MATERIAL AND SPECIMENS The investigations were performed on rolled 1.73 mm thick sheets of an aluminum alloy of the 2000 series, which is mainly used in aircraft and space industry. The base material is coated by a 50 ÷ 80 µm thick layer of pure aluminum as a protection against corrosion. Second phase particles have been identified by a chemical analysis as iron and copper together with Al12Mn2Cu segregations, with a total volume fraction of 0.12 %. Various specimens have been tested to characterize the deformation and fracture behavior of the material, namely smooth, U- and V-notched flat tensile specimens, Kahn-specimens, see Figure 1, and large M(T) specimens. Kahn-specimens have originally been proposed for the investigation of fracture behavior in ship steel plates [5] and were applied for the determination of fracture properties of aluminum sheets, later [6]. They are C(T) like specimens without fatigue crack, a/W = 0, of dimensions 35 × 60 mm2. Their advantage is their small size which reduces test and material costs in relation to the M(T) specimens of dimensions 760 × 1350 mm2. All specimens were loaded in longitudinal orientation. Whereas smooth and notched tensile specimens failed macroscopically unstable, Kahn- and M(T) showed stable crack growth. The crack initiated normal to the loading direction but changed to slant fracture incliced by 45°, see right hand side of Figure 1. The same mechanism was observed on the M(T) specimens. 60° 15 mm 60 mm 35 mm 10 mm 5 mm 30 mm Figure 1: Kahn specimen: size and geometry (left), fracture surface with normal and slant fracture (right) MODELS FOR DESCRIBING DUCTILE DAMAGE The Gurson-Tvergaard-Needleman-Model (GTN) The model of Gurson [7] for porous metal plasticity with extensions by Tvergaard und Needleman [8] modifies the von Mises yield potential by introducing a damage parameter, f*, which is a function of the void volume fraction, f, Φ( σe, σh, f, σY) = σe 2 σY 2 εp ( ) +2q1 f * cosh q 2 3 σh 2 σY ε p ( ) −1− q1f * ( )2 = 0 , f * = f for f ≤ fc fc + κ( f − fc) for f > fc , (1) where σe is the von Mises effective stress, σh the hydrostatic stress, and σY( ε p) the actual yield stress of the matrix material. The model was implemented as a "user supplied material" (UMAT) of the FE program ABAQUS. In accordance with metallographic observations, it is assumed in the present simulations that voids have nucleated with beginning plastic deformation, f(t=0) = f0, and damage evolution occurs due to the growth of
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