Chapter 2 - Tensile test & Hardness test1) Elastic Limit - amount of stress where plastic deformation starts 2) Yield Strength - 0. 2% of strain. (slightly above elastic limit ) 3) Ultimate Tensile Strength - Max stress before necking occurs. (All deformations before UTS are uniform) 4) Stress = Normal Force / Cross section area . Therefore, True Stress-Strain Curve defers from theoretical due to necking → X-area decreases. → (True) Stress increases! →(True) Strain = Ln (length/ original length)→Strength of material increases 5) Ductility - Measure of amount of plastic deformation before fractures occur. After fracture: a)% of elongation = (final gauge length - original gauge length)/(original length) x 100% →(change in length / original length) x 100% b) % of reduction = (Original X -sect area - X-sect at fracture site)/(Original X-sect area) x 100% Brittle materials → exhibits strains less than 5% at fracture Ductility is temperature dependent. UTS gives a rough indication of ductility. 6) Toughness (Tensile) - measure of ability to absorb energy up to fracture. →Toughness = Area under stress -strain curve → Work done per unit volume.Tough material = Strength & Ductility. Tough material exhibit much plastic deformation before fractured Key points to take note: a)Ductility - Strain dependent b)Toughness - Energy (absorption) dependent → Area under stress-strain curvec)Strength - Stress dependent 7) Hardness - measure of resistance to a surface indentation. →Hardness is related to the size or depth of the depression →determines the softness/hardness of the material →A relationship between hardness and strength can be determined emprically. →Hardness testing is the easiest way to determine the strength of a brittle material.
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3) Ultimate Tensile Strength - Max stress before necking occurs. (All deformations before UTS are
uniform)
4) Stress = Normal Force / Cross section area . Therefore, True Stress-Strain Curve defers from
theoretical due to necking
→ X-area decreases. → (True) Stress increases!
→(True) Strain = Ln (length/ original length)
→Strength of material increases
5) Ductility - Measure of amount of plastic deformation before fractures occur.
After fracture:
a)% of elongation = (final gauge length - original gauge length)/(original length) x 100%
→(change in length / original length) x 100%
b) % of reduction = (Original X-sect area - X-sect at fracture site)/(Original X-sect area) x
100%
Brittle materials → exhibits strains less than 5% at fracture
Ductility is temperature dependent.
UTS gives a rough indication of ductility.
6) Toughness (Tensile) - measure of ability to absorb energy up to fracture.
→Toughness = Area under stress-strain curve → Work done per unit volume.
Tough material = Strength & Ductility.
Tough material exhibit much plastic deformation before fractured
Key points to take note:
a) Ductility - Strain dependent
b) Toughness - Energy (absorption) dependent → Area under stress-strain curve
c) Strength - Stress dependent
7) Hardness - measure of resistance to a surface indentation.
→Hardness is related to the size or depth of the depression →determines the
softness/hardness of the material
→A relationship between hardness and strength can be determined emprically.→Hardness testing is the easiest way to determine the strength of a brittle material.
→Rate of diffusion is limited (dependent) by the number of vacancies.
Interstitial diffusion - diffusing atoms move from one interstitial site to an adjacent empty
interstitial site.
→Interstitial diffusion is limited to small solute atoms which are small enough to squeeze
into the interstitial sites between lattice atoms.→ No vacancies required.
→At lower temperatures, interstitial diffusion is generally faster than vacancy diffusion since
there are far more interstitial sites than vacancies at low temperatures.
→Interstitial atoms are smaller and more mobile!
Concentration and Flux
When there is a difference in concentration (composition), random atomic jumps will result
in a net flow of atoms from high to low conc. until the diffusing atoms are uniformly
distributed and concentration gradient becomes ZERO.
→The rate of mass transfer is measured by the Diffusion Flux, J → mass (or the number of
atoms) passing through a unit cross section area of the solid per unit time.
→J = -D ( dC/dx)
3) Factors affecting Rate of Diffusion
Flux of atoms is proportional to the concentration gradient. Magnitude of D is indicative of
the rate at which atoms diffuses.
