Application of Fractal Geometry to Fracture Forensics, Research and Production
The fracture surface records past events that occur during the fracture process by leaving characteristic markings. The application of fractal geometry aids in the interpretation and understanding of these events. Quantitative fractographic analysis of brittle fracture surfaces shows that these characteristic markings are self-similar and scale invariant, thus implying that fractal analysis is a reasonable approach to analyzing these surfaces. The fractal dimensional increment, D*, is directly proportional to the fracture energy, γ, during fracture for many brittle materials, i.e., γ = ½ E a0 D* where E is the elastic modulus and a0 is a structural parameter. Also, D* is equal to the crack-size-to-mirror-radius ratio. Using this information can aid in identifying toughening mechanisms in new materials, distinguishing poorly fabricated from well prepared material and identifying stress at fracture for field failures. Examples of the application of fractal analysis in research, fracture forensics and solving production problems are discussed.
J.J. Mecholsky Jr. "Application of Fractal Geometry to Fracture Forensics, Research and Production ", Advances in Science and Technology, Vol. 45, pp. 1646-1651, 2006