Fractal simulation and characterisation : novel methods for analysing crack and fracture surface

Abstract

The visual characteristics of crack trajectories and fracture surfaces of common construction materials, such as concrete and rocks, are tortuous and irregular, owing to their disordered microstructure and pre-existing material inhomogeneities. With the development of fractal geometry founded by Benoit Mandelbrot since 1982 and the following research studies, fracture surfaces and crack profiles are believed to be fractal in nature. By understanding the fractal nature of materials and describing the surface morphology quantitatively, the underlying fracture mechanisms can be better understood, and the relationship between fracture surface characteristics and material fracture properties can then be established and studied. Before extensive work begins on correlating fractal dimension with other fracture-associated variables, it is important to choose appropriate methods of fractal analysis and to understand the limitation of different methods. This study builds on the fractal theory and contributes to the fractal simulation and characterisation techniques that capture the visual characteristics of crack pattern and fracture surface of common construction materials. It seeks to examine the possibility of simulating cracks and fracture surfaces by a random fractal model – fractional Brownian motion (fBm), and to assess the reliability and validity of different proposed fractal characterisation methods. Various fractal characterisation techniques on fractal profiles and fractal surfaces were performed and evaluated. Computer programmes in the Pascal programming language were written to generate synthetic fractal profiles and surfaces simulating cracks and fracture surfaces, and to implement the fractal characterisation algorithms. The results indicate that the generalised variation method, for both 1D profile and 2D surface, gives the best approximation of fractal dimension.

Date of Award	2014
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology