LEC 1

- Break down into sub assembly if needed-

LEC 2

6 main material classifications:

- Metals/Alloys- Ceramics- Polymers- Hybrids- Glasses- Elastomers

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-

ELASTICITY- All mats are elastic (have bulk modulus)- Only solids have non zero Youngs / shear modulus- Solids usually have large moduli (elastic strains are

small)- NO MATERIAL is incompressible- Isotropic means only 2 elastic constants- Elastic strains are recoverable and store energy (can

find from area under graph) - Most common mats are approx linear- High modulus applications incude: structural members, con rods, springs, gears, machinery- Low modulus include: skateboard decks, other springs, vaultingpole, seat cushions-

3 METHODS OF MEASURING ELASTIC MODULI

UNUSUAL ELASTIC BEHAVIOUR

Rubber – E at room temp = 0.1GPA, E at -196C = 2GBA. Diffrence in bonds, minor bonds are T sensitive, above Tg minor bonds melt at E lowers.

- No cross linking; Tg = Tm

- Light crosslinking, Tg -> major reduction in Modulus on HEATING- Moderatre cross linking, Tg -> becomes leathery- Heavey cross linking; Tg-> little influence on properties- Complete cross-linking; No Tg

COMP MATERISL

- E perp to fibers can be up to 20x less than E parallel

- Parallel ε is ~ same from both mats

- - adds in series- Perp ε is VERY DIFF .

- - adds in parallel- In theory, comps can access any value in range of

mats- Practical range is Vf = 20-65%

- 9 eqn, 81 unkowns- Symmetry reduces this to 21 unkowns in

gen case- Orthotropic (i.e. 3 mutally perpen axes)

reduce to 9 elastic constants

- We can calc the value of ANY ELASTIC CONSTANTS IN ANY DIRECTION by using tensor transformation

- -

EXAMPLE:

SUMMARY:

- Some mats high nigh non-lin elastic properties, affects FEA, can be advantage e.g. apply constant force over large range of movement

- Some mats have elastic prop that change majorly with small change in temp- Some mats have high anistropic elastic props, e.g. single crystals, textured alloys.

o Can be adv or disadvo Can be modified in comps by fibre lay up but at reduced strength and modo 2D layups are simple but still have low modulus in 3rd D (transverse to lamella)o Comp modulus is a sens fn of fibre vol fraction.

WEEK 2:

- Ideal bong strength of homogeneous solid; σ ~ E/15- In reality, much lower Why? Defects and flaws- In metals, DEFECTS ARE DISLOCATIONS- Can be describes as extr ahalf plane of atoms inserted in structure, leading to LINEAR

DEFECT at base of extra h plane- We define the BURGERS VECTOR or SLIP VECTOR b, as the closure errror around the

dislocation, or distance moved in single dislocation jump.

- L = length, G = Shear modulus, b- length of Burgers vector, v = Poissons ratio.- Note, diclocation energy is proportional to burgers vector squared- Means dislocations will for most easily in DENSELY PACKED planes of atoms, where b Is small- Structures with large unit cells will have very large energies, therefore fewer dislocations.

(Major reason why ceramics do not plastically deform)- Line tension T associated with curved dislocations. i.e. DISCLATIONS WILL TRY TO REMAIN

STRAIGHT- Annealed metal typically has 103-= cm of dislocation line per cm3

How do dislocations move?

- Respone to shear stress ONLY- Apllies axiel force- Arbitary shear plane- Sher force is Fsin(theta)

Ds

- We can use dislocation analysis to determine relo between yield strength in tension, and yield strength in shear

- Dislocation facilitate plastic deformation in matelas bv instead of having to shear entire plane of bonds, same net effect can be achieved by dislocation hopping

- This way breaks one row of bonds at a time and allows plastic def at lower stress.

- The dislocation will move if the shear stress τ > f /b where b= slip vector

How do we stop them from moving?

- Lattic resistance force fi – (intrincis)- Disloc are surrounded by ε field, which interact with certain microstruc features- So if mincro struc can be manipulated, dislocs can be blocked

Increasing individual crystal strength – Solid soln hardening

- In a hard-sphere description, ZN atoms are slight bigger than Cu atoms, so slip plane is not uniform.

