numero25

G. Qian et alii, Frattura ed Integrità Strutturale, 25 (2013) 7-14; DOI: 10.3221/IGF-ESIS.25.02 10 high cycle to VHCF regime for Region A. The values of K I for Region B are between 35 and 60 MPa  m 1/2 , which correspond to the material fracture toughness K Ic . K I for Region A and B is used to calculate the plastic zone size r p around the crack tip based on the expression 2 p y 1 3 K r            (2) where Δ K is the amplitude of K I , σ y is the yield stress of the material. The calculated plastic zone size for Region A is 32.6 μm, which approximately equals to the size of 2-3 grain sizes. In the crack initiation and early propagation stage (Region A), grain boundary serves as a microstructural obstacle. In Region B, the calculated plastic zone size is 1449 μm. As the increase of the plastic zone, the crack propagation rate increases significantly. In Region C, as the decrease of the ligament of the specimen, the specimen displays a plane stress state. Thus, the fracture morphology shows a shear fracture with an angle of 45 degree along the tension direction. For the tested specimens, the fracture is plane strain condition in the crack initiation stage and the crack tip has a high constraint effect as a result of the small plastic zone size and high stress triaxiality. With the decrease of ligament in Region C, the crack tip has a small constraint which causes large plastic deformation. However, the crack tip constraint effect during the crack propagation needs a further quantification by using a K-T or J-Q method. The SIF ranges for inclusions and fisheye patterns are calculated by the following formula [2, 6] 0.5 a K area     (3) where area is the square root of the area for inclusions or fisheyes. Fig. 4 (a) shows the relationship between Δ K and N f . Δ K for inclusions is about 2.83 MPa  m 1/2 irrespective of the fatigue life, which is smaller than the threshold SIF range (Δ K th ) of the material. Δ K for fisheyes is about 10 MPa  m 1/2 , which is somewhat higher than Δ K th of the material. Therefore, it is understood that a crack that originates at an inclusion can propagate until it forms a fisheye pattern. According to Murakami’s model [2], fatigue strength at 10 8 cycles, denoted as σ w , is predicted by 1 6 1.56( 120) ( area ) w HV    (4) where HV is the Vickers hardness of the material. Fig. 4 (b) shows the relationship between σ max /σ w and number of cycles to failure. The ratio is between 1 and 1.2, indicating that the fatigue strength of the material in the present study is well predicted by the Murakami model. 10 6 10 7 10 8 0 4 8 12 16 Number of Cycles to Failure  K (MPa  m 1/2 ) SIF of inclusion SIF of fisheye 10 7 10 8 10 9 0.0 0.5 1.0 1.5 Number of Cycles to Failure  max /  W Figure 4: (a) Δ K for inclusions and fisheyes, (b) relationship between σ max / σ w and number of cycles to failure. (a) (b)