Fractal Research of Pore-Structure in Porous Titanium Fibers

Abstract

This paper adopted the vacuum sintering technology to prepare titanium fiber porous material with a three-dimensional spatial network fiber backbone and connectivity pore structure. With the help of fractal geometry theory and scanning and digitizing the image, the fractal research of pore-structure in porous titanium fibers is executed and we studied the influence of adopting the box-counting dimension method to calculate the fractal dimension. Additionally, we determined the quantitative relationship between fractal dimension and the porosity of the porous in titanium fiber, while described the physical meaning of the fractal dimension.

An experimental and analytical study based on fractal theory of satin fabrics in unsaturated permeability

“…Studies show that fiber preform is a fractal. [37][38][39] Thus, based on fractal theory, fiber preform satisfies the following equations 28 NðÞ¼…”

“…Studies show that fiber preform is a fractal. 37–39 Thus, based on fractal theory, fiber preform satisfies the following equations 28 where p(λ) is a density function of the equivalent diameter and L represents the characteristic quantity that is used to describe a fractal medium. L 0 is the representative length of a channel, L t ( λ ) is the physical length of the channel of which equivalent diameter equals λ (see Figure 3), ϕ is the porosity of the porous medium, λ is the equivalent diameter of a tortuous channel, and N ( λ ) the number of channels whose diameters are greater than λ .…”