PSI - Issue 33

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

437

10

3 h z h    .

(30)

2

2

In formulae (28) – (30), the values of the modulus of elasticity in tension at the upper and the lower surfaces of the beam are denoted, respectively, by tUP E and tLW E , the values of the coefficient of viscosity in tension at the upper and the lower surfaces of the beam are tUP  and tLW  , respectively, t n and t m are parameters which control the distributions of the modulus of elasticity and the coefficient of viscosity in tension along the beam thickness.

cLW E E /

/ tUP E E

0.5

 cUP

Fig. 7. The strain energy release rate in non-dimensional form plotted against

ratio (curve 1 – at

,

cUP

/ tUP E E

1.5

/ tUP E E

2.5

 cUP

 cUP

and curve 3 – at

).

curve 2 – at

c E , and the coefficient of viscosity, c  , in compression along the

The distributions of the modulus of elasticity,

beam thickness is expressed as

n

h z



    2

  

c

c h E E E E   n cLW cUP c

cUP

,

(31)

3

m

h z

  





    2

  

c

cUP  

cLW

cUP

,

(32)

3

c

m

h

c

where

3 h z h    .

(33)

2

2