PSI - Issue 33

5

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 428–442 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

432

1 1 h z h   

1

.

(11)

2

2

In formula (10), 1 1 n z are, respectively, the vertical centroidal axis and the coordinate of the neutral axis of the lower crack arm (Fig. 3). It should be noted that the neutral axis shifts from the centroid since the beam is functionally graded in the thickness direction. D  is the curvature of the lower crack arm, 1 z and

Fig. 3. Cross-section of the lower crack arm (the position of the neutral axis is marked by 1 1 n n  ). By substituting of (10) in (9), one obtains the following distribution of the time-dependent strain energy density along the thickness of the lower crack arm:     Et n D D u E z z e    2 1 1 2 0 1 . (12) The distribution of the time-dependent stress along the thickness of the lower crack arm is found by subtitling (10) in (4)      Et n D E z z e    1 1 1 . (13) The time-dependent strain energy cumulated in the un-cracked beam portion is expressed as 2 1