# Topic Outline Topic Outline Types Slip What is by benbenzhou

VIEWS: 9 PAGES: 15

• pg 1
```									    Topic Outline
Types
Slip
What is Slip?
Where does Slip Occur?
Slip Systems
Example
Burger’s Vector
Schmid’s Law
Slip Bands and Critical Stress
Sample Calculations

CHE 294   1
Types
We recognize two types of line defects.
Looks as though we are
Screw                             tearing apart the material.
A dislocation line marks
the boundary of the tear.
As we walk around
the line, we spiral
through the crystal
like a cork screw.                               Edge
Looks like it could contain an additional
plane of atoms ... this is not the case
because one plane is
missing.
Line defects are commonly called dislocations.
CHE 294   2
What is Slip?
Slip is atom motion due to stress.
unit cell under
no stress
apply a stress

bonds stretch to                                obtain a strain
their limit before                                apply more
breaking                                                stress

atoms slip

broken bond                                          release the
leads to a                                       stress, and the
defect inside                                        atoms relax
the material     the defect caused by slip remains         back

CHE 294   3
Where does Slip Occur?
Compare these two planes.
So slip occurs on
lattice planes       close packed
can easily slip     planes in close
packed
now apply          directions.
a stress
lattice planes do not slip as easily

a (110) plane

versus
BCC Crystal
a (100) plane

CHE 294   4
Slip Systems
Slip Planes + Slip Directions gives Slip Systems.
Lattice Slip Planes    Slip Directions # of Slip Systems
FCC         {111}           <110>            4 x 3 = 12
BCC         {110}           <111>            6 x 2 = 12
{112}           <111>               12
{123}           <111>               24
HCP        {0001}          <1000>                3

You are responsible for learning
• placements of all slip systems in FCC
• placements of all {110}<111> slip systems in BCC
• the total number of slip systems in FCC, BCC, and HCP

CHE 294   5
Example
What are the Miller indices for each of the following directions?

[001]

[111]               z

[110]

y
x
[111]

(1 1 0) plane of BCC crystal

CHE 294   6
Defining the Burger’s Vector
The Burger’s vector completes a loop around
the dislocation line.
start here to
Edge Dislocation                   make a loop
+1 in x                  (this is arbitrary)

+4 in y                           +3 in x    The length of the
Burgers vector |b| is
the distance between
the two atoms that
Burger’s                                      complete the loop.
Vector                                       You should learn
-4 in x           -4 in y       how to determine
|b| for cubic metals
Dislocation
and ceramics.
Line
CHE 294   7
Slip in Ceramics
Slipping ions is difficult!

+               +
+
+            +
+               +           Consider slip along
+               +
+                   <100> in NaCl
+               +
We cannot move a cation into the slot
of an anion during this slip.
We have to slip the cation past other cations into
the slot of the next closest cation.

Slip in ceramics is limited by both ionic repulsion (like charges
repel each other) and the different sizes of the ions (cations
are larger, making the slip plane less smooth).

CHE 294   8
Line and Atom Motion
How do the lines and atoms move during slip?

b
Atoms move parallel to b
(in the slip direction
on the slip plane)
Line moves parallel to b
(on the slip plane)

How does this picture change for a screw dislocation?

CHE 294   9
General Characteristics
These are the general characteristics of dislocations.

b Vector             Line            Atoms
Type        Points             Moves            Move
Edge          to line           || to b             || to b
Screw       || to line            to b              || to b

means perpendicular      || means parallel

Atoms are always moving parallel to the Burgers vector in the
slip direction on the slip plane.
Convince yourself that you understand this table.

CHE 294 10
Force Required for Slip
How much applied force is needed to cause slip?
Consider a
single crystal       Fresolved         3. Resolve that force on
to the slip plane ... in the slip direction.
rod.                      slip
1. Apply a
direction              τresolved = Fresolved / As
tensile force
4. The resolved
λ
along its
axis.                                                            stress is a shear
F                                    As                   stress.

Ao          φ            slip plane            5. Express the
resolved shear

σ = F /Ao
stress in terms of
the applied
normal to                            tensile stress.
2. Calculate the
τrss = σ cos φ cos λ
slip plane
applied tensile stress.

This formulation is known as Schmid’s law.
CHE 294 11
Vector Notation
Schmid’s law can
be expressed in
R
vector notation
with Miller              cos λ = T • R / | T | | R|
indices.
λ
You already know how           T
to calculate angles
between vectors using                             φ
Miller indices and dot
products.
n
An example using                               cos φ = T • n / | T | | n |
Miller indices is ...
(hT hR + kT kR + lT lR)
cos λ =
(hT2 + kT2 + lT2 ) (hR2 + kR2 + lR2 )
CHE 294 12
Example
What is τrss in terms of σ for this example in a BCC crystal?

slip    τ along [1 1 1]

σ
σ along [1 1 0]

φ = 90o (by inspection)
λ = 35.3o (by calculation)
(110) plane             τrss = 0!           Why?

CHE 294 13
Slip Bands and Critical Stress
Consider stress applied to a single crystal rod or grain.

σ

n

Slip causes bands to
appear in a single crystal or             τ
within a grain.

The stress needed to start slip is the
critical resolved shear stress τcrss
CHE 294 14
You should learn ....
• the slip systems given previously
• where to locate the Burgers vector in screw
and edge dislocations
• how to calculate the length of the Burgers
vector in metals and ceramics
• the direction of motion of dislocation lines
and atoms relative to the Burgers vector in
edge and screw dislocations
• how to use Schmid’s law backwards and
forwards
CHE 294 15

```
To top