Elucidation of pore connection mechanism during ductile fracture of sintered pure iron by applying persistent homology to 4D images of pores: Role of open pore

Abstract 4D pore configurations including an open pore were visualized by synchrotron X-ray laminography during the ductile fracturing process and then interpreted quantitatively using persistent homology (PH), a topological measure. In particular, this study used the zeroth PH, where the radius of an equivalent volume sphere for each pore and the distances to the other pores can be estimated for pairs of pores. The pore configurations were quantified as a set of birth and death values { ( b i , d i ) } and changes due to increasing strain were tracked. As a result, the zeroth PH revealed the following information at the final stage before fracturing. First, the pair configurations between the open pore and closed pores decreased owing to the adsorption of closed pores by the open pore. Second, the configuration between the elongated closed pore and the open pore, where equivalent volume spheres are overwrapped, increased. These configurational changes in pores predict the pore connection between the open pore and surrounding closed pores that eventually generates a ductile crack perpendicular to the tensile stress. This study demonstrated the effective interpretation of the pore connection process that is essential to ductile crack generation.