KINETICS OF SECONDARY RECRYSTALLIZATION IN GRAIN-ORIENTED SILICON STEEL STUDIED BY HIGH-TEMPERATURE BACKGROUND

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KINETICS OF SECONDARY RECRYSTALLIZATION

IN GRAIN-ORIENTED SILICON STEEL STUDIED

BY HIGH-TEMPERATURE BACKGROUND

Y. Iwasaki, K. Fujimoto

To cite this version:

JOURNAL DE PHYSIQUE

CoZZoque CS, suppZe'men% au nOIO, Tome 42, octobre 1981 page C5-493

KINETICS OF SECONDARY RECRYSTALLIZATION

I N

GRAIN-ORIENTED SILICON

STEEL STUDIED

BY

HIGH-TEMPERATURE BACKGROUND

Y.

Iwasaki and K.

Fujirnoto

Research Laboratories, Kawasaki Steel Corpo~ation, Kawasaki-cho, Chiba 260, Japan

Abstract.- Secondary recrystallization id grain-oriented silicon

steel is studied by the high-temperature background damping.

Abnormal grain growth involves an abrupt drop of the background.

The temperatures of initiation and completion of the secondary

recrystallization are, thus, determined for the sane sample from

the definite change in background with increasing temperature.

The background measured on isothermal annealing yields a trans-

posed sigmoidal curve consisting of three stages when plotted as

a function of annealing time. Each stage except for the third

is argued on the basis of the dislocation model of grain bounda-

ries, involving Avrami's equation of the fraction recrystallized

and following the theories of Johnson-Mehl and Avrami. Time law

of growth is investigated. Activation energy is obtained for

the second stage which is the principal stage of the secondary

recrystallization in the steel.

1. Introduction.- The subject of nucleation and growth in recrystalli-

zation of

3%

silicon iron has been extensively investigated with acute

interest both from technological and scientific points of view. The

material commercially produced today is singly oriented steel having a

highly develo~ed

preferred orientation as a {110)<001> texture. The

texture develops as

a

result of secondary recrystallization during

which a relatively few grains aligned to the orientation grow at the

expense of the surrounding primary grains, finally up to many times

the sheet thickness.

The microstructural change accompanying the {110}<001> texture

formation has been mostly studied by metallographic examination of X-

ray methods. These methods are convenient to know texture development,

whereas they provide little information about elementary atomic proc-

esses involved in recrystallization. Internal friction which readily

reflects motion of lattice defects has been considered employable for

this purpose (1)-(3). There have been, however, few quantitative stud-

ies utilizing the high-temperature background, the origin of which is

presumably due to dislocation motion at high temperatures

(4)-(6).

The

present report furnishes a method to correlate results of the back-

ground damping with those by conventional metallographic techniques.

2.

Experiment.- The material was essentially 3% silicon iron contain-

JOURNAL DE PHYSIQUE Grain-oriented silicon steeI at 850.C for

/

~ ~ ~ ~ Temperature, OC indicated time in min.

2

t

50

/I

1

Temperature, 'C F i g . 1 : Temperature dependence F i g . 2 : E f f e c t o f g r a i n - c o a r s - of i n t e r n a l f r i c t i o n . f R T : f r e q . e n i n g on h i g h - t e m p e r a t u r e back- a t room t e m p e r a t u r e . ground damping.

i n g 0.058%Yn, 0.015Se and 0.Q23Sb w i t h minor i m p u r i t i e s . P r o p e r l y p r e - p a r e d from i n g o t s ( 7 ) , c o l d - r o l l e d s h e e t o f 0 . 3 mm t h i c k n e s s w a s d e c a r - b u r i z e d t o 0.002C a t -800°C f o r 5 min, and a t t h e same t i m e p r i m a r y

recrystallizationoccurredproducing a f a i r l y s t a b l e f i n e - g r a i n e d m a t r i x o f a mean g r a i n s i z e of 1 5 pm i n d i a m e t e r . Specimens 100 l o n g and 5mm wide were made from t h e p r i m a r y r e c r y s t a l l i z e d s h e e t u s i n g a s l i c i n g machine w i t h a c u t t i n g p r e c i s i o n o f h e t t e r t h a n 5 pm. The specimens were mounted on a n i n v e r t e d t o r s i o n pendulum. D e t a i l s o f t h e a p p a r a t u s a r e r e p o r t e d e l s e w h e r e ( 7 ) . I n t e r n a l f r i c t i o n measurements were made o n h e a t i n g up t o 1100°C a t a r a t e o f Z°C/min o r h o l d i n g a t 85Q°C i n a vacuum o f 2 . 1 0 - ~ t o r r .

