ME2151 Summary Pointers

Chapter 2

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Tensile test & Hardness test

1) 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 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.

Chapter 3 - Atomic Structure 1) Electronic Structure - Arrangement of electrons [Shells: K,L,M,N. Subshells: s,p,d,f.] →Table on pg 4! 

Electrons tend towards the lowest energy states (Greater Stability)

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Partially filled outermost shells → Valence electrons.

2) Primary Bonds - Ionic, Covalent and Metallic   

Ionic Bonding - Transfer of electrons (Non-directional) Covalent Bonding - Sharing of electrons (Fixed directional relation) Metallic Bonding - Electrons are delocalized → Forming a sea of randomly moving electrons.

3) Secondary Bonds a) Van der Waals Bonding - Attraction between atomic or molecular dipoles. (Induced polarity by temporary dipoles) b) Hydrogen Bonding - Special type of VDW bonding between molecules and hydrogen (Permanent dipoles) 

Hydrogen bonding is stronger than VDW bonding.

c) VDW bonding between layers of covalently bonded C atoms. ie graphite. 4) Bonding Forces and Energies  

There will be a attractive Force when 2 atoms are brought together. → Force increases with decreasing atomic separation (Brought closer). At short separations, a repulsive Force arises due to resistance of closed inner shells.

→ At Equilibrium = Force(Separation + Attractive) = 0 →Potential Energy due to interaction between atoms, min(max) Energy @ F = 0 →At this point, the atom only posses PE, →KE=0. →Energy-Atomic separation curve! @ 0 K(elvin). With KE, atom vibrates back and forth the width of the well. →When temperatures increases → total energy increase to above= material is in gaseous state. 5) Bonding Type and Properties a) Thermal Expansion, (alpha) - Thermal expansion coefficient can be determined by the depth and width of the potential well. Deep and narrow → thermal expansion coefficient is small. → Materials that are ionically and/or covalently bonded tend to have deep and narrow walls.

→Metals experience slightly greater expansion. →Materials with secondary bonding have very Large coefficient of expansion. 

Low expansion coefficients are generally preferred → Better thermal stability.

6) Melting Point - Measure of bond strength → Given by the Depth of the potential well. →Deeper the well, the greater thermal energy required to reach levels where bonding energy are low(liquid) or ZERO (gas). →Primary bonds have generally deeper wells → higher melting points. Secondary bonds does not! 7) Elastic modulus - Measure of a material's stiffness. →Elastic modulus is related to the slope of the force-separation curve near the equilibrium point. →The steeper the slop → the greater the force required to move the atoms away from their equilibrium positions → higher the module! 

Primary bonds tend to have higher stiffness, not for secondary bonds.

7) Hardness, Ductility and Toughness a) Ionic solids - A displacement of ions might lead to like charges being adjacent to each other, resulting in a repulsive force. b)Covalent solids- Strong mutual repulsion between negatively charged election clouds limit atomic movement. Thus, Ionic and Covalent solids are very hard, but low ductility and toughness. c) Metals- Because of the sea of free electrons, positive ions can slip from one to the other without any electrical-charge constraints. Therefore, metals are relatively ductile and tough.

Chapter 4 - Crystal structures 1) Atomic Arrangement - No order, Short range, Long range →Crystalline materials exhibit short and long range order. Repetitive pattern → Lattice! 2) Lattice - A collection of points arranged in a fixed periodic pattern. Points that make up the lattice are called Lattice Points. →Unit cell is the smallest subdivision of a lattice. Properties of a unit cell are the same as the lattice(whole crystal). →Each unit cell is described by the lattice parameters, ie the lengths of the cell edges and angles between axis. Bravais lattice → Types of lattice. ie. BCC, FCC. →When a group of atoms are located at the a lattice point, it is called the basis! Coordination number = Number of nearest touching atoms. Atomic packing factor = fraction of space occupied by atoms in a unit cell →APF= Vol of atoms in a cell / Vol of a unit cell. = (No. of atoms in a cell x Vol of an atom) / Vol of a unit cell. Theoretical density = Mass of unit cell / Vol of unit cell → (No. of atoms in a cell x Mass of an atom) / (Vol of a unit cell) 3) Metal Crystal Structures 

