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

1143

7

(a) P 1/+1 end

(b) NP 1/+1 end

(S)

(L)

(C)

(S)

(L)

(C)

g

g

1.22

1.22

0.00

0.00

(d) NP 1/+1 end

(c) P 1/+1 end

m 0.11

m 0.11

(S)

(L)

(C)

(S)

(L)

(C)

0.00

0.00

Fig. 7. Equivalent plastic strain γ after (a) proportional and (b) non-proportional loading; equivalent damage strain µ after (c) proportional and (d) non-proportional loading

the longitudinal cut (L), see Fig. 7(c). The distribution of the equivalent damage strain after proportional and non proportional loading history is very similar (Fig. 7(d)) although di ff erent damage processes have been predicted.

4. Conclusions

The paper discussed a continuum framework to model damage of ductile materials. The phenomenological model takes into account di ff erent branches in the damage criteria and damage rule corresponding to di ff erent stress-state dependent damage and failure processes on the micro-scale. Evolution of plastic and damage strains is modeled by rate equations which are numerically integrated by the inelastic predictor–elastic corrector method. Validation of the continuum damage model has been performed by new experiments with the biaxially loaded H-specimen and results have been compared with those taken from corresponding numerical simulations. Focus was on biaxial loading conditions and on di ff erent loading paths with the same final loading ratio. The analysis revealed the e ff ect of non proportional loading histories on the inelastic deformation and the damage behavior in ductile steels compared to proportional ones. In the critical notched regions of the specimen di ff erent stress states have been predicted leading to di ff erent stress-state-dependent damage processes expected on the micro-level. Thus, evolution of damage and fracture mechanisms is remarkably a ff ected by the loading conditions and the loading histories and have to be considered in validation of accurate material models predicting failure and lifetime of engineering structures.

Acknowledgements

The project has been funded by the Deutsche Forschungsgemeinshaft (DFG, German Research Foundation) – project number 322157331, this financial support is gratefully acknowledged.