100 500 1000 5000

Annealing Time

,

min

F i q . 3 : T h r e e s t a g e s o f h i g h - t e m p e r a t u r e background f o r i s o t h e r m a l a n n e a l i n g a t 8 5 0 ° C . t h a t t e m p e r a t u r e . F r e a n n e a l i n g a t 8 5 0 ° C y i e l d s c u r v e s o f i n t e r n a l f r i c t i o n which d e c r e a s e s w i t h i n c r e a s i n g t i m e o f p r e a n n e a l i n g ( F i g . 2 ) . The r e s u l t s e x p l a i n t h e s t e e p d e c l i n e i n F i g . 1 o v e r t h e t e m p e r a t u r e r a n g e o f 9 0 0 ° C t o 9 5 0 ° C . Such c o n s i d e r a b l y s t r u c t u r e - s e n s i t i v e back-

ground wzs examined o n specimens d u r i n g i s o t h e r m a l a n n e a l i n g a t 8 5 0 ° C ( F i g . 3 ) . The i n t e r n a l f r i c t i o n spectrum i s composed of t h r e e s t a g e s . The f i r s t s t a g e from t h e b e g i n n i n g t o 9 0 0 min shows a g r a d u a l change f o l l o w e d by a l a r g e d e c r e a s e i n t h e second s t a g e from 9 0 0 min t o 2 0 0 0 min. I n t e r n a l f r i c t i o n i n t h e l a s t s t a g e g o e s d o w n t o a s a t u r a t i o n v a l u e .

4 . D i s c u s s i o n . - Most o f t h e t h e o r e t i c a l t r e a t m e n t s o f t h e background assume t h a t t h e e x p o n e n t a l l y r i s i n g i n t e r n a l f r i c t i o n i s c a u s e d by t h e v i s c o u s motion o f d i s l o c a t i o n s which o s c i l l a t e under an a p p l i e d s t r e s s i n v o l v i n g e m i s s i o n and a b s o r p t i o n o f v a c a n c i e s

(4)

- ( 6 ) . A s t r e s s - s t r a i n r e l a t i o n s h i p d e r i v e d on t h e a s s u m p t i o n y i e l d s t h e e x p r e s s i o n o f t h e background:

= CA exp ( - H / ~ T )

,

(1)

where C i s a c o n s t a n t once t h e f r e q u e n c y o f o s c i l l a t i o n and t h e t e m p e r - a t u r e of a n n e a l i n g a r e g i v e n , and A t h e d e n s i t y o f d i s l o c a t i o n . The background a l s o o c c u r s i n s i n g l e c r y s t a l s , a l t h o u g h t h e magnitude i s much s m a l l e r t h a n i n p o l y c r y s t a l s .

Concepts o f t h e s t r u c t u r e of b o t h low and h i g h a n g l e g r a i n boun- d a r i e s have been g r e a t l y advanced. Recent models have been emphasized

C5-496 JOURNAL DE PHYSIQUE

leading to dislocation structure which is closely examined by electron microscope(l0),(ll). The grain size dependence of the background sug- gests that grain boundary dislocations contribute to the internalfric-

tion. Dislocations both in the matrix and at the grain boundaries, thus, participate in the dislocation density in eqn.(l), designated by AM and AB, respectively. The total density of dislocation is given by h

+

gh /L, with the mean grain size L and a geometrical constant g .

M B

During the process of the secondary recrystallization, some of the boundaries are partitioned by primary and secondary grains. By intro- ducing a fraction secondary-recrystallized X, a portion of the dislo- cation density hB(l

-

X), is associated with dislocations at the boun- darles of primary grains and the rest h X belongs to those of secon-

B

dary ?rains. The background is, thus, the sum of three dampings -1 -1

QM

,

Q p

,

~5~

corresponding to the location of dislocations, respec-

tively in the matrix, at primary and secondary grain boundaries. They -1

are expressed as OM = AMAM, 0;' = A h (1

-

X) /lpl 0;' = A ~ A ~ X / L ~ ~ B B

where A ~ , ~ , are constants and LP

LS the grain sizes of primaries

- . . . , 1 l

.

. . .

and secondaries. Secondary grains are usually distinguished from primaries with an optical nicro- scope by their size at least 100 times larger than the primaries,

-

1

so that the quantity (2, isnegli- gible before .';Q

he-damping

due to grain boundary dislocations Q-1 is, thus, A (1

-

X)/L, where A = G

P P

ABAB

,

L = L At the beginning

P '

-

1

/.'-

1

:

. .

. . . l

.

