Brittle failure of high toughness steel structures tends to occur after ductile crack initiation/propagation. Damages to steel structures were reported in the Hanshin Great Earthquake. Several brittle failures were observed in beam-to-column connection zones with geometrical discontinuity. It is widely known that triaxial stresses accelerate the ductile fracture of steels. The study examined the effects of geometrical heterogeneity and strength mismatches (both of which elevate plastic constraints due to heterogeneous plastic straining) and loading rate on critical conditions initiating ductile fracture. This involved applying the two-parameter criterion (involving equivalent plastic strain and stress triaxiality) to estimate ductile cracking for strength mismatched specimens under static and dynamic tensile loading conditions. Ductile crack initiation testing was conducted under static and dynamic loading conditions using circumferentially notched specimens (Charpy type) with/without strength mismatches. The results indicated that the condition for ductile crack initiation using the two parameter criterion was a transferable criterion to evaluate ductile crack initiation independent of the existence of strength mismatches and loading rates.