Issue 62

A. S. Yankin et alii, Frattura ed Integrità Strutturale, 62 (2022) 180-193; DOI: 10.3221/IGF-ESIS.62.13

If there is one fatigue curve and a point on another curve, we can assume that they are equidistant, then b 1 =b 0 , the model will be rewritten in the form:

   

   

 ' f

  

  

max

min

mean

max min





I

I

I

I

I

1

1

1 1

mean

2

2

   2

1

1

 



I

1

(15)

     0 ' 2 b f N

1

  2 N

b

2

2 B

 '





2



 ' f

3

3

0

B

f

B

If there is one fatigue curve, we can assume that the tensile-compression and torsional curves coincide, then σ′ f = √ 3 τ′ f , the model will have the form:

  

  

max

min

mean



I

I

I

1 1

mean

2

2

   2



I

1

(16)

     0 ' 2 b f N

1

2

2 B







3

B

B

If there is only one static test, we can take σ B = √ 3 τ B , the model will look like this:

max

min

mean



I

I

I

2

2

  2

1

(17)

     0 ' 2 b f N

2

2 B



C ONSIDERATION OF THE PHASE ANGLE BETWEEN LOADING MODES

I

t can be shown that in the variants of notation (14)-(17) the model of multiaxial fatigue will not consider the phase shift between the normal and tangential stress components, which does not always correspond to the experimental data. In this regard, let us introduce an additional summand into the radical expression:

max min

max

min





I

I

I

I

mean

mean

min

1

1

2

2











A

A I

A

A I

A I

1

(18)

1

2 1

3

4 2

5 2

2

2

The last term of the radical expression will be nonzero only if there is a phase shift between the tangential and normal loading modes. The setup experiment to determine the constant A 5 can be as follows:







         sin ; t

      2 t

sin

a

a

11

12

(19)

     0;

    33 13 23 22

  3

a

a

thus

max min

mean

mean

  I

 2 ; a





I

I

I

0;

0

1

1

1

2

2







1 sin

  

  

  

  





     sin t

    cos t

2

2

2

 

      t

2 I t per

2

2



 t

 

 a



  

sin

a

a

a

3

2

(20)

max

  min I

2

 a

I

2

2

2

   

   

1

3

1

2

 a A A 2 3

2

 a



     1 A







A

3

     0 ' 2 b f N

a

1

5

5

  2 N

  2 N

  2 N

b

b

b

2

 '

 '

 ' f

phase

1

0

phase

f

184