Crack initiation at a V-notch tip has been studied extensively under various configurations. In particular, the matched asymptotic approach has proven to be effective when combined with the Coupled Criterion (CC) to predict crack initiation. Previous studies have shown that, depending on the notch angle and the mode mixity, an optimal crack angle configuration exists, which may be misaligned with the pure mode I direction. However, these studies have primarily focused on straight crack initiation, while nonstraight cracks could also be optimal. In this work, various crack shape are investigated using the matched asymptotic approach and the CC to assess crack initiation. The influence of crack curvature on the stress and energy criteria is investigated, and different stress criteria are compared. Increasing crack curvature leads to less favorable stress conditions, while the energy aspect remains relatively unaffected. The CC solution becomes optimal when the shape converges towards a straight crack. Finally, numerical results are compared with experimental data from epoxy matrix samples to validate the proposed approach.