An Application of Fractal Theory to Complex Macrostructure: Quantitatively Characterization of Segregation Morphology

Abstract

Segregation of solute elements is an inherent characteristic of alloy solidification. Macro/semi-macro segregation seriously affects the mechanical properties of the final products. High-carbon steel billets is an important base material for producing high-end rod wire, while macro/semi-macro segregation is more serious due to its high carbon element content and low distribution coefficient. In order to control the segregation defects of high-carbon steel delicately, the morphology characteristics of segregation in 82B cord steel billet (the carbon content is 0.82 wt%) produced by continuous casting were studied based on fractal theory. It is shown that segregation morphology has fractal characteristics. Different calculation methods of fractal dimension describe segregation characteristics from different angles; fractal dimension calculated by perimeter-area method (D_PA) can quantitatively characterize the complexity of segregation profile, while fractal dimension calculated by the box-counting method (D_BC) reflects the spatial distribution characteristics of segregation in billets. Secondary dendrite arm spacing (SDAS) mainly affects the complexity of segregation profile. In additional, negative-correlation is shown between D_PA and cube root of local solidification time (the fitting coefficient is 0.79). This result demonstrated the potential of D_PA as a parameter for estimating local solidification time of the billet in which the measurement of SDAS is difficult.