PSI - Issue 79

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

48

Froustey & Lasserre criterion [4] The authors considered:  2 1 1 1 ln 1 a a a W V dT e      

W

m



and V

m

1















  

  

  



1

1





1 ln 1 





m dT e

1

1









dT

dT

1

 

1 1 e



a

m

The fatigue criterion of Froustey-Lasserre is: 2 1 a m FL V V E A B  

(28)

where

   

    

2

0 A E F    (



1 2 





1

2  

2





/ ( E G 

 



, ) 8 

A

and B

1

0

1 2 



E

2

3

, ) 

2

3

 

1



1

The domain of validity is defined by:



3



1

9. VALIDATION OF THE FATIGUE CRITERIA We propose the fatigue criterion for alternate rotating bending and torsion (22) depends on the threshold stress. We have been using the field of application using different criteria [13-18] and our own criterion by comparison with results found in the literature. The numerical analyzes refer to the experimental results of mechanical behavior fatigue. The material S65A steel testing by the Gough [19] on combined bending and torsion. In Table 3, the comparative study of all criteria is established using 16 tests: MD , Marhabi; FL , Froustey-Lasserre ; KK , Kakuno and Kawada; DV2 , Dang Van; RB , Robert; MD2, Mac Darmid2 and SI , Sines; On all the simulations of the critical plane, the MaDiarmid 2 criterion lead to conservative predictions. The others criteria are satisfactory and give fairly optimistic forecasts. 10. STATISTICAL ANALYSE OF CRITERIA RESULTS The analysis of Table 3 makes the criteria satisfying the rules of multiaxial fatigue over an interval per approach: The critical plane Criteria (CPC) case interval: 0.81 . . 1.08 C PC   The Global Approach Criteria (GAC) interval: 0.82 . . 1.07 GAC   The most relevant range corresponds to the McDiarmid2 criterion: 0.84 2 2.00 MD   All criteria are put to the test by an analysis of predictions for each test which are classified into three cases: 1- Correct forecast if the difference E-1 is less or equal to 2% 2- Conservative forecast if E> 1.02. Non-conservative forecast if E <0.98 Analysis of Forecast Performance by the Fatigue Criteria We want to obtain a ranking of the criteria based on a single variable. Thus, we represented the performance indicator I as a function of the mean deviation EM and the mean � : *( 1) I EM m   As we are looking for an average � closest to 1 therefore 1 m  closest to 0 and an average deviation closest to 0, the most efficient criterion will be the one whose performance index I will be the closest of 0. We can also know the