The effect of the roll-gap shape factor on internal defects in rolling

Journal of

ELSEVIER

Journal of Materials ProcessingTechnology60 (1996) 275-282

Materials Processing Technology

The effect of the roll-gap shape factor on internal defects in rolling S. Turczyn

Faculty of Metallurgy and Materials Science, Akademia Gdrniczo-Hutnicza, Mickiewicza 30, 30-059 Krak6w, Poland

Abstract

One of the main aims of the paper is to update the study on internal defects which can arise during rolling. First part of the work describes an upper-bound model of an appearance and growth of voids. The model refers to both the internal central bursts and the splitting of the ends during rolling. This solution allowed the formulation of an energetic criterion for the appearance of central bursts and splitting of the ends. The second part of the work contains the experimental verification of the model. The results confirmed the correcmess of the assumptions in the model and they agree well with the theoretical predictions. Agreement is particularly observed in the comparison between the measurements and the predictions of the splitting of the ends during rolling of aluminum samples. Criteria developed in the work, based on the minimum power requirement in rolling, show increased probability of the appearance of central bursts and split ends during rolling of products with the large relative thickness when small reductions are applied. The dangerous range of rolling parameters begins when the roll-gap shape factor exceeds 0.75-0.79.

Keywords: an upper-bound model of rolling defects, the roll-gap shape factor, central bursts and split ends defects

1. Introduction

The occurrence of some defects in rolling processes is an important problem for industry, especially for mass production like slab or plate rolling. The prevention of particular defects which can arise during rolling plays important role and is a mean for improving the quality and increasing quantity of products.Two research activities are known in the solutions of this problem, one deals with the improvement of metal formability by controlling the inclusion content and predicting the microstructure. The other one interests in improving the rolling process itself, through better roll pass design, deformation-zone geometry control, temperature and friction selection. Defects prediction in rolling processes is a complex problem because of the superposition of multiple parameters influences in a context of complicated geometries and boundary conditions. The resolution of these problems requires better understanding of the basic phenomena, involving the prediction of stress and strain state, flow- and deformation induced fracture that can occur in rolling. Rolling defects such as split ends or "crocodiling" [1,2] and central bursts [3,4] take place during various rolling processes. The consequences of these defects are not limited only to yield loss or rolling disturbances but they can also cause damage to the rolls and mill accessories. The phenomenon of split ends is a defect which initiates as a crack, forming along the center plane of the deformed material. The crack can vary in the severity from a slight separation of the upper and lower halves of the material rolled to complete separation or encasement of the rolls. Sometimes the splitting can 0924-0136/96/$15.00 © 1996 Elsevier ScienceS.A. All rightsreserved PI10924-0136(96) 02342-4

also be formed at any position along the length of the rolled material. Typical split ends defects arising during rolling are presented in Fig. l and Fig. 2.

Fig. 1. Split ends defect arisen during rolling of aluminium alloy. The phenomenon of internal voids or central burst is a defect which can occur during rolling of flat products. This defect, found in wire or strip drawing, has been reported by Rogers and Coffin [4] and Avitzur [5]. Early work by Avitzur, Van Tyne and Turczyn [3] has provided some criteria for the prevention of central burst during rolling. One of the main aims of the present work is to update the study on split ends and central burst defects arising in the flat rolling process. An energetic criteria for avoiding defects formation in

S. Turczyn / Journal of Materials Processing Technology 60 (1996) 275-282

276

by the velocity discontinuity surfaces has been described by Johnson and Mellor [10] and then by Avitzur and Pachla [11]. 2.1. Admissible flow patterns An essential step in the application of the upper-bound theorem is the determination of the strain rate field which is usually derived from kinematically admi.~sible velocity field. The number of admissible flow patterns, called velocity fields, is unlimited. It is presumed, however, that in order to get higher solution accuracy, the velocity fields should be as close as possible to actual ones. In this analysis three patterns of the triangular rotational velocity field are applied to model defects formation during rolling. These patterns are illustrated in Fig. 3, 4 and 5.

