J-A2 characterization of crack-tip fields:: Extent of J-A2 dominance and size requirements

The requirements for J-dominance, limits of the single-parameter criterion to characterize the fracture of engineering structures, and two-parameter fracture analyses are first reviewed. Through comparison, it is argued that the two-parameter fracture methodology based on the J-A(2) theory is a reasonable extension of the single parameter (J-integral) fracture methodology. Consequently the extent of J-A(2) dominance in various specimens under either tension or bending is investigated in detail in this paper. Using the J(2) flow theory of plasticity and within the small-strain framework, full field finite element solutions are obtained for both deep and shallow crack geometries of single edge notch bar under pure bending [SEN(B)] and central cracked panel in uniform tension [CC(T)]. These crack-tip stresses are compared with those in the HRR singularity fields and the J-A(2) asymptotic fields at the same level of applied J. The comparison indicates that the size R of the region dominated by the J-A(2) field is much larger than that of the HRR field around the crack tip. Except for deeply-cracked SEN(B) in low hardening material (n = 10) under fully plastic conditions, the numerical results near the crack tip in both SEN(B) and CC(T) match very well with the J-A(2) asymptotic solutions in the area of interest 1 < r/(J/sigma(0)) < 5 from well-contained to large scale plasticity. The implications of these results on the minimal specimen size requirements essential to a two-parameter fracture criterion based on the J-A(2) asymptotic solution are then discussed.