PSI - Issue 13

Steffen Gerke et al. / Procedia Structural Integrity 13 (2018) 39–44 S. Gerke et al. / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 3. X0-specimen: (a) Photo and (b) corresponding notation

the damage condition (Eq. 1(a)) and the damage law (Eq. 1(b)) are given. Here I 1 = tr T and J 2 = 1 / 2 dev T · dev T are invariants of the Kirchho ff stress tensor T and σ reflects the damage threshold. Furthermore, N = 1 / ( 2 √ J 2 ) dev ˜ T is the normalized deviatoric stress tensor while ˙ µ represents the equivalent damage strain rate measure. The damage mode parameters α and β and the kinematic parameters ¯ α and ¯ β correspond to di ff erent stress-state-dependent damage mechanisms on the micro-level. They depend on the stress triaxiality η and the Lode parameter ω given by

2T 2 − T 1 − T 3 T 1 − T 3

I 1 3 √ 3 J 2

σ m σ eq

(a)

and ω =

with T 1 ≥ T 2 ≥ T 3 (b)

(2)

η =

=

where σ m = 1 / 3 I 1 is the mean stress, σ eq = √ 3 J 2 is the von Mises equivalent stress and T 1 , T 2 and T 3 are the principal Kirchho ff stress components. In this context it is important to point out that the corresponding stress-state dependent behavior has to be validated experimentally with appropriate specimen geometries. In continuation new biaxial experiments with the X0-specimen are presented which can provide this missing information.

3. Experiments with X0-specimen

The X0-specimen (Fig. 3(a), photo) is double-symmetric with four uniform notched regions which have been arranged in a 45 ◦ angle. The aluminum alloy EN AW 6082 (AlSiMgMn) is characterized by minor hardening behavior and the sheets have an initial thickness of 4.0 mm while within the notches it was reduced to 2.0 mm. Due to its geometry the specimen can be used under shear, tension and intermediate loading conditions. Fig. 3(b) reflects the appropriate displacement measures: ∆ u ref . 1 = u 1 . 1 − u 1 . 2 and ∆ u ref . 2 = u 2 . 1 − u 2 . 2 while F 1 . 1 = F 1 . 2 = F 1 (and corresponding F 2 . 1 = F 2 . 2 = F 2 ) holds with marginal deviations. Experiments with the X0-specimen have been performed under di ff erent, throughout the experiment constant, loading ratios, see Fig. 3(b). Details on the experimental technique can be found in Gerke et al. (2017). The load– displacement–curves shown in Fig. 4(a) indicate clearly the influence of the load case. In this context it is important to notice that the material behaves most brittle under the tension dominated load case F 1 / F 2 = 1 / + 2 while for rather shear like load cases 1 / − 0 . 5 , 1 / − 1 or 1 / − 2 distinct ductile behavior is characteristic. In contrast, the highest loads are achieved for tension dominated load cases 1 / + 2 , 1 / + 1 or 1 / + 0 . 5 while the maximum load drops with decreasing F 2 , see Fig. 4(b). Accumulation of damage leads to final fracture of the specimen. The influence of the loading ratios on the fracture behavior is indicated in Fig. 5. The upper row shows photos of the fractured specimens of all load cases. The surface shows the speckle pattern for the DIC evaluation while arrows indicate the loading conditions. The fracture pattern of the notches was not consistent: Frequently two opposite notches fractured but also the case that two neighboring notches fractured or that even three notches fractured occurred. The shape of the central area indicates nicely the influence of F 2 : Under 1 / − 1 loading the central area is elongated while this e ff ect reduces to a complete homogeneous enlargement ( 1 / + 1 ). The fractured specimens (upper row) can be directly related to the principal strains before fracture