Issue 35

V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 35 (2016) 114-124; DOI: 10.3221/IGF-ESIS.35.14 117 this way, the relations between the relative crack depth a/t and the aspect ratio a/c can be measured using a comparison microscope. In addition, based on periodically measured increments of surface crack length  c , the curve of surface crack propagation versus cycle numbers dc/dN can be obtained. Afterwards, utilizing the relation of crack depth versus surface crack length, it is possible to obtain the crack growth rates da/dN in the depth direction. Another interesting result pointed out in the present study is the aspect ratio increasing under biaxial loading as a function of crack depth a/t (Fig.4,a) whereas the aspect ratio decreasing under bending loading (Fig.4,b). a) b) Figure 4 : Aspect ratio versus crack depth under (a) different biaxial loading and (b) bending. N UMERICAL RESULTS rom Figs. 2 and 3 can be seen that the length of the arc of semi-elliptical crack front depends on the loading conditions of the CS and BP specimens. Moreover, the crack propagation process in CS samples can be divided into two stages. During the first stage a semi-elliptical crack is a part-through-thickness. On the second stage semi- elliptical crack completely crosses the wall and becomes a through-thickness. To compare the parameter distributions along the semi-elliptical crack front is convenient to introduce the dimensionless coordinates in the following form 2     . In the following representation of numerical results, we will use variable  changing in the range from 0 to 1. Constraint parameters Characterization of the constraint effects in the present study was performed using the non-singular T -stresses, the local triaxiality parameter h and the T Z -factor of the stress-state in a 3D cracked body to illustrate the features of the behavior of surface cracks in the CS and BP specimens . T-stress Using the crack flank nodal displacements technique, the T -stress distributions in various specimen geometries were determined from numerical calculations. To this end, the commercial finite element code, ANSYS [8], was used to calculate the stress distributions ahead of the crack tips. In this part of the FEA calculations, the material is assumed to be linear elastic and characterized by E =76.5 GPa and  =0.3. 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 (1) 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. F