Pure metals → only one metal ions occipies each lattice point.

a) Face-Centered Cubic FCC Unit cell length = 2RxRoot2. Because unit diagonal length = 4R. Coordination Number = 6, Atoms per cell = (0.25 x 8) + (6 x 0.5) = 4. → APF=0.74 b) Body-Centered Cubic BCC Unit cell length = 4R/(Root3) Coordination number = 8, Atoms per cell = 2, APF = 0.68 c) Hexagonal closed-packed HCP Lattice parameters: a (width) =2R , c(height) = 4a/(Root6) Coordinate number of central atom = [6 +2(3)] = 12, APF = 0.74 (Same as FCC)

4) Allotropy/Polymorphism - Ability to assume more than one crystal structure in the solid state. (eg, FCC, BCC at different temperatures) → Such property changes are useful for hardening/softening → Could also be detrimental. Distortion and cracking due to changes in vol. 5) Close-Packed Crystal Structures      

Metal atoms packed closely, at equilibrium bond length → Lowest energy, most stable Closed packed directions → directions/plane which atoms are in direct contact. Plastic deformation in metals occurs most readily along close-packed directions Number and relative positions of close-packed directions/planes affect ductility. Packing same-sized atoms in FCC and HCP gives the smallest volume(Highest density, APF =0.74). Therefore, FCC and HCP are close-packed structures. Arrangements of close-packed planes differs in HCC and FCC. Therefore, ductility/plastic deformation is different.

→ HCP only has close-packed planes at hexagon. 6) Interstitial Positions and Sizes →Interstices are 'holes' between lattice atoms    

Size of an interstitial site = r (radius of hole) / R (radius of lattice atom) Tetrahedral interstitial = 0.225 (Bounded by 4 atoms) Octahedral = 0.414 (Bounded by 6 atoms) Cubic = 0.732 (Bounded by 8)

→Atoms occupying interstitial sites must be larger than the size of the hole! Smaller ones are not allowed to "rattle" around loose sites. 7) Family of Directions (use [ ] brackets)    

Miller indices (3 axis) → use < > brackets. eg. = *100+ / *010+ / *001+. Miller-Bravais Indices (4 axis) Planes use ( ) brackets - at where the planes intersect the axis Family of planes use { } brackets

8) Crystalline Materials   

Single crystals have same orientation and alignment of unit cells throughout entire crystal. However, most materials are polycrystalline → structures composed of many small crystals (grains) with identical structures but different orientation. Grain boundaries are formed when different orientated crystals coincide.

Single crystal materials (with the absence of grain boundaries) 

very hard and strong.

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exhibit directionality → magnetism, electrical conductivity, elastic modulus and creep resistance. - anisotropy. At grain boundaries, atoms are displaced from their equilibrium → posses more energies. Interfacial energy makes grain boundaries preferential sites for chemical reactions. They are attacked more aggressively. → scatter light better → appear darker under microscope.

Chapter 5 - Crystal Defects and Diffusion 1) Crystal Defects -

Point Defects - zero dimensional → involve a few atoms at most → vacancies and impurities. Linear Defects - 1 dimensional → Local fault lines along a line → Dislocations Planar defects - 2 dimensional → Serve as boundaries between regions. → Grain Boundaries. Volume defects - macroscopic scale (Large) defecs that represent inhomogeneities in a solid. → Inclusions such as precipitates/cracks/voids.

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At a given temperature, the average KE of a material is fixed. However, KE of individual atom at any time is not constant, but randomly distributed over a wide range. Sometimes an atom might posses sufficient energy to break its bond from its neighbours and jump to another lattice site. The amount of energy to break the bonds is known as Q, the activation energy. Rate of successful jumps of atoms is proportionate to the number of atoms with energy more than Q. Rate = Ce^(-Q/RT) → lower activation energy = higher rate!

