PSI - Issue 19

J. Srnec Novak et al. / Procedia Structural Integrity 19 (2019) 548–555 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

553

6

N =757

N =1

ε vM,pl

a)

b)

Fig. 4. Von Mises plastic strain: (a) first cycle; (b) stabilized cycle.

As shown in Fig. 5(a), the stress increases (i.e. material exhibit cyclic hardening) up to 100 cycle when saturation is reached, whereas strains progressively decrease over cycles, see Fig. 5(b). Hence, the “ stabilization criterion ” (used to identify the number of cycles at which material stabilizes) cannot be defined in terms of stress, but of strains. Here it is proposed to compute the relative difference of the equivalent strain range between two subsequent cycles:

   

   

( ) i

( 1)  i







 

eq,notch

eq,notch

100

eq,notch   e



(8)

( ) i





eq,notch

and to compare it with a given threshold (0.002). According to the adopted criterion, ∆ e eq,notch ≤ 0.002, stabilization is reached after 757 cycles. If, instead, the procedure described in Srnec Novak et al. (2018) is followed, in which the cycles to stabilization are estimated through Eq. (4) by using the plastic strain range calculated after five cycles ( Δ ε pl,5 ), a much lower number would result ( ≈260 cycles). This significant difference can be probably explained by taking into account the cyclic hardening that causes gradually decreasing of the plastic strain range over cycles and, therefore, an underestimated value of N stab is obtained when Δ ε pl,5 is considered. After stabilization, a maximum equivalent strain range Δ ε eq,notch =0.0199 is recorded. This value is in good agreement (1.53% relative difference) with that obtained by Saiprasertkit et al. (2012), see also Table 2. Fig. 5(b) confirms that the numerical model well describes the aforementioned experimental procedure. In fact, in that case the experimental set-up guarantees a constant imposed strain in the reference position, which is actually observed also in the present simulation. On the other hand, the previously mentioned stress redistribution makes the strain range not constant in the area close to the fictitious notch.

0.03 0.04 0.05 0.06 0.07

200 300

  eq,notch   x,notch   x,ref

Notch position

Reference position

-100 0 100

 

 x (MPa)

0 100 200 300 400 500 600 700 800 0 0.01 0.02

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 -300 -200 N=1-5 N=20 N=100 N=757

a)

b)

 x

N

Fig. 5. (a) Combined model: stress-strain cycles in x -direction; (b) strain range versus number of cycles.