o 9. f

/ B

Fig. 2. Split ends defect arisen during rolling of steel bar. the centre plane of the rolled material is discussed. Using an upper bound method with the assumption of a rigid body uni-triangular velocity field for deformation zone the model of these defects is proposed. The power solutions obtained for the analysed flow patterns allowed to classify roiling parameters into safe and defect expected ranges. The roll-gap shape factor [6-8] plays an important role in this study. The criteria for avoiding split ends and central burst are sought so that preventive steps can be taken during the rolling process to eliminate these defects. Finally, the results of experimental rolling of copper and aluminium alloy are presented. It has been found that split ends and cenlral bursts are more likely to occur in thick plates and sheets when small reductions are applied.

td

,c

I

I

<

2. Mathematical model of defects formation

Fig. 3. Assumed flow pattern for central burst arising. An upper bound method of limit analysis in a classical formulation has been applied to model failure modes during rolling. According to Prager and Hodge [9] a statement of the upper bound theorem is that "among all kinematically admissible strain rate fields the actual one minimizes the following expression" J*

:

2k

eijeijdV + V

f

Sr

~'[Av [dS r

•

-

f

Sr

Tivi

• dSr

(1)

where k - yield stress in shear, e~ - kinematically admissible strain rate, "r - shear stress, Av" - velocity discontinuity, vi° kinematically admissible velocity field, V - volume. The upper bound theorem states that the externally supplied power J" is less than or equal to the sum of internal power, frictional power losses, power losses due to the surfaces of velocity discontinuity and losses or gains due to external tractions T i. For a rigid body motion and absence of front and back tractions, the deformation energy is assumed to be dissipated along the surfaces of the velocity discontinuity Sr. The upper bound analysis for a process where rigid body motion is separated

The workpiece of thickness 1% enters the roll gap with a velocity Vo (zone I) and exits from it with a thickness 1~ and a velocity vf (zone III). The rolls of radius Ro rotate at an angular velocity too, thus, their peripheral velocity is v, = to° Ro. In general case, Fig. 3, the deformation region (zone II) is separated by three surfaces of velocity discontinuity F~, r2, r3 and rotates as a rigid body with angular velocity to. The material is assumed to be an isotropic strain-hardening body. Surfaces PI and r2 separate a linear body motion from the one with rotational motion. The velocity field contains two pseudo-independent parameters X, and Y,. These parameters are used to position the apex A of the triangle within the deformation zone. The values of X, and Ya are determined from the principle of minimum energy. The parameter Y, is the half distance of the deformation zone apex A from the center line of workpiece, Fig. 3, and is used to permit the formation of an internal voids if it is energetically favorable. This flow pattern is employ to model central burst generation during rolling process. An assumption of Y, = 0 leads to another flow pattern which describes sound flow without the defects formation, Fig. 4.

277

S. Turczyn / Journal of Materials Processing Technology 60 (1996) 275-282 (ho

-

Ya)vo = (Ra2

-

Ro2) O = (hf

(2)

Ya)Vf

-

From Eq. (2), the kinematically admissible velocity field in the deformation zone is derived in the form to _ vf h f / R o ' - Y . / R o oo Vr (R,/Ro) 2 - 1 ~-

o

\

r,',~o'--e

~

_

Xa

(3)

.!

'~J~O2

Fig. 4. Sound flow pattern. When point A of the deformation zone is located at the exit plane, the value of Y. and X. can be set equal to zero. Furthermore, the surface of the velocity discontinuity P2 can be removed. The triangle (zone II) would continue to rotate around the roll axis and split ends would develop. This flow pattern, shown in Fig. 5, is used to simulate the phenomenon of split ends formation during rolling of flat products.

The relative power losses (divided by 2koRoVr) for a strain hardening material are given by the following equations: - surface I'~ and F2

J'r,

R 2 _,ki ,o (--r,/,

(4)

1

2 ko O o ~ R o )

- surface I~3 1 kma

J'r~ = 2ko

to

(5)

~l-~o - 11

- losses or gains due to tensions

hf tO

J"--

Ya

~]

hf ( 1 + RF / h° R° R°

~oRo

Ro) hf h o _ Y . Ro

~b-~f

(6)

Ro

- associated with surfaces of fiat crack

(7) jr

Fig. 5. Assumed flow pattern for splitting during rolling. The computation of the upper-bound on power for each flow pattern enables the prediciont which scheme is prevailing during deformation. The domain where the lowest power required is for the field that describes the flow with defects formation indicates the process parameters under which the rolling failures are expected. This results in establishing a proper criteria in order to eliminate occurrence of such defects during fiat rolling. 2. 2. Power equations f o r specific flow pattern

