J-A ₂ Characterization of Crack-Tip Fields: Extent of J-A ₂ Dominance and Size Requirements

Abstract

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/σ₀)<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.