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 twenty
§ 5.8 The Stress Around a Dislocation
? Ⅰ,Screw dislocation,Displacement:
Strain,
)(2200 1 xytgbbuuu zyx ????? ???
0
d
d0
d
d
0
d
d ??????
z
u
y
u
x
u z
z
y
y
x
x ???
0)( 12 ???????? xuyu yxxy ??
)(2z 22
z
yx
ybu
x
u x
xz ?
???
?
??
?
??
?
?
)(2z 22
z
yx
xbu
y
u y
yz ?
??
?
??
?
??
?
?
Stresses,0z ??? ??? yx
)(2)(20 22z22z
yx
xGb
yx
yGb
yxxy ?????? ?????
? Ⅱ.Edge dislocation
222
22
)(
)3(
)1(2 yx
yxyGb
x ?
?
??? ???
222
22
)(
)(
)1(2 yx
yxyGb
y ?
?
?? ???
)(z yx ???? ??
0)( )()1(2 zz222
22
??? ??? yxxy yx yxxGb ?????
if y=0,0z ??? ??? yx
r
Gb
x
Gb
xy )1(2)1(2 ????? ????
For either edge or screw dislocation shear stress on slip
plane along S.D.
?
?
?
?
?
?
?
?
??
nd i s l oc a t i os c r e w
2
nd i s l oc a t i oe d g e
)1(2
s
?
??
???
G
G
r
b
??
§ 5.9 Elastic Energy and Line
Tension of Dislocation
? Ⅰ,Wtot = Wcore+ Welast = Wmisfit+ We
l
P
?
?
1,We of an edge dislocation.
Model,see figure.
consider an area element x→x+ dx which displaced
from b'→ b'+db'.
then
lGb
r
RG l b
bx
x
blG
bxlW
R
r
xye
2
2
b
0
)ln (
)1(4
dd
1
)1(2
d)d(
o
?
??
??
?
?
?
?
?
?
?
?
??
??
? ?
?
2,We of a screw dislocation:
)ln (
4
2
e
?r
RG l bW
?
?
3,We of a mixed dislocation:
l
?cosb
?sinb
b?
?
)l n (]4 )c o s()1(4 )s i n([
22
m ix
?r
RlbGlbGW
?
?
??
? ?
??
? Ⅱ.Line tension
2e
d
dt e n s i o nl i n e Gb
l
WT ???
Examples and Discussions
Exercise
Thank you !
20