Issue 30

Yu.G. Matvienko, Frattura ed Integrità Strutturale, 30 (2014) 311-316; DOI: 10.3221/IGF-ESIS.30.38 314 conditions, namely, Plane Stress and Plane Strain. Moreover, when specimen thickness increases, the shape and size of the plastic zones tend to zones which are typical for plane strain conditions. Thus, the results clearly show that triaxiality of the stress state around the crack tip should be taken into account by means of both non-singular xx T -stress and zz T -stress according to Eq. (6). The validity of analytical equations for calculation of the plastic zone around the crack tip is demonstrated by means of finite element analysis [4, 5]. The deviation between analytical and numerical results does not exceed 20% in the angular range (0  , 30…45  ) and (90  …100  ,135  …145  ). It should be noted that the deviations between the results of the numerical analysis and the analytical calculation in the angular range (0°–145°) can be explained by the fact that the T - stress components around the plastic zone can be not constant and depend on angle  as reported in Ref. [4]. Loading parameters B / W =0.25 B / W =0.40 B / W =0.50 P, kN 6.0 9.6 12.0 K I , MPa  m 1/2 66.0 66.0 66.0 T xx , MPa 186.59 182.36 176.28 T zz , MPa -159.47 -106.81 -84.97 Table 1 : Loading conditions of the CT specimen. T HE EFFECT OF THICKNESS ON THE NON - SINGULAR T- STRESSES UNDER MIXED MODE LOADING Loading conditions inite element analysis of 3D stress fields in the vicinity of the crack front is performed for the center cracked circular disc (CCCD-specimen) with the thorough-thickness crack of arbitrary space orientation. The specimen is loaded by 2 compressive forces acting in the vertical direction. This configuration of the specimen is very suitable to create different conditions of mixed mode (I + II) loading [6]. The orientation of the crack plane with respect to the disk is determined by the angle α. Changing the angle can provide almost any relationship between the magnitudes of stress intensity factors, namely, I K and II K . Loading mode mixity is characterized by the following parameter 2 ( ) I e II K M arctg K   (8) Calculation of fracture mechanics parameters The evaluation of the stress intensity factor is based on the well-known approach that includes the calculating this parameter in a number of points (at varied r ) using relations from formulas (1) and extrapolation of the obtained values of the stress intensity factors to the point r =0   0 2 | | | 2 I xx xx xx r K                (9)   | | 8 II xx xx r K            . (10) The computational procedure considers the nodes of the finite element mesh as the calculation points, but the nodes are located at some small distance from the crack front. To obtain the distribution of the stress intensity factor along the crack front, this procedure is used for a number of planes (x0y) orthogonal to the crack front [7- 9]. Their location is characterized by local coordinate s along the front and starts from the center of the crack front. The calculation of the xx T - and zz T -stress is performed using the stresses in the points on the crack surface 1 2 xx xx xx T               (11) F