D is related to the frequency at which atoms jump from sites to sites.→D = Do e^(-Q/RT)
→D is temperature dependent
Temperature
→ At higher temperature → D becomes larger → rate of diffusion increases!
Diffusion Mechanism
→Activation energy, Q , depends on diffusion mechanism (vacancy or interstitial).
→When Q is high, D is low → Diffusion is slow.
→In vacancy diffusion, vacancy must first be created before an atom can jump into it. Q
then consists of the energy required for vacancy formation plus energy required for an atom
to jump in.
Interstitial diffusion, interstitial spaces are always available → Q is simply the energy
required for the atom to jump in.
→ Therefore Q Interstitial < Q Vacancy
Atomic Bonding
→Q is also dependent on the atomic bond strength. Q can be reflected by the melting pointsof material. Strong bonds → Require more energy to 'break free' .
Actual yield strength of metals are at least 1000 10000 times lower than theoretical values.
This is due to slips occurring in real metal crystals via the movement of dislocation
→ Dislocation is when only a small fraction of atomic bonds are broken at one time, causing
minimal disruption to the crystal lattice. Dislocations are linear or 1 dimensional → local fault → forming a line.
Can be introduced during solidification, plastic deformation or thermal stresses by rapid
cooling.
2 types of dislocations.
a) Edge dislocation - Inserting a half plane into the crystal.
→Dislocation line is at the bottom of the extra half plane.
→ Top region of dislocation line is in compression
→Bottom region of dislocation line is in tension
b) Screw dislocation - Skewing the 2 halves of the crystal by 1 atomic spacing.
Most dislocation are mixed dislocations, containing both edge and screw dislocation.
If shear stress applied to edge dislocation is high enough, bonds beside the 'extra' plane will
be broken to form with the extra plane, eventually causing the last plane of atoms to slip by
1 atomic distance.
→Therefore, only small amount of shear stress is required to operate in the immediate
vicinity of the dislocation in order to produce a step-by-step dislocation.
Although edge, screw and mixed dislocation move in different direction, the result is the
same shear.
Shear stress in bulk ceramics is at least 2-4 times more than in metals. Not only becausecovalent and ionic bonds are stronger, but ions in the more complex structures must move
greater distance between equilibrium lattice positions. (Just like BCC vs FCC)
Bonding in ceramics which are predominantly ionic → contain very few slip systems.
Therefore, slips in certain directions would generate strong electrostatic repulsion →
resisting slips!
Bonding in ceramics which are predominantly covalent → bonds are directional. Therefore,
very difficult to cause displacement in atoms.
Therefore, shear force required to cause slips are higher than that required to cause a
fracture. →Ceramics are hard and brittle! →Do not undergo plastic deformation except at
high tempertures.
3) Strengthening Mechanisms in Metals
Since plastic deformation in dependent on the ability of dislocations to move,
and hardness and stress of metallic alloy are related to the stress at which plastic
deformation can be made to occur.
2 ways to harden or strengthen a metal:
a)Eliminate all crystal defects - such as dislocations. This will allow metals to be very strong,
almost equivalent to theoretical yield strength. However, this is almost impossible. Most
materials exist in polycrystalline. This can only be done on single crystals = very small.
b)Creating more crystal defects to restrict/hinder one another. However, actual yield
strength is still much lower than theoretical.
Atoms around a dislocation are displaced from their equilibrium position → resulting in
elastic strain → elastic stress field around a dislocation. (Strain energy)
Around an edge dislocation → Top: Compression, Bottom: Tension. Around a screw dislocation → lattice spirals around the centre of dislocation!
Stress fields can overlap one another by 'combining' or 'cancelling' each other out. →
Doubling the strain energy or lowering the overall strain energy. However, they must be on
the same plane and of equal magnitudes!
Probability is very low as most dislocations are random and mixed. Thus, dislocation
interactions tend to be mutually repulsive. (More likely)
Repulsive interactions obstructs the motion of interacting segments of different dislocations,
while non interacting ones continue to move (grow), creating dislocation tangles during
plastic deformation. → Therefore, act as obstacles of other dislocations.