Assuming the plane strain and the unit width of the workpiece, the incompressibility condition for a general flow pattern, Fig. 3, can be written as follows

= 1+ 5

koRo

where m - friction ~tc - contact angle, ~f, ~b - front and back tension coefficient, ¥s - surface energy per unit area. Consequently, the total relative power for the unit width of the material rolled is obtained by summing up above mentioned power losses along three surfaces r i and power losses or gains due to tensions, if applied. For a general flow pattern it yields: J* - 2koRoVrJ* - 2 ( j ' r , ÷ J*r 2 ÷ J'r3) ÷ Js* - Jr"

(8)

Substitution of Eqs. (4-7) into Eq. (8) and optimizing the resulting formulae with respect to pseudo-independent parameters leads to a final equation which is presented symbolically as the function of the process independent parameters k , ho

J' f ro

Y~ /

(9)

278

S. T u r c ~ n / Journal o f Materials Processing Technology 60 (1996) 275-282

Power for sound flow pattern. As stated earlier in the cases where sound flow occurs, the value of Y, is equal to zero and the apex A of the deformation zone is located on the workpiece center line. Using an assumption Y,/Ro = 0 in Eqs. (3-6) and optimizing Eqs. (4-6) with respect to pseudo-independent parameters leads to the power equation for a sound flow

=2kl Rrl/2qbl + 2 T_~( Rr2]2qb2÷ h~f (1

(I0)

These figures show the range of independent process parameters where sound flow is expected (labeled as "safe zone") and the range where centralburst is energetically more favorable. Besides that, Fig. 6 indicates that external tractions promote central bursting and that the relative back stress has a greater effect on it as compared to the relative front stress. For the strain-hardening materials the central burst zone is slightly larger then for perfectly plastic one, Fig. 7. 0.5

safe zone

#, s,

Power for split ends pattern. In the velocity field assumed for split ends, the point A lays on the exit plane, thus X, = 0. Moreover, there is not the velocity discontinuity surface I'2 at the exit and, therefore, there is not shear loss Jr2 in the power equation for split ends. By eliminating the friction losses (from optimization procedure m = 0) and assuming the lack of external tensions, the power equation (Eq. 8) transforms into that for split ends pattern (ll) ko ~ Ro)

-2Ro koRo

I/ iI

0.4

-

-

-

~

-

-

-

-i- -

-

I • --I . . . .

~s,1-

I

I

I I I I.-

I

,,//' //

I

k)

°-0

I/,

" 2q I

/

I/

------4 central

0.3

. . . .

l---

burst z o n e

"0

[ c/J/Fi

2--u 0.2

3. Prevention criteria fer internal defects

.... .

.

.

.

.

.

.

.

.

.

.

o

,,F"

In establishing an energetic criteria for central bursts in rolling, the determination of an optimal value of the parameter Y,/Ro has been required. As stated earlier, when the optimal value of Y,/Ro is greater than zero, the model indicates that the flow pattern with central burst is energetically more favorable. The critical point is the condition where the optimal Y,/R~ ratio becomes zero. Such points identified for a wide range ofprocess parameters give the central bursts criteria for flat rolling, shown in Fig. 6 and 7.

0.5

//,

I

!

#|

0.1

L~. . . . . . . . . . .

--i. . . .

r---

1.~_~ perfectly p l a s t i c AI505 I - T 5 AI6Ofil-T5

0.0 -~

0.0

0.1

0.2

Relative

0.3

thickness,

hardened annealed

0.4

0.5

0.8

ho/Ra

safe zone

Fig. 7. Central burst criteria for aluminium A16061-T6 rolling.

0.4

........

J, .......

,J ....

i

/i

1,1 0.a

.............. , % aentral

burst zone

0 "U

/I j

Q

"5 o.2

[

. . . . . . . . t'J. ,.. . . . . . .

