PSI - Issue 33

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

409

8

RH 1 ( )     i n i

U a RH 

u dA RH 0

,

(23)

i

A

i

i RH u 0 are the area of the cross-section and the strain energy density

where RH n is the number of layers, i A and

of the i -th layer, respectively.

Fig. 5. The strain energy release rate in non-dimensional form plotted against the non-dimensional time (curve 1 – for delamination crack located between layers 1 and 2, curve 2 – for delamination crack located between layers 2 and 3). The strain energy density is written as

2 1

RH i u 0



  i .

(24)

By combining of (13) and (16), one derives

   

n t

   

2 1

2 1







2 2

e v t i 2

1

u

E v t pri 

n E E 







.

(25)

0

1

RH

i

i

pri



i

The strain energy in the un-cracked beam portion is written as

UN     A 1 ( ) i n i

(  

)

U

l a

u dA UN 0

,

(26)

UN

i

i

where the number of layers and the strain energy density are denoted by UN n and i UN u 0 , respectively. The distribution of strains, UN  , along the thickness of the un-cracked beam portion is expressed as