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IM465 – Segundo Semestre de 2010 - Análise de artigo
Exercício de caráter estritamente individual. Envie-o para meu e-mail até 29/10/2010.
O artigo apresentado a seguir trata da texturização e anisotropia de uma liga de
alumínio. Os autores comentam sobre diversos conceitos que temos discutido nas
aulas.
Responda as seguintes questões a partir do conteúdo do artigo:
1) O que diferencia os processos CC e DC, considerando os próprios processos,
seus produtos e o recozimento posterior?
2) O que pode levar à formação de orelhas nas chapas laminadas de alumínio?
3) Justifique as duas rotas utilizadas no procedimento experimental: recozimento
prévio, laminação a frio, recozimento final, ensaios de textura e anisotropia.
4) Por quê os autores afirmam que o recozimento a 204 oC por 3 horas não afeta a
textura?
5) Por quê os autores optaram ensaio de embutimento das chapas?
6) Quais foram as diferenças encontradas nas texturas dos produtos recozidos a
454 oC por 3 horas e como essas diferenças afetaram a anisotropia?
7) Como a deformação por laminação a frio modificou a textura do material
recozido e como isso influenciou a anisotropia?
8) Como ocorre a transição de quatro para oito orelhas?
9) Como a temperatura de recozimento da segunda rota de processamento afetou
a textura e anisotropia das chapas?
10) Quais são as condições de processamento que devem ser utilizadas para se
obter produtos com a qualidade adequada para estampagem profunda?
Jou
rnal
of
Mate
rials
Pro
cess
ing
Tech
no
log
y2
10
(2
01
0)
20
07
–2
01
5
Co
nte
nts
lists
av
ail
ab
lea
tS
cie
nce
Dir
ect
Jou
rnal
of
Mate
rials
Pro
cess
ing
Tech
no
log
y
jou
rn
al
ho
me
pa
ge
:w
ww
.els
ev
ier.c
om
/lo
ca
te/j
ma
tpro
tec
Co
mp
ari
son
of
eari
ng
beh
av
ior
betw
een
con
tin
uo
us
cast
an
dd
irect
chil
l
cast
AA
51
82
alu
min
um
all
oy
sd
uri
ng
cold
roll
ing
an
dan
neali
ng
J.Lia
,W.C
.Liu
a,∗
,H.Y
uan
a,Y
.K.G
ao
b
aK
eyLa
bora
tory
of
Met
ast
ab
leM
ate
rials
Sci
ence
an
dTec
hn
olo
gy,C
oll
ege
of
Mate
rials
Sci
ence
an
dE
ngin
eeri
ng,Y
an
shan
Un
iver
sity
,
No.4
38
Heb
eiA
ven
ue,
Qin
hu
an
gd
ao
06
60
04
,Heb
ei,C
hin
ab
Bei
jin
gIn
stit
ute
of
Aer
on
au
tica
lM
ate
rials
,Bei
jin
g1
00
09
5,C
hin
a
articleinfo
Art
icle
his
tory
:
Rece
ived
26
Marc
h2
01
0
Rece
ived
inre
vis
ed
form
11
July
20
10
Acc
ep
ted
17
July
20
10
Key
word
s:
Alu
min
um
Ro
llin
g
Tex
ture
Eari
ng
Xr
ay
dif
fract
ion
abstract
Th
eev
olu
tio
no
fte
xtu
rean
deari
ng
du
rin
gro
llin
go
fco
nti
nu
ou
sca
st(C
C)
an
dd
irect
chil
l(D
C)
cast
AA
51
82
alu
min
um
all
oy
sw
as
inv
est
igate
d.T
he
resu
lts
sho
wed
that
the
CC
all
oy
po
ssess
ed
asi
gn
ifica
ntl
y
weak
er
cub
ete
xtu
reth
an
the
DC
all
oy
aft
er
an
neali
ng
at
45
4◦C
for
3h
.Th
eev
olu
tio
no
fte
xtu
rean
deari
ng
du
rin
gro
llin
gw
as
stro
ng
lyaff
ect
ed
by
the
init
ial
tex
ture
.T
he
45
◦eari
ng
valu
eo
fth
eC
Call
oy
incr
ease
d
wit
hin
creasi
ng
roll
ing
red
uct
ion
,w
hil
eth
e0
/90
◦eari
ng
valu
eo
fth
eD
Call
oy
decr
ease
d.A
fter
45
%co
ld
roll
ing
red
uct
ion
,th
ed
eep
dra
wn
cup
of
the
DC
all
oy
ex
hib
ited
eig
ht
ears
at
0◦,4
5◦
an
d9
0◦
toth
ero
llin
g
dir
ect
ion
.Th
eD
Csh
eet
wit
hm
inim
um
eari
ng
was
ob
tain
ed
at
ab
ou
t8
3%
roll
ing
red
uct
ion
.Th
eev
olu
tio
n
of
tex
ture
an
deari
ng
du
rin
gan
neali
ng
of
the
CC
an
dD
Call
oy
sw
as
com
pare
d.A
nem
pir
ical
rela
tio
nsh
ip
betw
een
the
eari
ng
valu
ean
dte
xtu
rev
olu
me
fract
ion
sw
as
est
ab
lish
ed
.Min
imiz
ati
on
of
eari
ng
cou
ldb
e
ach
iev
ed
by
bala
nci
ng
the
cub
e,r
cu
be
an
db
fib
er
com
po
nen
ts. ©
20
10
Els
ev
ier
B.V
. A
ll r
igh
ts r
ese
rved
.
1.
Intr
od
ucti
on
Tw
inb
elt
con
tin
uo
us
cast
(CC
)p
roce
ssin
go
falu
min
um
all
oy
sheets
has
rece
ntl
yatt
ract
ed
ex
ten
siv
eatt
en
tio
nb
eca
use
of
its
hig
hp
rod
uct
ivit
yan
dlo
wco
nv
ers
ion
cost
.In
the
con
tin
uo
us
cast
pro
cess
ing
,th
em
olt
en
meta
lis
po
ure
db
etw
een
two
rota
tin
g
steel
belt
sto
pro
du
cea
cast
slab
,w
hic
his
imm
ed
iate
lyfe
din
to
thre
eco
nse
cuti
ve
ho
tro
llin
gm
ills
,fo
rmin
gh
ot
ban
dp
rod
uct
s.
Du
eto
dif
fere
nt
pro
cess
ing
rou
tes,
there
are
dis
tin
ctd
iffe
ren
ces
inm
icro
stru
ctu
rean
dte
xtu
reb
etw
een
CC
an
dd
irect
chil
l(D
C)
cast
ho
tb
an
ds,
wh
ich
aff
ect
the
ev
olu
tio
no
fm
icro
stru
ctu
rean
dte
x
ture
du
rin
gsu
bse
qu
en
tp
roce
ssin
gan
dh
en
ceth
efo
rmab
ilit
yo
f
alu
min
um
all
oy
sheets
.
Liu
an
dM
orr
is(2
00
3)
inv
est
igate
dth
ete
xtu
reev
olu
tio
no
fC
C
an
dD
CA
A5
18
2alu
min
um
all
oy
sd
uri
ng
cold
roll
ing
.T
hey
fou
nd
that
the
mic
rost
ruct
ure
an
dte
xtu
reo
fth
eC
Ch
ot
ban
dw
ere
sig
nifi
can
tly
dif
fere
nt
fro
mth
ose
of
the
DC
ho
tb
an
d.T
he
CC
ho
tb
an
d
po
ssess
ed
aty
pic
ald
efo
rmed
stru
ctu
rean
da
stro
ng
bfi
ber
roll
ing
tex
ture
,wh
ile
the
DC
ho
tb
an
dex
hib
ited
afu
lly
recr
yst
all
ized
stru
c
ture
an
da
stro
ng
cub
ete
xtu
re.
Aft
er
an
neali
ng
at
45
4◦C
for
3h
,
the
CC
AA
51
82
alu
min
um
all
oy
ex
hib
ited
asi
gn
ifica
ntl
yw
eak
er
cub
ete
xtu
reth
an
the
DC
cou
nte
rpart
.T
he
tex
ture
ev
olu
tio
nd
ur
ing
cold
roll
ing
was
stro
ng
lyaff
ect
ed
by
the
init
ial
cub
ete
xtu
re.
