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Several authors have recently discussed the use of fractals to describe fracture energies and their relationships to fracture surface geometries. A fractal is a self-similar geometric construction with non-integer dimensionality. Self-similarity means that the fractal appears the same under all magnifications. Dimensionalities are described below and more rigorously. Fracture energies (E) are quantified according to the scale of observation (L), e.g., J integrals on the macroscopic scale or interatomic potentials on the lattice scale. Surface geometries have been described by roughness parameters (R) or by the fracture surface dimensionality: D/sub s/ ..cap alpha..ln(R)ln(L). Another fractal dimensionality for fracture has been defined in terms of energy: D ..cap alpha..ln(E)ln(L). A frequently employed assumption is that D/sub s/ is the same for all scales, or that a plot of ln(R) versus ln(L) is linear. However, others have found that this is in general not true for fracture surfaces. It appears that the sigmoidal scaling behavior of fracture energies could be as common as others have observed for fracture surface roughnesses. In the present work, fracture energies are found to exhibit the same sigmoidal behavior when plotted versus an apparent material structure parameter. This parameter is herein called a ''characteristic structural unit formore » fracture'' (L/sub o/). Arguments leading to this conclusion are given.« less |
