PSI - Issue 5

Sabrina Vantadori et al. / Procedia Structural Integrity 5 (2017) 761–768 Sabrina Vantadori et al. / Structural Integrity Procedia 00 (2017) 000 – 000

766

6

The equivalent stress amplitude related to the critical plane, according to the Carpinteri criterion, is given by:

2   

  

 

(8)

af

, 1 

2

2

N

C







, eq a

, a eq

a

af

, 1 

a eq N , is expressed by:

where



 m u  /

a eq N N ,

N

 



(9)

a

af

, 1 

being m N and a N the mean value and the amplitude of the normal stress to the critical plane, respectively, u  is the ultimate tensile strength of the material, and a C is the amplitude of the shear stress acting on the critical plane, computed according to the procedure proposed by Araujo et al. [16] . The number of loading cycles to failure, f N , is determined by solving the following equation:         m f af a m f m f af af a eq N N N N N N C N 0 , 1 2 * 2 0 2 0 2 , 1 , 1 2 , / / / /          (10) By employing the fatigue life f N results obtained from Eqs (6) and (10), the value of damage D at the verification point 1 C is computed applying both the Basquin relationship:

k   

S

  

S

af

, 1 

(11)

N

N



ref C

S

, 1

0

S

eq,a

and the Miner rule:

, 1 ref C f N

D 

(12)

N

  k k S

  0 0 N N S when the Findley criterion is applied, whereas

, 1   af af S 

eq a eq a S , ,   ,

being

,

, and

, 1 

, 1    af af S  , , 1

eq a S ,

, k k S  ,

0 0 N N S  when the Carpinteri criterion is applied.

 

eq a ,

The damage values according to the Findley criterion are constants since D is independent of both n and  : D = 1.22 by employing the welding fatigue properties, and D = 1.37 by employing the C25E steel fatigue properties. The damage values according to the Carpinteri criterion depends on n (Fig. 5).

1.0

1.0

0.8

0.8

0.2 DAMAGE, D 0.4 0.6

(a) DAMAGE, D 0.2 0.4 0.6

0.5(10) 5 1.0(10) 5 2.0(10) 5 n Carpinteri et al.

0.5(10) 5 1.0(10) 5 2.0(10) 5 n Carpinteri et al.

(b)

0.0

0.0

0

30

60

90

0

30

60

90

PHASE SHIFT,  [°]

PHASE SHIFT,  [°]

Fig. 5. Damage determined by employing (a) the welding fatigue properties, and (b) the C25E steel fatigue properties.