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/sigma(0))) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/sigma o) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress sigma(e), the hydrostatic stress c, and the stress triaxiality R-sigma, the three-parameter J-Q(T)-T-z 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 T-z and the Q(T) term, which is determined by matching the finite element analysis results, the J-Q(T)-T-z 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 phi equals about 31.5 degrees for different a/c and n. Finally, the empirical formula of T-z and the stress components are provided to predict the stress state parameters effectively. (C) 2008 Elsevier Ltd. All rights reserved.