To elucidate the correlation between crack initiation strengths obtained from different testing protocols, this study conducted three-point bending (TPB) and semicircular bending (SCB) tests on AC-13 modified asphalt mixtures under varying displacement rates. Digital image correlation technology was employed to monitor the real-time evolution of displacement and strain fields. Results indicate that the standard vertical displacement rate applied at the specimen top fails to align the two methods. Instead, the proposed “equivalent strain rate at the crack initiation point”—which integrates the time-dependent evolution of the internal stress-strain state—serves as a superior index for characterizing the relationship between TPB and SCB tests. Specifically, when this equivalent strain rate exceeds 0.006, the strength metrics derived from both testing methods demonstrate high consistency. Consequently, the SCB test shows significant potential as a reliable alternative to the traditional TPB method for evaluating the fracture performance of asphalt mixtures.