PSI - Issue 5

O. Plekhov et al. / Procedia Structural Integrity 5 (2017) 438–445 A. Vshivkov et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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3. Results of fatigue experiments

During the experiments, a series of samples was tested where the crack length and the heat flux were recorded. Figures 5 show the characteristic time dependences of heat flux during the experiment. The heat flux during the experiment can be divided into two stages. In the first stage (up to point *), cyclic loading in the elastic mode with a constant amplitude of the applied load is carried out to achieve the required value of the stress intensity factor. In the second stage (after the point *), the load is controlled to maintain a constant value of the stress intensity factor, while the rate of the fatigue crack propagation also remains constant (Fig. 7). This stage is the subject of investigation.

*

Fig. 5. The characteristic heat flux during the experiments with constant stress intensity factor.

Fig. 6. The characteristic crack length during the experiments with constant stress intensity factor.

According to the classical concepts the heat flux from the top of the crack should remain constant with constant stress intensity factor. However, in the experiment a monotonic decrease in the heat flux is observed.

4. Energy dissipation at crack tip under cyclic loading

Following the work Raju (1972), we can propose a relation between elastic and real deformation at crack tip:

2 1   

  

E

ef

el

,







(2)

ij where – the Young’s modulus, - secant plasticity modulus. Equation (2) was originally proposed by Dixon (1965) as results of photo elastic experiments data treatment based on the Ramberg-Osgood relationship (1943): ij s E

n   

  

.     We can write a following estimation for octahedral stress and couple it with an elastic solution: 0 A G  

2 1





  

  

n

1



B

3 1 2(1 ) 



el oct



,





(3)

oct

n

1



B

1





n

  

,    

 

e oct    ,

e

B GA 

where

- elastic limit.



e



0 0