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Vacancies     

a vacant (missing) lattice site from which an atom is missing. Equilibrium number of vacancies, Nv = Ne^(-Q/RT) A crystal will always have vacancies at any temperature above 0 K(elvin). Nv will increase with temperature. Vacancies are the basis(Cause) of movement of atoms → Diffusion

2) Diffusion - Spontaneous movement of atoms within a material as a result of atomic vibration. 

Self diffusion → constant, random, movement of atoms within the pure material → occurs in the absence of a concentration gradient → no net flow of atoms → effects are insignificant to material properties

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Inter diffusion → movement of atoms from one material to the other. → Occurs in the presence of a net flow of atoms. High conc to low conc. → Affects material properties. →Known as heterogeneous diffusion.

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Vacancy diffusion - diffusing atoms from its normal lattice position to an adjacent vacancy. → This is the mechanism for self-diffusion and inter diffusion. →Only if the diffusing atoms are of comparable size of the host atoms (hole/vacancy).

→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!

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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

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Temperature → At higher temperature → D becomes larger → rate of diffusion increases!

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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.

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Interstitial diffusion, interstitial spaces are always available → Q is simply the energy required for the atom to jump in. → Therefore QInterstitial < QVacancy

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Atomic Bonding →Q is also dependent on the atomic bond strength. Q can be reflected by the melting points of material. Strong bonds → Require more energy to 'break free' .

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Crystal Structure → It is more difficult to squeeze through regions that are densely packed. It is more difficult for atoms to squeeze through regions that are densely packed. Therefore, generally, Q is higher and D is lower for close-packed structures (FCC)→ Slower diffusion!

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Crystal defects Such as dislocations, grain boundaries and surfaces provides open, disordered regions which atoms can move easily. Therefore, Q along such defects are much lower → D is much higher. →Cross sections of these areas are usually small → therefore only at low temperatures, these short circuit diffusion are significant. →In nanocrystalline materials where there are many grain boundaries, surface diffusion can still dominate. → diffusion in microelectronic devices.

Chapter 6 - Dislocations, Deformation and Strengthening in Metals 1) Plastic Deformation by Slip  

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Slip → involves the sliding of one plane of atoms to another under an action of shear stress. →Slip plane and slip direction is where slip occurs. → Slip system Slip does not take place in any arbitrary plane/direction. → preferred slip plane/direction is where atoms are most densely packed. →Slip occurs in steps of one atomic spacing, so moving atoms from one stable site to the next would involve the least energy. (Atoms are close together.) Since most engineering alloy are polycrystalline, different orientations of each grain → each grained is strained differently by an applied stress. Slip will begin on slip system when the resolved shear stress acting on the slip plane in the slip direction reaches a critical value. Multiple planes can slip all together with sufficient shear stress. In polycrystalline solid, the deformation in each grain must be compatible with its neighbours to maintain the integrity and coherency of the grain boundaries. Metals with FCC and BCC structures are ductile because they have large number of slip systems. (Close-packed planes) Slip systems in FCC and BCC are well-distributed such that at least one slip system is favourably orientated for slip at low applied stress. Slip systems in FCC and BCC intersect → resulting in cross slip, whereby one system can intersect with another to continue on another. (not blocked) However, BCC does not have close-packed planes → slipping atoms must move a greater distance from one equilibrium lattice to another. Therefore, higher shear stresses are necessary for slip in BCC than in FCC. → Higher strengths in BCC than FCC> Although HCP contains close-packed planes, slip systems can only be parallel along the hexagonal plane. Thus, cross slip is not possible. → HCP is relatively brittle!

→No. of slip planes and its orientation affect ductility.

2) Dislocations and Slip  

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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 because covalent 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.    

