PSI - Issue 42

D.I. Fedorenkov et al. / Procedia Structural Integrity 42 (2022) 537–544 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

542

6

(

)

1

s

   

   

pl

2 2 1 1

− − −

 

u 

u

.

(8)

r

=

2

E

c 

4.3. Kinematic hardening The kinematic hardening constants (2) are determined depending on the aims and objectives of the subsequent interpretation of the results. If the aim is to simulate only monotonic loading, it is possible to find a and b by the least squares method, taking as a basis the expression described in Ellyin’s (1997) work: ( ) 1 exp e Y pl a b b       −  − −   = = . (9) If the aim is to model the kinetics of plastic strain accumulation under cyclic loading, the determination of the parameters becomes somewhat more complicated. It is necessary to know the first loop width – first cycle on the nominal stress curve from the low-cycle fatigue tests, thanks to which the Weller diagram (Fig. 1) was obtained. The back stresses are calculated from the obtained set of the first cycles at different levels of cyclic loading. The back stress value is the difference between the maximum axial stress and the yield stress in compression. The compressive proportional elastic limit is the decrease in the tangent angle of the tangent to the curve compared to the compression elasticity modulus by two times. Thus, the dependence of back stresses on the plastic strain of 25Cr1Mo1V steel at room temperature was obtained (Fig. 3, a).

Fig. 3. (a) dependence of back stresses on plastic strain; (b) the rate of change of back stresses from changes in plastic strain depending on the back stresses of 25Cr1Mo1V steel.

For uniaxial tension in equation (2) the plastic strain tensor rate coincides with the total equivalent plastic strain rate. Let ’ s write (2) in the form:

e pl d a b d  

 −  = .

(10)

Then, the dependence of back stresses on plastic strain is represented as a function In this dependence, the slope of the resulting curve ( ) f  uniquely determines a , the shift along the abscissa axis – b . Thus, the parameters of Voce isotropic hardening, Armstrong-Frederick kinematic hardening and Lemaitre damage model for structural steel were obtained (Table 2). ( ) e pl d d f    = (Fig. 3, b).