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

Abstract

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/ σ 0)) are relatively small, while the approach can hardly characterize it very well with the increase of r/( J/ σ 0) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ e, the hydrostatic stress σ m and the stress triaxiality R σ , 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 φ equals about 31.5° 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.