Dislocations

Question 1

What are the 3 types of defects?

Answer 1

0d, Point - vacancies, inclusions
1d, Linear - dislocations
2d, Planar - grain boundaries

Question 2

What is the vacancy concentration?

Answer 2

Nv = N e ^-QV/kt
N = concentration of atomic sites, Qv = formation energy, k = Boltzmann constant, t = temp

Question 3

What is the inclusion concentration?

Answer 3

Xb = Nb/N x 100
Xb = At% of b, Nb = number of b atoms, N = number of atoms

Question 4

Define twin boundaries and plastic deformation

Answer 4

Twin boundaries - when stacking sequence in crystal is disrupted
Plastic - dislocations moving through a material

Question 5

What’s the difference between simple shear, pure shear and normal stress?

Answer 5

Simple - opposite forces acting on opposite face
Pure - forces acting on all faces (pairs in opposite directions)
Normal - object will elongate/compress in direction of stress

Question 6

What atomic displacement caused by shear becomes in equilibrium?

Answer 6

When displacement = 0, a/2 or a atoms will stay in position when shear removed
Any other and atoms move back to closest equilibrium site when shear removed

Question 7

What is the maximum shear stress that can be applied to a material?

Answer 7

G/2π

Where G = shear modulus

Question 8

Draw an edge dislocation

Answer 8

Extra 1/2 plane of atoms with tensile field below and compressive field above (when extra plane above)

Question 9

How are the strains fields of a dislocation set up and what is there importance?

Answer 9

Due to bonds being stretched or compressed
Strain fields interact with eachother which means dislocation interact with eachother - increase stress needed for movement

Question 10

Why does plastic deformation require energy?

Answer 10

Occurs when dislocations move - this involves bond breaking and reforming as half plane moves = energy needed = stress needs io be applied

Question 11

What is the critical resolves shear stress?

Answer 11

Minimum energy needed for dislocation movement

Question 12

What is the Burgers vector?

Answer 12

Describes the magnitude and direction of a dislocation

Question 13

How is a slip plane found?

Answer 13

Cross product of the Burgers vector and line direction

Question 14

Why is there no slip plane in a screw dislocation?

Answer 14

Because the Burgers vector and line direction are parallel

Question 15

Find the Burgers vector of an edge dislocation

Answer 15

Start at a point in the crystal, connect a square around the dislocation and count the atoms between corners, redraw the box on a perfect crystal (shouldn’t connect fully), distance between start and finish = Burgers vector

Question 16

What is meant by dislocation loop?

Answer 16

Set up when dislocation doesn’t end at the end of the material
Burgers vector is the same at all points in the loop

Question 17

How can the Burgers vector and line direction be used to find the type of dislocation?

Answer 17

If B perpendicular to line = pure edge
If B parallel to line = pure screw
If angle in between = mixed edge and screw

Question 18

What roles are there for dislocations?

Answer 18

Dislocations can’t terminate inside a crystal (must be at a free surface/form a loop)
Dislocations can be split into x and y components

Question 19

What is a dislocation node?

Answer 19

Location where dislocation splits/joins with other dislocations
At this point Burgers vectors must be conserved = combine b3= b2 + b1

Question 20

Describe how dislocation loops are formed

Answer 20

Dislocation pinned between two points, shear applied causing dislocation to lengthen, points still pinned until loop surrounds points and new dislocation forms between points

Question 21

How can dislocations be seen?

Answer 21

Etching attacks strain field of dislocation or by using TEM

Question 22

What affect does packing density and atom-atom spacing have on slip?

Answer 22

Plane with highest packing factor will observe slip first (easiest for dislocations to move through), Burgers vector must lie in this plane

Question 23

Define a slip system

Answer 23

Combination of symmetrically identical slip planes and easiest slip directions
Ie highest packing density planes and shortest atom-atom spacing direction

Question 24

Describe slip in BCC

Answer 24

Highest packing factor in {110} = slip plane
Shortest atom spacing in {110} plane = <111> direction
Burgers vector = 0.5<111>
Burgers magnitude = 0.5a.root 3
Slip system = {110}<1-11> -> changes due to dot of line and plane = 0 to be valid

Question 25

Describe slip in FCC

Answer 25

Highest packing factor in {111} = slip plane Shortest atom spacing in {111} plane = <110> direction Burgers vector = 0.5<110> Burgers magnitude = a/root 2 Slip system = {111}<1-10> -> changes due to dot of line and plane = 0 to be valid

Question 26

What is the strain energy causes by a dislocation?

Answer 26

E = 0.5 G.b2 | Where G = bulk shear modulus, b = Burgers vector

Question 27

What are partial dislocations and when might they occur?

Answer 27

When an atom dislocation in two steps rather than one, happens when Eperfect > Epartial1 + Epartial2 + Estacking This is energetically favourable, atom displacement is continuous

Question 28

What are the two changes that occur to a dislocation loop?

