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O. A. Hilders and D. Pilo, “On the Development of a Relation between Fractal Dimension and Impact Toughness,” Materials Characterization, Vol. 38, No. 3, 1997, pp. 121-127. doi:10.1016/S1044-5803(96)00148-9

has been cited by the following article:

• TITLE: Relationship between Fracture Toughness and Fracture Surface Fractal Dimension in AISI 4340 Steel

  AUTHORS: Luis R. Carney, John J. Mecholsky

  KEYWORDS: Fractal Fracture; Ductile Failure; Brittle Failure; Mechanical Behavior

  JOURNAL NAME: Materials Sciences and Applications, Vol.4 No.4, April 30, 2013

  ABSTRACT: This study analyzes the relationship between fracture toughness and the fracture surface fractal dimension for a set of twenty-four CT-type AISI 4340 steel specimens heat treated to a variety of tensile strengths. Specimens were tested in accordance with ASTM E 399. Their respective fracture surfaces were plated, polished, photographed under an SEM in BSE mode and measured according to the Richardson method to obtain fractal dimensions. For brittle materials the limited results are consistent with previous literature: increasing fractal dimension with increasing toughness. For partially or fully ductile materials the results indicate a decrease in fractal dimension with an increase in fracture toughness. The data are modeled using a variation of the function applied to ceramics. Fracture in a ductile mode is characterized by the formation of dimples which exhibit fractal characteristics. The results are discussed in terms of the micromechanisms of fracture.