- Easy motion for disloc RELIES on slip-place being uniform/smooth. The solute atoms will therefore procude additional resistance force that adds to intrinsic lattice resistance. (First eqn)

- Alpha? (omitted in slide) Inversely proportional to mean spacing of solute atoms on slip plane., eqn 2. C – solute concentration

- Size of constant depends on whether solute in another metal dissolving substitionally (i.e. replacing host atoms) or non0metal dissolving interstitally (i.e. in spaces between atoms).

- Interstital atoms are most effective, partly bc they migate to trained regions around disloc and LOCK them.

- Very effective strengthening mech per unit concentraition HOWEVER solubility of interstitial elements usually very low before new phases begain to appear.

- Effectiveness of substitutional solutes depends on size compared with solvent and whetehr they have similar electronic configs

Precipitation and dispersion strengthening

- Regardkess wheter fored by precititation from super sat soln OR by dispersion of 2nd phase- Presence of obstacles inside metal crystals obstructs dislocation passage- Dislocations interact with ε field rather than precipitates- Although dispersed particles are incoherent with matrix phase and disloc interact directly

with them- Disloc is forces to curve between obstacles. - Line tention increases requiring increased shear stress.- Yield criterion, F > 2T/L- Provides additional res force due to obstables given by eqns above. - IT IS BEST TO HAVE STRONG CLOSLEY SPACE PARTICLES.

Work Hardening

- A metal/alloy that is plastic deformed to a certain stress level, adopts that stress as its new yield.

- If subsequently loaded to any stress at which it was plastically deform, it will deform only elastically.

-- Recall annealed metal has low disloc density, while CW metal has far greater- Greater number of dislocs DO NOT make slip easier as slip planes interact with each other,

several cases:o Disloc on intersecting slip plans PIN each other if they meet. DOESN’T prevent motion

but now requires much greater forceo Disloc on parallel slip attract or repel due to ε fields around

On diff slip plans, disloc align themselves, energy of crustal can be reduces by cancellation of ε fields

On same, like dislocs repec bc overlap of ε fields is energetically unfav.

- As a result, disloc in mats form into dense tangles, usually subdiving crystals into much smaller regions.

- Within regions, much harder for disloc to move bc of repulsive forces bw dislocations- As a result becomes increasingly hard to cause slip and work hardening occurs- Total yield strength of SINGLE CRYSTAL given by eqn above

Polycrystalline metals

S

Combining

- Combining exp for polycrys mat with infinite g size, and hallpatch eqn we obtain an expression for total yield strength of poly mat

- Particulary metals + alloys

- Ceramics contain some dislocations- Become active at very high temps, usually immobile at r temp- In tension, ceramics fail rapidaly + immobile- In comprasssion, failure begains locally by micro-craking- Preventing m-cracking relies on putting obstacles in the way of micro-cracks (instead of

dislocs)

- As with metals, strength defined as onset of plasticity- Plastic flow in poltmeers occure by relative motion of polymer chains w/ little disruption by

FAILURE OF van der waals bonds and cross linkinge- STRONGLY time dependant- Strenght is GREATLY increased by cross-linking- Obstacles are also effective (e.g. fillers)

- Steels canbe made very strong via heat treatment and alloyin- This can effect forming machining welding and toughess properties- HSLA steels are desgined to avoid this by compression of small alloying additions and special

processing

-

-

Grain size effects – Mn in soln inhibits grain growth. V, Nb etc carbines in Austenite inhibit growth

- Some carbides dissolve during high T processing- Reform during cooling and give precipitation hardening effect, total effect in figure aboce

PLASTICITY – True strain and Stress-

- Definitiions are flawed due to STRESS not taking account of changing cross section area

- Remember Volume is conserved, in tension doubling length gives 100% strain, but in compression 100% strain makes sample disspear. There for STRAIN is flawed too

- Tension and compression sides now match on curve

INTERNAL WORK OF PLASTIC DEFORMATION PER UNIT VOL

- Test machine strates/uses energy on sample- Consider energy dissipation during plastic deformation:

--- Variables include tool geom, temo, strain strain, flow stress- S-S state of mat in deformation zone is too complex to model analytically- Assumptions that can be made to SIMPLIFY:

o Plastic strain is large, elastic strain ~ 0o Assume NO WORK HARDENING (adequate for hot, poor for cold working)o Assume uniform and homogeneous metal (poor for cast feed and latter stages of

