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
Strategies for Strengthening:
3. Cold Working (%CW)
Cold working, also known
as strain hardening, is
when a material is
plastically deformed
Straining a material of
yield strength σ sub(y0) to strain
D results results in plastic
deformation
Releasing the force and
then straining again will
give an increased yield
strength (σ sub(yi))
Room temperature deformation.
* Common forming operations change the cross sectional
area: Forging, Rolling, Extrusion and Drawing all put the material under strain.
Percent cold work: Equation
%CW = A(o) - A(d) / A(o) x 100
A(o) initial cross sectional area
A(d) changed cross sectional area
Dislocations During Cold Work
-Dislocations entangle with
one another during cold
work.
-Dislocation motion
becomes more difficult
Result of Cold Work
Dislocation density equation
Does yield stress increase or decrease as dislocation density increases? and why?
Rho sub(d) = total dislocation length / unit volume
Yield stress increases as Rho sub(d) increases.
The number of dislocations increases after cold working.
* As the dislocation density increases, the chances of dislocations being closer to one another increases.
- Dislocations can repulse (if two compressed zones interact/ align) or cancel out one another (if the two dislocations are oppositely sensed i.e tensile above compression below and vise versa for the other dislocation, the tensile and compressive forces cancel each other out and attract each other, Dislocation Annihilation)
- On average, dislocation-dislocation strain interactions are repulsive.
Therefore to summaries
As cold work increases: (3)
Yield strength (sigma sub(y)) increases.
* Tensile strength (TS) increases.
* Ductility (%EL or %AR) decreases, because of the dislocation, saturation and repulsion.
We have shown how cold working increases the
yield strength of a material but lowers its
ductility.
We are now going to consider the opposite
where the ductility is increased but, as a
consequence, the strength decreases.
What is the process the material must undergo?
Annealing (heating without melting)
Effects of cold work are reversed!
What are the stages of Annealing?
Recovery- Polycrystalline materials possess a range of different
lattice strains.
* Removal of these lattice strains is achieved by heat
treating the material in a process known as annealing.
* The increased thermal energy of the atoms in the lattice
allow diffusion to occur and reduce the number of
dislocations.
* The reduction in dislocations is called recovery .
Recrystallisation- Annealing at elevated temperature allows atoms to move and form new crystals.
* These new crystal grains are small, relatively defect free and
consume cold worked grains that possess a high dislocation density
Further Recrystallization (as time enfolds)
All cold-worked grains are consumed.
Recrystallization of cold worked metals can be used to refine
the grain structure.
Recrystallization temperature,T sub(R)=
temperature at which
recrystallization is complete within 1 h
Annealing:
Grain Growth (why does it happen)
At longer times, larger grains consume smaller ones.
Grain boundary area (and therefore energy) is reduced.
Dislocations are observed primarily in what materials? (2)
metals and alloys
Strength is increased by making … …
difficult.
dislocation motion
Heating (annealing) can reduce … …
and increase … …
This decreases the strength
dislocation density
grain size
Methods to increase strength are: (3)
- decrease grain size
- solid solution strengthening
- cold work
Grain Growth
Empirical Relation: Equation
d^n - d sub(o) ^n = Kt
k - coefficient dependent
on material and T
t - time elapsed
d - grain diam. at time t.
n - exponent typ. ~ 2
There is a strong correlation between microstructure
and what kinda property
mechanical properties.
The development of microstructure of an alloy is
related to the characteristics of its phase diagram.
Phase diagrams show…
equilibrium states
What is the difference between solutions and mixtures
– Solutions – solid solutions, single phase
– Mixtures – more than one phase
Solubility Limit:
Max concentration for
which only a single phase
solution occurs.
Think of the graph, temp against C(o), composition (wt% e.g sugar)
Components:
The elements or compounds which are present in the mixture
(e.g., Al and Cu)
Phases:
The physically and chemically distinct material regions
that result (e.g., alpha and beta).
What can you say about phases, and what happens across phase boundaries?
Give 2 examples
Phases are homogeneous and have uniform physical
and chemical properties.
* Across phase boundaries, physical and/or chemical
characteristics change abruptly.
* Example 1: water and ice are chemically identical but
physically dissimilar.
* Example 2: polymorphism (metals existing in more
than one crystal structure)
Microstructure is determined by: (3)
(to do with phases)
what does microstructure determine?