. . . . a

1

of isothermal annealing, QG be-

comes Ap/LO with the initial prain

10

102

103

I

o4

Annealing time, min size L,. According to Avrami's

equati:n, the boundary component

Three

segments character-

-1 lstlc of growth kinetics in secon-

QG is written as dary recrystallization.

Table 1 Index m in Avrami's equation for grain growth. Dim. of grain _Johnson-Nehl

growth Avrami

*

Avrami's eqn.:

X = 1

-

exp(-6tm). 3 -dim. 4 3

2

m (

4

*

Assumption.on nuclea-

2-dim, 3

₅

_m

₂

tion rate

N

Johnson-Mehl~

fi

= cst. l-dim. 2 l c m 5 2 svrami:

fi

= Nvexp(-v-r)

,

N: number of preferred nucleation sites each having

a

nucleation frequency

v.

Table 2 Characteristic parameters of recrystallization.

Temp. ('C)

Stage I

Stage I1

Stage I11

a n c1 n N n

Q

,

'

= (A,/L)

exp

(

-6

tm)

,

B = B

0

exp

(

- H ~ ~ / * T )

,

( 2 )

where t is the annealing time and HSR is the activation energy for

secondary recrystallization; m, 6 are constants. The index m takes

0

values of 1 to 4 corresponding to the dimension of growth (Table 1) (12).

The ratio Q$/Q~-~, denoted by q, is

a

function of grain size expressed

a

S

q =

(L/Lo)exp(~tm)

,

whence l n q

=

ln(L/LO)

+

6 t m .

(3)

Figure 4 shows a graph of log(1nq) against logt

,

composed of three

segments, Each stage in Pig.

3

is determined from the intersection of

segments. A straight line in Fig.

4

is expressed in the form: l n q

=

atn

,

where

a and n are called the characteristic parameters of g r a m

growth. Their values for each stage are given in Table 2.

4.1

~ ~ g ~ ~ ~ - & ~ ~ g ~ j ~ g - j ~ - ~ _ ~ g g g ~ ~ . ~

In an early stage, primary grains of

the order of 10 pm can grow three-dimensionally regarding the sheet

thickness of 0.3 mm. Three-dim. qrowth gives

3

2

m

2

4

,

while the

characteristic parameter n for the stage is 0.67. Therefore, the prin-

cipal term in this stage is necessarily the first one in eqn.(3). The

exponent n is equal to 1 for normal qrain growth (13). A value of

n

less than

1

implies that the growth is retarded. On the other hand,

the parameter n increases up to a value larger than 1 with increasing

temperature of annealing; at 920°C abnormal qrain growth may partially

occur resulting in n

=

1.4 (13).

4.2

Gggyt_h_-k_~ne~jc_s_-&~-~_t_a_qe-IZ.-

The characteristic exponent n takes

in this stage a value of 3. If normal grain qrowth is dominant, the

parameter n is about 1 and the first term in eqn.(3) related to the

primary grain size L becomes principal one. The second term is,

there-

fore, predominant. According to Table 1, the grain growth is two-dim.

In fact, o ~ t i c a l

microscopic observations reveals that secondarygrains

grow through the sheet thickness in the early period of this stage

which is nucleation of secondary recrystallization in the sense of

Cohen

(14).

Prom eqns.

(2)

and

( 3 ) ,

one obtains

In

t

=

~ ~ ~ / m k T

+

(l/m)

ln[ln(qLo/60L)

l

.

( 4 )

