Issue 51

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

2

2

   

    +    

   

I

I



2

a

2

m

H

max

+



(11)

1

a

b

c

(

)

1 3



=



+



+



(12)

H

max

11max

22max

33max

where σ H max

is the maximum hydrostatic stress, a , b , c are the model parameters, which were determined as follows:

- the parameter a was determined by means of the torsional S-N curve τ a 0 ( N )

0 = ,

=





m m  = = = 



=





0 = ,

I

I

( ) N

0

( ) N

,

,

(13)

a

a

a

0

H

max

2

m

2

a

a

0

=



a

( ) N

(14)

a

0

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

1

1

0 = ,



=





0  = = = , m m 

=





=



I

( ) N

,

,

(15)

I

0 3 N

( )

0 3 N

( )

a

a

0

a

2

m

2

a

a

H

max

a

0 ( ) 3 3 ( ) a a N   − 0

=

с

(16)

N a

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

= 126 MPa

1 max 3 =

1

=





0  = = ,



=



=







I

( ) N

I

( ) N

( ) N

,

,

,

(17)







a

m

a

a

2 m m

2

a

a

H

a

3



m

=

b

(18)

2

2

  

      −

  





( ) N

( ) N





a

a

−

1

3

c

3

a

S-N curves τ a 0 ( N ) and σ a τ ( N ) were plotted according to the experimental data from Tab. 2 similarly to curve σ a 0 ( N ) (see section 3.1, Eq (9)). The advantage of this model is that it takes into account the beneficial effect of the mean compressive axial stresses and that the Marin method does not predict. Also, by using the σ H max term in the multiaxial function (11), the mean stress effect in the axial direction is increased compared with the torsion case. It is worth notice that this method is quite complicated, compared to the Marin method, and requires a great number of adjusting experiments (at least three S-N curves τ a 0 ( N ), σ a 0 ( N ) and σ a τ ( N )).

E XTENSION OF THE S INES METHOD

Extension of the Sines method to take into account the static torsional mean stress effect (Sines+) he Sines method [5] can be expressed through Eqn. (19): T

156