-number of phases present
- proportions of phases
- distribution and arrangement of phases
Microstructure determines mechanical properties
Effect of T & Composition (Co)
Changing T can change number of phases
Changing Co can change number of phases
Phase equilibria
When are equilibrium conditions met?
Equilibrium condition: the Gibbs free energy
is at a minimum.
Time period required to attain equilibrium can
be very long, particularly in solid systems.
Time period required to attain equilibrium can
be very long, particularly in solid systems.
Systems in non-equilibrium where rate of
approach to equilibrium is extremely slow
are called …
metastable
Phase diagrams indicate phases as function
of … (3)
Phase diagrams indicate phases as function
of Temperature, Composition, and Pressure
What is the process called when substances goes from solid to gas
Sublimation
(reverse called deposition)
For this course:
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
Phase Diagrams:
What info do you need to work out the number and types of phases, and the compostion (%) of each phase
Number and types of phases:
If we know T and composition (Co), then we know:
- the number and types of phases present.
composition of phases:
If we know T and Co, then we know:
–the composition of each phase.
weight fractions of phases:
If we know T and Co, then we know:
–the amount of each phase (given in wt%).
The Lever Rule
(Tie Line)
W sub(L) = S / R + S
W sub(alpha) = R / R + S
alpha- for the solid
Tie line – connects the
phases in equilibrium with
each other - essentially an
isotherm
Metal Fabrication in general
How do we fabricate metals?
– Blacksmith - hammer (forged)
– Molding - cast
* Forming Operations
– Rough stock formed to final shape
Hot working*
T high enough for recrystallization
* Larger deformations
Cold working
well below Tm
work hardening
smaller deformations
What are metal alloys?
Metal alloys are mixtures of metal types along
with other elements
– E.g. Fe with carbon
- Weight %, temperature
– Define the microstructure via phase
diagrams
Volume fractions
- For multiphase alloys…
- For multiphase alloys, relative phase amounts can be
specified in terms of volume fraction rather than mass fraction - Phase volume fractions can be determined from examination
of the microstructure - For an alloy consisting of phases α and β: V (alpha) + V (beta) = 1
Therefore V (alpha) = V (alpha) / V (alpha) + V (beta)
Now sub in V (x) = W(x) / Rho(x) for where x = alpha and beta respectively
What is meant if a system (solution) is binary?
System is:
–binary
i.e., 2 components:
Cu and Ni.
What is meant if a system (solution) is isomorphous?
i.e., complete solubility of one component in another;
alpha phase field extends from 0 to 100 wt% of a chosen element on the phase diagram.
Metal Fabrication Methods (3)
Forming
Casting
Rolling
Metal Fabrication Method
Casting
mold is filled with metal
– metal melted in furnace, perhaps alloying
elements added. Then cast in a mold
– most common, cheapest method
– gives good production of shapes
– weaker products, internal defects
– good option for brittle materials
Metal Fabrication Method
Forming (list all variations): 4
Forging (Hammering; Stamping)
Rolling (Hot or Cold Rolling)
(I-beams, rails, sheet & plate)
Drawing
(rods, wire, tubing)
die must be well lubricated & clean to reduce friction and prevent impurities
Extrusion
(rods, tubing)
ductile metals, e.g. Cu, Al (hot)
Metal Fabrication Method
Casting (list all variations): 4
Sand Casting
(large parts, e.g.,auto engine blocks)
* trying to hold something that is hot
* what will withstand >1600ºC?
* cheap - easy to mold => sand!!!
* pack sand around form (pattern) of desired shape
Investment Casting
(low volume, complex shapes e.g., jewelry, turbine blades)
plaster die formed around wax prototype
- pattern is made from paraffin.
- mold made by encasing in plaster of paris
- melt the wax & the hollow mold is left
- pour in metal
Die Casting
(high volume, low T alloys)
Continuous Casting
(simple slab shapes)
visual filter, molten metal poured in, comes out as a solidified tube like structure.
Metal Fabrication Method
Joining (list all variations): 2
Powder Metallurgy
(materials w/low ductility)
point contact at low T (of three seperated atoms) –> densify –> densification by diffusion at higher T.
Welding
(when one large part is impractical)
Heat affected zone:
(region in which the microstructure has been changed)
