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.