材料科学基础
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson fourteen
§ 4.4 Rotation of Crystal during
Slip
? Ⅰ.The cause of rotation:
Due to constraints,or boundary conditions,
imposed on the crystal.
? Ⅱ.The rule of rotation,
1) axis of rotation
∥ ∥
R?
R? lL ??? lb ???
bnllL ????? )( ???
2) During slip,the S.D,tends to approach to loading
direction in tension.
During slip,the S.P,tends to approach to compression
plane in compression.
F
F
F
F
F
F
F
F
? Ⅲ.The consequence of rotation,
1,Change in length of the specimen
????? 22 c o sc o sc o s21 ??? lL
① In tension
bnllL ?????? )( ??? ?
?
?
?
?
c o s
c o s
s in
s in 00
l
L b
?? n??
② In compression
nbaaA ?????? )( ??? ?
② Geometrical softening in tension
Schmid’s law
at the onset of slip,
???? c o sc o s?
c o n s t,?? C??
ooy ??? c o sc o s?
o
o
o
o A
F
A
F
??
?
?
? c osc os
)
c os
(
c os
??
????? ???
o
C
?
???
c osc os ?
2,Change in orientation
① Orientation change and multislip
Example:
Given,a FCC crystal held in tension ∥
Determine:1,Single slip system
2,Rule of rotation
3,and orientation at the onset of duplex of slip
4,Rule of rotation during duplex slip
5,Final orientation,i.e,the state position
F? ]521[
?
1,slip system,
2,locus,F tend to,∥ ∥
3.
]110)[111(
]110[ ]110[?FR ?? ]211[R?
2
]110[
3
]111[]512[
)(
???
???
bnl
bnllL
???
?????
?
6
6
6
261202
]110[6]512[
2
]110[
)
3
]111[
]512([]512[][
][l e t
?
?????????????
??
????
?
w
vu
uv w
uv wl
??
?
?
?
]311[//]622[//F? ?
]011)[111(]110)[111(:s y s t e m ss l i pd u p l e x ?
Solution:
4.
5,stable:
]011[21 ??? RRR ???
][,wvuF ????
]110[][]011[][ 21 ?????????? wvuRwvuR ??
r o t a t i o nnoa n ds t a b l e]000[W h e n 21 ??? RRR ???
§ 4.5 Surface Morphology of Crystal
After Slip
The following deformation marks can be seen
on the surface of the crystal after slip.
1,Slip lines,the steps formed on surface due to slip.
2,Slip bands.
3,Deformation band formed due to inhomogeneous
rotation.
4,Kink bands
§ 4.6 Strain Hardening (Work-
hardening)
?Ⅰ.What ’s strain hardening?
(working hardening)
By strain hardening we
means the increase in tensile
stress for polycrystals or in
shear stress (the flow stress) for
single crystals necessary for
keeking on plastic deformation.
The shear strain necessary for slip to continue
increases with the amount of shear strain,This
Phenomenon is called strain hardening or work
hardening of single crystal.
Strain Hardening curve of single crystal —— curve.
It can be divided in to three stages:
1,for Ⅰ, Easy-glide
2,for Ⅱ, Linear hardening is very great
3,for Ⅲ, Parabolic hardening ↓
flow stress
???
rd
d?
rd
d?
???? ???
I Ⅱ
Ⅲ
?Ⅱ.Hardening Curve
1,Characteristic of hardening curve
How to obtain curve???
?
?
?
?
?
?
???
??
??
?
?
?
??
?
?
???
?
?
?
c o ss i n)(
c o s
1
c o sc o s
c o s
c o s
22
l
L
A
F
①
②
?
?????
????
??
??
s ins in
c o sc o s
lLblbL
lLnlnL
?????
?????
?
?
?
?
s in
s in
c o s
c o s ?? ???
l
L ③
?? ????
22 s in)(1c o s
l
L??? ④
?Ⅲ.Surface Morphology
slip line slip band cross slip line and band? ?
slip band —— 滑移带
deformation band —— 形变带
rink band —— 弯折带
§ 4.7 Twinning(Ⅰ)
—— Microscopic Aspect
? Ⅰ,Basic feature of twinnings.
Twinning is a translational movements of one portion of
the crystal with respect to the other on a specific plane
called twinning plane and along a specific orientation
relationship between the two portion of crystals.
? Ⅱ.Twinning system.
1,A Twinning plane plus a twinning direction lying on it is
called a twinning system.
2,Twinning systems for FCC,BCC and HCP.
3,It is more difficult for twinning systems to occur than
slip systems,because (twinning).
??
??
??
0110}2110{:H C P
111}11 2{:B C C
211}11 1{:FC C
c?? ?
FCC,{111}<112>
FCC
{111}
<112>
BCC
<111>
{112}
BCC,{112}<111>
c
a1
a2
a3
HCP,?? 0111}2110{
?? 0111
}2110{
? Ⅲ.Atom movements in twinning of FCC
To show movements,all atoms should be projected
onto shear plane and contains twinning direction.
FCC
basic requirement,symmetrical
relationship
]121[
)111(
Discussion
1,Orientation relation-ship
2.
3,Before twinning,ABC ABC ……
After twinning,BCA
AB
C
4,Twinning can be considered as continuous stacking
fault.
70 7.0
2
2
3
2
6
???
a
a
r
0 1 32
Examples and Discussions
Exercise
Thank you !
