Practical application of empirical formulation of the stress concentration factor around equally sized dual spherical cavities to aluminum die cast

An empirical method is developed for obtaining the stress concentration factor for a pair of equally sized spherical cavities embedded in a large continuum in three-dimensional space. For practical applications such as die-cast materials containing many pores, we construct a simple and robust closed-form equation to evaluate the stress concentration factor considering the interaction between two cavities. The stress concentration factor can be used to evaluate the effect of pores on the material strength and the probable location of pores that will initiate a fatigue crack. Three-dimensional finite element linear elastic analysis was carried out to evaluate the stress concentration factors for arbitrary locations of the two cavities. The effects of the inter-cavity distance and the orientation of the inter-cavity axis with respect to the loading direction on the stress concentration factor are numerically obtained by systematically changing each of these parameters. Two empirical equations are proposed to fit the stress concentration factor data calculated by finite element analysis after considering various boundary conditions from a mechanical standpoint, and the parameters of the empirical formula are obtained by non-linear curve fitting with regression analysis.