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
Chapter Ⅳ
Plastic Deformation of Crystal
Lesson twelve
§ 4.1 Introduction
1,Deformation process of polycrystalline materials
Deformation process of industrial material consists of
three stages:
? Elastic,which is reversible
? Plastic or permant
? Fracture
2,Deformation mode of crystals
1) Slip
2) Twinning
3) Grain boundary sliding followed by g.b,migration
4) Diffusion
3,Basic feature of slip and twinning
Both slip and twinning are shear
processes under shear stresses,i.e,it is a
translational movement of one portion of the
crystal with respect to the other on a specific
plane and along a specific direction.
slip
twinning
The main difference between slip and
twinning is that the former does not cause any
change in orientation in the sense that any
crystallographic direction remain the same
with respect to the laboratory coordinate
systems,While the latter results in change in
orientation,After twinning the two parts of
the crystal,twinned and untwinned,are
symmetrical to some plane or orientation,Or
say,one is the twin of the other.
§ 4.2 Slip Systems
? Ⅰ,Definition,
Slip Systems is the combination
of a crystallographic plane and a
direction lying on it,On the plane
and along the direction slip takes
place.
A slip plane plus a corresponding
slip direction is called a slip system.
?
?
? Ⅱ,Slip systems of typical crystals
FCC,S.S,(Slip Systems) is {111} <110> at R.T,
(temperature),There are 12 S.S,in all.
HCP,S.S.
BCC,
CsCl,{110}<100>
????? 0211}0110{0211}0001{
for metals with large c/a for other HCP metals
}123{
111}112{
}110{
??
}1110{
0211}0110{
)0 00 1(
???
for metals with large c/a
for other HCP metals
? Ⅲ,Schmid ’s law (The condition for
slip to start)
1,The shear stress acting on slip plane along slip
direction is,?
????
?
?
? ??? c o sc o s
c o s
c o s
oo A
F
A
F
?
??
?
90
),(
)..,(
??
?
?
?
?
??
?
?
nF
DSF
5.0f a c t o rno r i e n t a t i o:
ssn o r m a l s t r e:
m a x ???
?
Slip occurs when the resolved shear stress
acting on slip plane along slip direction reaches a
Critical value,called the Critical stress,Critical
Resolved Shear Stress (C.R.S.S) and is
characteristic of the crystal in question.
When,slip starts as when slip
starts,
depends on material and temperature.
For FCC,
For BCC,and other structure,
c?
c?? ? c??? ?
c?
M P a1~c?
M P a1 0 010~ ?c?
Condition for slip to start:
???? c o sc o s?
C?? ? ??? c o sc o s?
Orientation factor
??? ?C
Soft orientation
Hard orientation
5.0M a x ??
0.1 0.2 0.40.3 0.5 0.4 0.3 0.2 0.1
? ?
?
2,Discussion
① is a material constant
② Which one will first slip in crystallographiclly
equivalent slip systems?
③ It is an approximate law.
④ For single crystal is not a material
constant.
c?
S?
The determination of active slip system(s)
? ?112
? ?101
angle
⑤ Application of Schmid’s law
Examples and Discussions
Exercise
Thank you !
12
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
Chapter Ⅳ
Plastic Deformation of Crystal
Lesson twelve
§ 4.1 Introduction
1,Deformation process of polycrystalline materials
Deformation process of industrial material consists of
three stages:
? Elastic,which is reversible
? Plastic or permant
? Fracture
2,Deformation mode of crystals
1) Slip
2) Twinning
3) Grain boundary sliding followed by g.b,migration
4) Diffusion
3,Basic feature of slip and twinning
Both slip and twinning are shear
processes under shear stresses,i.e,it is a
translational movement of one portion of the
crystal with respect to the other on a specific
plane and along a specific direction.
slip
twinning
The main difference between slip and
twinning is that the former does not cause any
change in orientation in the sense that any
crystallographic direction remain the same
with respect to the laboratory coordinate
systems,While the latter results in change in
orientation,After twinning the two parts of
the crystal,twinned and untwinned,are
symmetrical to some plane or orientation,Or
say,one is the twin of the other.
§ 4.2 Slip Systems
? Ⅰ,Definition,
Slip Systems is the combination
of a crystallographic plane and a
direction lying on it,On the plane
and along the direction slip takes
place.
A slip plane plus a corresponding
slip direction is called a slip system.
?
?
? Ⅱ,Slip systems of typical crystals
FCC,S.S,(Slip Systems) is {111} <110> at R.T,
(temperature),There are 12 S.S,in all.
HCP,S.S.
BCC,
CsCl,{110}<100>
????? 0211}0110{0211}0001{
for metals with large c/a for other HCP metals
}123{
111}112{
}110{
??
}1110{
0211}0110{
)0 00 1(
???
for metals with large c/a
for other HCP metals
? Ⅲ,Schmid ’s law (The condition for
slip to start)
1,The shear stress acting on slip plane along slip
direction is,?
????
?
?
? ??? c o sc o s
c o s
c o s
oo A
F
A
F
?
??
?
90
),(
)..,(
??
?
?
?
?
??
?
?
nF
DSF
5.0f a c t o rno r i e n t a t i o:
ssn o r m a l s t r e:
m a x ???
?
Slip occurs when the resolved shear stress
acting on slip plane along slip direction reaches a
Critical value,called the Critical stress,Critical
Resolved Shear Stress (C.R.S.S) and is
characteristic of the crystal in question.
When,slip starts as when slip
starts,
depends on material and temperature.
For FCC,
For BCC,and other structure,
c?
c?? ? c??? ?
c?
M P a1~c?
M P a1 0 010~ ?c?
Condition for slip to start:
???? c o sc o s?
C?? ? ??? c o sc o s?
Orientation factor
??? ?C
Soft orientation
Hard orientation
5.0M a x ??
0.1 0.2 0.40.3 0.5 0.4 0.3 0.2 0.1
? ?
?
2,Discussion
① is a material constant
② Which one will first slip in crystallographiclly
equivalent slip systems?
③ It is an approximate law.
④ For single crystal is not a material
constant.
c?
S?
The determination of active slip system(s)
? ?112
? ?101
angle
⑤ Application of Schmid’s law
Examples and Discussions
Exercise
Thank you !
12
