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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3

(c)

(a)

0 10 20 [mm]

(d)

(b)

0 20 40 [mm]

0 10 20 [mm]

Fig. 2. New biaxial specimens

Classical biaxial specimen geometries (for example Fig. 1(j, k), taken from the overview Kuwabara (2007)) have been designed to determine the yield surface and the subsequent plastic behavior. They are characterized by an ex tended central part where at the beginning of the experiment a relatively homogeneous distributed stress and strain state is obtained, but with ongoing deformation more localized damage processes, for instance at the transition zone between leg and central zone, take place which lead to final failure. Consequently, this type of cruciform specimen is not suitable to study the damage and failure processes in a well controlled way. Based on these observations several new specimen geometries have been proposed and investigated numerically and experimentally: The Z-specimen (Fig. 1(a) and detail (b)) has been tested first in a one–dimensional testing device consecutively in tension and shear direction (Driemeier et al. (2010)), then in a biaxial divice under shear–tension load cases (Bru¨nig et al. (2015)) and finally under shear–compression loading (Bru¨nig et al. (2018)). The Z-specimen has shown good applicability for a wide range of loading conditions, but the strong coupling of two legs is from an experimental point of view di ffi cult to handle. The H-specimen (central part shown in Fig. 1(d)) is characterized by four independent notched regions which are arranged in direction of one axis. First numerical and experimental studies have been published (Gerke et al. (2017)) and a detailed study on the geometry can be found in Gerke et al. (2018). Furthermore the X0-specimen (central part shown in Fig. 1(c)) has been proposed. After an iterative process this geometry has been established and numerical studies have been published (Gerke et al. (2017)). In section 3 experimental results with the X0-specimen are presented in detail.

2. Continuum damage model

Large inelastic deformations including the evolution of damage and final failure in ductile metals can be modeled by the continuum framework presented in Bru¨nig (2003); Bru¨nig et al. (2008, 2015). Here the stress-state-dependent damage behavior is briefly outlined. The phenomenological approach takes into account damaged and fictitious un damaged configurations. The damaged configurations are considered to characterize the anisotropically damaged behavior. With

1 + ¯ β N (b)

= ˙ µ ¯ α

1 + β J 2 − σ = 0 (a) and ˙ H da

1 √ 3

f da = α I

(1)