Relationship between fractography, fractal analysis and crack branching

Abstract

A critical part of failure analysis is to understand the fracture process from initiation through crack propagation. Crack propagation in brittle materials can produce crack branching patterns that are fractal in nature, i.e., the crack branching coefficient (CBC). There is a direct correlation between the CBC and strength, σf: σf∝CBC. This appears to be in conflict with the fractal dimensional increment of the fracture surface, D*, which is independent of strength and related to the fracture toughness of the material, Kc: Kc=E a01/2D* 1/2, where E is the elastic modulus and a0, a characteristic dimension. How can D* be constant in one case and CBC be a variable in another case? This paper demonstrates the relationship between D* and CBC in terms of fractographic parameters. Examples of fractal analysis in analyzing field failures, e.g., that involve comminution, incomplete fractures of components, and potential processing problems will be demonstrated.