PSI - Issue 28

Wei Song et al. / Procedia Structural Integrity 28 (2020) 200–207 Author name / Structural Integrity Procedia 00 (2020) 000 – 000

205

6

additional hardening caused by non-proportional loadings and notch gradient. To quantify the notch gradient distribution of damage factors, it is necessary to obtain the local stress or strain for notch fatigue analysis of related engineering components. Different damage parameters are defined according to the maximum principle strain, shear strain or energy amplitude by combining the critical plane, which meets the need of materials with tensile or shear dominant failure mechanism. These models are summarized in Table. 1.

Table 1 Multiaxial fatigue damage models considering the notch effect.

Multiaxial notch fatigue model

Expression

f t 

      

     

max

k

1



g

n 

( ) 2 f N

( ) 2 f N

b

c

f g 

1



+

=

+

max

FS model [2]

(

)

( )

2

n x 

G

y 



f t 

max

1

k



g

n 

( ) 2 f N

( ) 2 f N

b

c

f 

1



+

=

+

g

max

FS-M model [4]

(

)

( )

2

n x 

G G g  



f  

2

1

c b c b  −   +   

( ) f N

( ) f N

2

b

b c +



f f  e  

( ) ( , )  

4

W r  

r dr

=

+

ZSP model [1]

w

2

2

L

E

eff

f  

2

  max ( ) eq W t

(

)

(

)

2

b

b c +

f f  e  

2

2

N

N

=

+

Macha model [9]

f

f

E

f 

( n x E   e  = ) ( ) x ( ) a

(

)

(

)

b

c

f e 

2

2

N

N

+

Mäde model [10]

f

f

f  

2

2

(1

)

f



+

1 e



  

  

(

)

(

)

2

b

b c +

f f  e  

2

2

N

N



=

+

n 

NP

Proposed model

,max

f

f

2

2

k

E

t

3.3. Multiaxial fatigue life prediction The FS model considering the notch gradient gives conservative fatigue life predictions for all the cyclic loading conditions. While, the FS-M model provides relatively accurate fatigue life estimations for the test data, which are most within a life scatter of ±3 for different notch specimens. Similar to FS damage model, a trend of conservative fatigue life predictions for in-phase proportional loading by Made model was observed for base metal. Fatigue life correlations for these test data, computed by MATLAB, are shown in Fig. 6 along with the corresponding life prediction curve based on uniaxial fatigue properties. The proposed fatigue damage model considering the notch concentration factor gives good fatigue life predictions for in-phase proportional and 90  out-of-phase proportional loading. Multiaxial fatigue life predictions by the proposed model are also compared with FS, FS-M, ZSP, Macha, Mäde models. The proposed model on the basis of SWT model and stress concentration factors give acceptable fatigue life predictions comparing with the other models.