[en] Significant advances in elastic-plastic fracture became possible with the introduction of Rice's path independent J-integral which has two physical meanings. First, the J-integral is equivalent to the energy release rate associated with a virtual crack advance. Secondly, J can be regarded as the strength of the stress and strain singularity near a stationary crack tip. As a result of several experimental studies, the J-integral is generally accepted as a valid parameter to characterize a material's resistance to the onset of crack growth under large-scale yielding. Driven by simplicity and the practical benefits that could be derived from a geometry and size-independent material resistance curve for large amounts of crack growth, J_M, a modified J parameter was introduced. Initial results using J_M were encouraging but subsequent studies did not support the earlier results. The present computational study presented in Volume 1 of this report investigates several forms of this parameter, how they are derived and the validity of these parameters for small and large amounts of crack growth. It is concluded that neither J nor J_M (nor any single parameter) can satisfactorily capture the full range of near-tip fracture states. A discussion on the range of validity of J_M is given in Volume 2. This work is relevant for assessing structural integrity of nuclear pressure vessels and piping