PSI - Issue 2_A

Stefan Kolitsch et al. / Procedia Structural Integrity 2 (2016) 3026–3039 Stefan Kolitsch/ Structural Integrity Procedia 00 (2016) 000–000

3031

6

dN da

( ) p m p C F R a K K K R a ( , ) ( , ) = ⋅ ∆ ⋅ ∆ ∆ − ∆ ∆ −

,

(4)

th

where F( R , Δ a ) is calculated as

   

   

m

  

     

   ∆ − l

R f R

a

−

∑ = n i 1

  

  

− 1 ( , ) 1 1 1 ( ) ∆ = − − F R a

v

⋅ − 1

exp

⋅

(5)

i

i

by using Newman’s crack opening function depending on the stress ratio R :

    

+ + + 2 R A A R A R A R R , 3

; max(

0

≥

0

1

2

3

f R

− + , A A R A A 1 0 2 , 1 0

− ≤ < 2 R

( )

0

=

(6)

R

2

< −

with the parameters

1/

α

  

     

  

πσ

(

)

2

A

=

0,825 0,34 0,05 − + α

cos

α

max

0

2

σ

F

F σ σ α max

(

)

1 = + − = − − − A A A A A A A A 2 1 0,415 0,071 − 1 0 2 1 =

(7)

3

3

0

1

where σ max / σ F = 0.3 for the load levels investigated and α = 3.0 for plane strain conditions. For the long crack threshold Δ K th,lc ( R ) a linear dependence on the stress ratio R is assumed, (1 ) ( ) 0 th,lc K R K R = ∆ ⋅ − ∆ .

(8)

For evaluation of the parameters in Eqns 4 to 8, several fracture mechanics experiments are required. For this purpose, pre-cracked single edge bending (SE(B)) specimens were tested at different load ratios R = -1, R = 0.1 and R = 0.7 followed by a statistical analysis. In Fig. 3 the results of these experiments and their statistical evaluation are shown. Different colors mark different load ratios R . Experimental results are illustrated by single dots, whereas the continuous and dashed lines represent the mean estimate as well as the upper and lower predictions (denoted by COV-up and COV-low) obtained by combining the respective upper (97.5%) and lower (2.5%) confidence limits of the parameters, cf. Table 2.