Materials Engineering (Week 3) Flashcards
When does plastic deformation occur?
Plastic deformation occurs when bonds are
permanently broken during increasing strain.
Plastic deformation = motion of large number of dislocations
In crystalline materials, plastic deformation is
related to what?
In crystalline materials, plastic deformation is
related to the presence of defects and
imperfections in the solid
What is Plastic deformation by slip?
Plastic deformation by slip where one plane of atoms
slides over adjacent plane by dislocation motion
The movement of the dislocation is called…
Slip
What is the slip plane
and the slip direction?
The crystallographic plane along which the
dislocation line travels is the slip plane.
The direction it moves in is the slip direction.
Slip plane and slip direction form what?
The slip system.
The slip system is defined by what?
the crystallographic
structure of the material
The slip plane will move: (2)
– Along the path of least resistance
– Along a crystal plane where the density of atoms
is highest
Dislocation moves along what? (2)
slip plane in slip direction
Dislocation density in metals is typically …
give range
10^3 – 10^10 mm^-2
Edge dislocation
Edge dislocation moves in response to
shear stress in stress direction.
Screw dislocation
Screw dislocation
moves perpendicular
to stress direction.
Slip direction
direction of movement - Highest linear
densities
Slip plane
- plane allowing easiest slippage
- Wide interplanar spacings - highest planar densities
BC, FFC, HCP
which has the most number of slip systems, and hence is more likely (highest potential) to experience dislocation movement
Body Centered Cubic
Face-Centered Cubic
Hexagonal Close-Packed
Stress and Dislocation Motion
Crystals slip due to
.
a resolved shear stress, tau sub(R)
Applied tension can produce such a stress.
Stress and Dislocation Motion
Equation for a slanted (diagonal) plane:
normally Applied tensile stress: sigma = F/A
Resolved shearstress: t sub(R) =Fs/As
Fs - shear force acting parallel to the slip direction
As - is the cross sectional area of slippage plane (actually larger)
Fs = f x cos(lambda)
As = A / cos(phi) phi- think water potential symbol
Final equation: Tau = sigma x cos(lambda) x cos (phi)
as F = sigma x A
Critical Resolved Shear Stress
When does a slip system occur?
when the resolved shear stress is
larger than a critical value
tau sub(R) > tau sub(CRSS)
CRSS - Critical Resolve Shear Stress
What variation can make slippage easier or more difficult?
Crystal orientation can make slip easy or difficult
Tau = sigma x cos(lambda) x cos (phi)
Remember cos(lambda) and cos (phi) are angles
Slip Motion in Polycrystals
We have previously been considering
single crystals only
* Many materials are polycrystalline
containing a number of single crystals
what can you say about shear stress in polycrystals?
Slip planes & directions (lambda, phi) change from
one crystal to another.
- tau sub(R) will vary from one crystal to another.
- The crystal with the largest tau sub(R) yields first.
- Other (less favourably oriented) crystals
yield later. - Stronger - grain boundaries pin
deformations - Deformation of one grain constrained by
neighbouring grains
Alteration in grain structure can make the material more malleable as majority of the grains are now isotropic
Slip in polycrystalline materials
Strength of metals and alloys can be
increased if slip motion is made more difficult
Slip motion in polycrystalline materials (such
as metals and alloys) hindered by (made more difficult):
– Reducing grain size
– Making a Solid solutions (by adding an impurity to it)
– Cold working (form of deformation under ambient or slightly elevated temp)
Strategies for Strengthening:
1. Reduce Grain Size
(number of grains)
Each single crystal in a polycrystalline material is known as
a grain. The junction between grains is the grain boundary.
* Grain boundaries are barriers to slip.
* Barrier “strength“ increases with increasing angle of
misorientation.
The greater the angle between the two grains the greater the misalinement and hence the bigger the barrier.
If we consider how the grain size is related to the amount
of grain boundaries
* Smaller grain size: more barriers to slip.
Strategies for Strengthening:
1. Reduce Grain Size
(number of grains)
Hall-Petch Equation:
sigma sub(yield) = sigma sub(o) + (k sub(y) x d^1/2)
where k sub(y) and sigma sub(o) are constants
and d is the grain size (length)
Conclude: if the grain size goes down, yield stress goes up
Strategies for Strengthening:
2. Solid Solutions
-Impurity atoms distort the lattice & generate stress.
-Stress can produce a barrier to dislocation motion.
If we consider dislocations, the lattice is already
distorted. This distortion is lattice strain
Impurity atoms tend to concentrate at
dislocations in order to lower lattice strain
If the atoms are bunched up above the slip plane,
small impurity atoms will lower the lattice strain
Large impurities concentrate at dislocations on low
density side
It can be a large or small impurity atom (in comparison to the pure metal atoms)
*refer to diagram for these concepts
Why impurity atoms reduce slip
Impurity atoms lower the lattice strain
For slip to initiate, the bonds between the impurity atoms
need to be extended and broken. This increases the lattice
strain significantly, indicating that more force is required to
both initiate and progress the slip system
