at low loads and elastic deformation of the larger asperity contacts dominates at high loads. The critical load signifying the transition from predominantly plastic to elastic deformation depends on the fractal parameters and material properties. In the low-load range, the static coefficient of friction decreases with the increase of the load, while in the high-load range it increases with the load. Numerical results for copper fractal surfaces illustrate the effects of normal load, surface topography, and interfacial shear strength on the static coefficient of friction.

Determination of the optimum sampling interval for rough contact mechanics

It is well known that roughness parameters such as slopes, asperity densities and curvatures, which are needed to calculate contact mechanics, are not intrinsic properties of the surface but depend on the sampling interval. A method for choosing this sampling interval is proposed, based on Archard's observation that repetitive contact must be elastic. From a description of the rough surface as a self-affine fractal, the second moment of the power spectrum can be expressed in terms of fractal parameters which are intrinsic properties of the surface. The moment integral is then solved for its lower limit, which defines the tribologically appropriate sampling interval. Thus a relationship can be derived between three dimensionless numbers: the ratio of this critical wavelength to the topothesy; the fractal dimension; and the material property ratio. Measurements on two commercial hard disk drives are interpreted in terms of the model, and it is predicted that under realistic operating loads the real separation between slider and disk at rest is about 100 nm, with between 40,000 and 80,000 discrete contacts of 12–15 nm radius.

Contact analysis of elastic-plastic fractal surfaces

Rough surfaces are characterized by fractal geometry using a modified two-variable Weierstrass–Mandelbrot function. The developed algorithm yields three-dimensional fractal surface topographies representative of engineering rough surfaces. This surface model is incorporated into an elastic-plastic contact mechanics analysis of two approaching rough surfaces. Closed form solutions for the elastic and plastic components of the total normal force and real contact area are derived in terms of fractal parameters, material properties, and mean surface separation distance. The effects of surface topography parameters and material properties on the total deformation force are investigated by comparing results from two- and three-dimensional contact analyses and elastic and elastic-perfectly plastic material behaviors. For normal contact of elastic-perfectly plastic silica surfaces and range of surface interference examined, the interfacial force is predominantly elastic and the real contact area is approximately one percent of the apparent contact area or less, depending on the mean interfacial distance. The analysis can be easily modified to account for anisotropic fractal surfaces and different material behaviors.