PSI - Issue 13

Florian Fehringer et al. / Procedia Structural Integrity 13 (2018) 932–938 Fehringer, F., Schuler, X., Seidenfuß, M. / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 2. (a) Incorrect plastic behavior (b) Incorrect prediction of shear failure (c) No description of kinematic hardening effects.

The new material parameter k  characterizes the influence of shear stress on the damage evolution. The material parameter can be calibrated by using results from torsion tests or shear tests (i.e. butterfly specimen).

Fig. 3. (a) Hosford yield criterion for different parameters (b) Back-stress tensor in Rousselier model.

3) To numerically describe multiple loading situations, a kinematic hardening term is added to the Rousselier model. The kinematic hardening effect is described by a back-stress tensor using the formulas of Drucker and Prager (1949), Armstrong and Frederick (1966) and Chaboche (1983). In contrast to the standard kinematic formulations, the back-stress tensor contains in addition to the deviatoric part a hydrostatic part as well. Therefore, the Rousselier yield surface is not only shifted perpendicular to the hydrostatic axis but also parallel to the hydrostatic axis (see Fig. 3 (b)).    2 1   X X and     X X X'    (4) + (5)

3 2

X B   

and

(6) + (7)

X' 

p         X





C

q n X'     





  







p



q







4. Experimental and numerical investigations

To evaluate the extended Rousselier model, many different types of specimens under various loading conditions were tested (see BMWi-project No. 1501474). More than 25 different types of specimen were tested with a total number of experiments of approximately 200. Experimental and numerical results of smooth tensile tests, notched specimen tests, C(T)25-specimen tests and pre strained notched tensile tests can be found in Fehringer et al. (2016). Exemplary, the experimental and numerical results for the torsion tests can be found in Fig. 4 (a). Unlike the standard Rousselier model, the shear enhanced model is able to predict the moment of failure for low stress triaxialities. To investigate size effects on limit strains, a series