PSI - Issue 40

V.N. Syzrantsev et al. / Procedia Structural Integrity 40 (2022) 411–417 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

415

5

Using function (8) for each obtained stress value , 

1,

we calculate the value:

j j

m



( )    , j f

(11)

f

j



knowledge of which allows calculating the value of relative duration of the j -th step for each step of the block of stresses , 1, j j m   by the relationship:

  

  

m 

/

t

j f   

f

.

(12)



j 

j 

j

j



1

j



Positioning the block steps  in the order of decreasing stress levels, we obtain the desired loading cyclogram for the case of setting the stress in a shape of a sample of finite length with an unknown distribution law. For function f  (  ) shown in Fig.2, the loading cyclogram is shown in Fig.3. , , 1, j  j t j m

Fig. 3. The loading cyclogram obtained on the basis of function f  (  ) in Fig. 2

3. Determination of the loading cyclogram steps duration The cyclogram in Fig.3 is built in the plane of parameters   t , where t j , loading block steps. To obtain the numbers of strain cycles j N , 1, j m  for each j -th block step for the period of registration of values, we use the information obtained by the original means of registration of cyclic strains – fatigue damage sensors (FDS) [Kopnov (2017 and 1992), Troshchenko (1985), Bojko (1981)]. The FDS design does not differ from the strain cells. The operation principle of the sensors is based on the measurement for irreversible changes in electrical resistance under action of the cyclic deformations, depending on the level and duration of loading. The change in electrical resistance can be registered at any desired time. FDS do not need electricity and constant connection to the measuring equipment. The FDS is calibrated when determining the number of deformation cycles ( j N , 1, j m  ) at each stage of the block. Calibration is performed in the cyclic deformation process of the samples. The FDS is glued on their working part. The dependency for the magnitude of the relative change in the electrical resistance for the FDS R  on the stress amplitude  and the number of deformation cycles N is determined because of the FDS calibration. The least squares processing of the FDS calibration data is presented in the study by Kopnov (2017). It makes it possible to describe the function ( , ) R N   in the regression dependency form: 1, j m  is a relative duration of the

2 ( ) ( ) R N V V N V N V N             , 3 ( , ) ( ) ( )

(13)

0

1

2

3