∗C
orr
esp
on
din
gau
tho
r.T
el.:
+8
61
58
33
35
62
75
;fa
x:
+8
63
35
80
74
54
5.
Em
ail
ad
dre
ss:
wcl
iu@
ysu
.ed
u.c
n(W
.C.L
iu).
Itw
as
fou
nd
that
the
CC
alu
min
um
all
oy
had
ah
igh
er
rate
of
for
mati
on
of
the
bfi
ber
com
po
nen
tth
an
the
DC
cou
nte
rpart
.Z
hao
an
dM
orr
is(2
00
5)
com
pare
dth
ete
xtu
reev
olu
tio
no
fC
Can
dD
CA
A
50
52
ho
tb
an
ds
du
rin
gis
oth
erm
al
an
neali
ng
.T
hey
fou
nd
that
the
CC
AA
50
52
ho
tb
an
dw
as
mo
red
iffi
cult
tore
cry
stall
ize
than
the
DC
AA
50
52
ho
tb
an
d.A
fter
com
ple
tere
cry
stall
izati
on
,th
eC
CA
A5
05
2
alu
min
um
all
oy
po
ssess
ed
aw
eak
er
cub
ete
xtu
reth
an
the
DC
AA
50
52
alu
min
um
all
oy
.Sark
ar
et
al.
(20
06
)co
mp
are
dth
eso
ften
ing
beh
av
ior
of
cold
ro
lled
CC
an
din
go
tca
st(I
C)
AA
57
54
alu
min
um
all
oy
s.T
hey
po
inte
do
ut
that
the
dif
fere
nce
sin
the
soft
en
ing
beh
av
ior
betw
een
the
CC
an
dIC
mate
rial
cou
ldb
ere
late
dto
solu
ted
rag
an
dco
ncu
rren
tp
reci
pit
ati
on
wh
ich
occ
urr
ed
du
rin
gan
neali
ng
of
the
CC
mate
rial
resu
ltin
gin
the
reta
rded
gro
wth
of
recr
yst
all
ized
gra
ins.
Th
ep
last
ican
iso
tro
py
of
alu
min
um
all
oy
sheets
can
be
att
rib
ute
dto
the
pre
sen
ceo
fcr
yst
all
og
rap
hic
tex
ture
dev
elo
ped
in
pro
du
ctio
np
roce
sses.
Th
eo
ccu
rren
ceo
feari
ng
du
rin
gd
eep
dra
w
ing
of
ate
xtu
red
sheet
isa
qu
ali
tycr
iteri
on
inin
du
stry
,si
nce
it
can
cau
sem
ajo
rp
rob
lem
sin
the
pro
du
ctio
no
fd
eep
dra
wn
con
tain
ers
fro
malu
min
um
sheet.
Th
ere
lati
on
ship
betw
een
eari
ng
an
d
tex
ture
has
been
dem
on
stra
ted
on
aq
uali
tati
ve
po
int
of
vie
w:
45
◦an
d0
/90
◦eari
ng
wh
ich
are
ass
oci
ate
dre
spect
ively
wit
hth
eb
fib
er
roll
ing
tex
ture
an
dcu
be
recr
yst
all
izati
on
tex
ture
.M
ore
ov
er,
An
ders
son
an
dN
aess
(19
86
)u
sed
em
pir
icalm
eth
od
sto
defi
ne
the
eari
ng
perc
en
tag
eas
ali
near
fun
ctio
no
fso
me
tex
ture
data
.In
the
pre
sen
tw
ork
,th
eev
olu
tio
no
fte
xtu
rean
deari
ng
du
rin
gro
llin
g
an
dan
neali
ng
of
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
sw
as
inv
es
09
24
01
36
/$–
see
fro
nt
matt
er
© 2
01
0 E
lsev
ier
B.V
. A
ll r
igh
ts r
ese
rved
.
do
i:1
0.1
01
6/j
.jm
atp
rote
c.2
01
0.0
7.0
17
20
08
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
Ta
ble
1
Ch
em
ical
com
po
siti
on
so
fth
eC
Can
dD
CA
A5
18
2alu
min
um
all
oy
s(w
t%).
All
oy
Si
Fe
Cu
Mn
Mg
Cr
Al
CC
0.1
10
0.2
12
0.0
41
0.3
50
4.5
95
0.0
13
Bal.
DC
0.0
84
0.2
18
0.0
44
0.3
27
4.3
51
0.0
10
Bal.
tig
ate
d.
An
em
pir
ical
rela
tio
nsh
ipb
etw
een
the
eari
ng
valu
ean
d
tex
ture
vo
lum
efr
act
ion
sw
as
est
ab
lish
ed
.
2.
Ex
pe
rim
en
tal
Th
em
ate
rials
use
din
the
pre
sen
tin
vest
igati
on
were
CC
an
d
DC
AA
51
82
alu
min
um
all
oy
s.T
he
chem
ical
com
po
siti
on
so
fth
e
two
all
oy
sare
giv
en
inT
ab
le1
.T
he
as
rece
ived
mate
rials
were
CC
an
dD
Ch
ot
ban
ds,
wh
ich
were
pro
du
ced
usi
ng
stan
dard
ind
us
tria
lp
ract
ices.
Th
eth
ick
ness
of
the
CC
an
dD
Ch
ot
ban
ds
was
3.0
7
an
d2
.64
mm
,re
spect
ively
.T
he
CC
ho
tb
an
dp
oss
ess
ed
aty
pic
al
defo
rmed
stru
ctu
rean
da
stro
ng
bfi
ber
roll
ing
tex
ture
,wh
ile
the
DC
ho
tb
an
dsh
ow
ed
afu
lly
recr
yst
all
ized
gra
inst
ruct
ure
an
da
stro
ng
cub
ete
xtu
re.I
no
rder
toach
iev
ea
sim
ilar
init
ial
state
pri
or
toco
ld
roll
ing
,th
eh
ot
ban
ds
of
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
sw
ere
an
neale
dat
45
4◦C
for
3h
foll
ow
ed
by
air
coo
lin
g.A
fter
an
neali
ng
at
45
4◦C
,th
eC
Ch
ot
ban
dw
as
full
yre
cry
stall
ized
.T
he
ho
tb
an
d
an
neali
ng
isre
ferr
ed
toh
ere
aft
er
as
pre
tre
atm
en
t.
Th
ean
neale
dC
Can
dD
Ch
ot
ban
ds
were
cold
roll
ed
tod
iffe
r
en
tre
du
ctio
ns
ran
gin
gfr
om
0to
91
%to
inv
est
igate
the
ev
olu
tio
n
of
tex
ture
an
deari
ng
du
rin
gro
llin
g.
At
larg
er
roll
ing
red
uct
ion
s,
the
deep
dra
wn
cup
sfr
act
ure
db
eca
use
of
the
low
pla
stic
ity
of
the
cold
ro
lled
sheets
.R
eco
very
of
cold
ro
lled
sheets
can
imp
rov
e
the
pla
stic
ity
,b
ut
do
es
no
taff
ect
the
tex
ture
an
deari
ng
beh
av
ior.
Th
us,
the
cold
ro
lled
sheets
were
an
neale
dat
20
4◦C
for
3h
tore
veal
the
vari
ati
on
ineari
ng
wit
hro
llin
gre
du
ctio
n.
Ino
rder
toin
vest
igate
the
ev
olu
tio
no
fte
xtu
rean
deari
ng
du
rin
gan
neal
ing
,th
eC
Ch
ot
ban
das
well
as
the
an
neale
dC
Can
dD
Ch
ot
ban
ds
were
cold
roll
ed
to7
1.5
%re
du
ctio
n,a
nd
then
an
neale
dat
dif
fere
nt
tem
pera
ture
sfo
r3
h.
Fig
.1
sho
ws
the
flo
wch
art
of
the
pro
cess
ing
rou
tefo
rth
eC
Can
dD
CA
A5
18
2alu
min
um
all
oy
su
sed
inth
is
stu
dy
.
