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, ${\sigma }_f$: ${\sigma }_f\propto CBC$. 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, $K_c$: $K_c=E{a_0}^{1/2}{D}^{*1/2}$, where $E$ is the elastic modulus and $a_0$, 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.

失效分析的关键部分是了解从引发到裂纹扩展的断裂过程。脆性材料中的裂纹扩展会产生本质上是分形的裂纹分支模式，即裂纹分支系数（CBC）。CBC与强度有直接关系，${\sigma }_F$： ${\sigma }_F\propto C乙C$。这似乎与断裂面的分形维数增加相抵触，$d^{*}$，它与强度无关，并且与材料的断裂韧性有关， ${ķ}_C$： ${ķ}_C=Ë{{\mathrm{一种}}_0}^{\mathrm{1个}/2}{d}^{*\mathrm{1个}/2}$，在哪里 $Ë$ 是弹性模量， ${\mathrm{一种}}_0$，一个特征尺寸。怎么能$d^{*}$在一种情况下为常数，而CBC在另一种情况下为变量？本文演示了两者之间的关系$d^{*}$ 和 $C乙C$在形貌参数方面。将演示分形分析示例，以分析现场故障，例如涉及粉碎，部件不完全断裂以及潜在的加工问题。