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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. → Metal strengthens! (Hall- Petch equation: yield strength = σo + (ky / (rootd) )

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Polycrystals are generally stronger than single crystals → fine grained metals are stronger than coarse grained. Grain size < 5 x 10^(-6). When grain size decrease below 20 nm, a reverse effect is resulted → softening. Grain size can be refined by cooling quickly from molten state, or extensive plastic deformation followed by annealing. Solid Solution Strengthening Impurities exists in all materials (Solute Atoms). Impurities may occupy interstitial sites or substitute atoms of the host material depending on their sizes. These solute atoms distort the surrounding lattice and increase the strain energy of the crystal. Solute stress field could interact with approaching dislocations → repulsion arises. → Higher applied stress is required to overcome the repulsion → Strengthens! Such stress field can also interact with dislocation to increase or decrease the strain energy within the region. However, when a low strain is established, further movement away of the dislocation would again raise the strain energy! → More solute atoms = greater strengthening Degree of solid solution strengthening depends of the relative sizes of the solute and solvent atoms. Larger the difference, greater the distortion → stronger the strain energy. However, too large a solute atom, lower its solubility. Dispersion Hardening (Precipitation in material) Precipitation or age hardening effect → Interaction between dislocation and dispersed particle depends on the nature of particle-matrix boundary. Most particle matrix are non coherent and disordered → particles do not distort the surrounding lattice. → dislocation would not be able to pass through them. This results in a bowing between particles. → Bowing dislocation causes a greater lattice distortion and higher strain energy. → Higher shear stress required → strengthens. Coherent particles will only further increase the stress field as new surfaces are often created → raises the interfacial energy. (More area of blockages)

4) Annealing (To get back original material before strain hardening) a)Recovery 

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Heat material sufficiently (0.4 x M.P.)→ dislocations in a strain hardened metal rearrange into lower strain energy → forming cell boundaries of a subgrain structure within the old grains → polygonization. Dislocation density decreases minimally. Hardness, strength and ductility remain almost unchanged due to the dislocation density. However, thermal and electrical conductivity restored.

b) Recrystallization 

Temperature I raised further to (0.6 x M.P.)

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New small dislocation-free grains nucleate at high energy cell boundaries of the polygonization subgrain structures , eliminating most of the dislocations and replace the strain hardened grains. Since recrystallized grains are relatively free of dislocations → physical properties restored back to original form (before strain hardening). → Hot work! Disadvantage → poor surface finish due to oxidation.

c) Grain Growth   

Main basis of grain growth is to reduce interfacial energy (Energy at grain boundaries) Grain growth results in fewer grains → decreasing grain boundaries This involves diffusion of atoms across grain boundaries such that some grains grow at the expense of others. → Reduces the strength and hardness due to less boundaries → less blockages.

Chapter 7 - Fracture and Fatigue 1) Fracture involves initiation and propagation    

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Slow application of external loads (Tensile test) Rapid application of external loads (Hardness test/ Impact) Cyclic or repeated loading (Fatigue) Time-dependent deformation (Creep) Stress concrentration Actual fractures occur at 10-1000 times lower than theoretical fracture strengths. This is because materials contain cracks within it → tensile load are transferred to the regions of cracks. Max Stress = 2 x (Applied Stress) *Root(length of crack/radius of crack tip)+ → Max stress is experienced at the crack tip. Brittle Fracture - Little or no plastic deformation before fracture (Low toughness) Separations of material tends to occur through grains → Cleavage fractures (transgranularly) are relatively flat and shinny. → Can also occur along grain boundaries (intergranularly) Yield strength of brittle material is higher than its fracture strength. (Easier to fracture than deform plastically) Crack grows (Longer) very rapidly (Speed of sound) → causing a cleavage crack. (use fomula to derive explaination) Cleavage fracture occurs in brittle ceramics, but also common in BCC and some HCP metals at low temperatures. True cleavage fracture is not observed in FCC metals due to their low shear stress required for slip → numerous slip systems →ability to cross slip.

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Ductile Fracture - undergo extensive plastic deformation before fracturing. →Absorbs a considerably amount of energy before failing. →Materials fail my ductile fracture are deemed as tough A cone and cup will be resulted. →Surface fracture will look dull, irregular and fibrous. Yield strength of ductile materials are lower than fracture strength (Plastic deformation will occur first) However, as material deforms, yield strength will increase again → due to strain hardening. Radius of crack tip will also increase due to deformation (unlike brittle)→ stress experienced at crack tip becomes a smaller fraction to fracture strength (or the new yield strength)! Well-annealed metals do not usually contain cracks since the heating process would have closed up most of the cracks. However, most engineering alloy contain precipitates which voids nucleate through decohesive of weak matrix-particle interface or fracture of brittle particles or grain boundaries. Such voids grow to become cracks. (Plastic deformation begins from these precipitates → merging with one another to grow in size → forming cracks.) Larger the plastic zones → the more energy it can absorb (Allowable regions of plastic deformation.)