Tex
ture
measu
rem
en
tsw
ere
perf
orm
ed
at
the
qu
art
er
thic
k
ness
of
the
cold
roll
ed
an
dan
neale
dsh
eets
.Th
e(1
11
),(2
00
),an
d
(22
0)
po
lefi
gu
res
were
measu
red
up
toa
max
imu
mti
ltan
gle
of
75
◦b
yth
eSch
ulz
back
refl
ect
ion
meth
od
usi
ng
Cu
Ka
rad
iati
on
.Th
e
ori
en
tati
on
dis
trib
uti
on
fun
ctio
ns
(OD
Fs)
were
calc
ula
ted
fro
mth
e
thre
ein
com
ple
tep
ole
fig
ure
su
sin
gth
ese
ries
ex
pan
sio
nm
eth
od
(lm
ax
=1
6)
(Bu
ng
e,1
98
2).
Th
eO
DFs
were
pre
sen
ted
as
plo
tso
fco
n
stan
tϕ
2se
ctio
ns
wit
his
oin
ten
sity
con
tou
rsin
Eu
ler
space
defi
ned
by
the
Eu
ler
an
gle
sϕ
1,˚
an
dϕ
2.T
he
vo
lum
efr
act
ion
so
fth
ete
xtu
re
com
po
nen
tsw
ere
calc
ula
ted
by
an
imp
rov
ed
inte
gra
tio
nm
eth
od
pro
po
sed
by
Liu
an
dM
orr
is(2
00
3).
Cu
pd
raw
ing
test
sw
ere
perf
orm
ed
on
ah
yd
rau
lic
pre
ss.F
or
the
sheets
wit
hth
ick
ness
es
ran
gin
gfr
om
0.2
6to
ab
ou
t3
mm
bla
nk
s
wit
ha
dia
mete
ro
f6
0m
mw
ere
defo
rmed
wit
ha
pu
nch
of3
3.3
mm
.
Aft
er
deep
dra
win
g,th
eeari
ng
pro
file
sw
ere
pro
bed
inst
ep
so
f1
◦
usi
ng
Hu
xle
yB
ert
ram
36
0◦
Au
tom
ati
cE
ari
ng
Test
Sy
stem
.D
ue
to
the
ort
ho
tro
pic
sam
ple
sym
metr
y,th
eeari
ng
pro
file
may
be
sym
metr
ized
wit
hre
spect
toth
ero
llin
gd
irect
ion
(RD
)an
dtr
an
svers
e
dir
ect
ion
.Fig
.2
sho
ws
two
ex
am
ple
so
fth
eeari
ng
pro
file
of
the
dra
wn
cup
sw
ith
fou
ran
deig
ht
ears
.T
he
eari
ng
valu
ew
as
calc
u
late
du
sin
gth
efo
llo
win
geq
uati
on
:
E=
hi−
hm
in
hm
in(1
)
wh
ere
hm
inis
the
heig
ht
at
the
vall
ey
,an
dh
iis
the
heig
ht
of
the
eari
ng
peak
s.Fig
.2(b
)d
ep
icts
ach
ara
cteri
stic
eig
ht
ear
pro
file
wit
h
ears
at
0◦,
45
◦an
d9
0◦
toth
eR
D.
Th
us,
the
45
◦an
d0
/90
◦eari
ng
valu
es
can
be
ob
tain
ed
fro
mth
em
easu
red
eari
ng
pro
file
s.Fo
rsu
ch
mix
ed
tex
ture
sw
ith
eig
ht
ears
the
delt
aeari
ng
valu
e,1
E,m
ay
be
use
ful,
wh
ich
isd
efi
ned
as
1E
=2
h4
5◦−
(h0
◦+
h9
0◦)
h0
◦+
h9
0◦
(2)
Neg
ati
ve
valu
es
of
1E
imp
lyth
at
the
av
era
ge
0◦/9
0◦
ears
are
larg
er
than
the
45
◦ears
or
the
deep
dra
wn
cup
ex
hib
its
fou
r0
/90
◦ears
.
Fig
.1
.Flo
wch
art
of
the
pro
cess
ing
rou
tefo
rth
eC
Can
dD
CA
A5
18
2alu
min
um
all
oy
su
sed
inth
isst
ud
y.
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
20
09
Fig
.2
.E
ari
ng
pro
file
so
fth
ed
raw
ncu
ps
wit
h(a
)fo
ur
an
d(b
)eig
ht
ears
.
3.
Re
sult
s
3.1
.E
volu
tion
of
textu
rean
dea
rin
gd
uri
ng
roll
ing
Fig
.3
sho
ws
the
tex
ture
of
the
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
saft
er
an
neali
ng
at
45
4◦C
for
3h
.It
isse
en
that
the
CC
all
oy
po
ssess
ed
asi
gn
ifica
ntl
yw
eak
er
cub
ete
xtu
reth
an
the
DC
all
oy
.
Th
ete
xtu
reev
olu
tio
nd
uri
ng
roll
ing
of
the
CC
an
dD
CA
A5
18
2
alu
min
um
all
oy
sh
as
been
rep
ort
ed
els
ew
here
by
Liu
an
dM
orr
is
(20
03
) .Fig
.4
sho
ws
the
vari
ati
on
inth
ev
olu
me
fract
ion
so
fth
e
cub
e,
bfi
ber
an
dre
main
der
com
po
nen
tsw
ith
roll
ing
tru
est
rain
.
As
the
roll
ing
tru
est
rain
incr
ease
d,
the
vo
lum
efr
act
ion
so
fth
e
cub
ean
dre
main
der
com
po
nen
tsd
ecr
ease
d,
wh
ere
as
the
vo
lum
e
fract
ion
of
the
bfi
ber
com
po
nen
tin
crease
d.
Th
eC
Call
oy
ex
hib
ited
ast
ron
ger
bfi
ber
tex
ture
than
the
DC
all
oy
at
ag
iven
roll
ing
red
uct
ion
.
Fig
.5sh
ow
sth
eev
olu
tio
no
feari
ng
du
rin
gro
llin
go
fth
eC
Can
d
DC
AA
51
82
alu
min
um
all
oy
s.T
he
an
neale
dC
Ch
ot
ban
dex
hib
ited
very
small
ears
at
45
◦to
the
RD
beca
use
of
the
weak
reta
ined
roll
ing
tex
ture
inth
ere
cry
stall
izati
on
tex
ture
.Th
e4
5◦
eari
ng
valu
e
an
dd
elt
aeari
ng
valu
ein
crease
dw
ith
incr
easi
ng
roll
ing
red
uct
ion
.
At
90
%ro
llin
gre
du
ctio
n,
the
eari
ng
valu
eo
fth
eC
Call
oy
reach
ed
ab
ou
t9
%.T
he
an
neale
dD
Ch
ot
han
dex
hib
ited
0/9
0◦
eari
ng
beca
use
itp
oss
ess
ed
ast
ron
gcu
be
recr
yst
all
izati
on
tex
ture
.A
sth
ero
llin
g
red
uct
ion
incr
ease
d,th
ecu
be
com
po
nen
tw
eak
en
ed
,w
here
as
the
bfi
ber
com
po
nen
tst
ren
gth
en
ed
.Th
isre
sult
ed
ina
decr
ease
inth
e
0/9
0◦
eari
ng
valu
e.
Th
eir
reg
ula
rv
ari
ati
on
inth
e0
◦eari
ng
valu
e
inth
eearl
yst
ag
eo
fd
efo
rmati
on
can
be
att
rib
ute
dto
the
eff
ect
of
sheet
thic
kn
ess
.Th
eth
ick
alu
min
um
sheet
an
dsm
all
size
of
pu
nch
Fig
.4
.V
ari
ati
on
inth
ev
olu
me
fract
ion
so
fth
ecu
be,
bfi
ber
an
dre
main
der
com
po
nen
tsw
ith
roll
ing
tru
est
rain
inth
eco
ldr
oll
ed
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
s.
rest
rict
the
form
ati
on
ofe
ari
ng
du
rin
gd
eep
dra
win
g.W
hen
the
cold
roll
ing
red
uct
ion
reach
ed
ab
ou
t4
5%
,th
ed
eep
dra
wn
cup
ex
hib
ited
eig
ht
ears
at
0◦,4
5◦
an
d9
0◦
toth
eR
D.A
sth
ero
llin
gre
du
ctio
n
furt
her
incr
ease
d,
the
0/9
0◦
eari
ng
valu
ed
ecr
ease
d,
wh
ere
as
the
45
◦eari
ng
valu
ein
crease
d.
