PSI - Issue 28

L.A. Igumnov et al. / Procedia Structural Integrity 28 (2020) 2086–2098 L.A. Igumnov, I.A. Volkov/ Structural Integrity Procedia 00 (2019) 000–000

2090

5

The evolution equation for the creep will formulate in the form:

W 

1   

  



   c

Z 

Z 

  exp( ) c c f k    .

c c c ij ij W e     ,

rc

c



(21)

1

,

;

;



c c Z W W 

f

Z







c

c

c

c

c

c

c

c

1

W

r



f

f

c

c

Summation of damage during fatigue and creep can be written as:

W W

  

 

(22)

с  ,

1     р

 

Н

p



 

a

where is H – the Heaviside function. As a criterion of completion of the development of disseminated disease (stage of formation of the macrocrack) was adopted for achieving the magnitude of damage its critical value: 1 f     . (23) 3. Numerical results In the work (Mozharovsky N.S., Shukaev S.I. (1988)), the authors experimentally study the effect of the deformation trajectory type on fatigue life of the 08Х18Н10Т steel under a combined effect of alternating torsion and uniaxial tension-compression. The experiments were varied: the amplitude of intensity of plastic deformation ( p u e ), the view angle of the deformed state (  ) and the angle of phase shift  between the amplitude of axial deformation and torsion deformation. Processing of the experimental results by regression analysis provided the regression equation of the form (Volkov I.A., Korotkikh Y.G. (2008)): The analysis of experimental information shows a significant effect of  and  on fatigue life of the steel. Fig. 1 shows the fatigue curves (dotted lines) obtained using the regressive equation (fatigue life under uniaxial tension-compression (curve 2), curve 1 corresponds to alternating torsion, curve 3 corresponds to the ‘square-type’ trajectory (a combined effect of uniaxial tension-compression and alternating torsion)). In Fig. 1, the solid line shows fatigue curves for various deformation trajectories. Points i A , i B , i C ( 1, 2,3 i  ) in Fig. 1 correspond to the results of computational evaluation of fatigue life for the same intensity amplitude of plastic strains p u e for the three deformation trajectories in question. The results of the comparison of the calculated and experimental data show that:  the kind of fatigue curves is strongly nonlinear in nature;  regression dependence of the type (24) do not describe the experimental data in the region of "small" and "large" longevity, so formula (24) should be used with caution;  under the joint action of uniaxial tension–compression and alternating torsion (trajectory of the type "square") with the same amplitude of plastic deformation p u e , the durability is reduced compared to the uniaxial tension compression is more than 6 times, and under alternating torsion over 14 times.  intensity or full plastic deformation, the length of the trajectory of plastic strain are not the criteria of equivalence for processes with low cycle fatigue and for disproportionate loadings lead to a significant increase in the calculated longevity than actual. 2 ln 10.50 7.50 1.71 10 6.367 10 p N e         5 2  2 1.5839 10 8.41 10      5 2  2 5 2 3 5 2  7 2 2   2.66 10 3.133 10 2.4 10 1.372 10 2.04 10 . f u p u e                        (24)