14
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson fourteen
§ 4.4 Rotation of Crystal during
Slip
? Ⅰ.The cause of rotation:
Due to constraints,or boundary conditions,
imposed on the crystal.
? Ⅱ.The rule of rotation,
1) axis of rotation
∥ ∥
R?
R? lL ??? lb ???
bnllL ????? )( ???
2) During slip,the S.D,tends to approach to loading
direction in tension.
During slip,the S.P,tends to approach to compression
plane in compression.
F
F
F
F
F
F
F
F
? Ⅲ.The consequence of rotation,
1,Change in length of the specimen
????? 22 c o sc o sc o s21 ??? lL
① In tension
bnllL ?????? )( ??? ?
?
?
?
?
c o s
c o s
s in
s in 00
l
L b
?? n??
② In compression
nbaaA ?????? )( ??? ?
② Geometrical softening in tension
Schmid’s law
at the onset of slip,
???? c o sc o s?
c o n s t,?? C??
ooy ??? c o sc o s?
o
o
o
o A
F
A
F
??
?
?
? c osc os
)
c os
(
c os
??
????? ???
o
C
?
???
c osc os ?
2,Change in orientation
① Orientation change and multislip
Example:
Given,a FCC crystal held in tension ∥
Determine:1,Single slip system
2,Rule of rotation
3,and orientation at the onset of duplex of slip
4,Rule of rotation during duplex slip
5,Final orientation,i.e,the state position
F? ]521[
?
1,slip system,
2,locus,F tend to,∥ ∥
3.
]110)[111(
]110[ ]110[?FR ?? ]211[R?
2
]110[
3
]111[]512[
)(
???
???
bnl
bnllL
???
?????
?
6
6
6
261202
]110[6]512[
2
]110[
)
3
]111[
]512([]512[][
][l e t
?
?????????????
??
????
?
w
vu
uv w
uv wl
??
?
?
?
]311[//]622[//F? ?
]011)[111(]110)[111(:s y s t e m ss l i pd u p l e x ?
Solution:
4.
5,stable:
]011[21 ??? RRR ???
][,wvuF ????
]110[][]011[][ 21 ?????????? wvuRwvuR ??
r o t a t i o nnoa n ds t a b l e]000[W h e n 21 ??? RRR ???
§ 4.5 Surface Morphology of Crystal
After Slip
The following deformation marks can be seen
on the surface of the crystal after slip.
1,Slip lines,the steps formed on surface due to slip.
2,Slip bands.
3,Deformation band formed due to inhomogeneous
rotation.
4,Kink bands
§ 4.6 Strain Hardening (Work-
hardening)
?Ⅰ.What ’s strain hardening?
(working hardening)
By strain hardening we
means the increase in tensile
stress for polycrystals or in
shear stress (the flow stress) for
single crystals necessary for
keeking on plastic deformation.
The shear strain necessary for slip to continue
increases with the amount of shear strain,This
Phenomenon is called strain hardening or work
hardening of single crystal.
Strain Hardening curve of single crystal —— curve.
It can be divided in to three stages:
1,for Ⅰ, Easy-glide
2,for Ⅱ, Linear hardening is very great
3,for Ⅲ, Parabolic hardening ↓
flow stress
???
rd
d?
rd
d?
???? ???
I Ⅱ
Ⅲ
?Ⅱ.Hardening Curve
1,Characteristic of hardening curve
How to obtain curve???
?
?
?
?
?
?
???
??
??
?
?
?
??
?
?
???
?
?
?
c o ss i n)(
c o s
1
c o sc o s
c o s
c o s
22
l
L
A
F
①
②
?
?????
????
??
??
s ins in
c o sc o s
lLblbL
lLnlnL
?????
?????
?
?
?
?
s in
s in
c o s
c o s ?? ???
l
L ③
?? ????
22 s in)(1c o s
l
L??? ④
?Ⅲ.Surface Morphology
slip line slip band cross slip line and band? ?
slip band —— 滑移带
deformation band —— 形变带
rink band —— 弯折带
§ 4.7 Twinning(Ⅰ)
—— Microscopic Aspect
? Ⅰ,Basic feature of twinnings.
Twinning is a translational movements of one portion of
the crystal with respect to the other on a specific plane
called twinning plane and along a specific orientation
relationship between the two portion of crystals.
? Ⅱ.Twinning system.
1,A Twinning plane plus a twinning direction lying on it is
called a twinning system.
2,Twinning systems for FCC,BCC and HCP.
3,It is more difficult for twinning systems to occur than
slip systems,because (twinning).
??
??
??
0110}2110{:H C P
111}11 2{:B C C
211}11 1{:FC C
c?? ?
FCC,{111}<112>
FCC
{111}
<112>
BCC
<111>
{112}
BCC,{112}<111>
c
a1
a2
a3
HCP,?? 0111}2110{
?? 0111
}2110{
? Ⅲ.Atom movements in twinning of FCC
To show movements,all atoms should be projected
onto shear plane and contains twinning direction.
FCC
basic requirement,symmetrical
relationship
]121[
)111(
Discussion
1,Orientation relation-ship
2.
3,Before twinning,ABC ABC ……
After twinning,BCA
AB
C
4,Twinning can be considered as continuous stacking
fault.
70 7.0
2
2
3
2
6
???
a
a
r
0 1 32
Examples and Discussions
Exercise
Thank you !
14