Neg
ati
ve
valu
es
of
1E
imp
lyth
at
the
av
era
ge
0◦/9
0◦
ears
are
larg
er
than
the
45
◦ears
.A
fter
90
%ro
llin
g
red
uct
ion
,th
eeari
ng
pro
file
on
lysh
ow
ed
fou
r4
5◦
ears
.
Fig
.3
.T
ex
ture
of
the
(a)
CC
an
d(b
)D
CA
A5
18
2alu
min
um
all
oy
saft
er
an
neali
ng
at
45
4◦C
for
3h
.
20
10
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
Fig
.5
.(a
)0
/45
◦eari
ng
valu
ean
d(b
)d
elt
aeari
ng
valu
eas
afu
nct
ion
of
roll
ing
red
uct
ion
for
the
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
s.
Th
ealu
min
um
sheets
wit
hm
inim
um
eari
ng
cou
ldb
eo
bta
ined
at
ag
iven
gau
ge
by
bala
nci
ng
the
45
◦an
d0
/90
◦eari
ng
ten
den
cies.
Fo
rth
eD
Call
oy
,th
em
inim
um
eari
ng
valu
eo
f3
.5%
was
ob
tain
ed
at
ab
ou
t8
3%
roll
ing
red
uct
ion
.T
he
eari
ng
valu
eo
fth
eC
Call
oy
incr
ease
dw
ith
incr
easi
ng
roll
ing
red
uct
ion
.At
larg
ero
llin
gre
du
c
tio
ns,
the
eari
ng
valu
eo
fth
eC
Call
oy
was
larg
er
than
that
of
the
DC
all
oy
.T
he
eari
ng
valu
eo
fth
eC
Call
oy
at
51
%ro
llin
gre
du
ctio
n
was
the
sam
eas
the
min
imu
meari
ng
valu
eo
fth
eD
Call
oy
.Th
ere
fore
,in
ord
er
toim
pro
ve
the
pla
stic
an
iso
tro
py
ofth
eco
ldr
oll
ed
CC
sheet,
the
cold
roll
ing
red
uct
ion
sho
uld
be
red
uce
db
yco
ntr
oll
ing
the
thic
kn
ess
of
init
ial
CC
ho
tb
an
d.
3.2
.E
volu
tion
of
textu
rean
dea
rin
gd
uri
ng
an
nea
lin
g
Fig
.6sh
ow
sth
eO
DFs
of
the
CC
ho
tb
an
dco
ldro
lled
to7
1.5
%as
well
as
the
CC
an
dD
Ch
ot
ban
dan
neale
dat
45
4◦C
for
3h
an
dth
en
cold
roll
ed
to7
1.5
%.
Inth
eco
ldr
oll
ed
state
the
CC
all
oy
wit
ho
ut
pre
tre
atm
en
tex
hib
ited
the
stro
ng
est
bfi
ber
roll
ing
tex
ture
.T
he
Fig
.6
.O
DFs
of
the
CC
ho
tb
an
dco
ldro
lled
to7
1.5
%as
well
as
the
CC
an
dD
Ch
ot
ban
ds
an
neale
dat
45
4◦C
for
3h
an
dth
en
cold
roll
ed
to7
1.5
%.
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
20
11
Fig
.7.
Rati
o(M
i/M
ira
nd
om
)o
fth
ev
olu
me
fract
ion
ofth
ete
xtu
reco
mp
on
en
t(M
i)to
that
un
der
ap
erf
ect
lyra
nd
om
con
dit
ion
(/M
ira
nd
om
)as
afu
nct
ion
ofan
neali
ng
tem
pera
ture
for
(a)
the
CC
ho
tb
an
dco
ldro
lled
to7
1.5
%as
well
as
the
(b)
CC
an
d(c
)D
Ch
ot
ban
ds
an
neale
dat
45
4◦C
for
3h
an
dth
en
cold
roll
ed
to7
1.5
%.
stre
ng
tho
fth
eb
fib
er
com
po
nen
td
ecr
ease
din
the
seq
uen
ceo
fth
e
CC
all
oy
wit
ho
ut
pre
tre
atm
en
t,th
eC
Call
oy
wit
hp
ret
reatm
en
t
an
dth
eD
Call
oy
wit
hp
ret
reatm
en
t,w
here
as
the
stre
ng
tho
f
the
cub
eco
mp
on
en
tin
crease
d.
Th
eD
Call
oy
wit
hp
ret
reatm
en
t
reta
ined
the
mo
stre
main
ing
cub
eco
mp
on
en
t.
Du
rin
gan
neali
ng
ofth
eco
ldr
oll
ed
sheets
,reco
very
an
dre
cry
s
tall
izati
on
tak
ep
lace
.T
he
ev
olu
tio
no
fre
cry
stall
izati
on
tex
ture
can
be
an
aly
zed
qu
an
tita
tiv
ely
by
the
vari
ati
on
inth
ete
xtu
rev
ol
um
efr
act
ion
sw
ith
an
neali
ng
tem
pera
ture
.Fig
.7
sho
ws
the
rati
o
(Mi/
Mi
ran
do
m)
of
the
vo
lum
efr
act
ion
of
the
tex
ture
com
po
nen
t
(Mi)
toth
at
un
der
ap
erf
ect
lyra
nd
om
con
dit
ion
(/M
ira
nd
om
)as
a
fun
ctio
no
fan
neali
ng
tem
pera
ture
.T
he
tex
ture
vo
lum
efr
act
ion
s
of
the
cub
e,
rcu
be,
Go
ss,
rG
oss
,b
/Ran
dre
main
der
com
po
nen
ts
are
5.4
1,
5.6
4,
6.4
5,
9.0
9,
16
.90
,an
d5
6.5
0%
ina
perf
ect
lyra
n
do
msa
mp
le,
resp
ect
ively
(Liu
an
dM
orr
is,
20
04
).It
isn
ote
dth
at
reco
very
of
the
cold
ro
lled
sheets
did
no
talt
er
the
stre
ng
tho
f
the
bfi
ber
roll
ing
tex
ture
.Sig
nifi
can
tch
an
ges
inte
xtu
reco
mp
o
nen
tso
ccu
rred
du
rin
gre
cry
stall
izati
on
.Fo
rth
eco
ldr
oll
ed
CC
all
oy
wit
ho
utp
ret
reatm
en
t( F
ig.7
(a))
,th
em
ajo
rch
an
ge
thro
ug
hre
cry
s
tall
izati
on
was
are
mark
ab
led
ecr
ease
inth
eb
fib
er
com
po
nen
t.
Mo
reo
ver,
recr
yst
all
izati
on
als
od
ecr
ease
dth
eG
oss
com
po
nen
tan
d
incr
ease
dth
ecu
be,r
cu
be,r
Go
ssan
dre
main
der
com
po
nen
ts.F
or
the
cold
ro
lled
CC
all
oy
wit
hp
ret
reatm
en
t(F
ig.
7(b
)),
recr
yst
al
lizati
on
decr
ease
dth
eb
fib
er
an
dG
oss
com
po
nen
tsan
din
crease
d
the
cub
e,
rcu
be
an
dre
main
der
com
po
nen
ts.
Th
er
Go
ssco
mp
o
nen
tch
an
ged
slig
htl
yth
rou
gh
recr
yst
all
izati
on
.Fo
rth
eco
ldr
oll
ed
DC
all
oy
wit
hp
ret
reatm
en
t(F
ig.7
(c))
,recr
yst
all
izati
on
decr
ease
d
the
bfi
ber,
Go
ssan
dcu
be
com
po
nen
tsan
din
crease
dth
er
cub
e,
rG
oss
an
dre
main
der
com
po
nen
ts.
Fig
.8sh
ow
sth
eco
mp
ari
son
of
recr
yst
all
izati
on
tex
ture
am
on
g
the
thre
eco
ldr
oll
ed
sheets
.T
he
CC
all
oy
ex
hib
ited
asl
igh
tly
weak
er
recr
yst
all
izati
on
tex
ture
than
the
DC
all
oy
. Liu
et
al.