Brittle vs Ductile 

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Ductile fracture is generally preferred → crack growth is relatively slow and steady. Time allows preventive measures can be taken before fracture. → Able to absorb more energy prior to fracture Brittle fracture is catastrophic as it occurs suddenly → too fast.

Effects of Temperature and Strain Rate: Ductile to Brittle Transition 

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Ductile fracture is accompanied with plastic deformation → involving dislocation motion (deformation is related to dislocations). Materials with high critical shear stress (BCC metals) → thermal energy helps in overcoming the energy barrier. At low temperatures, material tends to be more brittle as thermal activation for dislocation motion is reduced. → Yield strength increases as temperature. (Yield strength is inversely proportionate to ductility). Since ductility reduces, plastic zone decreases → ability to absorb more energy decrease. → Fracture tends to be more cleavage. Such materials show a dependence on strain rate because thermal activation is less effective at faster rate of deformation. Higher strain rate → higher yield strength. Generally, slip systems in BCC and some HCP becomes active only when there is sufficient thermal energy for dislocation motion. (There do not have close-packed planes) →Consider yield strength consists of 2 components → Thermal activation and shear stress!

Impact Testing 

Charpy test - hammering the material to test for impact toughness.

Fatigue 

When a material is subjected to repeated stress cycles, they can fracture below UTS or even yield strength.

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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 fast 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)

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Criteria for corrosion to take place in a system →Potential difference →Electrically connected →Electrolyte Tendency to lose electrons → how negative the potential is

2) Forms of Corrosion a) Galvanic Corrosion - when 2 metals of different composition are electrically connected in an electrolyte    

The alloy with more negative potential becomes the anode and corrodes. → Greater the potential difference → greater the corrosion. Rule of thumb: Ratio of electrons through anodic and cathodic reaction must be equal! Small anodes vs Big cathode →Corrosion will be severe Big anodes vs small cachode → less severe.

b) Uniform Corrosion - Special case of galvanic corrosion occurring at microscopic regions. 

Alloys with more than one phase would undergo uniform corrosion. Single phase alloys are more resistant compared to multi phase.  Galvanic couples may develop at grain boundaries, leading to intergranular corrosion. →Segregations of impurities at grain boundaries could make these regions anodic to the bulk of the grains. c) Intergranular corrosion - could arise from precipitates forming at grain boundaries.  Alloys with corrosion protection, such precipitaion reactions at the grain boundaries deplete adjacent areas of solute, resulting these areas to be less resistant to corrosion than the surrounding grain material.  Sometimes, Individual grains are loosened and lost from the material.  Or, localised loss of grain boundary material can lead to an appearance similar to cracking. Differential Aeration Corrosion 

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When there is a difference in oxygen concentration between two regions, the low oxygen region will become the Anode, the region with higher conc. of oxygen will be the Cathode. →Cathode requires oxygen to allow reactions to take place. Differential aeration is responsible for crevice (protruding) corrosion and pitting(hole) corrosion. Small crevices and pits are produced by uniform corrosion → eventually leading to localised corrosion due to differential conc. of oxygen. Differential aeration is also the mechanism behind waterline corrosion. Oxygen unable to reach metal near the waterline than regions far away. →Metal just inside waterline (edge) becomes cathodic, while immersed metal becomes anodic.

Other Concentration Cells

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A metal after cold worked (Strain hardening) contains high density of dislocations. Dislocations are associated with high energy. High energy regions becomes Anodes to less stressed regions (Cathodes). Grain boundaries (with higher energy) are anodic to bulk grains and tend to corrode more severely. Rate of corrosion at grain boundaries that do not contain segregated impurities or precipitates is not significantly higher than the grain interior, since the potential difference between boundaries and interior is only minimal.

