Analysis of Earring in Circular-shell Deep-drawing of bcc and hcp Sheet Metals

on topic "Analysis of Earring in Circular-shell Deep-drawing of bcc and hcp Sheet Metals"

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Engineering

Procedía Engineering 81 (2014) 887 - 892 =

www.elsevier.com/locate/procedia

11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014,

Nagoya Congress Center, Nagoya, Japan

Analysis of earring in circular-shell deep-drawing of bcc and hcp

sheet metals

Tetsuro Ohwue, Yoshikazu Kobayashi*

Akita National College of Technology, 1-1,Bunkyo-cho, akita-city, 011-8511, Japan

Abstract

The occurrences of earrings in circular-shell deep-drawing tests for two different types of crystal materials were investigated. The simulation was conducted with whole 360°circumference analysis. As the first result, the earring height is proportional not only to AR/R cve but also to ATLave ((R90-R00)/Rave). Secondly, the optimum m-value in yield function for the pure titanium and the low-carbon aluminum-killed steel, which led to the fairly good reproduction of experimental results, is 8 and 2 respectively. Furthermore, the blank mesh pattern is assumed to clarify the influence of R-values of three directions.

© 2014 PublishedbyElsevierLtd.Thisisan open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University Keywords: Deep-drawing; FEM-analysis; Aluminum-killed steel; Pure titanium; R-value; Anisotropy; Earring

1. Introduction

The earring of circular-shell drawn cup has been mutually related with R-values of three directions [1]. However FEM analyses of the earring for pure titanium drawn cup [2] and aluminum alloys [3] are reported, there are few reports with different crystal type analyses. In this report, a circular-shell deep-drawing test and an FEM simulation utilizing LS-DYNA with YLD89 [4] anisotropic yield function were conducted in order to investigate the occurrence of the earring for the low-carbon aluminum killed steel (bcc) and the pure titanium (hcp). In order to clarify the influence of R-values of three directions, the new parameter ATLave ((R90-Roo)/Rave) and the whole 360°

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* Corresponding author. E-mail address: Ohwue@canvas.ocn.ne.jp

1877-7058 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi: 10.1016/j.proeng.2014.10.093

circumference blank-mesh were adopted and experimental cups and analyzed figures were compared respectively. 2. Experimental and analyzing procedure

A circular-shell deep-drawing test was conducted with 780 kN double-action oil-hydraulic press. Punch diameter is 75 mm with 5 mm punch shoulder radius and die diameter is 8 0mm with 5 mm die shoulder radius. Materials used were a low-carbon aluminum killed steel (Material A) and a pure titanium (Material B) with 1mm thickness. Mechanical properties and R-values of three directions are shown in Table 1 and Table 2. In Table 2, R00, R45, R90 show R-value of longitudinal direction (0°), diagonal direction (45°), transverse direction (90°) respectively. Rave, AR and new parameter ATL and ATLave values are calculated by Eq. (1)-(4), and also shown in Fig.1. Drawing ratio is 2.2 and Teflon lubricant is used for both sides of the blanks. Frictional coefficient used in the simulation between blank and tool surface was assumed to be 0.05 by the experimental result. An FEM simulation utilizing LS-DYNA with YLD89[4] anisotropic yield function (Eq. (5)) was conducted with the blank-mesh as shown in Fig.2. The m-value of Eq. (5) was changed from 2 to 12 in the simulation.

R = R00 + R"0 + 2R45

AR = + - R45,

ATL = R"o - Roo, ATL = R"0 " R00

= a\K 1 + K 2\m + a\K 1 - K 2+ c\2 K 2|m = 2 a e

Table 1. Yield stress (YS), tensile strength (TS), total elongation (T.El), and uniform elongation (U.El) of materials in three directions.

Material Direction YS TS T.El U.El

(MPa) (MPa) (%) (%)

A L (0°) 165 302 4".7 23.3

D (45°) 173 314 43.6 1".3

T (90°) 164 2"" 48.3 24.0

Ave. 16" 307 46.3 21.5

B L (0°) 218 334 40.3 24.0

D (45°) 25" 318 41.0 ".8

T (90°) 307 351 37.1 6.7

Ave. 260 330 3"." 12.6

0° 45° 90° (L) (D) (T)

Direction

Fig. 1. R-values of three directions and AR and ATL values.

Table 2. R-values of three directions (R00, R45rR90) , Rave, AR, ATL and ATLave values of materials.

Material Roo R45 R90 Rave AR AR/Rave ATL ATT ave

A 1.84 1.31 2.13 1.65 0.68 0.41 0.2" 0.18

B 0.83 2.1 3.32 2.0" -0.02 -0.001 2.4" 1.1"

3. Results

Fig. 3 shows the comparison of the experimental photo and simulation figure of material A (low-carbon aluminum killed steel). In Fig. 4, the comparison of experiment and simulation shows the wall height distributions of Material A from 0° to 360°. In Fig. 5, the comparison of the experiment and simulation figures of material B (pure titanium) is shown. In Fig. 6, the comparison of experiment and simulation about the wall height distributions of Material B from 0° to 360° is shown. The best m-value of Eq. (5) used in the simulation of Material A is 2, and that of Material B is 8 respectively. This result of Material A does not coincide with the paper of YLD894). For both materials, the more m-value becomes, the less the earring height becomes. From these figures, the experimental results and the simulation results comparatively coincide well.

