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 thirteen
3,Application of Schmid’s law
① How to determine the active S.S,for all the equivalent
S.S.
② Determine the active S.S,by Reflection Rule.
? Orientation cell for cubic crystals.
? Given,BCC Crystal having {110}<111>slip system.
Determine, active slip system in response to tensile
loading along
Solution:
a,Draw a orientation cell.
b,Label the loading direction in the cell.
c,Determine the active S.S,by reflection rule.
4,Determine the active slip systems by
Schmidt's law
① Draw a standard projection
x=z line
x=y line
y=z line
② Label the loading direction in standard projection.
③ Mirror rule
m a xm a x )c o s( c o s ??? ??
case1.
along
FCC,orientation triangle,
slip system is
]124[
]1 0 0][011][111[
]101)[111(
case2,
along
orientation triangle,
according to the mirror-refraction
rule the active slip system is
]215[
]011)[111(
given [u v w],determine active slip system
]0 0 1[]1 1 1[]1 0 1[ ??
5,Determine the active slip systems by
Reflection Rule,
Example:
Given,BCC crystal having {110}<111> slip system
Determine active slip system in response to tensile loading
along,]231[
Solve:
① Draw a standard projection.
② Label the loading direction in
standard projection.
③ Determine the active S.S by
Reflection Rule.
④
a) locate inside the orientation triangle ( ),single slip.
b) locate at the edge of the orientation triangle ( ),double
(duplex) slip.
c) locate at the corner of the orientation triangle,multiple
slip.
F? 1F
F? 2F
When the axis of load is in the edge or corner of the
orientation triangle,muli-slip occurs.
]011)[111(
]101)[111(]011)[111( ?
F?
001
111 101 111
011
F1 F2
F3
6,A tensile force is applied on a BCC
cylindrical bar with across section of 25mm2,
The initial axis is, The CRSS is
0.4MPa, The slip plane is,
]124[
}110{
Determine:
① initial S.S.
② P
③ duplex S.S.
④ the shear strain and the indices of the axis at the moment
when duplex starts
⑤ stable position
?
Solution:
Draw a standard projection
Determine orientation triangle:
]1 0 0[]011[]111[ ??
① initial S.S.
mirror refraction rule
②
]111)[101(
cP ??
??,??
F3
oc c o sc o s ???? ?
73
5
321
]111][124[c o s ?
??? ?
42
5
42
14
221
]101][124[c o s
o ?
??
???
N2066374
4263
25
254
c o sc o s
AA
?????
??????
o
cP
??
??
③ duplex S.S., ]111)[110(]111)[1 0 1( ?
at the beginning of initial slip
④ at the beginning of duplex slip
]111[65]124[3 ]111[2 ]101[]124[]124[][ ?? ??????u v w
?
?
?
6
5
1
6
5
2
6
5
4
??
???
??
w
v
u
0?w
5
6??
?
0
3
5
?
??
?
w
v
u
0]3[5L ?? at the beginning of duplex slip
⑤ stable position is ]011[
§ 4.3 Change in Reference Direction
& Reference Places during Slip
? Ⅰ.Change of reference direction
after slip
O
A
d?
b?
before slip
O
B
D?
From the figure udD ??? ??
1
??? ?? tg
n?
d?
1
?
?
????? )( ndu ??
B
b?
A
O
n?
u?
d? D
??
Examples:
[given]
[ ask ]
[solve]
?,)S, D, a lo n gr u n it v e c t o(,,bnd ???
D?
bnddD ????? )( ??? ?
Where is the unit vector along the normal to the S.P.
is the unit vector along S.D.
n?
b?
Discussion:
1,for compression
2,if located on S.P,
then
and
bnddD ????? )( ??? ?
d?
0??nd ??
dD ?? ?
? Ⅱ.Change of reference planes
take two vectors in the reference plane.
let
after slip
dd ??? and
ddm ??? ???
DdDd ???? ????
DDM ??? ???
mnbnmbm
bmnm
bddnm
bdnddndm
dbndbdndm
bnddbnddM
???????
????
?????
????????
?????????
?????????
][][
][
)]([
])()[(
)()(
))(())((
?????
????
??????
????????
?????????
?????????
??
?
?
?
??
??
mnbmM
nmbmM
?????
?????
][
][
???
????
?
?,for tension
,for compression
Examples and Discussions
1,All directions which lie on slip plane do not
change after slip.
2,Slip plane remains unchanged after slip.
if on slip plane
then
m?
bm ?? ?
mM
mb ???
??
??? 0
Exercise
Thank you !
13