Issue 51

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

2

2

2

(

) (

) (

)

(

)

2

2

2

1

=



−



 + −



 + −



+



 + +



I

6

(5)

2

m

11

m

22

m

22

m

33

m

11

m

33

m

12

m

23

m

13

m

6

where σ -1

is the fully reversed axial fatigue limit, σ u

is the ultimate tensile strength, I 2 a

and I 2 m

are the amplitude and the mean

value of the second invariant of the stress deviator tensor. In order to predict the material fracture with an arbitrary number of N cycles, let us replace the fully reversed axial fatigue limit σ -1 in Eqn. (3) with the axial S-N curve σ a 0( N ) .

2

2

   

    +    

   

3

I

3

I

2 ( ) a N

2

m



1

(6)





a

0

u

Let us rearrange Eqn. (3) for two types of multiaxial loadings given in the second part. For the first case (see Eq (1)), we will write as follows

2



  



3

m

=



=









− 

I

3

I

( ) 1 N

,

,

(7)

a

a

0

2

a

a

2 m m





u

For the second one (see Eq 2), it will be

2

m    −     u 



( ) N

a

0

=



=







I

I

3

,

,

(8)

1

2 a

a

2

m m

a

3

The Marin method requires the ultimate tensile strength and the axial S-N curve. The ultimate tensile strength σ u of the alloy is equal to 450 MPa. The axial S-N curve was plotted according to the experimental data ( σ a = 0.5 · σ y ; τ m = 0 and σ a = 0.61 · σ y ; τ m = 0 from Tab. 2) and was interpolated through a function σ a 0 ( N ).

( ) ' 2 f N N   = ( )



(9)

a

0

( ) 0 ' 2 f N N   = ( )



(10)

a

0

where coefficients σ f = -0.051. For different alloys one can observe an increase of fatigue strength in the compression area (at negative static tensile stresses σ m ) [32]. However, the Marin method (see Eq 6) does not make it possible to consider this. One can observe the same value of the second invariant I 2 m (see Eq 5) at positive and negative values of static tensile stresses σ m . Also, the disadvantage of the method is that it predicts the same reduction of fatigue life at constant torsional τ m and tensile σ m mean stresses (see Eq 6). And, as has been mentioned above, for ductile materials an increase of the mean stress in torsion direction leads to a decrease of fatigue strength lower than in axial direction. In order to take into account this effect one can add, for example, the maximum hydrostatic stress (see Eq 11) how was made in [31]. The advantage of the model is its relative simplicity and a small number of adjusting experiments ( σ u ; σ a 0 ( N )) necessary ’ = 1478 MPa, τ f ’ = 370 MPa, and exponents β = -0.156, β 0

to determine its parameters.

The modified Crossland method (Crossland+) The Crossland method does not take into account the static torsional stress effect. Therefore, authors in Ref. [31] proposed the modified Crossland method:

155