Strain Hardening - a ductile metals becomes harder and stronger as it plastically deforms.
This process is known as cold working because temperature at which deformation takes
place is 'cold' relative to its melting point.
During plastic deformation, dislocation interactions often end up repulsive, thus higher
applied stress is required to overcome this mutual repulsion and that dislocation movement
can continue moving (Force them through). → Metal becomes stronger.
Many new dislocations are created during continuous plastic deformation → dislocation
density increases. Therefore, average distance between dislocation decreases → greater
'blockage' → Metal becomes stronger. Crystals that have intersecting slip systems often strain-harden rapidly because slip tends to
occur in more than one slip system → causing more dislocations to intersect → more
blockage. (BCC & FCC)
Yield strength and tensile strength increases by 'cold work' but ductility decreases. Physical
properties such as thermal and electrical conductivity decreases due to electrons and
photons scattering.
Strain hardening explains why true stress-strain curve in a tensile test shows a rising stress
from start of yielding to fracture.
→ Relation between ductility vs strength (strain hardening)!
Methods to strengthen → rolling, stamping.
Grain Size strengthening - in polycrystal, each grain has different orientation to its
neighbours, and dislocations cannot move from one grain to another. Therefore grain
boundaries acts as a barrier for dislocations. (Block)
When dislocations pile up at the grain boundary, the strain energy increases locally, creating
a back stress that repels other dislocations from approaching. Therefore a higher stress is
required to overcome this repulsion
→ More grain boundaries ( smaller the grain size in a material) → more obstacles → higher
the stress required to overcome the repulsion to cause plastic deformation. → Metalstrengthens! (Hall- Petch equation: yield strength = σo + (ky / (rootd) )
Fatigue fracture is also catastrophic → very sudden with little visible plastic deformation
even in ductile materials.
Cracks grow slowly under stresses less than the yield strength until cracks become so large
that the remaining cross sect area can no longer support the load and suddenly fractures.
Fatigue failure generally starts form surface where bending or torsional stresses are the
highest.
Fatigue cracks may be pre-existing or initiated by plastic deformation, or due to surfaces.
Under cyclic stress, tensile produces a small plastic zone at crack tip → stretching open the
crack tip → creating larger surface. As tensile stress is removed/reversed, the crack closes up
and new surface folds → extending the crack length. By formula → Stress max increases!
As crack grows, cross sect are that supports the load decreases → stress increases →
eventually fractures. → Exhibit beachmarks/ripple lines (striations).
At eventual last supporting end, stress experienced will be larger than the fracture strength
→ leading the f ast fracture.
Fatigue Testing
Stress amplitude = (Stress max - Stress min)/ 2
Mean stress = (Stress max + Stress min)/ 2
Stress amplitude can be plotted against number of Cycles to failure. (For a constant mean
Stress)
Fatigue limit for metals → max stress amp which does not cause a fracture regardless of N.
Non ferrous alloys → fatigue strength (failure at N cycles) or Fatigue life (failure at stress x)
→Different curves represent different mean stress.
Fatigue life can be improved by selecting a stronger material or increasing surface hardness
→ shot peening →Act as compressing the surface, inducing compressive surface stresses.
Non-Destructive Testing
Methods of identifying fatigue cracks
Small surface cracks → Dye penetrant
Surface and Internal fatigues
-Ultrasonics
-Radiography
Chapter 8 - Corrosion
Corrosion occurs in an aqueous environment → Relatively Humidity (RH) > 60-70%
1) Electrochemical Reactions
Metals dissolve in electrolyte to produce positive metal ions in electrolyte
→Metal becomes negatively charged as electrons remain in metal.
When another metal of different electrochemical potential in added to the same
electrolyte, connected with a thin wire, a potential difference in resulted.
The metal with higher E.P (more negative potential) will have more electrons → where
electrons will flow to the less reactive metal → Cathode (Takes in electron) Corrosion then take place at the more negative potential → Anode (produces elecrons)
Component with higher melting points segregates at the centre of the solid while regions
between grains are rich in the lower-melting point component.