CW)- Metal working is muti-dimension optimisation problem, we want:

o Minimum force per unit deformationo High deformation rates (high strain, high prod rates)o No fracture of work pieceo Nminimum reducant deformation (i.e. defor take makes no contributions to final

shape)o Min friction losses

- Many of these work gainst each other / mutally exclusive

- eo- Metalworking theory requies:

o Static Equilibrium of force eqno Relo between stresss and straino Yielding criterion e.g. Von Mises

- Various approaches, most comprehensive is finite element analysis, an appromimation is Uniform Deformation Energy method

-

NECKING AND PLASTIC INSTABILITY- Normal S-S curvs of ductile mats show

DECREASE in stress past UTS- Part of this can be corrected by using

TRUE S-S.- However part of it persist due to

LOCALISED DEFORMATION/ NECKING due to phenomenon known as PLASTIC INSTABILITY

- Once a neck is visible, most of plastic flow is confined to it bc stress is higher here (leading to rapid failure)

- If work hardening is less than effects of reduces A, the neck is UNSTABLE (grows)-

- Critical point is when Asigma = F = constant for whole material

-- When considering this in NORMAL S-S, unstable necking begains at UTS and causes failure

as expecte

WEEK 3 PROP OF MATERIALS + FRACTURE TOUGHNESS

FRACTURE TOUGHNESS

Failure in Service

- Mechanical Failutreo General Yieldingo Fast Fractureo Fatigueo Creep

- Corrosion + Oxidation- Wear and Abrasion

These arnt necessary independent:

- Degredation mechanisms (wear corrosion etc) can reduce loaracking)d bearing cross section of componenent and therefore induce mechanical failure

- Converwsely, pressense of high stress can accelerate certain corrosions (e.g. stress corrosion)

Many imcongrous behaciers, e.g. Why is Untempered Marensitic steel bittle under impact when tensile strength = 2000GPA? Due to fracture toughness

Fractuve toughness is the property govering a materials susceptibility to fast fracture

FAST FRACTURE IS HE CATASTROPHIC gROWth OF Pre EXISITING CRAKS/FLAS IN COMPONENET

Crack growth can occur at speed of sound in material, virtually impossible to crack to be arrested once propgating.

Fast fracture is important bc:

- Often occurns in large structures- Very rapid- Can cause massive damage- Increased use of mats susceptible to f fracture in modern engineering

- System would like to be in minimum energy state- Fracture is way to release stored energy- For e.g. a full boloon, introducing flaw causes fast fracture AND

o Whilist table at los pressure, a pre-existing flaw can propagate at high pressure (high stress)

o Note stored energy is released as kinestic energy, sound and heat. o Not that also failure was independent on both the existence of flaw AND the applied

stress

- TO propagate, crack MUST TO WORK on structure (i.e. assosicated energy cost)- If it costs more energy to advance crack than the strain energy potentially recovered, the

crack will not propagate. - In this case, crack is NON-CRITICAL- Once energy gain exceeds energy cost, CRITICAL.

Consider a plate containing crack loading in tension, and relate to diagram avoce.

DEFINITON OF FRACTURE TOUGHNESS

- Eqn is σ(πa)0.5 = (EG)0.5

- LHS = Stress intensity (object + application properties)– K- RHS = Critical stress intensity (material properties) Kc

- Fast fracture occurs when σ(πa)0.5=K>Kc=(EGc)0.5

- Critical combiniatio nof stress and crack length ONLY DEPNDS on Youngs mod and Gc (toughness)

Remember

- Tensinle strengths or ceramics are low due to low fracture toughness AND processing flaws- Quenched steels become brittle due to Gc being reduces- Glass fibres are strong as they cannot contain significant flaws- Large structures are weaker due to flaws from assmelby

-

- We have K1C, K11C, K111c respectiviley, and K1<k11<k111

- Therefore K1C gives safest predictions and also takes into account of mode changing

- BC internal cack is like 2 smaller cracks facing opposite direction, we take internal crack length as 2a.

