The main goal of this paper is to provide the theoretical background for the fracture phenomena in marine structural steels. In this paper, various fracture criteria are theoretically investigated: shear failure criteria with constant failure strain and stress triaxiality-dependent failure strain (piecewise failure and Johnson-Cook criteria), forming limit curve failure criterion, micromechanical porosity failure criterion, and continuum damage mechanics failure criterion. It is obvious that stress triaxiality is a very important index to determine the failure phenomenon for ductile materials. Assuming a piecewise failure strain curve as a function of stress triaxiality, the numerical results coincide well with the test results for smooth and notched specimens, where low and high stress triaxialities are observed. Therefore, it is proved that a failure criterion with reliable material constants presents a plastic deformation process, as well as fracture initiation and evolution.