;:!7// ,,,'y i 1 1

1

o.1 .--#' o.o

~ o.o

0.1

Perfectly plastic material - ~b = 0 , 0 0 ~'f _ _ ~% = 0 , 0 o ~, ___ (% = 0 , 2 5 ~f .... ~b = 0 , 2 5 ~t 0.2

Relative

0.3

thickness,

0.4

0.5

l 0,00 I o,251 0,00 0,25 0.6

The criterion of split ends defect is developed through the following procedure. If, for a given set of process parameters, the power consumption for sound flow is higher than that for split ends pattern, the split ends defect is likely to occur. The criterion of split ends defect will be established when the whole range of the independent process parameters e and hJRo is covered. The power consumption for sound flow pattern can be acquired by Eq. (10) through a numerical optimization procedure with respect to pseudo-independent parameter X,/Ro, while the power requirement for split ends flow pattern can be directly calculated from Eq. (ll). The obtained solution can be applied for both the perfectly plastic and the strain-hardening materials. For the first one the substitution k/ko = 1 is made in the computations. For the strain-hardening materials, the yield stress variation along the deformation zone is calculated from the relation applicable to the plane strain conditions 2k =

Yo 1 +-~-2 B l n

ha/R.

Fig. 6. Central burst criteria in the rolling process with tensions.

where Yo, B and n are the material parameters.

(12)

S. Turczyn I Journal of Matermls Processing Technology 60 (1996) 275-282

These parameters used in the calculations for annealed aluminium alloy AI6061-T6 are: Yo = 43 MPa,. B = 50, n = 0.204 and for annealed SAE-1020 steel: Yo = 232 MPa, B = 58, n = 0.294. The criteria obtained for perfectly plastic material and for aiuminium alloy are presented in Fig. 8 and for the SAE-1020 steel in Fig. 9. To the right and below the line split ends defects are expected while to the left and above the line a sound flow prevails.

279

0.5

0.4

14

0.4

~, o . ~

I

0.3

~_~

. . . . . . . . . i. . . . . . T

J . . . . . . . .

tO

'

"!

P 0.2 >

U

perfectly plalflo I AI6061-T6 hardened I AI6061-T6 annealed I

~

"o II

¢• . . . . . . . i

•• . . . . . . . i

I i i i

I i i i

I

l

i i i

i i

i

i

, i i

, i i

/

~ /,

g

I s i o'j i ,~ i ~, /

,,,'r

0.1

iaf. z,n. ! ........ , " - " . " ~ ' 7 ~ : , , /,,4," , , .2./1 ~

Q

o 0.2

.1_ ....... i

i ~ ~_

i i

I

i

,J.Y

...... /.~

il__~

i i

i i

0.0

0.1

i

~1

........ : .... ~ i

1,~

~,

Ii

|

!

...... b-----4

i

l

i

l

i

i i

i l

i i

;

...... , ....... i

l

I

B

Relative thickness,

l

h./R.

i i

Fig. 10. Joint ('riteria for central burst and split ends defects. 0.0

0.1

0.2

Relative

0.3

0.4

0.5

0

hJR,

thickness,

Fig. 8. Split ends criteria for ah]mirtium AI6061-T6 rolling.

0.4

___ k)

i T

0.3

i _ ~

tO

1 ] i

psrfectlyplaetlc 5AE- 1020 hardened SAE-1020 annealed , I

, I

i i I

i

i!i

i!| s "

! i

.

:

.

.

:

.

,"

h° - 0.57 e Ro (1 - e)

safe zone i , :

II 0 O

IZ

i

i

:

I

I

1

0.1

-"

h° - 1.81 e Ro (1 - e)

,

i

: "/7,

I

/

• )

i L---4~

'+ 1 ,',:Y i1 i . . . . . . . . ~. . . . rT",~l". . . . . . . t ' - - - - ' ~ . . . . . . . -~. . . . . . . i

I+ +J/ +//:

0.0

[ +" f/ :, / / f . . _ { ,¢1

i

0.0

0.1

/

i

i

1

1

i

i

l]

I'

I,

I,

0.3

11.4

0.5

:

1

i

0.2

Relative thickness,

h,/R,

Fig. 9. Split ends criteria for carbon steel rolling.

