PSI - Issue 35

86 Toros Arda Akşen et al. / Procedia Structural Integrity 35 (2022) 82 – 90 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 Here, dλ and d are the proportionality factor and the plastic strain increment, respectively. 4. Damage Model

5

In general, damage models are classified into two groups, namely coupled and uncoupled models. Coupled models establish a relation between the internal damage and the deformation of the material (Lian (2015), Zhang et al. (2019)). However, the identification procedure of coupled models may be toilsome (Park et al. (2020)). In contrast, uncoupled models are salient for simplicity, and they require fewer mechanical test in order to calibrate the damage model parameters. It is assumed for uncoupled models that the failure occurs when a weight function over the plastic strain reaches a limit (Park et al. (2020)). Generalized plastic work is an uncoupled phenomenological damage model that considers the plastic work as damage indicator (Freudenthal (1950)). This criterion was incorporated into the Hypela2 user subroutine and can be expressed as follows (Freudenthal (1950), Ozturk et al. (2002), Aksen et al. (2020)). (10) In the equation above, σ eqv and ε eqv are the equivalent stress and strains respectively, C represents the critical damage parameter known as damage indicator. In Hypela2 subroutine, plastic work based - failure was calculated as a percentage as given in Eq. (11). , eqv f    =  0 . eqv d C eqv



eqv

0 

eqv eqv d

 

(11)

%

.100

Failure

=

C

5. Material Characterization HomPol4 criterion has 9 coefficients defining the in-plane anisotropy of the sheet. The calculated parameters of HomPol4 were listed in the Table 3 for TRIP590 and TWIP940 steels, separately. Out of plane properties were assumed as isotropic due to the lack of the information in thickness direction.

Table 3. Anisotropy parameters of HomPol4 yield function

α 1

α 2

α 3

α 4

α 5

α 6

α 7

α 8

α 9

TRIP590 TWIP940

1 1

-2.02

3.06 2.24

-2.36 -2.02

1.048

6.3

-6.51

7.109 6.366

7.236 8.836

-1.797

0.88

4.767

-4.556

Yield loci contours, yield stress and r value directionalities predicted by HomPol4 are given in Fig. 1 and 2.

0 0.5 1 1.5 2

TRIP590 TWIP940

Normalized Stress Along TD

0 0.5 1 1.5 2 Normalized Stress Along RD

Fig. 1. Predicted yield loci contours