Algorithm for three-dimensional analysis of cleavage facet and its application for brittle fracture surface of steels

Computer image processing technology has been applied to cleavage fracture surface analysis and an algorithm for the estimation of 3-dimensional cleavage facet boundaries and 3-dimensional facet areas has been developed. An angle α_i,j between relative normal vectors of one mesh P_i,j and adjacent mesh plane P_i+1,j was calculated and the α_1,j was compared to the threshold one α_th. If α_i,j is larger than α_th and the α_i+1,j calculated between the mesh planes P_1+1,j and P_i+2,j along X axis is smaller than α_th, the P_i+1,j mesh plane was the facet boundary. The same calculation was continued along both X- and Y-axes, and facet numbers being contained in the analyzed area were obtained. After the estimation of facet boundaries, 3-dimensional facet areas were calculated by dividing the 2-dimensional facet areas by cos β_k which is the angle between average normal vector of facet and vertical vector. By this algorithm, the cleavage fracture surfaces were analyzed of JIS SS41 and HT80 steels and the effect of the threshold angles α_th is discussed using the facet numbers estimated, the distribution of the values of α, and the 3-dimensional facet areas. The method is useful to analyze cleavage facet size and discuss the relationship between the cleavage fracture and microstructures such as ferritic grain size and prior austenitic grain.