Fig. 3 Example to demonstrate the anomalous growth behavior of a short surface crack individually traced throughout one of the virtual CAL tests with a stress amplitude equal 390 MPa.
As given by the present simulation, the FCG rate of crack 4 during its three stages presented in Fig. 3I (A)-(C) is plotted in Fig. 3I (D)-(F). The crack starts its growth with a very low rate and continues to propagate with an increasing rate, see Fig. 3I (D). Beyond its first coalescence, the crack growth is relatively slower, Fig. 3I (E). During the third stage of its propagation, see. Fig. 3I (F), the crack continues its growth with decreasing rates. According to the present model, that behavior is due to the local variation in the yield stresses of the involved surface grains and the extents of the plastically deformed zones ahead of the tips of the interacting cracks.
The interaction and evolution of short fatigue cracks and their coalescence were clarified in the literature via replica and acoustic microscopy observations, e.g. 57. However, the number of static images, typically = 7-15 for each specimen is too small to describe all the kinematic events possibly taken place over the specimen surface throughout its life. For example, the advance rate of the two tips of a crack may be different, the coalescence of neighboring cracks may be missed and the events taken place during the period of successive replicas are not observed. To simulate the replica technique, an illustrating example follows considering the behavior of crack 4 presented in Fig. 3.
Figure 4 shows the fatigue crack growth behavior of that crack should its surface length be measured at intervals of (1) 10000 cycles, Fig. 4(A), (2) 20000 cycles, Fig. 4(B), and (3) 30000 cycles, Fig. 4(C). The behavior corresponding to the three intervals is different as compared with each other and with that behavior presented in Fig. 3I(D-F). Thus, to have reliable experimental results, the number of replicating actions should be thought of.