→This phenomenon is called hot shortness → regions around grain boundaries melt before
equilibrium solidus temperatures are met.
Mechanical Properties of Isomorphous Alloys
Since isomorphous alloys form a single solid phase at all compositions → each component will
experience solid-solution strengthening by additions of other component.
→Strength and Ductility is inversely proportionate.
3) Binary Eutectic System
This system is for 2 components that are only partially soluble.
Eutectic composition and Eutectic temperature!
Eutectic temperature is the lowest temperature which liquid phase exists and also thelowest solidification/melting point.
Hypoeutectic → composition lower than eutectic point.
Hypereutectic →composition more than eutectic point.
Solidification of Eutectic Alloy
Alternating layers (lamellae) of alpha/ beta are formed because such structure requires the
different compost atoms to diffuse only relatively short distances → minimise diffusion path.
Solidification of Off-Eutectic Alloy
Proeutectic / Primary → the solids form before eutectic temperatures!
Due to presence of proeutectic alpha, the final composition in 100% solid state is slightly
different. →proeutectic + lamellae.
alpha lamellae composition = final composition of alpha - composition of proeutectic alpha
Alloys without Eutectic Reactions
Only alloys with composition lying within the alpha and/or beta regions do not undergo
eutectic reactions → undergoes reactions just like the isomorphous alloys. (single solid)
Alloys exceeding the solubility limit at room temp. but within max. solubility limit forms atwo-phase microstructure that has a different morphology from the standard eutectic 2
phase. → non-lamellae (the other composite will precipitate in the structure)!
Mechanical Properties of Eutectic Alloys
Greater number of boundaries = greater strengthening effect.
Eutectic lamellae → very strong. More Eutectic → higher strength.
5) Other Binary systems
alpha and beta are called terminal solid solutions. (Appear at the ends of a phase diagram)
→At a particular temp. there will be a equilibrium phase, it is can be checked if it is
spontaneous by calculating the G, if it is negative → spontaneous!
G may be regarded as the 'driving' force for transformation.
Nucleation
Atoms in liquid are in continual random movement
Time to time, a small group of atoms will come together to form tiny crystal nucleus by
chance!
The nucleus must be of critical size, r*, or larger in order to remain stable and grow.
→If it is smaller than r, it will redissolve back.
Increase in degree of undercooling, (Change in T), decreases the required critical nucleus
radius.
Probability of atoms randomly clustering to form small groups is higher than larger ones
→Nucleation becomes easier and faster! (with larger Change in T)
However, random clustering of atoms requires local diffusion → temperature dependent! →Therefore, rate of diffusion decreases.
Net nucleation rate is therefore balanced between ease of nucleation and atomic mobility.
Nucleation occurs preferentially at sites such as walls of containers or suspended impurities.
In solid to solid phase transformation, preferential nucleation sites
→grain boundaries
→Dislocations
→Phase Boundaries
→Surfaces of impurities and precipitate.
Growth
Once nucleus of critical size or larger is formed, spontaneous and sustained growth occurs.
Growth includes transport atoms into the nucleus, and rearranging them to form crystal
structures.
→This process is diffusion dependent → Prefer high temperatures
Overall rate of (kinetics) of phase transformation depends on nucleation and growth rates.
Characteristics of phase transformation:
i) Incubation period to allow nucleation
ii) Transformation is slow initially (S curve)
iii) New phase starts growing at the expense of the other once nucleated. Rapid increase in
amount of new phase present
iv) Growth rate of new phase decreases eventually due to depletion of solute atoms.
2) Isothermal Transformation Diagrams
Equilibrium phase diagrams only show the microstructures that develop under equilibrium
conditions
Rate of cooling/heating and actual temperature transformation determines the actual
resultant microstructure. (Different form Equilibrium phase diagrams)
Isothermal Transformation (IT) or Time-Temperature-Transformation (TTT) diagrams showthe progress of transformation with time and their final microstructure,