PSI - Issue 5

Martin Krejsa et al. / Procedia Structural Integrity 5 (2017) 1283–1290 Martin Krejsa et al./ Structural Integrity Procedia 00 (2017) 000 – 000

1287

5

The probable course of the growth of the fatigue crack is shown in Fig. 1. (a). The probabilities (8) - (10) can be determined in any period of time, t , using the probabilistic methods. The probabilistic calculation is carried out in time steps where one step typically equals to one year of the service life of the construction. When the probability of failure P ( F ( t ) ) reaches the designed failure probability P d , an inspection t I should be carried out in order to find out fatigue cracks, if any, in the construction element. The inspection provides information about conditions of the construction. Such conditions can be taken into account when carrying out further probabilistic calculations. The inspection in the t time may result in any of the three mentioned random phenomena U , D or F . Using the inspection results for the t time, it is possible to define the probability of the mentioned phenomena in times T > t I . For that purpose, the conditional probability should be taken into consideration. it can be defined the probability of event F in time T with respect to the results of structural inspection in time t I :                             I I I I I t t T t t T t T P U P F P F P D P F D P F U .    (11)

and

      t T

    t

    t .

    T

    I t P D P F P F P U P F U   I I





.

(12)

  T P F D



I

  t I

Using conditional probability (11) and the designed failure probability P d is possible design the time of the following inspections t II , t III , t IV … focused on the structural elements susceptible to fatigue damage - see Fig. 1. (b).

4. Fatigue damage prediction of short edge crack under various load

The demonstration of using mentioned methodology was made for the single edge-cracked steel element with rectangular cross-section under short edge fatigue damage defined such as in Kruml et al. (2011). Calibration curve were derived for a relative crack length a/h : 0.01-0.5 loaded by tension, pure, three-point (3PB) and four-point bending (4PB) using expression:

  

.

(13)

   K

h a f a

 

    

In case of 3PB test is   equal to:

2 b h F s PB    3

3



.

(14)

  

2

The resulting calibration function for 3PB test and ration s / h =4 is:

2

3

  f a h s 3

h a

h a

h a

  

   

   

4    PB

(15)

1.0618 1.0658 

2.9787

1.0435

   

   

   

and for s / h =8 respectively:

2

3

  f a h s 3

h a

h a

h a

  

   

   

8    PB

.

(16)

1.0895 1.0022 

2.9389

1.0091

   

   

   