Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios (a/c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J–Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances (r/(J/σ0)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/σ0) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σe, the hydrostatic stress σm and the stress triaxiality Rσ, the three-parameter J–QT–Tz approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor Tz and the QT term, which is determined by matching the finite element analysis results, the J–QT–Tz solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/c and n. Finally, the empirical formula of Tz and the stress components are provided to predict the stress state parameters effectively.