(13)

- for split ends defects ,~

"0 e

L. 0.2

Fig. 10 shows the joint criteria for both failures: central burst and split ends. It can be observed that the range of process parameters where central burst is expected is much wider than that for split ends. The lines in Fig. 9 showing criteria for the perfectly plastic material can be approximated by the following expressions: - for central burst defects

0.6

(14)

Central bursts or split ends defects are expected when the relative thickness of the material is higher than the left side of the Eqs. (13) and (14), respectively. For strain-hardening materials (cold rolling processes) the split ends zone is slightly larger and this negative effect depends on strain-hardening characteristic of the deformed metals, Figs. (7-9). The developed criteria indicate that for a given material central bursts and split ends defects tend to be promoted by small roll radius Ro, large initial thickness of the workpiece ho and small thickness reductions e. Therefore, these defects can occur when the roll-gap shape factor A achieves a relatively high value, Fig. 11. Such conditions exist during rolling of the slabs, heavy gauge plates or in the roughing groups of hot strip mills [8,12].

280

S. Turczyn / Journal of Materials Processing Technology 60 (1996) 275-282

are analysed. Firstly, the material is assumed to have no defects which results in the one type of the stress field. Secondly, the stress fields are computed in the notched specimens subjected to rolling. Stress variation along the roll gap is presented in Fig. 12. The results of the stress analysis are compared with the upper bound predictions and they confirm an important role of the rollgap shape factor.

2.0 oentral burst Qnd split e n d s a x p s o t e d

h o + hf

A -

21

1.5

. . . . . .

~. . . . . . . . .

i1

1". . . . . . . . . Z

-

d

,". . . . . . . . . :

central burst expet."ted

@i

p

400 1 AI6061-T6

notohsd plans

centre

1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2oo-

[

~6 •

1

a. "i n¢ :

* 0.5

.........

safe

,L . . . . . . . . . l

~ .........

i

:

°°

ZOrle

~..

perfectly plastic material ~, = ~, = o 0.0

i

0.0

,

,

,

I

i

0.1

,

,

,

!

0.2

Relative

i

~ -20o

,

1 -400 i

i

i

i

|

,

0.3

i

0.4

,

,

i

='

i

_

0.5

reduotion, ¢

Fig. 11. Influence of the roll-gap shape factor on central burst and split ends defects during rolling.

-600

~ 6

8

10

12

14

16

Sample length, mm Fig. 12. Variation of ox, oy and o m stresses along roll gap.

In order to investigate closer the mechanical conditions under which the rolling defects are formed the stress analysis is performed. The elastoplastic Finite element approach developed by Malinowski and Lenard [13] has been employed to compute the stress field in the deformed material. Two types of the workpiece

4. Experimental results The analytically obtained split ends criteria have been compared with the results of experimental rolling. Two different

Fig. 13. Example of the folded copper specimens series of 3 mm in height after rolling (increasing reduction from 3.4% for sample No. 1 to 14.9% for sample No. 8).

S. TurczynI Journal of Materials Processing Technology 60 (1996) 275-282

281

Fig. 14. Examples of the most bent split ends obtained during rolling of aluminium specimens (relative thickness of the samples: No. 1 - 0.605, No. 2 - 0.452, No. 3 - 0.380, No. 4 - 0.310).

specimens shapes have been used. Firstly, copper samples, folded in the half of the length, were rolled. Four series of rolling experiments using constant specimens height 2, 3, 4 and 5 ram, respectively, were done. The rolls of 25 mm in diameter were used. During rolling both parts of the folded specimens were bent in opposite direction with various curvature, Fig. 13. The curvature of split ends obtained after partial rolling shows tendency to splitting. 0.4

---

A I 6 0 6 1 - T 6 annealed • split e n d l ~ . eeund flew

0.3

. . . . . . . . . . . . . . . . . . . . .

: i

j . . . . . . . . . . . . .

..l. ......

For the second part of the experiment solid specimens have been prepared. They were cut from AI6061-T6 aluminium alloy rectangular ba/s 6.35; 7.94; 9.53 and 12.70 nun of height and 25.4 nun of width. Two pairs of work rolls of 21 and 67 mm in diameter were used for the experiment, therefore, eight values of parameter tg/Ro, ranging from 0.095 to 0.605, were obtained. The most bent split ends occurred during rolling of four series of the aluminium specimens are shown in Fig. 14. Fig. 15 presents the comparison of experimental results with the analytically developed criteria. It can be seen from Fig. 15 that almost all split ends defects which have occurred during experimental rolling lay in the area below the line where "crocodiling" is expected. 5. Summary and conclusions

t._ ...~. f ,,¢

z,,

safe

i.

