Issue 51

A. S. Yankin et alii, Frattura ed Integrità Strutturale, 51 (2020) 151-163; DOI: 10.3221/IGF-ESIS.51.12

into account this effect because it predicts the constant ratio σ a 0 ( N i

) / τ a 0

( N i ) = √ 3. Therefore, the Eqn. (21) was

modified as follows:

2

2

) ( +

)

(

C I + +  D I

A I

B I

1

(28)

2 2

a

2 2

m

2 1

m

2 1

a

 = + + 



I

(29)

1

a

11

a

22

a

33

a

The parameters of Eqn. (28) are written in the numerator. It helps avoiding the division by zero (function jumps) at N k point, when σ a 0 ( N k ) / τ a 0 ( N k ) = √ 3. We think that such a formulation is more convenient for program implementation . The the model parameters A 2 , B 2 , С 2 and D 2 were determined as follows: - the parameter A 2 was determined by means of the torsional S-N curve τ a 0 ( N )

0 = ,

=

N 



m m  = = = 

0 = ,



=



0 = ,

I

I

( )

0

I

( ) N

I

,

,

(30)

a

1

m

a

a

0

1

a

2

m

2

a

a

0

2 0 1 ( ) a A N  =

(31)

was determined by means of the axial S-N curve σ a 0 ( N )

- the parameter D 2

1

0 = ,

0 = ,



=



=





0  = = = , m m 

=



I

I

( ) N

I

( ) N

,

,

(32)

I

0 3 N

( )

1

m

a

a

0

1

a

a

0

a

2

m

2

a

a

1

−

2 0 a A N 

1

( )

3

=

(33)

D

2



( ) N

a

0

was determined by means of the axial S-N curve σ a τ ( N ) with torsional mean stress τ m

the parameter B 2

= 126 MPa

1

=





0  = = ,

0 = ,



=



=



=



I

I

( ) N

I

( ) N

I

( ) N

,

,

,

(34)







a

m

1

m

a

a

1

a

a

2 m m

2

a

a

3

) 2

) ( 2 −

(

1

−

( ) D N A N   ( )

1



2 3 a 

2

a

=

B

(35)

2



m

the parameter С 2

was determined by means of the torsional S-N curve τ a σ ( N ) with tensile mean stress σ m

= 202 MPa

1

=





0  = = ,

=





=



0 = ,

=



I

( ) N

I

( ) N

I

I

,

,

,

(36)





a

m

1 m m

a

a

1

a

2

a

a

2

m

m

3

) 2

) ( 2 +

(

1

−

( ) A N B 



1



2

a

2 3 m

=

C

(37)

2



m

Thus, the approach presented above has all the advantages of the previous model and allows taking into account the different slopes of the fatigue curves under tension-compression and torsion, however, it requires even more experimental data (four S-N curves τ a 0 ( N ), τ a σ ( N ), σ a 0 ( N ) and σ a τ ( N )).

158