EXAMPLE

i) Lmax = 100,000/2 (2 plates) = 0.49 MNσmax = Lmax/A = 108.9 Mpa.This is much less than yield stress of 900Mpa therefore no general yielding

ii) F fracture occurs when σ (π a)0.5 > K1C

σc=kc/(πa)0.5 = 40E6/ (π*0.025)0.5

142.4MPA > 108.9Since critical σ is > than L (108.9 MPA) hook can still upport up to 100T (no f frac)’

iii) Safety factor, S = critical stress / load, = 142.7/108.9 = 1.31iv) For S – 3, σm=142.7/3 = 47.6Mpa

Lmax=σm*A = 47.6E6-0.0045 = 0.214MN PER PLATE

To calculate how large crack must grow before it causes fast fracture at Lmax

- Let σ = σm = 108.9Mpa- Crack will propagate when σ(πa)0.5 = K1c

- Solve for a, we get 0.043mm- Meaning of Gc – energy cost of creating a unit projected area e.g. 1m2

- Several mechanisms add to this cost, e.g. surface energy- True surface area > projected surface area due to roughness- Each new cracked region produces new surface area and hence costs energy- Another contributor is the need for crack to do work against microstructure.-For e.g Plastic deformation requires lots of work, relative size of contributions to

Gc allow us to distinguish bw 2 extreme cases, Ductile tearing and Brittle fracture.

- All mats are somewhere on this spectrum- Fracture surface of ductile mats show large

amounts of plastic deformation- But in f fracture we talk about failure below

yield stress. How?- Cracks act as a stress CONCENTRATION- Local stress is approx. by 1st eqn, where r is

distance ahead of crack tip assuming semi elliptical crack.

- Local stress will excees yield strength of aductile mat in a region BOUNDED BY ry

- Failure usually begains adhjacent to flaws- Some work hardening take place and crack

blunting due to void formation- These ensure crack propagation isslowed down and requires large amount of energy

BRITTLE FRACTURE

- Little/no plastic defo (low fracture toughness)- σlocal now exceeds BOND STRENGTH between atoms - 2 Types

o Cleavage in which atomically flat fracture planes are formed – leads to fractures with very smooth/flat surfaces. Stress conc ahead of crack tip exceeds theoretical strength. In rrality, quite common in certain ytpes of minerals, but RARE in engineering materaisl. Some steels and hcp metals at low temps do this

o Conchoidal (shell like) in which concentric riges form on fracture surface. Non-crystallyne usually therefore no plans of metals to park

- No plastif def occurs therefore crack can propagate at speed of sound in material.- Creation of new surface is the ONLY ENERGY cost to resist craking- In polycrystal mats (most metal and ceramics) britlle facture propagates from graint to g and

takes slightly diff path in each. Size of crack expands as it propagates and leaves distinctive features on face (chevron marks)

- Chevron markes often point back to fracture origin-

- Some ductile mats remain ductain over full range of temps (e.g copper at 4K)

- Some mats undergo ductile to brittle trans as temp is reduces

- This had lead to steels in shpis breaking, ski lifts failing, etc

- We can study transition via impact test, and plot absorbed energy as a function

of room temp, and look for transition

- 1) Lower shelf energy- 2) Trainsition temp- 3) Uppershelf energy

- Transition temp is definted as temp at where absorbed energy is midway bw upper and lower shelf

- We can see mat B high much higher transition temp than A, and is not suitable for use at low temp

- FRACTURED SAMPOLES ARE ALSO INSTRUCTVE- Ductile mats have fibrous (rough and dark) fractures and cross sectional area is deformed- Brittle sample has pale non fibrous fracture and area does not change.remains square- Usually lots of cleavage fracture in brittle zone

STEELS

- Majpr influence on transformation is Carbon conten- 3 Major changes when increasing carbon content

o Upper shelf energy decreaseso Transition temp increaseo Transition becomes spread out over grater range

- Only SOME steels are susceptible to this effect (usually strongest of the unaklloyed steels)- To aboud low T britltlness, in addition to using lowest C, we can use steels with V SMALL

GRAIN SIZES- High alloyed steels often immune from transformation, same as austentic and ferritic

stainless steels- Impact energy and Kc are closely related

MICROSTRUCTUAL STRATEGIES

- G size reduction has similar benefit on Kc as it does with yield strength- Fabrication techniques cause anisotropy of inclusions, leads to Kc variation of up to 50%

depending on direction.- Often detrimental in service (e.g. rolled steel plates, fracture toughness is diff in directions,

need to be considered in orientation)- 2 phase + comp mats oftens have enhanced fracture toughness due to other meachinisms.

