PSI - Issue 42

Michael Brünig et al. / Procedia Structural Integrity 42 (2022) 1137–1144

1141

M. Bru¨nig et al. / Structural Integrity Procedia 00 (2019) 000–000

5

F i [kN] (a) P 1/+1

F i [kN] (b) NP 1/+1

15.0

15.0

10.0

10.0

5.0

5.0

0.0 1.0 2.0 3.0 4.0 Exp a1 Exp a2 Sim a1 Sim a2 Δ u i [mm]

0.0 1.0 2.0 3.0 4.0 Exp a1 Exp a2 Sim a1 Sim a2 Δ u i [mm]

0.0

0.0

Fig. 3. Load-displacement curves: (a) proportional path, (b) non-proportional path

(a) P 1/+1 end

(b) NP 1/0 switch

(c) NP 1/+1 end

Exp

Sim

Exp

Sim

Exp

Sim

1.06

0.36

0.91

0.00

0.00

0.00

Fig. 4. Principal strain fields

by the corresponding numerical simulation (Sim). On the other hand, for the non-proportional loading path a localized band of the first principal strain with slightly diagonal orientation after the first load step (NP 1 / 0 switch) appears in the experiment (Exp) with maxima of 36%. At the end of the non-proportional path (NP 1 /+ 1 end) the strains increase up to 91% localized in a band with diagonal orientation from top right to bottom left. This strain behavior is also predicted by the numerical simulation (Sim). The strain fields in Fig. 4 clearly show that the loading history has an influence on the deformation and localization behavior of the investigated steel. Based on the numerical analysis the stress state in the notched regions of the H-specimen can be predicted, see Fig. 5. In particular, after the proportional loading path the stress triaxiality reaches the maximum of η = 0.3 in the center of the notch (Fig. 5(a)). The corresponding Lode parameter is ω = -1.0 (Fig. 5(d)). In the case of the non-proportional loading path the stress triaxiality after the first load step reaches η = 0.0 in the center of the notch and η = 0.3 at its boundaries (Fig. 5(b)). The corresponding Lode parameter is ω = -0.1 in the center and ω = -1.0 in the boundaries (Fig. 5(e)). After further non-proportional loading the stress triaxiality at the end of the test (shortly before fracture occurs) is η = 0.3 (Fig. 5(c)) and the Lode parameter is ω = − 1 . 0 (Fig. 5(f)). Thus, the final stress state is nearly una ff ected by the loading history. Di ff erent mean values are computed as averages over the cross section of the notch. For example, more information on the stress history is shown in Fig. 6 where evolution of di ff erent mean parameters is visualized over the increasing mean equivalent von Mises strain ¯ eq . In particular, the stress intensity ¯ σ I (defined as the maximum principal shear stress) increases with increasing equivalent strain and the behavior is very similar for the proportional and the non proportional loading path, see Fig. 6(a). In addition, the formation of the mean stress triaxiality ¯ η and the mean Lode parameter ¯ ω is shown in Fig. 6(b). For the proportional loading path the mean stress triaxiality is at the beginning of loading ¯ η = 0.25 and slightly increases to ¯ η = 0.40. For these mean stress triaxialitites damage is caused by simultaneous growth of voids and formation of micro-shear-cracks. In the case of non-proportional loading the mean