For a given qo, the logarithm of annealing time until q reaches qo

exhibits a linear relation to 1/T if L

/L

for q=qo is independent of

0

annealing temperature; the slope is H

SR/mk. The activation energy

H

S

R

is, thus, obtained when m is determined; in this case, m

2

3. Anappre-

C5-498 JOURNAL DE PHYSIQUE

s l o ~ e o f t h e l i n e y i e l d s a n a c t i v a t i o n e n e r g y f o r growth o f 1 3 1 k c a l / mol. I n comparison w i t h a c t i v a t i o n e n e r g i e s o f 70 kcal/mol f o r secon- d a r y g r o w t h i n c u b e t e x t u r e ( 1 5 ) and 75.5 kcal/mol f o r t h e growth o f s e c o n d a r y g r a i n s i n 3%Si-Fe ( 1 6 ) , t h e v a l u e i n t h i s c a s e i s t w i c e l a r - g e r . The a c t i v a t i o n e n e r g y f o r d e s u l f u r i z a t i o n i n commercial s i l i c o n i r o n c o n t a i n i n g manganese i s r e p o r t e d a s h i g h a s 98 kcal/mol ( 1 6 ) . R e c e n t work i n t h i s l a b o r a t o r y h a s shown t h a t t h e i n h i b i t i o n o f normal g r a i n growth by MnSe p a r t i c l e s i s s i g n i f i c a n t l y s t r o n g e r t h a n by MnS p a r t i c l e s . The h i g h a c t i v a t i o n e n e r g y o b t a i n e d f o r s t a g e I1 a p p e a r s t o be a s s o c i a t e d w i t h s u c h a l a r g e back s t r e s s e x e r t e d by t h e f i n e l y d i s p g r s e d second p h a s e o f NnSe p a r t i c l e s . 5 . C o n c l u s i o n s . - An i n v e s t i g a t i o n a t t h e i n e r n a l f r i c t i o n l e v e l i s a v i t a l supplement t o t h e s t u d i e s c a r r i e d o u t by c o n v e n t i o n a l m e t a l l o - g r a p h i c t e c h n i q u e s . The h i g h - t e m p e r a t u r e background i s s o s t r u c t u r e - s e n s i t i v e t h a t it e n a b l e s o n e t o f o l l o w i n - s i t u t h e r e c r y s t a l l i z a t i o n p r o c e s s f o r t h e same b u l k sample. The k i n e t i c s o f g r a i n growth i s s p e c i f i e d by t h e d i m e n s i o n o f g r o w t h . The growth i s e s t i m a t e d by t h e c h a r a c t e r i s t i c e x p o n e n t n . R e t a r d e d growth i n s t a q e I v h i c h i s a l m o s t u n o b s e r v a b l e by t h e c o n v e n t i o n a l m e t a l l o g r a p h i c t e c h n i q u e s , i s d e t e c t e d by t h e i n t e r n a l f r i c t i o n . S t a g e I1 c o r r e s p o n d s t o a t y p i c a l abnormal growth. The a c t i v a t i o n e n e r g y f o r t h e growth o f s e c o n d a r y g r a i n s i s

1 3 1 k c a l / m o l . P o t e n t i a l t o a p p l y t h e h i g h - t e m p e r a t u r e background t o r e c r y s t a l l i z a t i o n s t u d y i s shown t o b e c o n s i d e r a b l e . To e s t a b l i s h t h i s i n t e r n a l f r i c t i o n t e c h n i q u e , f u r t h e r i n v e s t i g a t i o n s a r e e a r n e s t l y d e s i r e d . Acknowledgments.-The a u t h o r s w i s h t o t h a n k D r . H . Shimanaka f o r h e l p f u l i n f o r m a t i o n o n commercial s i l i c o n s t e e l , and M r . M . K o n i s h i f o r s t i m u - l a t l n g d i s c u s s i o n s . R e f e r e n c e s . (1) T. S . K&: T r a n s . AIME, 1 8 8 , 5 8 1 ( 1 9 5 0 ) .

( 2 ) P. M. Robinson and P . ~ X i c h a r d s : P h i l . Maa.. 11. 4 0 7 ( 1 9 6 5 ) . ( 3 ) A. I s o r 6 , W. B e n o i t and P . Stadelmann: p h i 1 1 { l a c ;

34,

811(1976)

.

( 4 ) J . F r i e d e l , C. B o u l a n g e r and C . C r u s s a r d : A c t a Met.,

2,

3 8 0 ( 1 9 5 5 ) . ( 5 ) B. E s c a i g : A c t a Met., 1 0 , 8 2 9 ( 1 9 6 2 ) .

( 6 ) J. Woirgard: Thkse D r

&s

S c i . P h y s . , Univ. P o i t i e r s ( 1 9 7 4 ) .

( 7 ) Y. I w a s a k i and K . F u j i m o t o : P r o c . ICIFUAS-7, Ed. P h y s . , P a r i s ( l 9 8 1 ) ( 8 ) W. Bollmann: C r y s t a l D e f e c t s and C r y s t a l l i n e I n t e r f a c e s , S p r i n g e r

B e r l i n ( 1 9 7 0 ) .

( 9 ) Y . I w a s a k i : A c t a C r y s t . , A s , 59 (1976)

.

( 1 0 ) T. Schober and R. W. B a l l u f f i : P h i l . Mag.,

21,

109 (1970)

.

(11) Y . I s h i d a , M. Mori and F. I i d a : Acta M e t . , 25, 8 1 5 ( 1 9 7 7 ) . ( 1 2 ) J. E . Burke a n d D. T u r n b u l l : Prog.Met. phys, 3 , 2 2 0 ( 1 9 5 2 ) . ( 1 3 ) Y . I w a s a k i and K. F u j i m o t o : ( t o be p u b l i s h e d )

.-

( 1 4 ) M . Cohen: T r a n s . AIME, 212, 1 7 1 ( 1 9 5 8 ) .