PSI - Issue 42

708 Toru Yagi et al. / Procedia Structural Integrity 42 (2022) 702–713 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 7 normalized by Rose’s equation, shown in equation (1) -(3). Since d value is dependent on the crack velocity, it is normalized to compare the gradient of d value as the crack propagates.

Fig. 3.1 Mesh division of crack surface d ( ) = ( ) d (0) ( ) ≈ (1 − ) √1 − ℎ ℎ ≈ 2 1 ( 2 ) 2 [1 − ( 2 1 )] 2

(1) (2)

(3) The results of this FEM analysis are shown in Fig. 3.2. (a) is the result of the bending model. The trend of d is decreasing as the crack propagates. When the crack velocity 400 m/s or more, d decreases more rapidly than the static solution. (b) is that of the tensile model. The trend of d is unchanged or slightly increasing on the tensile mode. This is against the experimental results showing the facts of arrest even in tensile mode specimens. Based on the previous study done by Willoughby, d of low crack velocity should decrease more rapidly than that of high crack velocity, but the results of the analysis are completely opposite. The traditional theory of reflected stress waves cannot describe the pop-in phenomenon.

Fig. 3.2 Crack extension and normalized dynamic stress intensity factor of (a) three-point bending model and (B) tensile model