(20
03
)
fou
nd
that
the
dif
fere
nce
inth
ere
cry
stall
izati
on
tex
ture
betw
een
the
CC
an
dD
Call
oy
sco
uld
be
att
rib
ute
dto
dif
fere
nt
init
ial
tex
ture
san
dp
art
icle
size
dis
trib
uti
on
sp
rio
rto
cold
roll
ing
.T
he
pre
tre
atm
en
tp
rio
rto
cold
roll
ing
als
oaff
ect
ed
the
recr
yst
all
iza
tio
nte
xtu
reo
fth
eC
Calu
min
um
all
oy
.Th
ere
cry
stall
izati
on
tex
ture
of
the
CC
all
oy
wit
ho
ut
pre
tre
atm
en
tex
hib
ited
ast
ron
ger
cub
e
com
po
nen
tan
da
weak
er
Rco
mp
on
en
tth
an
that
of
the
CC
all
oy
wit
hp
ret
reatm
en
t.
Fig
.9sh
ow
sth
ev
ari
ati
on
inth
e4
5◦
eari
ng
valu
ean
dd
elt
aeari
ng
valu
ew
ith
an
neali
ng
tem
pera
ture
for
the
cold
ro
lled
CC
AA
51
82
alu
min
um
all
oy
wit
han
dw
ith
ou
tp
ret
reatm
en
t.In
the
defo
rmed
an
dre
cov
ere
dst
ate
s,th
eC
Call
oy
wit
ho
ut
pre
tre
atm
en
tp
oss
ess
ed
asi
gn
ifica
ntl
yh
igh
er
45
◦eari
ng
valu
eth
an
the
CC
all
oy
wit
hp
re
treatm
en
t.T
he
45
◦eari
ng
valu
ean
dd
elt
aeari
ng
valu
ed
ecr
ease
d
wit
hin
creasi
ng
an
neali
ng
tem
pera
ture
.A
fter
com
ple
tere
cry
stal
lizati
on
,th
eC
Call
oy
stil
lsh
ow
ed
45
◦ears
,an
dth
e4
5◦
eari
ng
valu
e
of
the
all
oy
wit
ho
ut
pre
tre
atm
en
tw
as
slig
htl
ylo
wer
than
that
of
the
all
oy
wit
hp
ret
reatm
en
t.Fig
.1
0(a
)sh
ow
sth
ere
lati
on
ship
betw
een
the
0/4
5◦
eari
ng
valu
ean
dan
neali
ng
tem
pera
ture
for
the
cold
ro
lled
DC
AA
51
82
alu
min
um
all
oy
.In
the
defo
rmed
an
dre
cov
ere
dst
ate
s,th
eD
Call
oy
ex
hib
ited
eig
htears
at0
◦,4
5◦
an
d9
0◦
toth
e
RD
.Aty
pic
aleari
ng
pro
file
issh
ow
nin
Fig
.2(b
).T
he
0◦
eari
ng
valu
e
was
larg
er
than
the
45
◦eari
ng
valu
e,w
hil
eth
e9
0◦
eari
ng
valu
ew
as
very
small
.D
uri
ng
recr
yst
all
izati
on
an
neali
ng
,th
est
ren
gth
of
the
cub
eco
mp
on
en
tw
eak
en
ed
(Fig
.7
(c))
,le
ad
ing
toa
decr
ease
inth
e
0/9
0◦
eari
ng
valu
e.
Aft
er
com
ple
tere
cry
stall
izati
on
,th
eD
Call
oy
als
oex
hib
ited
45
◦ears
.Th
ev
ari
ati
on
inth
ed
elt
aeari
ng
valu
ew
ith
an
neali
ng
tem
pera
ture
issh
ow
nin
Fig
.1
0(b
).It
isn
ote
dth
at
the
valu
eo
f1
Ein
crease
dw
ith
incr
easi
ng
an
neali
ng
tem
pera
ture
.
4.
Dis
cu
ssio
n
4.1
.E
ffec
tof
the
pro
cess
ing
met
hod
(CC
vs.
DC
)on
eari
ng
beh
avio
r
Ho
tb
an
ds
of
AA
51
82
alu
min
um
all
oy
pro
du
ced
by
the
DC
an
d
CC
pro
cess
ing
ex
hib
itsi
gn
ifica
ntl
yd
iffe
ren
tfe
atu
res
ofm
icro
stru
c
ture
an
dte
xtu
re.T
he
DC
ho
tb
an
dp
oss
ess
es
are
cry
stall
ized
gra
in
stru
ctu
rean
da
stro
ng
cub
ete
xtu
re,
wh
ere
as
the
CC
ho
tb
an
d
ex
hib
its
ad
efo
rmed
stru
ctu
rean
da
stro
ng
bfi
ber
roll
ing
tex
20
12
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
Fig
.8
.R
ecr
yst
all
izati
on
tex
ture
of
the
cold
ro
lled
CC
AA
51
82
alu
min
um
all
oy
(a)
wit
ho
ut
an
d(b
)w
ith
pre
tre
atm
en
tan
d(c
)co
ldr
oll
ed
DC
AA
51
82
alu
min
um
all
oy
wit
h
pre
tre
atm
en
t(T
=3
71
◦C
).
ture
.A
fter
an
neali
ng
at
45
4◦C
for
3h
,th
eC
Ch
ot
ban
dis
full
y
recr
yst
all
ized
.T
he
cub
ere
cry
stall
izati
on
tex
ture
of
the
CC
all
oy
is
sig
nifi
can
tly
weak
er
than
that
of
the
DC
all
oy
.Du
rin
gro
llin
gin
itia
l
ori
en
tati
on
sare
gra
du
all
yro
tate
dto
the
bfi
ber
com
po
nen
t.T
he
ev
olu
tio
no
fte
xtu
red
uri
ng
roll
ing
isst
ron
gly
aff
ect
ed
by
the
init
ial
tex
ture
. Liu
et
al.
(20
04
a)
stu
die
dth
eeff
ect
ofin
itia
lte
xtu
reo
nte
x
ture
ev
olu
tio
nin
cold
ro
lled
AA
51
82
alu
min
ium
all
oy
.Th
ey
fou
nd
that
the
cub
eo
rien
ted
gra
ins
rota
tem
ore
slo
wly
tow
ard
sth
eb
fib
er
com
po
nen
tth
an
the
oth
er
gra
ins
wit
hu
nst
ab
leo
rien
tati
on
s.
Th
est
ron
gin
itia
lcu
be
tex
ture
inth
eD
Call
oy
giv
es
rise
toa
weak
bfi
ber
roll
ing
tex
ture
wit
hm
ore
rem
ain
ing
cub
eo
rien
ted
gra
ins
aft
er
ag
iven
roll
ing
red
uct
ion
.T
he
bfi
ber
roll
ing
tex
ture
inalu
min
um
all
oy
sp
rom
ote
seari
ng
ess
en
tiall
yat
45
◦w
ith
resp
ect
toth
e
RD
,w
here
as
the
cub
ere
cry
stall
izati
on
tex
ture
pro
du
ces
sym
met
rica
l0
/90
◦ears
.T
he
ev
olu
tio
no
feari
ng
du
rin
gro
llin
gd
ep
en
ds
on
the
ab
ilit
yto
bala
nce
the
two
typ
es
of
tex
ture
s.E
ng
ler
et
al.
(20
07
)
dem
on
stra
ted
the
form
ati
on
of
asu
itab
lero
llin
gte
xtu
rew
ith
min
imu
meari
ng
req
uir
ed
the
op
tim
um
com
bin
ati
on
of
the
stre
ng
tho
f
Fig
.9
.V
ari
ati
on
inth
e(a
)4
5◦
eari
ng
valu
ean
d(b
)d
elt
aeari
ng
valu
ew
ith
an
neali
ng
tem
pera
ture
for
the
CC
AA
51
82
alu
min
um
all
oy
wit
han
dw
ith
ou
tp
ret
reatm
en
t.
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
20
13
Fig
.1
0.
Vari
ati
on
inth
e(a
)0
/45
◦eari
ng
valu
ean
d(b
)d
elt
aeari
ng
valu
ew
ith
an
neali
ng
tem
pera
ture
for
the
DC
AA
51
82
alu
min
um
all
oy
wit
hp
ret
reatm
en
t.
cub
ete
xtu
rein
the
init
ialm
ate
rialan
dam
ou
nt
of
sub
seq
uen
tco
ld
roll
ing
. Fig
.5sh
ow
sth
atth
eco
ldro
llin
gre
du
ctio
nco
rresp
on
din
gto
min
imu
meari
ng
isab
ou
t8
3%
for
the
DC
AA
51
82
alu
min
um
all
oy
.
