PSI - Issue 13

Marco Schmidt et al. / Procedia Structural Integrity 13 (2018) 91–96

93

M. Schmidt et al. / Structural Integrity Procedia 00 (2018) 000–000

3

F kN [ ] 2

(b)

(a)

1

F

2

0.5

F

F

1

1

Exp. Sim. LF -3:1 -7:1

u mm [ ] 2

0

F

0.8

0.4

1.2

0

2

Fig. 1. (a) Z-specimen with force directions; (b) Force-displacement-curves of F 1 : F 2 = − 3 : 1 and F 1 : F 2 = − 7 : 1.

describes the formation of macroscopic strains caused by growth of micro-defects on the micro-scale, where

1 2 √ J 2

1 dev ˜ S

dev ˜ S with dev ˜ S = dev ˜ T dev ˜ T − 2 3

N =

dev ˜ T

M =

J 2 1

and

(9)

are normalized deviatoric stress-based tensors. In addition, the equivalent damage strain rate ˙ µ characterizes the amount of irreversible damage strain rates, and the stress-state-dependent parameters ¯ a , ¯ β and ¯ δ are kinematic variables characterizing the ratio between isotropic and anisotropic damage deformations. With ¯ α ( η ) =   0 for η cut < η ≤ 0 0 . 5714 η for 0 < η ≤ 1 . 75 1 for η > 1 . 75 (10) the volumetric portion corresponding to evaluation of micro-voids is weighted, and with ¯ β ( η, ω ) = ¯ β 0 ( η ) + f β ( η ) ¯ β ω ( ω ) , (11) containing ¯ β 0 ( η ) =   0 . 87 for η cut < η ≤ 1 / 3 0 . 97875 − 0 . 32625 η for 1 / 3 < η ≤ 3 0 for η > 3 , (12) f β = − 0 . 0252 + 0 . 0378 η (13) and ¯ β ω ( ω ) = 1 − ω 2 for η cut < η ≤ 2 / 3 0 for η > 2 / 3 , (14) here taken to be the isochoric portion corresponding to development of micro-shear-cracks is balanced. In this context the parameter ¯ δ is neglected based on results of numerical simulations of biaxial experiments with di ff erent loading conditions (Bru¨nig et al. (2016)).

3. Biaxial experiments and numerical simulations

To validate the continuum damage model and to investigate the influence of negative stress triaxialities on ductile damage behavior, an experimental series with various biaxial load ratios is performed. The experiments are carried out with a biaxial testing machine that uses four independent electro-mechanically driven cylinders with a maximum load of ± 20 kN . The test specimen (Fig. 1(a)) is characterized by a tension-compression-axis ( F 1 ) and a shear-axis ( F 2 ). In addition, the central region has notches in two directions to localize the strains and damage. The used material is an aluminum alloy of the 2017 series and was selected for its pronounced ductile behavior.