Effect of reduction ratio, inclusion size and distance betweeninclusions on wire breaks in Cu fine wiredrawing

Hoon Choa,*, Hyung-Ho Joa, Sang-Gon Leeb,Byung-Min Kimc, Young-Jig Kimd

aKorea Institute of Industrial Technology, 472 Kajwa-4Dong, Seo-Ku, Incheon 404-254, South KoreabSchool of Precision Mechanical Engineering, Busan National University, Busan, South Korea

cERC for NSDM, Busan National University, Busan, South KoreadSchool of Metallurgy and Material Engineering, Sungkyunkwan University, 300 Chunchun-Dong,

Jangan-Gu, Suwon, Gyounggi-Do 440-746, South Korea

Abstract

The presence of an inclusion in wire makes wire breaks easy to occur even with a high reduction ratio. The investigation presented here is

mainly aimed at determining the reduction ratio when size of an inclusion, application of back tension and distance between inclusions are

considered. In order to investigate the effect of back tension on wire breaks, the applied back tension in a slip type continuous drawing

machine is calculated quantitatively using some parameters such as diameter and peripheral speed of capstan and coiling number. The effect of

an inclusion size and reduction ratio on wire breaks is investigated when quantitatively calculated back tension being 28% of drawing force is

applied. The size of an inclusion varies 5, 7 and 10 mm, the reduction ratio varies 10, 13 and 16%, the distance between inclusions is set to be

0.25 and 0.5 mm, respectively. Conical dies with a half angle a of 78, which is the value generally used in commercial production. As the FEM

code, the commercially available software DEFORM-2D is used. Copper is used for fine wire drawing process that initial diameter is 1 mm

and final diameter is up to 50 mm. Accumulated strain and mean stress are simultaneously calculated to obtain damage value in the multistage

wiredrawing. The defects of central burst type are generated at a smaller total reduction ratio with decreasing unit reduction ratio and with

increasing inclusion size. Furthermore, damage value rises because the tensile stress in deformation zone increases by applied back tension.

The distance between inclusions would not affect wire breaks because the distance is expanded excessively through multistage wiredrawing.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Cu wiredrawing; Wire breaks; Reduction ratio; Inclusion size; FEM analysis

1. Introduction

The suppression of the wire breaks in manufacturing fine

Cu wires is still one of the significant industrial problems

and the efforts to solve the problems also have been made

[1–4]. The wire breaks maybe caused by adoption of impro-

per drawing conditions such as die design, pass schedule,

lubricant and annealing or/and by existence of inclusions,

and Cu2O, segregations. It is well known that the existence

of the inclusions in Cu materials acts as the main cause of

wire breaks in Cu wiredrawing process [5].

By recent development in the FEM for the analysis of

stress and strain around inclusion during plastic deformation

process such as wiredrawing, it has been possible to prevent

the wire breaks more efficiently [6]. FEM simulation of

multistage drawing is more adaptable than that of single pass

drawing, because most of wiredrawing factories are

equipped with the continuous type of facilities. Doege [7]

attempted to determine the optimal parameters based on a

FEM analysis in multistage wiredrawing when the material

is assumed that initial defect such as inclusion is not con-

tained.

The multistage analysis presented here is mainly aimed at

investigation of effect of inclusion size and reduction ratio

on wire breaks in Cu wiredrawing considering back tension.

Furthermore, the effect of the distance between inclusions is

also investigated.

2. Experimental procedure

Table 1 shows the analysis variables and conditions used

in this study to investigate an effect of inclusion size,

reduction ratio and distance between inclusions on wire

Journal of Materials Processing Technology 130–131 (2002) 416–420

* Corresponding author.

0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 7 1 9 - 7

breaks. The initial diameter of wire is set to be 1 mm. The

wiredrawing speed is in the range of 0.43–1000 mm/s for the

first and the last drawing step, respectively.

Commercially available Deform-2D software is used for

FEM simulation of multistage wiredrawing. FEM simula-

tion is performed on the assumption that the inclusion is

poisoned at the center of the wire and its shape is circle.

