PSI - Issue 33

9

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 402–415 Author name / Structural Integrity Procedia 00 (2019) 000–000

410

2



z

UN  

h DUN

,

(27)

2

where

2 h z h   

.

(28)

2

2

0 .3

Fig. 6. The strain energy release rate in non-dimensional form plotted against 11 q (curve 1 – at 21  q

, curve 2 – at

0 . 5

0 . 7

21  q

21  q

and curve 3 – at

).

DUN  and 2 z are the strain at the lower surface of the beam and the vertical centroidal

In formulae (27) and (28),

UN v  , of the strains is written as

axis of the cross-section of the beam, respectively. The distribution of the speed,

2

v



v

z



.

(29)

DUN

2

UN 

h

where DUN v  is the speed at the lower surface of the beam. The variation of the stress, UNi  , in the i -th layer of the beam with the time is expressed as   UN n t pri i i pri UN UNi e v E v t n E E i         1 1 . (30)

   

   

The strain energy density that is involved in (26) is obtained as