Application of elastic-plastic fracture mechanics techniques to the problems of welded structure toughness evaluation is relatively new. In recent times, a subject of increasing interest is the correlation of Rice's path independent J-integral and its extended formulations to crack growth initiation in materials under plastic deformation. The circumferentially notched implant weldability test specimen is now widely used to evaluate the fracture characteristics of weld-base metal composites due to its advantages of small size and associated low cost. In this paper, an incremental finite element analysis, suitably modelled to admit linear work hardening of materials, has been carried out for this specimen under monotonic load histories. As a sequel to an earlier work, the domain-independent property of suitable J solutions available in the literature have been critically examined from the viewpoint of applying J-criterion to this specimen. Some new results about J and the associated notch tip deformation patterns are obtained here. Also, the role of surface and line contributions under the integral signs in axisymmetric J has been discussed in the context of the present problem. Solutions presented demonstrate that the J-integral can be used as a useful notch-tip characterizing parameter for this test specimen.