From the tensile test, the resultant relationship between the

effective stress and the effective strain of Cu, which is used

in this study, is acquired as follows:

�s ¼ 532:02_�e0:41976 ðMPaÞ (1)

The Cockcroft and Latham [8] criterion is used as the

damage value to estimate if and where a defect of central

burst type will occur during the wire drawing process. The

equation is expressed as follows:

Z �ef

0

s�

�s

� �d�e ¼ C (2)

where s� is the maximum principle tensile stress, �s the

effective stress, �ef the fracture strain, �e the effective strain

and C is the Cockcroft–Latham constant. For the FEM

analysis, Eq. (2) can be approximated as follows:

Xn

i¼1

ðs�ed�eeÞi ¼ C0 (3)

where n is the number of steps in the simulation, s�e the

maximum tensile stress inside the element and d�ee is the

incremental effective strain or �ei � �ei�1. If the summation of

Eq. (3), C0, exceeds the critical damage value, defect of

central burst type should occur around the inclusion.

The critical damage value of Cu materials used in this

study was obtained by using Bridgman method [9]. The KS-

14A tensile test specimen is used and critical damage value

of material is measured in the necked region. The measured

critical damage value is 1.424.

In particular, in this study, the applied back tension in a

slip type continuous drawing machine is calculated quanti-

tatively by using Eq. (4). In Eq. (4), back tension force of

ði þ 1Þth depends on the drawing force of ith dies, the

number of coiling in the ith capstan and the friction coeffi-

cient between wire and the ith capstan.

Fiþ1;b ¼ 1

expð2pnimÞFi;d (4)

where Fiþ1;b is the back tension force of ði þ 1Þth dies, ni the

number of coiling in the ith capstan, and m the friction

coefficient between wire and the (i)th capstan.

For calculating drawing force (Fi,d) in Eq. (4), Geleji’s

equation [10] was applied. As a result of analysis, the back

tension force is 25–28% of drawing force at each drawing

pass. FEM simulation of wire breaks is performed when

back tension is applied or not applied in wiredrawing

process.

3. Results and discussion

3.1. Effect of inclusion size on wire breaks

As regions of compression and tensile stress appear

repeatedly around an inclusion in the wire drawing process,

a defect caused by accumulated stress maybe mostly central

burst type. A defect of central burst type is considered to

occur when damage value reaches the critical value. This

defect grows in size when they exceed the critical values,

finally resulting in wire breaks. In the present study, total

reduction ratio means overall reduction ratio, which can be

drawn without occurrence of central burst defect.

Fig. 1 shows the analysis result to investigate the effect of

inclusion size on wire breaks when unit reduction ratio is set

to be 16%. The damage value obtained from accumulated

strain approaches critical damage value rapidly as inclusion

size increases.

As shown in Fig. 2, it is possible to draw the wire without

occurrence of central burst until total reduction ratio reaches

98.7% when an inclusion is not contained in wire. The

diameter of drawn wire is 113 mm when total reduction

Table 1

Variables and condition for FEM simulation

Material Semi-die

angle (a)

Friction

coefficient (m)

Reduction

ratio (%)

Inclusion

size (mm)

Distance between

inclusion (di/dw)

5N–Cu 78 0.05 10, 13, 16 5, 7, 10 0.25, 0.5

Fig. 1. Relationship between damage value and drawing step in variation

of inclusion size.

H. Cho et al. / Journal of Materials Processing Technology 130–131 (2002) 416–420 417

ratio is 98.7%. As a result of FEM simulation, a defect of

central burst type is observed in a smaller total reduction

area with increasing inclusion size; the total reduction ratio

decreases from 97.84 to 96.94% as inclusion size increases

to 5, 7 and 10 mm when back tension is not applied.

The inclusion is hard and negligibly deformed, in con-

trast, only the Cu located between the die and the inclusion is

subjected to deform in large strain [11]. In addition, the area

of cross-section between die and inclusion decreases as size

of an inclusion increases. Based on the above-mentioned

discussion, it can be mentioned that damage value accumu-

lates and reaches critical damage value rapidly as size of an

inclusion increases.

Fig. 3 shows the distribution of the damage value in

multistage wiredrawing of Cu wire containing an inclusion

of 5 mm when reduction area is 16% and back tension is not

applied. The small solid circle indicates inclusion contained

in the wire. After the wire passes through the first die in Fig. 1,

the damage value around the inclusion starts from 0.206, and

after 11 drawing step, it becomes 0.774 in Fig. 1. The region

that damage value approaches its critical value (1.424) is

generated 21 drawing step and the defect of central burst type

is observed when damage value exceeds the critical damage

value; after 22 drawing step. A defect of central burst type is

observed along the center line in drawn wire. Since tensile

stress acts in the drawing direction at the center of the wire,

an internal crack is easy to occur in front of or at the back of

the inclusion when wire passes through a die.

The effect of applied back tension on wire breaks is

investigated and the result is shown in Fig. 4. It has been

generally known that the optimal back tension can be up to

Fig. 2. Effect of inclusion size on wire breaks.

