Issue 33

V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 33 (2015) 335-344; DOI: 10.3221/IGF-ESIS.33.37 338 Two different stress ratio R f values (0.1 and 0.5) were applied several times to the specimens in order to highlight the crack front geometry during propagation: during each test, beach marks were produced on each specimen by increasing the applied stress ratio from 0.1 to 0.5 at constant value of maximum cyclic nominal stress, when the surface crack length was approximately increased to a  0.1mm. The typical beach marks on the post mortem cross section of different specimens are shown in Figs. 3 and 4 for tension and torsion, respectively. From the crack front shape obtained in this way, the relations between the relative crack depth a/D and the surface crack chord length c/D can be measured using a comparison microscope. In addition, based on periodically measured increments of surface crack chord length  b , the curve of surface crack propagation versus cycle numbers db/dN can be obtained. Afterwards, utilizing the relation of crack depth versus surface crack chord 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 crack front and aspect ratio stabilization (Fig.3,b) with respect to different initial notch geometry, when considering the analyzed multiaxial loading condition. It can be seen that the crack propagation paths differ with diverse initial flaw forms, but converge to the same configuration when the crack depth ratio is larger than about 0.25. N UMERICAL RESULTS Dimensionless coordinates rom Figs. 3 and 4 can be seen that the length of the arc of semi-elliptical crack front depends on the loading conditions of the hollow specimens. Moreover, the crack propagation process in hollow 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 cylinder 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: 0 0 cos x     , 0 0 sin y     (1) cos c c x     , sin c c y     cos i i x     , sin i i y     ,   0 , i c     , 0 c       0 0 i i c x x X x x    ; 0 0 i i c y y Y y y    (2) 2 2 1 2 i i i R X Y   ,   0, 1 R  (3) where  0 is angle determining position of initial point of the semi-elliptical crack front whereas  c is angle corresponding to the deepest point of the crack front. In the following representation of numerical results, we will use variable R changing in the range from 0 to 1. Constraint parameters Recently, several two parameter models describing elastic-plastic fracture mechanics were introduced to explain some of the restrictions inherent in the one parameter approach based on the J -integral. The different sources of changes in the in- plane and out-of-plane constraint are associated with the crack size, the geometry of the specimen and the loading conditions and notch effects on the fracture resistance characteristics of structural materials. 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 hollow specimen . T-stress The T -stress has been recognized to present a measure of the constraint for the small-scale yielding conditions. Few methods have been proposed for calculating T . This study explores the direct application of FEM analysis by using the crack flank nodal displacements for calculating T -stress. Using this 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 =74 GPa and  =0.3. F