For slip to occur in polycrystalline materials,
5 independent
slip
systems are required (von Mises criterion). Hence, materials
which are ductile in single crystalline form, may not be as ductile
in polycrystalline form. FCC crystals (Cu, Al, Au) have excellent
ductility.
At higher temperatures more slip systems may become active
and hence polycrystalline materials which are brittle at low
temperature, may become ductile at high temperature.
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31
ǀ
Middle East Technical University
ǀ
Çağla
Meral
ǀ
[email protected]
ǀ
Plastic deformation by slip
For a material, which crystalline structure is more ductile
(deform more readily under load before breaking): HCP, BCC or
FCC?
12/1/2015
32
Q

12/1/2015
17
ǀ
Middle East Technical University
ǀ
Çağla
Meral
ǀ
[email protected]
ǀ
Single Crystal Slip
12/1/2015
33
Unslipped
single crystal
Slip
plane
Direction
of force
Zinc
crystal
ǀ
Middle East Technical University
ǀ
Çağla
Meral
ǀ
[email protected]
ǀ
Crystals slip due to a
resolved shear stress,
τ
R
.
Applied tension can produce such a stress.
Resolved shear stress
Tuesday, December 01, 2015
34
normal to slip
plane,
n
s
Resolved shear stress
τ
R
= F
S
/ A
S
Shear
area A
S
τ
R
τ
R
F
S
Relation
between
s
and
τ
R
F
cos
λ
A
/
cos
φ
λ
F
F
S
φ
n
S
A
S
A
Applied tensile stress
s
=
F
/
A
F
Area A
Force F
τ
R
= F
S
/ A
S
𝜏
𝑅
= 𝜎 cos 𝜆 cos 𝜙

12/1/2015
18
ǀ
Middle East Technical University
ǀ
Çağla
Meral
ǀ
[email protected]
ǀ
Critical resolved shear stress
12/1/2015
35
critical resolved shear stress =
minimum stress that initiates
slip
Ø
:
Angle between the
normal to the slip plane and
the applied stress directions.
λ:
Angle between the slip
and stress directions.
τ
CR
= σ . cos λ . cos Ø
ǀ
Middle East Technical University
ǀ
Çağla
Meral
ǀ
[email protected]
ǀ
Angle between two directions
Sometimes the angle between two directions may be
necessary.
Vector A:
[h
1
k
1
l
1
]
Vector B:
[h
2
k
2
l
2
]
α
:
angle between A and B
Tuesday, December 01, 2015
36
cos
a
=
(h
1
2
+k
1
2
+l
1
2
) (h
2
2
+k
2
2
+l
2
2
)
h
1
h
2
+ k
1
k
2
+ l
1
l
2
A . B=|A| |B| cos
a