Answer 28

Expansion - when shear grows the loop | Contraction - when shear shrinks the loop

Question 29

What affect does heating have on dislocations

Answer 29

Heating causes atoms to vibrate and move which can cause dislocations to move +ve will move away from eachother, +ve and -ve towards eachother and annihilate Basis of annealing

Question 30

What is the force on a dislocation?

Answer 30

Stress x Burgers vector

Question 31

What affects the critical resolve shear stress?

Answer 31

Made of intrinsic (pierles stress) and extrinsic properties (strengthening mechanisms) Temperature adds energy to system so reduces the CRSS

Question 32

What is peierls stress?

Answer 32

Intrinsic material property, stress needed to Overcome lattice resistance to dislocation movement, Materials with higher Ym and Tm generally have higher peierls stress Stress decreases as temp increases

Question 33

Describe interstitial strengthening

Answer 33

Atoms on interstitials cause strain fields when they strain the lattice, this interacts with dislocation strain fields (if annihilate energy needed for dislocation to regain energy so can love again) Atoms can also diffuse to edge dislocation and cause it to be pinned = increased energy to move

Question 34

How can there be more than one yield point present in a material?

Answer 34

Interstitial atoms can diffuse to dislocations, when enough stress applied they move from dislocation = reduced stress needed for dislocation movement -> upper and lower yield stress present Can only occur in BCC materials

Question 35

What is Schmidt’s law and the Schmidt factor?

Answer 35

Yield only commences when stress > CRSS Factor = cosθcosλ Where θ = angle between force and slip plane, λ = angle between force and slip direction

Question 36

How can you tell which slip system is active?

Answer 36

The one that requires the least energy = the one with the highest Schmidt factor (sign irrelevant) Or use OILS rule

Question 37

Use OILS rule to find the active slip system on a FCC material with tensile axis [123]

Answer 37

[123] FCC slip direction = <110> O - move 0 to positon of Intermediate value in axis = [101] FCC slip plane = {111} - reverse sign number in position of Lowest tensile axis = (-111) Slip system = [101](-111) for tensile axis [123]

Question 38

When doesn’t work hardening occur?

Answer 38

When planar slip occurs - this is when only one slip system is active = no dislocation interaction = constant CRSS

Question 39

Describe stage 2 work hardening

Answer 39

Multiple slip planes are active due to crystals rotating = Schmidt factors becoming equal, this means dislocation stress fields interact with eachother

Question 40

What is the primary slip system?

Answer 40

The first slip system to move/act

Question 41

Describe lock and jog formation

Answer 41

Lock - edge dislocations collide + merge to form one dislocation (Burgers vector conserved), line direction cross of two combining directions, is slip plane isn’t valid = sessile Jogs - two dislocations can cause a slip step = increase dislocation area = increased energy, of jog no longer in slip plane = sessile Both cause CRSS to increase

Question 42

How many slip systems are needed in polycrystalline materials?

Answer 42

5 active systems for slip to occur

Question 43

Describe stage 3 work hardening

Answer 43

Dislocations pile up at obstacles (grain boundaries/inclusions) and extra energy is needed to overcome them Screw dislocations can move slip planes to get around the obstacle

Question 44

Explain grain size strengthening

Answer 44

Dislocations can’t move through grain boundaries, they pile up = back stresses on dislocation source = prevents dislocation creation and means CRSS is increased Smaller grains = more boundaries = more strength

Question 45

Explain precipitate hardening

Answer 45

Coherent precipitates are split by dislocations = energy requirement Incoherent precipitates cause dislocations loops to be formed around them = energy requirement Small precipitates have higher SA:volume ratio = higher strengthening

Question 46

How do you calculate the magnitude of a Burgers vector?

Answer 46

Multiply the Burgers vector by a, and then Pythagoras it all (find the magnitude of a vector)

Question 47

What’s the shortest distance a dislocation can travel?

Answer 47

Always from the edge of a corner of the cube to the centre | b = 0.5 root(2a^2)

Question 48

How are bulk and Young’s modulus related?

Answer 48

G = E/2+2u | Where u = poisons ratio

Question 49

How would you work out the stacking fault energy from a micro graph?

Answer 49

Measure the stacking fault length (D) | Then use Estack = Ga2/12D

Question 50

How can the CRSS of a crystal be calculated?

Answer 50

τ = σy.schmidt factor (cosθcosλ) σ = yield stress, τ = CRSS Replace σy with σ to get the shear felt on a crystal

Question 51

What stress is needed for dislocation generation?

Answer 51

``` τ = Gb/2r G = shear modulus, b = Burgers vector, r = radius of dislocation ```

Question 52

How is yield stress calculated?

Answer 52

σy = 2τmax Yield stress = 2.max shear Max shear = G/2π

Question 53

When working out the number of vacancies in a material, how is N worked out?

Answer 53

Number of sites/molar volume | = avagadros number.density/molar mass

Question 53

What affect does atom-atom spacing have on slip?

Answer 53

Shortest atom-atom spacing will slip first, means that line direction must be in this direction