PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 416–427 Author name / Structural Integrity P o edi 00 (2019) 000–000

425

10

  

UN  

UN  

       UN 

  

  





 

 













t t

t

  

1

1

1

1





u

e

e











0

.

(39)

1

01

0

2

2

E

E





1

1

The curvature and the coordinate of the neutral axis of the lower crack arm are determined by using the equations for equilibrium (26) and (27). For this purpose, is replaced with . The stress, , is expressed as a function of the curvature and the coordinate of the neutral axis by combining of (4) and (25). The curvature, the coordinate of neutral axis and the strain energy in beam portion, , are found in analogical manner. 0  UN  UN 

1 2 B B

0.5  F 

1.0  F 



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

(curve 1 – at

, curve 2 – at

and

2.0  F 

curve 3 – at

).

The strain energy release rate in the phase of unloading is derived also by applying (31). The fact that the strain energy release rate obtained by (31) is exact match of that calculated by (20) confirms the correctness of the fracture analysis in the phase of unloading. 3. Parametric investigation In this section of the paper, results of a parametric investigation of the time-dependent longitudinal fracture behaviour in both loading and unloading phases are presented. The strain energy release rate is expressed in non dimensional form by using the formula . The variation of the strain energy release rate with time is analyzed. The effects of crack location, crack length and continuous material inhomogeneity on the strain energy release rate are evaluated. It is assumed that m, m, m, m and N. The variation of the strain energy release rate with time is shown in Fig. 3 where the strain energy release rate in non-dimensional form is plotted against the non-dimensional time in phases of loading and unloading (the time is expressed in non-dimensional form by the formula ). At the magnitude of the external force is decreased from 3 N to 2 N. It can be observed in Fig. 3 that in both phases the strain energy release rate increases with time (this behaviour is attributed to creep). The instantaneous decrease of the strain energy release ) /( 1 G G E b UPF N  0.010  b 0.012  h 0.100  l 0.030 1  l 3  F UPF UPF N t tE  / 1  8  N t