Th
e4
5◦
eari
ng
valu
eo
fth
eC
Call
oy
incr
ease
sw
ith
incr
easi
ng
roll
ing
red
uct
ion
.It
isab
ou
t7
.5%
wh
en
the
cold
roll
ing
red
uct
ion
reach
es
83
%.
Ino
rder
too
bta
inth
esa
me
eari
ng
valu
eas
the
DC
all
oy
,th
e
cold
roll
ing
red
uct
ion
of
the
CC
all
oy
mu
stb
ere
du
ced
to5
1%
sin
ce
the
CC
all
oy
do
es
no
th
av
een
ou
gh
rem
ain
ing
cub
eco
mp
on
en
tto
bala
nce
the
bfi
ber
roll
ing
tex
ture
.
Th
eco
ldr
oll
ed
CC
all
oy
po
ssess
es
ast
ron
gb
fib
er
roll
ing
tex
ture
,le
ad
ing
tola
rge
45
◦ears
.A
sre
cry
stall
izati
on
pro
ceed
s,th
e
vo
lum
efr
act
ion
ofth
ecu
be
com
po
nen
tin
crease
s,w
here
as
the
vo
l
um
efr
act
ion
ofth
eb
fib
er
com
po
nen
td
ecr
ease
s.T
here
fore
,th
e4
5◦
eari
ng
valu
ed
ecr
ease
sas
recr
yst
all
izati
on
pro
ceed
s.A
fter
com
ple
te
recr
yst
all
izati
on
,th
eC
Call
oy
stil
lE
xh
ibit
s4
5◦
ears
du
eto
its
rela
tiv
ely
stro
ng
Rco
mp
on
en
t.T
he
deep
dra
wn
cup
of
the
cold
ro
lled
DC
all
oy
ex
hib
its
eig
ht
ears
at
0◦,4
5◦
an
d9
0◦
toR
D,a
nd
the
0◦
ear
ing
valu
eis
hig
her
than
the
45
◦eari
ng
valu
e.
As
recr
yst
all
izati
on
pro
ceed
s,th
ev
olu
me
fract
ion
so
fth
ecu
be
an
db
fib
er
com
po
nen
ts
decr
ease
,le
ad
ing
toa
decr
ease
inth
e0
◦eari
ng
valu
e.
Aft
er
com
ple
tere
cry
stall
izati
on
,th
eeari
ng
pro
file
isch
an
ged
fro
meig
ht
ears
tofo
ur
ears
,an
dth
e4
5◦
eari
ng
valu
eis
slig
htl
ylo
wer
than
befo
re
recr
yst
all
izati
on
.
Th
ep
ret
reatm
en
to
fth
eC
Call
oy
pri
or
toco
ldro
llin
gals
oaff
ect
s
the
eari
ng
beh
av
ior
of
cold
ro
lled
an
dre
cry
stall
ized
sheets
.In
the
cold
ro
lled
state
,th
eC
Call
oy
wit
ho
ut
pre
tre
atm
en
th
as
larg
er
45
◦
ears
than
the
all
oy
wit
hp
ret
reatm
en
td
ue
toit
sst
ron
ger
bfi
ber
roll
ing
tex
ture
.In
the
recr
yst
all
ized
state
,th
eC
Call
oy
wit
ho
ut
pre
treatm
en
tex
hib
its
asl
igh
tly
low
er
eari
ng
valu
eth
an
the
all
oy
wit
h
pre
tre
atm
en
t.
Fig
.12
.C
om
pari
son
betw
een
the
calc
ula
ted
an
dm
easu
red
45
◦eari
ng
valu
es
for
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
s.
4.2
.R
elati
on
ship
bet
wee
nea
rin
gvalu
ean
dte
xtu
revolu
me
fract
ion
s
Fig
.11
sho
ws
the
sim
ula
ted
eari
ng
pro
file
so
fth
esi
xsi
ng
lete
x
ture
com
po
nen
tscu
be,
rcu
be,
Go
ss,
S,
B,
an
dC
.T
he
sim
ula
tio
ns
were
con
du
cted
base
do
nth
efo
rmu
lafo
rth
ean
gu
lar
dep
en
den
ce
of
the
qv
alu
ed
eri
ved
by
Man
(20
02
),w
hic
hw
ere
ex
ten
ded
to
qu
an
tify
the
eff
ect
ofcr
yst
all
og
rap
hic
tex
ture
on
eari
ng
pro
file
.Th
e
Fig
.11
.E
ari
ng
pro
file
so
fin
div
idu
alte
xtu
reco
mp
on
en
ts.S
ixte
xtu
reco
mp
on
en
ts(a
)cu
be,r
cu
be,G
oss
,(b
)B
,San
dC
are
sele
cted
.Th
ese
eari
ng
pro
file
sca
nb
eg
rou
ped
into
two
typ
es:
45
◦ty
pe,s
uch
as
rcu
be,B
,San
dC
wh
ose
eari
ng
peak
sap
pear
near
45
◦to
the
RD
,an
d0
/90
◦ty
pe,s
uch
as
cub
ean
dG
oss
wh
ose
eari
ng
peak
sap
pear
inth
ero
llin
g
an
dtr
an
svers
ed
irect
ion
s.
20
14
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
Fig
.1
3.
Rela
tio
nsh
ipb
etw
een
the
eari
ng
valu
ean
dte
xtu
rev
olu
me
fract
ion
sfo
rC
Can
dD
CA
A5
18
2alu
min
um
all
oy
s.(a
)4
5◦
eari
ng
valu
ean
d(b
)d
elt
aeari
ng
valu
e.
mate
rialp
ara
mete
rsin
the
form
ula
were
ob
tain
ed
fro
mth
ew
ork
of
Man
an
dH
uan
g(2
00
1).
Fo
rth
ecu
be
ori
en
tati
on
,ears
ap
pear
at
0◦
an
d9
0◦
wit
hre
spect
toth
eR
Dw
ith
an
idealo
rth
otr
op
icsy
mm
etr
y.
Th
er
cub
eo
rien
tati
on
can
be
tran
sfo
rmed
toth
ecu
be
ori
en
tati
on
by
the
45
◦ro
tati
on
ab
ou
tth
en
orm
ald
irect
ion
(ND
).T
hu
s,th
eear
ing
beh
av
ior
of
the
rcu
be
com
po
nen
tis
ex
act
lyo
pp
osi
teto
that
of
the
cub
eco
mp
on
en
t.T
he
max
imu
mear
po
siti
on
islo
cate
dat
45
◦
toth
eR
D.
Inco
ntr
ast
toth
ecu
be
ori
en
tati
on
,th
eeari
ng
peak
so
f
the
B,
S,
an
dC
com
po
nen
tsap
pear
at
ab
ou
t5
6◦,
47
◦,
an
d3
2◦
to
the
RD
,re
spect
ively
.Fo
rth
eG
oss
ori
en
tati
on
,it
sm
ax
imu
mears
occ
ur
at
90
◦,a
nd
its
tro
ug
his
loca
ted
near
45
◦.T
he
rG
oss
ori
en
ta
tio
nca
nb
etr
an
sfo
rmed
toth
eG
oss
ori
en
tati
on
by
the
90
◦ro
tati
on
ab
ou
tth
eN
D.
Th
er
Go
sso
rien
tati
on
resu
lts
inm
ax
imu
mears
at
0◦.
Inp
oly
cry
stall
ine
mate
rials
,th
eeari
ng
beh
av
ior
of
alu
min
um
sheets
du
rin
gd
eep
dra
win
gd
ep
en
ds
stro
ng
lyo
ncr
yst
all
og
rap
hic
tex
ture
.Liu
an
dM
orr
is(2
00
3)
inv
est
igate
dth
ete
xtu
reev
olu
tio
n
du
rin
gco
ldro
llin
go
falu
min
um
all
oy
s.T
hey
est
ab
lish
ed
the
math
em
ati
cal
form
ula
eo
fth
ete
xtu
rev
olu
me
fract
ion
san
dtr
ue
roll
ing
stra
into
qu
an
tify
tex
ture
ev
olu
tio
n.
