Morphology characteristics of solidification structure in high-carbon steel billet based on fractal theory

Solidification structure, as solid skeleton, determines directly the properties of materials, and segregation defects (i.e., uneven distribution of alloy elements) are also affected by the morphology of solidification structure. The high-carbon steel is one of the typical high-end steels, and its solidification morphology is always more complicated and segregation defects are more serious. In this study, solidification morphology of high-carbon steel with 0.82 wt% carbon content in continuously cast was investigated based on fractal theory in order to evaluate solidification characteristics of the liquid steel and control the segregation defects. It was demonstrated that the fractal dimension calculated via the box count method is effective to characterize quantitatively the complexity of the overall morphology of solidification structure instead of only local features. Further, a positive linear correlation (fitting coefficients R2 > 0.95) between fractal dimension and solidification structure ratio (Rstr) was found, i.e., the fractal dimension increases with increasing Rstr. The phenomenon of dendrite morphology complexity, which increases with increasing Rstr, is called the increasingly complicated dendrite overall morphology. It can be attributed to the increasing constitutional undercooling. In addition, the entropy in solidification system calculated by fractal dimension increases gradually in direction from the outer to middle zones of the billet. This indicates that the chaos of the solidifying interface increases gradually, which contributes to the understanding the solidification process. This study proposed a new parameter that depicts the overall solidification morphology from self-similar perspective, thus providing guidance for us to control the solidification morphology and segregation defects delicately.