Issue 33

V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 33 (2015) 335-344; DOI: 10.3221/IGF-ESIS.33.37 339 T z -factor The T Z factor [9] has been recognized to present a measure of the out-of-plane constraint and can be expressed as the ratio of the normal elastic-plastic stress components zz z xx yy T      (4) where  zz is the out-of-plane stress, and  xx and  yy are the in-plane stresses. The variation of this parameter is important to characterize the thickness effect on the crack front stress distribution and the changes of the plastic zone size. Stress triaxiality As a secondary fracture parameter, a local parameter of the crack-tip constraint was proposed by the authors [10] because the validity of some of the above-mentioned concepts depends on the chosen reference field. This stress triaxiality parameter is described as follows:   3 , , 3 2 kk ij ij h r z s s          (5) where  kk and s ij are the hydrostatic and deviatoric stresses, respectively. Being a function of both the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the in- plane and out-of-plane constraint that is independent of any reference field. The distributions of the elastic and elastic-plastic constraint parameters along the crack front in the hollow specimen under cyclic tension are plotted in Fig. 5 under pure Mode I loading. These distributions correspond to the crack front positions at the accumulated number of loading cycles N 1 =0 (initial front), N 2 = 21000 (intermediate front), N 3 = 50000 (intermediate front), N 4 = 131500 (final failure front). The constraint parameter is plotted against the normalized coordinate R . In this plot R = 0.0 is the crack border (the specimen free surface) while R = 1.0 is the mid-plane of the hollow specimen thickness. It can be observed that all constraint parameters essentially changed along the crack front from the free surface toward the mid-plane. It should be noted that the front of the number four in the Fig. 5 corresponds to the second stage of crack propagation when it becomes completely through-thickness and intersects the cylinder wall. а) b) с) Figure 5 : Constraint parameter distributions under cyclic tension along crack front (1-initial, 2-3- intermediate , 4-final). Plastic stress intensity factor Here, our primary interests are to obtain an accurate description for the distribution along the crack front of the governing parameter for the elastic-plastic solution in the form of an I n -integral and to determine the accuracy that this type of calculation, which will later be used for the general 3D problem, provides for the plastic stress intensity factor (SIF). The method developed here for combining the knowledge of the dominant singular solution with the finite element technique to obtain accurate solutions in the neighborhood of a crack tip is also applicable to the treatment of problems involving cracks in finite bodies.