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A Study of the Influence of Plastic Strain upon Fractal Dimensional Increment of an Aged Al-Si-Ge Alloy Based on Synthetic Fractal Profiles and Dimple Pattern of Fracture

A theoretical model was developed to correlate the fractal dimension, D, of ductile tension fracture surfaces of an aged Al-0.57Si-2.03Ge alloy with the macroscopic fracture strain, e f , based on the general definitions of D and the roughness parameter, R, as well as on a linear relation developed between e f and the natural logarithm of the scaling factor, (1/n), irrespective to the self-similar system to which it is referred. Two examples of synthetic self-similar profiles were used to show the general connection between D, R and e f . The higher the scaling factor, the higher the fracture strain and the lower the fractal dimension. This result suggests an increase of the shear stress component as the ductility increases, which generates an increase of the fracture surface flatness.