PSI - Issue 13

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

95

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

5

(a1)

(b1)

(c1)

10 m

-0.66

0.50

-1.0

1.0

(c2)

(a2)

(b2)

10 m

Fig. 3. (a) Stress triaxiality; (b) Lode parameter; (1) F 1 : F 2 = − 3 : 1; (2) F 1 : F 2 = − 7 : 1.

of ω = 0 . 23. The stress triaxiality of η = − 0 . 29 and the Lode parameter of ω = 0 are achieved in the center of the cut plane. With increasing compression, it can be seen with load case F 1 : F 2 = − 7 : 1 that the distribution of the stress triaxiality and the Lode parameter becomes more inhomogeneous. The minimum value of the stress triaxiality for this load case is η = − 0 . 55 and the corresponding Lode parameter of ω = 0 . 26. Scanning electron microscope images of the fracture surfaces, see Fig. 3(c) were taken to visualize the relationship between stress triaxiality and damage mechanisms. In the load case F 1 : F 2 = − 3 : 1, in addition to significant shear mechanisms, some small voids which have already been compressed can also be detected in Fig.3(c1). With increasing compression, voids are hardly visible, as the load case with the load factor F 1 : F 2 = − 7 : 1 shows in Fig. 3(c2). These voids are more compressed due to the remarkable superimposed compression and only shear mechanisms can be seen. It should therefore be noted that damage mechanisms still occur even for these high negative stress triaxialities. In summary, a connection between the stress triaxialities of the numerical simulations and the damage mechanisms from the experiments can be seen, thereby confirming that a good approximation of the damage material behavior is achieved with the presented anisotropic continuum damage model. The minima of the stress triaxialities in both load cases discussed above reached a high negative value. Therefore, the cut-o ff value below which no damage should occur has to be discussed. In Bru¨nig et al. (2018) the function for the cut-o ff value η cut = − 0 . 6 + 0 . 27 ω for 0 ≤ ω ≤ 1 (15) was proposed and the stress state in the center of the fracture surface was evaluated. With this function the cut-o ff value of η cut = − 0 . 54 is obtained for the present load case F 1 : F 2 = − 3 : 1 with the Lode parameter ω = 0 . 23. The minimum stress triaxiality of this load case was η = − 0 . 39 and therefore does not fall below this limit value. For the second load case, the cut-o ff value is η cut = − 0 . 53. The minimum stress triaxiality reached η = − 0 . 55, which is slightly below the cut-o ff value. As a consequence of the results, the stress-state-dependent function for the cut-o ff value remains a good approach and should be further investigated for other specimens and load cases. 4. Cut-o ff value for negative stress triaxialities