PSI - Issue 79

D. Marhabi et al. / Procedia Structural Integrity 79 (2026) 34–52

45



   

  1 2 E  

2

2

, m Rb   

2

r        R

2

2

, a Rb

(19)

, m Rb   





(

)

W

Rb To 

 

, a Rb

E

2

So that the over-energy under rotating bending combined to torsion supplied on a cycle is:   * 2 2 * 2 2(1 ) , , (1 )(1 ) 2 2 Rb To Rb To r mRb a Rb W E R q                  

(20)

We consider the relationship by triaxiality:



1

( R dTa Rb To dTm Rb To   ( ), (

), 2.07)

(21)

From the relations (11), (15), (17), (19), (20) and (21) the new criterion is identified (Appendix A3). The following expression of fatigue criterion under combined rotating bending and torsion is :

2

2

2

2

2

* 2 Eq Rb ,







, Eq Te  

, m Rb    

1



, a To

Rb

, mTo

, 1     (22.a) This elliptical function (22.a) depends on experimental parameters from standard tests �� , �� , �� , �� . The damage factor E 0 of the criterion requires beforehand the choice of a data item among an equivalent tensile , ( , ) m Te Te   through some experimental test for initiating the small crack in material aerea. , 1 2 0 2 0 2 2 , 1 , 1  ( ) 1  2 Rb Rb E Rb To where E    

2

*2 2   

The criterion validity ifor damage Indicator E 0 is :

(22.b)





m

, Eq Te

2

Specimen 1

Specimen 2

Specimen 3

Specimen 4

, Eq Te  

516 MPa

Stress near small crack (MPa)

 *

 *

 *

 *

 m

 m

 m

 m

167,25

280

178,4

245

180

205

165,89

172

230,67

214,26

192,87

168,95

* 2 2 Eq Rb  ,

(MPa)

Table 2: Criterion validity for damage indicator

The minimum threshold stress, obtained by the relation (8) on the basis of fatigue test data in table 1 constitute an analysis validating the inequality (22.b). 8. SCIENTIFIC LITERATURE OF THE FATIGUE CRITERIA CHOSEN Two main approaches are used by [20], [21] and [23]: Critical plane models and global approaches. Some criteria from the literature are given below. A - Critical Plane Type Criteria The experimental observations show that the rupture of the test pieces takes place in certain privileged directions.