3) Protection Against Corrosion   

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Design materials to reduce exposed surface area Minimize conc. or galvanic differences. Protective coating → prevent contact between metal and electrolyte. →If coating is anodic to underlying metal, should coating be scratch, corrosion is still desirable. (Large anode) Inhibitors → chemicals added to electrolyte to from protective layers on surfaces or anode/cathode Cathodic protection → Use sacrificial anode. → Or use impressed current to counter current to neutralise the corrosion current.

Chapter 9 - Phase Equilibria & Phase Diagrams 1) Components and Phases  A phase is a region of material that has the same composition and structure throughout. Separated from the rest by a distinct interface. →may contain one of more components  Microstructure is the structure of a material on the microscopic scale. → Characterised by phases present, relative amounts, composition and structure of each phase, size, shape and distribution of phases.  Phase diagram describes the lowest energy (equilibrium) state of a system.  One component system → Unary system→ Phase diagram, Pressure vs Temperature →Triple point of water = 273.16 K  Two component system → Solubility in the solid states 

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A solid solution is a homogeneous single phase formed by solute atoms (either by substitution or in interstitial sites) into a host crystal. →Original structure of crystal is maintained with solute atoms randomly and uniformly dispersed. If solute and solvent atoms are similar in size → substitutional solid solution. If solute is smaller → interstitial solid solution. Unlimited Solubility : Components form substitutional solid solution. Limited Solubility : Solute atoms only dissolve up to a certain extent; excessive solute may combine with solvent to from separate new phases. Solubility of interstitial atoms

→ Difference in atomic radii , 15% →Must belong to the same group or adjacent groups in the Periodic Table to prevent compound formation. →Valences must be the same →Crystal structures must be the same Specification of Composition  

Mass percentage (wt%) = (Mass of composition A) / (Mass of composition A +B) x100% Moles percentage (at%) = (Mols of composition A) / (Mols of composition A +B) x100%

2) Binary Isomorphous System    

Phase diagram : Temperature vs Composition (under constant/ atm pressure) →shows the states/phases of composition (ie. liquid, (liquid + solid) and solid) Left and right vertical lines represent 100% composition of each component. Solidus line and Liquidus line Shows a unique melting temperature at each composition.

a) Determination of Phases Present 

Single phase or double phase at a particular composition and temperature!

b) Determination of Phase Compositions   

Draw a Tie Line (Isotherm) through the 2 phase fields Note the intersection between the tie line and phase boundaries on each side. Compositions of phases are given by the composition axis of the intersections. →CL , Ca and Co

c) Determination of Phase Amounts From the tie line intersections:   

Mass fraction = (Mass of phase) / (Total mass) = (Opp. length arm) / (Total length) Mass fraction of Liquid = (Ca - Co) / (Ca - CL) Mass fraction of Solid = (Co - CL) / (Ca - CL)

d) Non- Equilibrium Solidification  

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During solidification, composition of a and L changes constantly according to the solidus and liquidus line. These changes are accomplished by diffusion. Diffusion in solids is usually very slow, cooling is too fast for the diffusing atoms to establish equilibrium phases and compositions in the solid states → The 'old' composition of alpha composition is unable to diffuse fast enough due to cooling →Therefore, overall alpha composition is relatively higher than the solidus equilibrium. →Thus, forming layers of different composition (alpha). → Cored Structure. Faster cooling will result in greater deviation.

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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 the lowest 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 a two-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)

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Components in a binary system reacts chemically to form intermediate phases →Intermediate solid solutions and intermediate compounds.

6) Iron-Iron Carbide System     

Ferrite → BCC (Interstitial sites are small, this solubility of carbon atoms is low) Austenite → FCC Cementite → Fe3C Pearlite → lamellae layers of Cementite and Ferrite Austenite → Ferrite and Cementite (at Eutectoid point → lamellae layers→ pearlite)

Transformation in Hypo/Hypereutectoid Steels 

Pearlite and proeutectoid is formed.

Mechanical Properties of Steel   

Interphase boundaries between ferrite and cementite is an obstable to dislocation movement → greater the number of boundaries → greater the strengthening. Cementite is very strong → containing metallic and covalent bonds. →Does not undergo plastic deformation. Dislocations can only take place in ferrite. → More cementite in a steel → stronger it is.

