PSI - Issue 22

Z. Marciniak et al. / Procedia Structural Integrity 22 (2019) 393–400 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

396

4

3. Experimental results and discussion Fig. 3 shows relations between the shear stress amplitude  a and the normal stress amplitude  a for the tested round cross-section specimens and two different numbers of cycles to failure under proportional loading (  = 0°). Graph 1 shows the Gough-Pollard model (ellipse quadrant) describing the limit state for N f = 3  10 6 cycles, and solid line 2 for N f = 1  10 5 cycles. Dashed line 3 is related to the equivalent stress amplitude equal to 360 MPa, obtained according to the Huber-Mises hypothesis for different ratios of normal and shear stresses. The curve 1 can be described by the equation, which takes the following form at the fatigue strength for N f = 3  10 6 cycles

2

2





  

 

   

a

a

1

    

(1)

300

162

From Fig. 4 it appears that there is a good conformity of test results for the verified combinations of bending and torsion with the Gough-Pollard curve for N f = 1  10 5 cycles.

Fig. 3. Limit state for two numbers of cycles to failure N f under bending and torsion with phase shift  = 0°.

The following equivalent stresses criteria were used for the calculated number of cycles N cal to failure: - the modified Huber-Mises criterion (mode H-M)

2

2   

4   

  

    

  

  

2

2









  2 0 5625 2   .

a

a

a

a

4 1 3 

2 1 3

cos





(2)

eq







2

a

a

a

2 2 3  







 

where for  = 0  ,

a

H M 

a H M  ,

a

a

,mod

- the modified Tresca criterion (mod T-G)