Recall rubre reinforced comps are usually much tougher than polymers and ceramins from which they are made

- 2 major reasons,o Ceramic fibres are TOO THIN to contain significant flawso They act as crack stoppers/deflrectors (crack deflection) note does not work for

cracks along fibres which readly lead to splitting (de-lamination)- Rubber toughnes polymers - tougher than parent material due to crack bridging- Partially stabilised zirconia – ceramic mat with highest fracture toughnes. Very complex

microstructure to but to understand the mechanism we only need to consider it as a high volume fraction of tiny precipitates of the tetragonal phase of zirconia embedded withing other zirconia phases. In stress field of advancing crack, tetra phase undergoes martensitic trans to monoclinic phase which it 5% larger in vol. This swlling of precips causes crack closing forces to be exerted on crack. KNOWN AS TRANSFORMATION TOUGHENING.

WEEEK 4 FATIGUES OF MATS

Failure can occure not only when σ > σy and Kic>σ root π a but also if σm > σendurance

- In most engineering cases, failure if by slow crack growth – i.e. fatigue.

- Image shoes fractured face of fatigued railway axle

3 Types of Fatigue

1) Fatigure of uncracked components – No pre-existing cracks, initiation controlled fracture E.g. most small components like gudgeon pins, gear teech, crank shafts. This can lead to:

a. High Cycle fatigue. Failure > 104 cycles to fracture. E.g. all rotating / vibrating sysmtel

like wheel.s engine componenetsb. Low cycle Fatigue. Failure < 104 e.g core components of nuclear reactors, turbine

components, any component subject to occasional overload2) Fatigue of cracked structres – cracks pre0exists, propgration controlled fracture e.g. large

structures, particulary containing weld, bridges, ships etc

Fatigue Testing –

- Stress range Δ σ = σmax – σ min- Mean stress, take average of stress- Stress amplitures – σa=(σ max – σ min) /2- Many loading modes, e.g. Tension Tension, Tenstion Compression, Rotation Bending (easiest

for many cycles at high frequency.- Note that there is extreme sensitivity to stress concentration even at level of minor surface

imperfections E.g. hot rolled streel with 700MPa UTS has only 0.55 fatigue life of the same steel with a polished surface

- There are also several surface treatments that can greatly enhance fatigue life. These include shot peening, carburising, and nitriding. All include residual compressive stresses at surface (Any applied tensile stress must first overcome residual stress)

- F fracture of brottle mats is probabilistic- Usually necessary for most matls as distribution of failure strengths is so narrow- This cases to be the case uner cyclic loading conditions- Even mats with very well defined fracture strengths for a single stress cycle will have fatigue

lifetimes distributed over a very wide band

- For E.h. 300 torsion bar springs loaded identically, mea life is 134,000 cycles but standard deviation is 37,000 from this SMALL smaple. The span of first to fail was 5 times less than longest surviving

- Manufacturers only often quote mean fatigue props, where as for safe deisgn, entine distribution needs to be examined

Low Stress - > High Cycle fatigue

1) We can identiy these failures become component was able to survive until only a small fraction of cross area was uncracked

2) The effect of a stress conc is to make crack propagate more rapidaly at surface than centre due to inc surface stress

3) Reversed bending and rotation bending lead to the initiation of multiple cracks

4) In rotational bending, the crack normal processes against the direction of

rotation, allowing identificant of loading situation.

High Stresss - > Low Cycle Fatigue

Coomapred with previous we can see

1) At high load uncracked area just prior to failure is a large proportion of cross sectional area

2) Multiple Initiation points are more likely3) In torsion cracks are more definiate and occur at

45oC to torsion axis in absence of stress conc/

FATIGUE EQNS

1) Uncrack componentsa. HighCycle Fatigue

i. Zero Mean stressBasquins Law – Δ σ (Nf)a=C1 where a is constant usually between 1/8 and 1/15 and C is a material constantCan only use of ZERO MEAN STRESS ONLYConstnats can be calc from any 2 known S, N points and used to predict fatigue lifetimes at sresses between 2 known points (or beyond with caution)

ii. Non-Zero Mean StressGoodmans Rule - Δ σ m = Δ σ 0 (1-(|σm|/UTS)Where Δ σ 0 = stress range to give life Nf at zero mean stress σm=mean stressΔ σ m = stress range must be REDUCE to in order to still survie same Nf cycles at non zero mean stress- Stress in one dir is closed to yield than in other

b. Low Cycle Fatigue Coffin-Manson Law – Δ ε pl Nf

b = C2

In this same σ =/= to ε E (i.e there is plastic ε which dominates fatigue life) B and C2 are material constants with b ~ +0.5 - 0.6

c. Non-Uniform stress cyclesMost common in real world, we need statistic approach

At every stress range there is a fatigue lifetime.