Mo
reo
ver,
Liu
an
dM
orr
is
(20
05
)u
sed
the
Joh
nso
n–
Meh
l–A
vra
mi–
Ko
lmo
go
rov
(JM
AK
)eq
ua
tio
nto
desc
rib
eth
ere
lati
ve
chan
ge
inth
ete
xtu
rev
olu
me
fract
ion
s
du
rin
gis
oth
erm
al
an
neali
ng
.T
hu
s,th
ete
xtu
reev
olu
tio
nd
uri
ng
roll
ing
an
dan
neali
ng
can
be
pre
dic
ted
by
usi
ng
sim
ple
rela
tio
ns
betw
een
the
tex
ture
vo
lum
efr
act
ion
san
dp
roce
ssin
gp
ara
mete
rs.
Ino
rder
top
red
ict
the
eari
ng
valu
eb
ase
do
nte
xtu
red
ata
,it
is
desi
rab
leto
est
ab
lish
the
em
pir
icalr
ela
tio
nsh
ipb
etw
een
the
eari
ng
valu
ean
dth
ete
xtu
rev
olu
me
fract
ion
s.T
he
cub
e,G
oss
an
dr
Go
ss
com
po
nen
tsp
rod
uce
0/9
0◦
eari
ng
,w
hil
eth
er
cub
ean
db
fib
er
com
po
nen
tsg
ive
rise
to4
5◦
eari
ng
.T
he
eff
ect
of
the
rem
ain
der
com
po
nen
to
nth
eeari
ng
beh
av
ior
may
be
neg
lect
ed
beca
use
the
ori
en
tati
on
sin
the
rem
ain
ing
reg
ion
are
betw
een
the
cub
e,r
cu
be,
Go
ss,r
Go
ssan
db
fib
er
ori
en
tati
on
reg
ion
s.T
here
fore
,th
eeari
ng
perc
en
tag
e(E
)ca
nb
eex
pre
ssed
as
afu
nct
ion
ofth
ete
xtu
rev
olu
me
fract
ion
s,i.e.,
E=
f cu
be
Mcu
be
Mcu
ber
an
do
m+
f rc
ub
eM
rcu
be
Mr
cub
er
an
do
m+
f Go
ssM
Go
ss
MG
oss
ran
do
m
+f r
Go
ssM
rG
oss
Mr
Go
ssr
an
do
m+
f bM
b
Mb
ran
do
m
(3)
wh
ere
f iis
aco
effi
cien
tw
hic
hre
flect
sth
eeff
ect
ofth
ete
xtu
reco
m
po
nen
to
neari
ng
beh
av
ior.
Th
ev
alu
eo
ff r
cu
be
sho
uld
be
eq
ual
to
neg
ati
ve
f cu
be
acc
ord
ing
toth
eeari
ng
pro
file
so
fth
ecu
be
an
dr
cub
eco
mp
on
en
tssh
ow
nin
Fig
.1
1.B
yfi
ttin
gth
e4
5◦
eari
ng
valu
e
an
dte
xtu
rev
olu
me
fract
ion
su
sin
gE
q.(3
),th
ev
alu
eo
ff c
ub
e,f G
oss
,
f rG
oss
an
df b
was
dete
rmin
ed
tob
e−
4.3
3,−
0.3
7,−
1.1
5an
d4
.34
,
resp
ect
ively
.T
he
corr
ela
tio
nco
effi
cien
to
fth
eli
near
fit
was
0.9
62
.
Fig
.12
sho
ws
the
com
pari
son
betw
een
the
calc
ula
ted
an
dm
easu
red
45
◦eari
ng
valu
es
on
vari
ou
ssa
mp
les
un
der
dif
fere
nt
con
dit
ion
so
f
cold
roll
ing
an
dan
neali
ng
pra
ctic
e.
Neg
ati
ve
valu
es
of
f cu
be,
f Go
ss
an
df r
Go
ssin
dic
ate
that
the
cub
e,
Go
ssan
dr
Go
ssco
mp
on
en
ts
decr
ease
the
45
◦eari
ng
valu
e.T
he
ab
solu
tev
alu
eo
ff c
ub
eis
sim
ilar
toth
at
off b
.Hig
hab
solu
tev
alu
es
off c
ub
ean
df b
mean
that
the
cub
e
an
db
fib
er
com
po
nen
tsh
av
ea
mu
chla
rger
eff
ect
on
the
ov
era
ll
an
iso
tro
py
du
rin
gd
eep
dra
win
gth
an
the
Go
ssan
dr
Go
ssco
mp
o
nen
ts.I
fth
eeff
ect
of
the
Go
ssan
dr
Go
ssco
mp
on
en
tsis
neg
lect
ed
,
Eq
. (3
)ca
nb
esi
mp
lifi
ed
as
E=
f
(
Mr
cub
e
Mr
cub
er
an
do
m+
Mb
Mb
ran
do
m
−M
cub
e
Mcu
ber
an
do
m
)
(4)
Eq
.(4
)is
very
sim
ilar
toth
at
rep
ort
ed
by
An
ders
son
an
d
Naess
(19
86
).Fig
.1
3(a
)sh
ow
sth
ere
lati
on
ship
betw
een
the
45
◦eari
ng
valu
ean
dth
ev
alu
eo
fM
rcu
be/M
rcu
ber
an
do
m
+M
b/M
br
an
do
m−
Mcu
be/M
cub
er
an
do
m.
Th
ev
alu
eo
ff
was
dete
r
min
ed
tob
e4
.33
wit
ha
corr
ela
tio
nco
effi
cien
to
f0
.96
2.
Fo
rth
e
mix
ed
tex
ture
sw
ith
eig
ht
ears
,d
iffe
ren
t0
◦,
45
◦an
d9
0◦
eari
ng
valu
es
were
ob
tain
ed
.T
hese
data
of
eari
ng
an
dte
xtu
reca
nn
ot
be
sim
ult
an
eo
usl
yp
rese
nt
inE
q.
(4).
Acc
ord
ing
toE
ng
ler
an
dK
alz
(20
04
),1
Eis
very
use
ful
tore
pre
sen
tth
eeari
ng
lev
el
of
all
typ
es
of
eari
ng
pro
file
s.T
hu
s,th
ere
lati
on
ship
betw
een
the
valu
eo
f1
E
an
dte
xtu
rev
olu
me
fract
ion
can
be
est
ab
lish
ed
by
Eq
. (4
),as
sho
wn
inFig
.1
3(b
).In
this
case
,th
ev
alu
eo
ff
was
dete
rmin
ed
tob
e3
.79
.
Fig
.1
3(b
)sh
ow
sth
at
the
min
imiz
ati
on
of
eari
ng
can
be
ach
iev
ed
by
bala
nci
ng
the
cub
e,r
cu
be
an
db
fib
er
com
po
nen
ts.
5.
Co
nclu
sio
ns
Th
eev
olu
tio
no
fte
xtu
rean
deari
ng
of
CC
an
dD
CA
A5
18
2alu
min
um
all
oy
sd
uri
ng
roll
ing
an
dan
neali
ng
was
inv
est
igate
d.
Th
e
foll
ow
ing
con
clu
sio
ns
are
dra
wn
fro
mth
isst
ud
y.
(1)
Aft
er
an
neali
ng
at4
54
◦C
for
3h
,th
eC
CA
A5
18
2alu
min
um
all
oy
po
ssess
es
aw
eak
recr
yst
all
izati
on
tex
ture
,lead
ing
tov
ery
small
45
◦ears
.Th
e4
5◦
eari
ng
valu
ein
crease
sw
ith
incr
easi
ng
roll
ing
red
uct
ion
.A
tla
rge
roll
ing
red
uct
ion
s,th
eeari
ng
valu
eo
fth
e
cold
ro
lled
CC
sheet
isla
rger
than
that
of
the
cold
ro
lled
DC
sheet.
(2)
Th
eD
CA
A5
18
2alu
min
um
all
oy
po
ssess
es
ast
ron
gcu
be
recr
ys
tall
izati
on
tex
ture
,p
rod
uci
ng
0/9
0◦
eari
ng
.A
sth
eco
ldro
llin
g
red
uct
ion
incr
ease
s,th
ev
olu
me
fract
ion
of
the
cub
eco
mp
o
nen
td
ecr
ease
s,w
here
as
the
vo
lum
efr
act
ion
of
the
bfi
ber
J.Li
etal.
