PSI - Issue 33

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

436

9

  

  

1

h h z

  

  

   

   



G

z

dA







 



1

.

(27)

D n 1

2

U

n

2

2 2

b

1

n

D ( ) A

The MatLab computer program is used to carry-out the integration in (27). It should be noted that the strain energy release rate obtained by (27) is exact match of that found by (24). This fact is a verification of the analysis of the strain energy release rate with considering the stress relaxation developed in the present paper. A time-dependent solution to the strain energy release rate is derived also assuming that the material has different mechanical behaviour in tension and compression. In this case, the modulii of elasticity and the coefficients of viscosity in tension and compression have different values.

Fig. 6. The strain energy release rate in non-dimensional form plotted against the non-dimensional time for the case of material with different viscoelastic behaviour in tension and compression (curve 1 - at 0.5 /  cUP cLW   , curve 2 - at 1.5 /  cUP cLW   and curve 3 - at 2.5 /  cUP cLW   ).

t E , and the coefficient of viscosity, t  , in tension along the thickness

The distributions of the modulus of elasticity,

of the beam are written as

n

h z



    2

  

t

t h E E E E   n tLW tUP t

tUP

,

(28)

3

m

h z

  





    2

  

t

tUP  

tLW

tUP

,

(29)

3

t

m

h

t

where