Abstract This paper provides a rigorous incremental finite element procedure using both the conventional and hybrid‐displacement model to analyze in‐service situations of two‐dimensional eleastic‐plastic fracture mechanics problems under large‐scale yielding with arbitrary strain hardening material behaviors. To account for both the geometric nonlinearity and material nonlinearity, a tangent modulus incremental numerical method is employed. The fracture center‐cracked test specimen made of Ni‐Cr‐Mo—V rotor steel is solved. An acceptable JIC ductile fracture initiation criterion with finite deformation assumptions is constructed. Excellent correlations between the directly computed results and available experimental data are noted.