PSI - Issue 13

B.A. Stratula et al. / Procedia Structural Integrity 13 (2018) 1402–1407 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1406

5

min max / R    , the criterion will look like this

For uniaxial loading with the coefficient of asymmetry of the cycle



2 (1 ) 4 / 2) / 2 R 2

2 2 1 1/ 2 / (1 ) 4 F F n R      

F F S A N

max (   F

   

 

when

F

F



Comparing with Baskin formula for uniaxial fatigue curve

and having experimental

max (1 ) / 2 R 

N

R CR     

F

0 R we get

data for

1 R   and

3 1 )10 / 2 F   2

2 1 ) / 2

S

A

1 (        F F

(    B

)(      

,

,

F

F

F

F

1





2      2 

2  

(2 / (1 ) 1) R 

1 2 / (1 ) R 

/ / (4 / (1 ) ) R   





 

F

0

0

0

Here 1   and 0 R  are classical fatigue limits according to fatigue curves for with the cycle asymmetry coefficients 1 R   and 0 R , respectively, and B  is the ultimate strength, 0 1 / R      . An analysis of Findley's criterion for the pure-torsion reversible mode yields the following formulas:  After calculating these parameters from the results of two uniaxial tests with different cycle asymmetry coefficients, the problem of calculating the orientation of the critical plane and the durability for a multiaxial stress state is solved using the formulas obtained above for the normal components and the equation for the number of cycles before fracture N . It has now been established that relatively small cyclic stresses (less than the classical fatigue limit) acting at a high frequency (of the order of 1 kHz and higher) can lead to fracture of structure, Bathias and Paris (2005). High frequency loading leads to significant operating time ( N ~ 10 9 – 10 10 cycles) during the estimated service life of the product. The specified range of durability N >10 8 is known in the literature as very-high cycle fatigue (VHCF). In recent years, the VHCF tests have been developed and implemented Bathias (2006) for a very small set of cyclic loads, primarily for reversible and pulsating tensile-compression, Nikitin et al. (2012), as well as torsion of samples, Nikitin et al. (2015). However, in order to evaluate the durability of various structural elements subjected to high frequency long-term complex loading, the criteria for multiaxial VHCF fracture are necessary. In this paper we propose a simple and natural form of such criteria, based on the generalization of known multiaxial models for classical fatigue regimes. Consider the generalization of multiaxial LCF-HCF criterion to the regime of VHCF (Fig. 1, right branch of bimodal fatigue curve: 8 10 N  ). The basis for the generalized, multi-axis criterion of the Findley type is the similarity of the behavior of the left and right branches of the bimodal fatigue curve. This generalization consists in replacing the parameters of the left branch of the bimodal fatigue curve by the parameters of the right branch: R    , 3 8 F F    , where 1   and R  are the "new" fatigue limits on the right branch of the fatigue curve for the asymmetry coefficients R = -1 and R=R 0 . For VHCF regime we get (all parameters are marked ~) 2 1 1 (1 / 1 ) / 2 F F          , 3 2 )(1 / 1 )10 / 2 F   1 (          c B F F 2. Generalization of the multiaxial fatigue fracture criterion in the VHCF mode 1 B     , 1 1      , R

8 1 )10 / 2 F   2

2 1 ) / 2

S

A

1 (        F F

1     (

)(      

,

,

,

0 1 / R     

F

F

F

F

1





2      2 

2  

(2 / (1 ) 1) R 

1 2 / (1 ) R 

/ / (4 / (1 ) ) R   





 

F

0

0

0



C N

1       a

becomes:

For the pure-torsion reversible mode

F

8 2 )(1 / 1 )10 / 2 F   

2 1 1 (1 / 1 ) / 2 F F          ,

(          

c

F

F

1

1