Relies on assumptions thatEach stress cycle no matter how small is doing damageDamage from each stress regime is simply additiveThere is no’memory’ in material (i.e. order of stresses doesnt effect)

=

2) Cracked Components

Note Δ K = f(N) bc crack size increases with every cycle..

Note long steady state region (where A, m are mat constants and m ~ 4)

We can usually estimate a (initial crack length) from NDT results. We can calculate final a before f fractire from the f fracture criterion

Therefore we can estimate safe number of cycles from intergration

Same mechanisms operate regardless of whether crack is originates as slip line intrusion or from manufacturing flaw.

Clean material – Local yielding creates new surface at crack tip

- Is incremental (hence micro beach marks)2 Phase or dirty material – enhances yielding due to stress conc

- Voids form ahead of creak- Growth much faster or at lower applied stress.

WEEK 5 MORE PROP OF MATS

CREEP – ELEVATED TEMP EFFECT OF MAT PROPS

- Recall heat is kinetic energy of atoms in system- Due to rigid framework of solids, atoms vibrate about the mean position- Interactions between atoms lead to wavelike bhavior- These lattice vibrations increase with temp and leads to greate mobement / diffusion of

atoms, and electrons in solids are also able to be excited into higher energy states- DEFINITION: Creep is slow continuous deformation

usually ending in failure/rupture- Time and temp are now functions of material properties

- Thereofor definition of yielding becomes blurred at high temps- Functionally we write intstead of the low temp approx. that we are accustomed to using- This behaviour is called CREP or VICRO-ELASTIC DEFORMATION

TEMP SCALE

- Use K- Observations;

o Lead creeps at room temp (300K) and melts at 600Ko Al alloys creep at >373K and mekt at ~900K

- Rule of thumbo Mettallic mats creep at 0.3 – 0.4 Tmaxo Ceramic mats creep at 0.4 – 0.5 Tmax

- Polymers do not have melting temp, instead have glass transition temp’

CREEP TESTING

- creep is multi dim, i.e. ε is function of stress, temp AND time.

- In real wor, temp is determined by thermos dynamic considerations e.g. engine efficiency increases with temp

- Stress is usually determined by design and service conditions e.g. gas pressures

- Therefore for given T, we can measure ε vs time

3 Stages

1) Initial, rpaid, sometimes added as invetible effect in design calcs2) Steady state, constant, dominates creep life3) Accelerating, followed by rupter. Creep damage begins to occur, voids formed in g

boundaries, and lead to failure (creep rupture)- Remember we are taking a 1D slice. Changing T and stress will change graph.- Note increasing stress or T shortens creep lifetimes, increases slop of all staes, increases

total creep stain, and stage 2 becomes less distinct.

EQUATIONS OF CREEP

Stage 1) Trainsient Creep (rate not constant)

- ε=βt1/3

- Valid for many metallic systems, but expononent differs in non-metallic system. - ε=(σ / E) + βtα

- More general form- Decreasing creep rate is due to exhaustion of creep mechanism OR dynamic recovery

process

Statge 2) Steady State Creep

- εss = B σ n

- Power law behaviour, n usually 3-8 - At low stresses n~1 - Strongly suggests 2mechanisms can operate, one at very low stresses and another over a

wider stress srange.- If we try to extrapolate low stresses form high stress data, we cross this boundary and this

leads to underestimates of ε rates or overestiemates of time till failure

ACTIVATION ENERGY

- R is universal gast const, T is ABSOLUTE temp, Q is creep Activation Energy- The simlilatieies bw numberical values of activation energy and self-diffusion provides the

key to creep mecahnisms.- Diffusion becomes appreciable at ~0.3Tmax, which is why creep in metals begins near there