Fig. 3. Distribution of damage value in multistage wiredrawing when size of inclusion is 5 mm.

Fig. 4. Influence of the back tension on increase of damage value.

418 H. Cho et al. / Journal of Materials Processing Technology 130–131 (2002) 416–420

30% of the drawing force because the increase of back

tension leads to increase of tensile stress in the deformation

zone inside the wire as well as increase of damage value

[12]. Therefore, excessive back tension make easy to occur a

defect of central burst type in wiredrawing. As shown in

Fig. 4, the damage value reaches critical damage value at a

smaller drawing pass through multistage wiredrawing when

back tension, which is 28% of drawing force, is applied; the

damage value reaches critical value after 20 drawing pass

when back tension is applied. In contrast, the damage value

reaches critical value after 21 drawing pass when back

tension is not applied.

For avoidance occurrence of wire breaks, in the present

study, it is necessary to reduce back tension up to 28% by

control process variable such as coiling number in a slip type

continuous drawing machine.

3.2. Effect of reduction ratio on wire breaks

The effect of reduction ratio on wire breaks is plotted in

Fig. 5 when inclusion size is set to be 10 mm. It is shown that

a defect of central burst type is observed at a higher drawing

pass and at a smaller total reduction ratio with decreasing

unit reduction ratio; the total reduction ratio decreases from

96.94 to 92.0% as reduction ratio reduces from 16 to 10%

when back tension is not applied. It has been reported that

small reduction ratio involves excessive redundant work

[13]. The redundant work contributes extra strain hardening,

particularly at the wire surface and limits total reduction

[14].

Since the rate of nucleation and the growth of voids

depends on the hydrostatic pressure, as does the strain at

fracture, the distribution of hydrostatic pressure has been

frequently used as an index to predict the generation of

defect of central burst type in wiredrawing. When the

hydrostatic pressure becomes lager than zero (positive),

which indicates that local tensile failure such as central

burst may take place in deformation zone during plastic

deformation. Fig. 6 shows the distribution of hydrostatic

pressure at a various unit reduction ratio when inclusion size

and total reduction ratio is assumed to same that being

10 mm and 91%. It is shown that positive hydrostatic pres-

sure, which indicates tensile stress, is observed around

inclusion and surface of the wire. It is also found that a

region that indicates positive value increases in size around

inclusion with decreasing reduction ratio. When the hydro-

static pressure results in large tensile stress, it is believed that

a large number of internal cracks can be generated. Because

the occurrence of tensile stress is easier than that of com-

pression stress when unit reduction is small, it is make easy

to occur a defect of central burst type at the center of drawn

wire.

3.3. Effect of distance between inclusions on wire breaks

The effect of distance between inclusions on wire breaks

is investigated; the result is shown in Fig. 7. The distance

between inclusions di/dw (where di/dw is the ratio of distance

to initial wire diameter) varies between 0.25 and 0.5,

respectively, because the mesh generation is difficult when

Fig. 5. Effect of reduction ratio on wire breaks.

Fig. 6. Distribution of hydrostatic pressure (MPa) in variation of reduction ratio.

H. Cho et al. / Journal of Materials Processing Technology 130–131 (2002) 416–420 419

distance is set to up to 0.25. It is shown that remarkable

difference is not observed as shown Fig. 7; the defect of

central burst type is observed at same total reduction ratio

(96.94%) and drawing pass though distance varies. It can be

mentioned that the expansion of distance between inclusions

result from multistage wiredrawing leads to similar analysis

result. The expanded distance between inclusions is mea-

sured 6.751 and 11.33 mm after 20 drawing pass, respec-

tively, when the distance is set to be 0.25 and 0.5 mm.

4. Conclusion

The defect of central burst is observed at a smaller total

reduction with increasing inclusion size. In addition, the

application of back tension, which is 28% of drawing force,

leads to decrease of total reduction ratio.

As unit reduction ratio decreases, the central burst defect

is observed at a higher drawing pass and at a smaller total

reduction ratio. It is believed that small unit reduction ratio

causes excessive tensile stress around inclusion and it makes

easy to occur a defect of central burst type.

From investigation of effect of distance between inclu-

sions on wire breaks, it is not observed remarkable effect of

distance on wire breaks. Because the distance between

inclusions expanded during multistage wiredrawing process,

a reciprocal action between inclusions cannot be expected.

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Fig. 7. Effect of distance between inclusions on wire breaks.

420 H. Cho et al. / Journal of Materials Processing Technology 130–131 (2002) 416–420