Chapter 10 - Kinetics of Phase Transformations 1) Phase transformation 

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Phase transformation are not instantaneous, a change in phase requires a change in composition, crystal structure and/or the number of phases present. This can be achieved by rearrangement of atoms (often via diffusion) which requires a finite amount of time. Microstructures characterised by equilibrium phase diagrams are obtained at extremely slow change in temperatures. → State of equilibrium is maintained at all times. Phase diagrams does not reflect the time required for the equilibrium microstructures take to develop. Under non equilibrium conditions → resultant microstructure depends of the rate of heating/cooling and the actual temp. which phase transformation occurs. These factors also determined the rate of phase transformation. The desire microstructure can be tailored by controlling the rate (kinetics) of phase transformation.

The Driving Force for Transformation   

Thermodynamic state of system is defined by the Gibbs free energy, G, which is the measure of the internal energy and the randomness of the system. Equilibrium is a state of no spontaneous change → G is minimum. Phase transformation is possible only when changes is lower than G. → Change in G is < 0. → Final state - Initial state → Change in G < 0

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→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  

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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 show the progress of transformation with time and their final microstructure,

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TTT diagrams are derived by experimental sigmoidal curves a different temperatures. →Start and Completion Curve (Temp. vs Time axis)

Transformation in Eutectoid Steel →The transformation to pearlite form austenite:     

A redistribution of carbon atoms via diffusion is required. → the morphology (shape and size) of pearlite depends on the actual temperature of transformation. Near eutectoid temperatures, slow nucleation but fast diffusion. → Coarse pearlite → thick layers of ferrite and cementite → large interlamellar spacing. As undercooling increases, nucleation becomes faster → transformation to pearlite occurs earlier, but slow diffusion. → Fine pearlite with small interlamellar spacing. Coarse pearlite is more ductile → dislocations can move further →absorbs more energy. Fine pearlite is stronger! More dislocations → blocks one another.

→Further cooling produces bainite! → An even finer distribution of ferrite and cementite.   

However, bainite consists of extremely fine, elongated cementite particles between ferrite plates/needles. The difference in morphology is due to difference in temperature at which their transformation occur. Bainite is stable and will not transform directly to pearlite without reheating to form austenite.

→ However, when undercooling becomes so great, below MS, Martensite is formed.         

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Martensite is formed as carbon diffusion cannot occur, diffusive transformation to ferrite and cementite is suppresed. A diffusionless transformation to non-equilibrium martensite takes place Martensite has BCT (body centred tetragonal) structure, carbon atoms are trapped inside. Since carbon atoms are trapped inside, martensite has same composition as austenite. Transformation to martensite from austenite is purely due to temperatures. M50 means the temperate that 50% of austenite is transformed to Martensite. M temperatures are not fixed, but dependent on carbon content of steel. Retained austenite = left over austenite even though martensite is formed. Martensite is metastable, stable in room temperature, but upon reheating → martensite will decompose to even more stable phases of ferrite and cementite known tempered martensite. Martensite is the hardest phase in steel due to lattice distortion → the trapped carbon atom → However, it is brittle. Bainite is generally harder and stronger than pearlite due to much finer distribution.

Hypoeutectoid and Hypereutectoid Steels   

Transformation of austenite to proeutectoid phases requires the difussion of carbon atoms. Amount of proeutectoid phase that forms depends on undercooling More proeutectoid is formed when isothermal transformation are high.

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When undercooling is so large that bainite or martensite is formed, no proeutectoid.

3) Continuous Cooling Transformation Diagram (CCT)    

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Longer times and lower temperature as compared to TTT diagram. No bainite formation in constant cooling rate as all austenite would have transformed to pearlite by the time bainite transformation is possible Cooling lines are curved (over a range of temperatures) instead of a single temperature. Critical cooling rate that misses the 'nose' at which pearlite transformation begins → represents the minimum cooling rate that will avoid pearlite formation → produce only martensite at temperatures MF The opening of the start stop curves is the cooling range where there is insufficient time to complete austenite to pearlite.