DISLOCATIONS

- Stage 1 Creep

Arises from thermally activated dislocation glide. Stage 1 creep rate decreases with time bc dislocations eventually meet obstacles too big for thermally activated glide, and the supply of mobile dislocations is gradually used up by work hardening processes (i.e. thermally activated glide can overcome things like intrinsic lattic res, small ε fields, vacencies, but are not able to overwith without an increase in the stress)

- Stage 2

Consider a dislocation pinned by large precipitate. There Is a balance between glide for tb per unit length, and f the reaction force of precipitate. Dislocs not on the mid plane of precipitate (most_ also have component force of perpendicular to the slip plane, equal to tbtan(theta). This is known as the CLIMB FORCE and tried to push dislocation out of glide path.

Dislocations cannot glide in this dir, but can climb if atoms diffuse away from half plane.

Instead of being driven by conc gradient, climb is driven by stored mechanical energy in pinned dislocation. After sufficient climb, disloc is free to glide again.

Therefore stage 2 creep is linear bc work hardening (pinning) and recovery (unpinning) mechanisms are balance. The rate increases as stress increases bc climb force increases. Increases with temp bc diffusion rate increases

PURE DIFFUSIONAL MECHANISMS

- Remember creep vs stress has 2 regions- At low stresses, climb force is insufficient overcome most obstacles- This is pure diffusional creep. If diffusion of atoms can occur such that crystals bcome

narrower and longer, the stress at a constant load will be reducddes.- At T>0.5tmax this occurs by BULK DIFFUSION, and at 0.3-0.5Tmas occurs by grain boundary

and dislocation core diffusion

-

POLYMerS:

- Ciscoelastic solid – εss = C σ e-Q/RT

- Viscosity n=σ/3ε - Overall n=(1/3C)e+Q/RT

- Mot stpolymres don’t have well defined melting temp.- Above transition temp, mats show rubber like bhavioe (elastomers) or viscous liequid

behaviors (thermoplastics)- Viscous-liquid behaviour is more commong and governed by Newtonian-viscous flow, a type

of creep- Q is activation energy, energy req to overcome ptentiall energy barrier bw atoms in lattice of

crustalline solid.- In polumers, relates to res of long branched polymer chains to sliding over each other.

PRACTICAL COMPONENTS

- Components that are subjected to high temps in service must be manufactured to keep creep in mind.

- Components loaded below yield will fail over time due to either creep or shape deformation- Components relying on elasticity for tightness will loosen over time. For example, we have a

bolt tightened to stress i. Total ε is constant and initially all elastic. As creep takes place, creep ε gradually replaces initial elastic strain

- Consider bolts in steam turbine. IF we decide we need to tighten every time clamping stress has relacted to half initial value, we can use eqn above right.

REPRESENTATION OF CREEP”

- Creep is 4D ε = f(σ, T, t) by creeo rupture diagrams usally are tr=f(σ)T, usful but limited- Assumes ε is not important, only time to failure is

LARSONS MILLAR CURVES

- Takes a rupture diagram- For constant t plot a stress vs T diagram- Make constant stress polt logtvs 1/T- Extrapolate to find 1/T = 0 to find c- Cinstuct a plot of stress vs LM paremeter- P=TA(logt+c)- Trues to combine time and temp into single parameter (easier to graph as multiple

combinations will have same constant)

EXAMPLE: Consider alloy loaded to 900MPA, how long till rupture at 600C?

σ=900, P = 46000 from figure

46000=(1.8T+492)(logt+25)

logt=29.26

t=18197h

MATS RES TO CREEP

- Metls and ceramicso Reduced Diffusion rate

Choose high Tm (reduces T/Tm)o Obstructions to dislocations

Solid solns Precipitaes

o Intrinic or lattic res to glide Covalent bonding Intermetallic compoints

- Polymerso Cross longing of polymer chains raises temp/ slows creepo High melting point addictive also reduces creep rates

Creep is not always detrimaentaql, it is exploited extensively in mat processing such as- Metal forming

Ceramics- Polymer shapingRolling forging- Hot presing- Injection moulding

WEEK 12 WELDING

- Requires 3 tihingso Source of intense localied heato Source of metal to melt and form the oin, and most often a filler mato A means of protecting the hot metal from burning or otherwise reaction with

surrounds dueing the joining process