/Jo
urn
alof
Mate
rials
Pro
cess
ing
Tec
hn
olo
gy
21
0 (
20
10
) 2
00
7–
20
15
20
15
com
po
nen
tin
crease
s.A
fter
45
%co
ldro
llin
gre
du
ctio
n,
the
deep
dra
wn
cup
ex
hib
its
eig
ht
ears
at
0◦,
45
◦an
d9
0◦
toth
e
RD
.T
he
alu
min
um
sheet
wit
hm
inim
um
eari
ng
iso
bta
ined
at
ab
ou
t8
3%
roll
ing
red
uct
ion
.
(3)
Th
e7
1.5
%co
ldr
oll
ed
CC
sheet
wit
ho
ut
pre
tre
atm
en
tp
os
sess
es
asi
gn
ifica
ntl
yh
igh
er
45
◦eari
ng
valu
eth
an
the
cold
ro
lled
CC
sheet
wit
hp
ret
reatm
en
t.T
he
45
◦eari
ng
valu
e
an
dd
elt
aeari
ng
valu
ed
ecr
ease
wit
hin
creasi
ng
an
neali
ng
tem
pera
ture
.A
fter
com
ple
tere
cry
stall
izati
on
,th
eC
Call
oy
stil
l
sho
ws
45
◦ears
,an
dth
e4
5◦
eari
ng
valu
eo
fth
eall
oy
wit
h
ou
tp
ret
reatm
en
tis
slig
htl
ylo
wer
than
that
of
the
all
oy
wit
h
pre
tre
atm
en
t.
(4)
Th
e7
1.5
%co
ldr
oll
ed
DC
sheet
ex
hib
its
eig
ht
ears
at
0◦,4
5◦
an
d
90
◦to
the
RD
,an
dth
e0
◦eari
ng
valu
eis
larg
er
than
that
the
45
◦
eari
ng
valu
e.D
uri
ng
recr
yst
all
izati
on
an
neali
ng
,th
est
ren
gth
of
the
cub
eco
mp
on
en
tw
eak
en
s,le
ad
ing
toa
decr
ease
inth
e0
/90
◦
eari
ng
valu
e.A
fter
com
ple
tere
cry
stall
izati
on
,th
eD
Call
oy
als
o
Ex
hib
its
45
◦ears
.
(5)
An
em
pir
ical
rela
tio
nsh
ipb
etw
een
the
eari
ng
valu
ean
dte
x
ture
vo
lum
efr
act
ion
sh
as
been
est
ab
lish
ed
.M
inim
izati
on
of
eari
ng
can
be
ach
iev
ed
by
bala
nci
ng
the
cub
e,
rcu
be
an
db
fib
er
com
po
nen
ts.
Ack
no
wle
dg
me
nts
Th
isw
ork
was
sup
po
rted
by
the
Nati
on
alN
atu
ralSci
en
ceFo
un
dati
on
of
Ch
ina
(Gra
nt
No
.50
87
40
97
).
Re
fere
nce
s
An
ders
son
,B
.,N
aess
,S.E
.,1
98
6.E
ari
ng
an
dte
xtu
rein
all
oy
sA
A5
05
2an
dA
A3
00
4.
In:
Sta
rke,
E.A
.,San
ders
,T
.H.
(Ed
s.),
Al
All
oy
s—T
heir
Ph
ysi
cal
an
dM
ech
an
ical
Pro
pert
ies,
vo
l.1
.In
tern
ati
on
al
Co
nfe
ren
ceh
eld
at
the
Un
ivers
ity
of
Vir
gin
ia,
Ch
arl
ott
esv
ille
,V
irg
inia
,1
52
0Ju
ne
19
86
,E
ng
ineeri
ng
Mate
rials
Ad
vis
ory
Ser
vic
es,
Vir
gin
ia,p
p.4
99
–5
11
.B
un
ge,H
.J.,
19
82
.T
ex
ture
An
aly
sis
inM
ate
rials
Sci
en
ce.B
utt
erw
ort
hs
Pu
bli
cati
on
,Lo
nd
on
.E
ng
ler,
O.,
Kalz
,S.,
20
04
.Sim
ula
tio
no
feari
ng
pro
file
sfr
om
tex
ture
data
by
mean
so
fa
vis
cop
last
icse
lfc
on
sist
en
tp
oly
cry
stalp
last
icit
yap
pro
ach
.Mate
r.Sci
.En
g.
A3
73
,35
0–
36
2.
En
gle
r,O
.,Lö
chte
,L.,
Hir
sch
,J.
,2
00
7.
Th
rou
gh
pro
cess
sim
ula
tio
no
fte
xtu
rean
dp
rop
ert
ies
du
rin
gth
eth
erm
om
ech
an
ical
pro
cess
ing
of
alu
min
ium
sheets
.A
cta
Mate
r.5
5,5
44
9–
54
63
.Liu
,W
.C.,
Mo
rris
,J.
G.,
20
03
.C
om
pari
son
of
the
tex
ture
ev
olu
tio
nin
cold
roll
ed
DC
an
dSC
AA
51
82
alu
min
um
all
oy
s.M
ate
r.Sci
.En
g.A
33
9,1
83
–1
93
.Liu
,W.C
.,M
orr
is,J
.G.,
20
04
.Qu
an
tita
tiv
ean
aly
sis
ofte
xtu
reev
olu
tio
nin
cold
ro
lled
,co
nti
nu
ou
sca
stA
A5
xx
xs
eri
es
alu
min
um
all
oy
s.M
eta
ll.T
ran
s.3
5A
,26
5–
27
7.
Liu
,W
.C.,
Mo
rris
,J.
G.,
20
05
.E
vo
luti
on
of
recr
yst
all
izati
on
an
dre
cry
stall
izati
on
tex
tu
rein
con
tin
uo
us
cast
AA
30
15
alu
min
um
all
oy
.Meta
ll.T
ran
s.3
6A
,28
29
–2
84
8.
Liu
,W
.C.,
Zh
ai,
T.,
Mo
rris
,J.
G.,
20
03
.C
om
pari
son
of
recr
yst
all
izati
on
an
dre
cry
stal
lizati
on
tex
ture
sin
cold
roll
ed
DC
an
dC
CA
A5
18
2alu
min
um
all
oy
s.M
ate
r.Sci
.E
ng
.A3
58
,84
–9
3.
Liu
,W
.C.,
Zh
ai,
T.,
Man
,C
.S.,
Rad
hak
rish
nan
,B
.,M
orr
is,J.
G.,
20
04
a.E
ffect
of
init
ial
tex
ture
on
tex
ture
ev
olu
tio
nin
cold
ro
lled
AA
51
82
alu
min
ium
all
oy
.P
hil
os.
Mag
.84
,33
05
–3
32
1.
Man
,C
.S.,
20
02
.O
nth
er
valu
eo
fte
xtu
red
sheet
meta
ls.
Int.
J.P
last
ic.
18
,1
68
3–
17
06
.M
an
,C.
S.,
Hu
an
g,M
.J.,
20
01
.Id
en
tifi
cati
on
ofm
ate
rialp
ara
mete
rsin
yie
ldfu
nct
ion
san
dfl
ow
rule
sfo
rw
eak
lyte
xtu
red
sheets
ofc
ub
icm
eta
ls.I
nt.
J.N
on
Lin
ear
Mech
.3
6,5
01
–5
14
.Sark
ar,
S.,
Well
s,M
.A.,
Po
ole
,W.J
.,2
00
6.S
oft
en
ing
beh
av
ior
ofco
ldro
lled
con
tin
uo
us
cast
an
din
go
tca
stalu
min
um
all
oy
AA
57
54
.Mate
r.Sci
.En
g.A
42
1,2
76
–2
85
.Z
hao
,Y.M
.,M
orr
is,J
.G.,
20
05
.Co
mp
ari
son
ofth
ete
xtu
reev
olu
tio
no
fd
irect
chil
lan
dco
nti
nu
ou
sca
stA
A5
05
2h
ot
ban
ds
du
rin
gis
oth
erm
al
an
neali
ng
.M
eta
ll.T
ran
s.3
6A
,25
05
–2
51
5.
