PSI - Issue 42

Michael Brünig et al. / Procedia Structural Integrity 42 (2022) 1137–1144 M. Bru¨nig et al. / Structural Integrity Procedia 00 (2019) 000–000

1142

6

(a) P 1/+1 end

(b) NP 1/0 switch

(c) NP 1/+1 end

+1.00 h

-0.33

(d) P 1/+1 end

(e) NP 1/0 switch

(f) NP 1/+1 end

w +1.00

-1.00

Fig. 5. Stress triaxiality η and Lode parameter ω

(a) Stress Intensity σ [MPa] I

1.0 (b) Triaxiality η , Lode parameter ω Triaxial ity □

1600

Lode parameter ○

1200

0.5

800

0.0

400

-0.5

P 1/+1 NP 1/+1

0 0.0 0.2 0.4 0.6 0.8 1.0 ε eq [-]

0.0 0.2 0.4 0.6 0.8 1.0 ε eq [-]

-1.0

Fig. 6. Evolution of stress variables: (a) stress intensity as well as (b) stress triaxiality and Lode parameter

stress triaxiality starts at ¯ η = 0.0 and only slightly increases in the first load step which corresponds to predominant formation of micro-shear-cracks. With increasing load F 2 in the second load step a jump in ¯ η can be seen up to ¯ η = 0.3 and, then, the behavior of the mean stress triaxiality is similar to that one of the proportional loading path. In this load step additional voids will nucleate and grow but the damage processes will be dominated by the early evolution of micro-shear-cracks. Similar behavior can be seen in the formation of the mean Lode parameter: for proportional loading it decreases from ¯ ω = -0.4 to -0.9 whereas for the non-proportional loading path it starts at ¯ ω = 0.0 and decreases to ¯ ω = -0.2 and with additional loading by F 2 it jumps to ¯ ω = -0.75 and follows the curve for proportional loading. Figure 7 shows distributions of the equivalent plastic strain γ and the equivalent damage strain µ after loading on the surface of the notch (S), in the longitudinal cut (L) and in the cross section (C). In particular, after proportional loading the equivalent plastic strain shows a widespread band on the surface up to γ = 1.22 which becomes smaller in the longitudinal cut (Fig. 7(a)). Similar behavior can be seen after non-proportional loading but the maximum is only γ = 1.13 (Fig. 7(b)). Damage mainly occurs on the surface of the notch (S) up to µ = 0.11 and is marginal in