Direct estimation of fractal dimension for an irregular surface using the roughness parameter approach

The fracture process of any material is a natural response towards external loading. These fracture surfaces exhibit a fractal pattern that can be analyzed quantitatively by measuring its fractal dimension (FD). Subsequently, this FD value can be correlated with different properties of the material. Various versions of the cubic covering method (CCM) can accurately describe the fractal patterns present on irregular surfaces with minimum approximation. However, these methods are not direct methods for determining the FD, as they rely on the covering process of cubes rather than considering the irregular surface area. Considering this, a new approach known as the Roughness Parameter Method (RPM) was studied. This method involves the surface area of an irregular surface to measure surface roughness parameters for the direct estimation of the FD. Comparative analysis between direct and indirect methods to measure FD was carried out using Takagi surfaces and real-world irregular surfaces.