The fracture process zone encodes information in the surfaces it leaves behind, which may be decoded to reveal the fracture mechanism. In order to quantitatively relate the surface topography to fracture mechanics, the directional roughness metric is proposed to describe the grooves left behind by the fracture process. A partitioning method is proposed to localize the perspective of roughness analysis and reassemble it into a form that permits further interpretation of the roughness of local features. The minimum directional roughness is shown to follow the propagation path and the maximum directional roughness measures the intensity of the grooves. Its application on various indirect tensile fractures show that this method can quantitatively describe the surface left behind by the fracture. A positive correlation was found between the strain energy release rate (GIC) and the maximum directional roughness metric. This relationship can suggest that the local maximum directional roughness calculated by the surface roughness partitioning method can reflect the stress intensity factor (KIC) during fracture.


Brittle fractures produce characteristic patterns that appear to have a relationship with the fracturing process that create them. This can potentially be another source of information that can improve the characterization of materials. Roughness characterization is proposed as a method of quantifying the surface characteristics of a produced fracture. However, an understanding of brittle fracture mechanics and current knowledge on fracture topography must be established before attempting to investigate this relationship.

Classical linear-elastic fracture mechanics (LEFM) starts with Griffith's crack theory (Griffith, 1921). Materials carry pre-existing crack defects that only start to grow once a critical stress is reached. The presence of these cracks is important for the initiation of failure. Although the failure process starts when these cracks start opening, material rupture still requires additional stress. Irwin, in 1960, proposed the concept of a stress region around the fracture tip, the intensity of which is described using the stress intensity factor (K). Irwin also defined stable and unstable fracture modes which is differentiated by K crossing a critical threshold (KC). These values can be individually defined for the tensile, shear, and tearing modes of fracture. In this work, KI and KIC are used to represent the tensile stress intensity factor and critical stress intensity factor, respectively. Stable fracture describes the state of fracture growth where it requires additional load to propagate. Unstable fracture describes the phenomenon where the fracture tip requires no additional load to propagate and ultimately the material experiences uncontrollable rupture. Bieniawski, (1967), later proved the applicability of Irwin's concepts to rock fractures by describing the stages of failure according to LEFM.

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