PSI - Issue 35

Andreas Seupel et al. / Procedia Structural Integrity 35 (2022) 10–17 A. Seupel et al. / Procedia Structural Integrity 00 (2021) 000–000

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Table 2. Calibrated model parameters. Para. Σ 0 c 1 c 2

H 0

H inf

q r c

Z 1

Z 2

Z 3

b 0

z b0

z b1

ϑ b0

ϑ b1

MPa K − 1

Unit

K MPa MPa -

-

MPa -

-

-

K

K -

-

Value 179.5 -9.12 · 10 − 4

373 1478 434.2 1 0.224 24.6 3.65 0.49 9.99 259.52 73.28 2.15 1.38

1 . 5

213 K 293 K 373 K

martensite volume fraction z

1 . 25

1

0 . 25 true stress | σ | in GPa 0 . 5 0 . 75

σ

z

0 . 2 0 . 4 0 . 6 0 . 8 1

0

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0

0

true strain | |

Fig. 3. Asymmetric strain hardening: simulated stress-strain and martensite evolution curves (compression–dotted lines, tension–solid lines).

4 · 10 − 4 s − 1 , parameter ˙ ε 4 s − 1 ). The obtained parameters are summarized in Tab. 2 and the calibration results are illustrated in Fig. 2. Additionally, predictions at various intermediate temperatures are shown. The simulated curves match the experimental ones well at calibrated temperatures. The predicted behavior is reasonable for temperatures in between with some deviations at higher strain levels. The martensite evolutions at all temperatures are excellently matched by the modified Olson-Cohen-model of Seupel et al. (2020). Furthermore, the model is able to reflect the sigmoidal shape of the hardening curves, if martensite evolution is highly activated. In Fig. 3, simulated stress vs. strain curves are plotted which illustrate the tension-compression-asymmetry: According to literature findings, e.g., Stout and Follansbee (1986) for TRIP-steel AISI 304L or Seupel et al. (2016) for TWIP-steel X6CrNiMn 15-9-6, higher stress levels are observed in compression compared to tension as long as special deformation mechanisms are present (TWIP-e ff ect at 373 K and / or TRIP-e ff ect at 213 K as well as 293 K for X3CrMnNi 16-6-6, see Rafaja et al. (2020)). The predictions of the calibrated temperature dependent model at higher strain rates are compared to the experi mental data in Fig. 4. The Norton-exponent m = 35 is chosen in order to capture the increase of the initial yield stress with higher strain rates, i.e., the initial positive strain rate sensitivity. This choice is close to the value of 40 for AISI 304 reported by Zaera et al. (2012). As experimentally observed, the simulations predict the drop in stress response below the static strain hardening curves at higher strain rate under both tension and compression, see Fig. 4 a) and b), respectively. The model’s stress response in tension is slightly better compared to compression, but overall a reasonable agreement is obtained. Furthermore, the predicted martensite evolutions are in excellent agreement with the experimental data. In Fig. 5, the temperature evolutions during straining are compared which have been measured for tension and compression. Near the center of the tensile specimen (thermocouple TC 2), a good agreement of the simulated and measured temperature increase can be concluded for the considered strain rates, see Fig. 5 a). In compression, Fig. 5 b), a higher deviation of the final temperature at ˙ t = 1 s − 1 is observed, but the qualitative change of the temperature curve from ˙ t = 1 · 10 − 1 s − 1 to ˙ t = 1 s − 1 is fully reflected by the model. The change in shape of the temperature curves is possibly due to the transition to adiabatic heating (parabolic shape of the curve, Wolf et al. (2014)). The simulated curve-crossing-e ff ect in yield curves mainly depends on the coupling between martensite evolution and the mixture rule for strain hardening of the proposed model. The considered experiments to study rate influence are conducted at a temperature, where strain induced martensite evolution is the dominant mechanism. To confirm the 0 = 4 · 10 −