PSI - Issue 5

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

1288

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

6

The allowable crack size a ac for the 3PB can be expressed by a following relationship respected the derived weakening of the cross-sectional area of the element (with the limit length defined by h /2 and ratio a/h =0.5), similarly as in Wang et al. (2015):

PB F s    b f

 2 3 3

.

(17)

ac a h

 

y

Deterministic and random input quantities are given in Table 1 and Table 2.

Table 1. Overview of input deterministic quantities. Quantity

Value

Material constant m Material constant C

3

2.2·10 13 MPa m m ( m /2)+1

Height of the rectangular cross-section h Width of the rectangular cross-section b

0.1 m

0.01 m

Span of the element s

0.4 m

Designed probability of failure P d

0.02277 (  d = 2)

Table 2. Overview of input random quantities expressed in a bounded histograms. Quantity Type of parametric Mean value

Standard deviation

probability distribution

Total number of stress peaks per year N

Normal

10 6

10 5

Yield stress f y

Lognormal

200 MPa

20 MPa 0.6 kN 0.05 mm 0.2 mm

Loading force in three-point bending test F 3 PB

Normal

6 kN

Initial size of the crack a 0

Lognormal

0.2 mm

Smallest detectable size of the crack a d

Normal

2 mm

If a period of time t is specified and the time step is 1 year, it is possible to determine resistance of the construction R ( a ac ) and R ( ad ) pursuant to (4) - see Fig. 2, load effects, E ( N ) , pursuant to (5) and reliability function G fail according (6) – see Fig. 3, as well as the probability of elemental phenomena, U , D and F , pursuant to (8) through (10) for each year of the structural operation – see Fig. 4, which are the basis for specification of inspection times.

(a)

(b)

Fig. 2. Resulting histograms of the structural resistance (a) R ( a d ); (b) R ( a ac ).