PSI - Issue 35

Toros Arda Akşen et al. / Procedia Structural Integrity 35 (2022) 82 – 90 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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steels. Subsequently, punch stroke at which the failure occurred, was predicted for both materials using the plastic work criterion. In the present study, the effect of out of plane stresses which are usually neglected in the previous works, were incorporated into the FE analyses as well by using solid elements. 2. Mechanical Tests In the present work, experimental data of UTT and HETs were procured from the literature study (Chung et al (2011)). Tension tests were conducted with a constant speed of 50 µm/s. Dimensions of the test specimen were selected according to the ASTM E8 standard corresponding to the 50 mm gauge length. Two different AHSS steels, namely TRIP590 and TWIP940 are studied. The thickness values of TRIP590 and TWIP940 steels are 1.2 mm and 1.47 mm, respectively. UTTs were conducted for RD, DD and TDs. Yield stresses and the r values for different material orientations are listed in the Table 1.

Table 1. Yield stress ratios and anisotropy coefficients for different directions (Chung et al (2011)) θ 0 45 90 Biaxial TWIP940 r θ 0.816 1.188 1.339 - σ θ [MPa] 445 447 459 600 TRIP590 r θ 1.02 0.78 1.29 - σ θ [MPa] 428 436 423 464

Here, θ represents the angle value between the related direction and RD. Experimental biaxial yield stress values were procured from different literature studies (Lee et al. (2012), Gösling and Thülig (2019)). Hardening curve parameters determined by curve fitting method are given in the Table 2 for both steels.

Table 2. Parameters of the Swift law K [MPa] n

ε 0

TRIP590 TWIP940

1240 2360

0.276 0.688

0.02 0.09

∗ σ true = K (ε 0 + ε p ) n Later, HETs of TRIP590 and TWIP940 steels were carried out. Blank holder force acting on the blank was 196.2 kN for both steels in the experiments. In this test, centered hole (with a 10 mm radius) of the blank was enlarged with the motion of the conical punch. The tool geometry was taken from the work of Chung et al. (2011). HER is an important parameter giving information about the stretch flangeability limit. In general, higher HER indicates higher flanging ability. Determination of HER in terms of percentage is given in Eq. (1).

final d d

initial − 

 

(1)

%

.100

HER

= 

 

d

initial

In the equation above, d initial , d final are the initial and the final hole diameters, respectively.

3. Plasticity model In this work, homogeneous fourth order polynomial-based yield function (HomPol4) was implemented through Hypela2 user subroutine in order to define the bound of the yield loci. First, polynomial yield criterion was proposed by Gotoh (1977). Later, Soare (2007) developed the Gotoh’s polynomial criterion considering convexity conditions. HomPol4 yield function can be expressed by following equation.

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