Fracture mechanics are of high interest for the engineering design and structural integrity assessment of polymeric materials; however, regarding highly ductile polymers, many open questions still remain in terms of fully understanding deformation and fracture behaviors. For example, the influence of the constraint and specimen size on the fracture behavior of polymeric materials is still not clear. In this study, a polymeric material with an elastic plastic deformation behavior (ABS, acrylonitrile butadiene styrene) is investigated with regard to the influence of constraint and specimen size. Different single-edge notched bending (SENB) specimen sizes with constant geometrical ratios were tested. The material key curve was used to investigate differences in the constraint, where changes for small and large specimen sizes were found. Based on a size-independent crack resistance curve (J–R curve), two apparent initiation parameters (J0.2 and Jbl) were determined, namely, the initiation parameter Jini (based on the crack propagation kinetics curve) and the initiation parameter JI,lim (based on an ESIS TC 4 draft protocol). It was found that J0.2 and Jbl could be used as crack initiation parameters whereby Jini and JI,lim are indicative of the onset of stable crack growth.