.

,-

:

0.2

.

.

; /

.

.

.

.

.

.

.

.

.

li

i i

: i

!i 0.1

i

.i . . . .

..... /

i

0

IO

II

q U l ~ ; li

i

i

,°

t

*: -"V i

ill

,,"

," i

lq,..i i

:i i

i• I

i

;~

i

i

ot

#k

1

i

D

0.0

li,,', l, ll!

I', , . , ? ' . . . .

0.0

0.1

!"

•

--~/: Ii

"1 •

I

,':Ill u

,

I ) / ~ ~ ~ s p i i t

,/

r m

Hi

li I

I

: At

j i

:

--

a.

a

1

erl.s expedsd D

"

" e

I' . . . . I' . . . . i . . . . I . . . . 0.2 0.3 0.4 0.5 0.6

Relative

thickness,

0.7

h,/R,

Fig. 15. Comparison of experimental results with analytically developed criterion.

The two-dimeusional model of the limit analysis is presented for the simulation of central burst and split ends formation during flat rolling. The determination of the total relative power for three flow patterns have allowed to establish the proper criteria that classify process parameters into safe and central burst or split ends zones, which are illustrated in Figs. 6+ 11 of the paper. The main conclusion of the study is that for a given material central bursting or splitting of the ends in rolling tends to be promoted by the following independent parameters of the process: - large initial thickness of the sample t~, - small thickness reductions e, - small work roll radius P~. The dangerous range of the rolling parameters begins when the roll-gap shape factor A exceeds value 0.75.-'0.79, Fig. 11. Moreover, it has been found that internal burst defects are more likely to occur than split ends; both failures are expected in thick plates and sheets when small reduction are applied. The stress fields computed for notched specimens showed high tensile stresses acting in the direction perpendicular to the sample centre plane, Fig. 12. Such stresses can lead to internal bursts or split ends formation. The comparison of the stress fields obtained

282

S. Turczyn /Journal of Materials Processing Technology 60 (1996) 275-282

for aluminium specimens confirmed the important role of inclusions or other material discontinuities in the creation of internal defects. Comparison of the analytically developed criteria for split ends defects with the results obtained during experimental rolling of aluminium specimens show generally good agreement, especially during rolling of aluminium samples. By using these criteria in the rolling practice, it has become possible to predict necessary rolling conditions in order to avoid split ends and central burst defects. References

[1] K. L. Barlow, P. R. Lancaster and R. T. Maddison, Metals Technology, 11 (1984) 14. [2] M. M. A1-Mousawi, A.M. Daragheh, S.K. Ghosh and D.K. Harrison, J. Mat. Proc. Tech., 32 (1992) 461. [3] B. Avitzur, C. J. Van Tyne and S. Turczyn, J. Eng. lna[, ASME Trans., 110 (1988) 173.

[4] H. C. Rogers and L. F. Coffin Jr., Proc. Manufact. Tech., Univ. of Michigan, 1967, 1137. [5] B. Avitzur and J. C. Choi, J. Eng. lna~, ASME Trans., 108 (1986). [6] W. A. Backofen, Deformation Processing, Addison-Wesley Publishing Co., Reading, Massachusetts, 1972. [7] S. Turczyn and M. Pietrzyk, J. Mat. Proc. Tech,. 32 (1992) 509. [8] S. Turczyn, Dissertation Monographies No. 31, Wyd. AGH 1995. [9] W. Prager and P. G. Hodge Jr., Theory of Perfectly Plastic Solids, Chapman and Hall, Ltd, London, 1951. [10] W. Johnson and P. B. Mellor, Engineering Plasticity, Van Nostrand Reinhold Co., Ltd, New York, 1973. [11] B. Avitz'ur and W. Pachia, J. Eng. Ind,, ASME Trans.,108 (1986) 295. [12] S. Turczyn, Steel Research, 63 (1992) 69. [13] Z. Malinowski and J. G. Lenard, Comput. Meths Appl. Mech. Eng., 104 (1993) 1.