Fractal analysis of the surface cracks on continuously cast steel slabs

Abstract

Data concerning the length of longitudinal cracks on the surface of continuously cast steel slabs were collected from two plants. The data were analyzed to find the relation between crack length and crack frequency. The analysis revealed the following. (1) After normalization to eliminate the effect of different casting conditions, the fractal relation characterizing the normalized cumulative frequency distribution (N (m−2)) and the crack length (L (mm)) of the primary surface cracks could be represented by the equation $$N = \gamma N_c = \gamma k_c L^{ - 1.5} $$ where Nc is the cumulative frequency before normalization, γ is the normalizing coefficient, and kc is a constant. (2) The values for γ varied over a wide range, but remained constant throughout a heat and were the same for both the upper and lower faces of the slab. (3) It was found that in some instances, when L exceeded a critical value (Lc), the value of L became δ times longer than the length predicted by the previous distribution. This increase in L was ascribed to secondary growth of the cracks. This occurred more frequently on the lower, rather than on the upper, face of the slab. The product of Lc and δ was approximately constant. The formation of the surface cracks is discussed in view of the fractal phenomena.