90° (T-direction)

Fig. 2. Blank-mesh used in simulation.

(a) Experiment (b) Simulation

Fig. 3. Comparison of experimental photo and Simulation figure of circular-shell deep drawing test of Material A (Low-carbon aluminium-killed steel).

4. Discussion

4.1 Influence of AR/Rave value

Figure 7. shows the relationship between AR/Rave and the average earring ratio. In Fig. 7, experiment data (solid marks) and simulation data (open marks) of imaginary materials by changing AR values with the same Rave value of Material A. Maximum and minimum lines of D.V. Wilson et a.l are also plotted in Fig. 7. The correlation between AR/Rave and the average earring height is not always true, because Material B is out of data from D.V. Wilson et al. [1].

85 80 75 70 65 60

_ m-2 (Simulation) -Experiment

45 90 135 180 225 270 315 360 Angle from rolling direction (°)

Fig. 4. Relationship between Fig.4 Angle from rolling direction and wall height compared with experiment and simulation (m = 2) in low-carbon aluminium-killed steel (Material A).

(a) Experiment (b) Simulation

Fig. 5. Comparison of experimental photo and Simulation figure of circular-shell deep drawing test of Material B (pure titanium)

4.2 Influence of ATL/Ravevalue

Figure 8 shows the relationship between ATL/Rave and the average earring ratio. In Fig.8, experiment data (solid mark) and simulation data (open marks) of imaginary materials by changing ATL/Rave values with the same Rave and AR value of Material B. From this figure, the larger the ATL/Rave value, the larger the average earring ratio becomes.

4.3 Influence of blank mesh

Table 3 and 4 show the circumference angle of ears and valleys of experiments and simulations compared with the four discontinuous points of blank-mesh in Material A,B. In Material A, the angles of valleys have the strong

"¡5 70

g 65 60

0 45 90 135 180 225 270 315 360 Angle from rolling direction (°)

Fig. 6. Wall height distributions compared with experiment and simulation in case of Material B (Pure titanium).

—O—Experiment ' m=8 (Simulation)

~\-1-1-r

Maximum line of Wilson et.al. I I I

Material A (Experiment)

-0.8 -0.4

0.4 0.8 1.2 AR/R^

Fig. 7. Relationship between AR/Rave and the average earring height.

< o ---

0 0.5 1 1.5

ÛTLave

Fig. 8. Relationship between ATLave value and average earring height in Material B (pure titanium) and imaginary materials changing ATL; value in case that AR values are nearly zero.

Table 3. Angle of valley and earring from longitudinal direction in case of Material A.

Number of vally and earring 1'st 2'nd 3'rd 4'th

Discontinuous point of blank I 42° 128° 222° 308°

Vally angle (Simulation) 40° 130° 220° 310°

Vally angle (Experiment) 45° 125° 215° 315°

Earring angle (Simulation) 0° 80° 180° 260°

Earring angle (Experiment) 0° 85° 165° 260°

Table 4. Angle of earring and valley from longitudinal direction in case of Material B.

Number of vally and earring 1'st 2'nd 3'rd 4'th

Discontinuous point of blank I 42° 128° 222° 308°

Earring angle (Simulation) 45° 140° 225° 315°

Earring angle (Experiment) 50° 135° 220° 315°

Vally angle (Simulation) 0° 85° 185° 265°

Vally angle (Experiment) 0° 95° 180° 265°

correlation to the angles of blank-mesh of discontinuous points. On the other hand, in Material B the angles of ears have the weak correlation to those of blank-mesh.

5. Conclusions

(1) The correlation between AR/Rave and the average earring height is not always true. Although AR/Rave is nearly zero pure titanium has large earring.

(2) In case of pure titanium, the occurrence of large earring is caused by the large ATL/Rave value.

(3) The best m-value of YLD894) yield function is 2 for aluminium-killed steel and 8 for pure titanium.

(4) The four discontinuous points of blank-mesh is assumed to clarify the influence of R-values of three directions to the earring.

Acknowledgements

Authors thank Prof. Dr. Toshihiko Kuwabara (Tokyo University of Agriculture and Industry), Dr. Kohsaku Ushioda and Dr. Tohru Yoshida (Nippon Steel and Sumitomo Metal Corporation), Mr. Kazuki Satoh and Mr. Yuya Ohyama (graduated students of Production Engineering course of Akita National College of Technology).

References

[1] Wilson, D.V. and Butler, R.D., 1961. "The Role of Cup-Drawing Tests in Measuring Drawability", Journal of the Institute of Metals, 90, 473-483.

[2] Kuwabara, T., Katami, C., Kikuchi, M., Shindo, T. and Ohwue, T., 2001. "Cup Drawing of Pure titanium Sheet-Finite Element Analysis and Experimental Validation", Proceedings of Simulation of Materials Processing (7'th NUMIFORM), 781-787.

[3] Yoon, J.W., Dick, R.E. and Barlat, F., 2011. "A New Analytical Theory for earring generated from Anisotropic Plasticity", International Journal of Plasticity, Vol.27, 1165-1184.

[4] Barlat, F. and Lian, J, 1989. "Plastic Behavior and Stretchability of Sheet Metals Part.1: A Yield Function for Orthotropic Sheets under Plane Stress Conditions", International Journal of Plasticity, Vol.5, 51-66.