Dislocations Flashcards
What are the 3 types of defects?
0d, Point - vacancies, inclusions
1d, Linear - dislocations
2d, Planar - grain boundaries
What is the vacancy concentration?
Nv = N e ^-QV/kt N = concentration of atomic sites, Qv = formation energy, k = Boltzmann constant, t = temp
What is the inclusion concentration?
Xb = Nb/N x 100 Xb = At% of b, Nb = number of b atoms, N = number of atoms
Define twin boundaries and plastic deformation
Twin boundaries - when stacking sequence in crystal is disrupted
Plastic - dislocations moving through a material
What’s the difference between simple shear, pure shear and normal stress?
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
What atomic displacement caused by shear becomes in equilibrium?
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
What is the maximum shear stress that can be applied to a material?
G/2π
Where G = shear modulus
Draw an edge dislocation
Extra 1/2 plane of atoms with tensile field below and compressive field above (when extra plane above)
How are the strains fields of a dislocation set up and what is there importance?
Due to bonds being stretched or compressed
Strain fields interact with eachother which means dislocation interact with eachother - increase stress needed for movement
Why does plastic deformation require energy?
Occurs when dislocations move - this involves bond breaking and reforming as half plane moves = energy needed = stress needs io be applied
What is the critical resolves shear stress?
Minimum energy needed for dislocation movement
What is the Burgers vector?
Describes the magnitude and direction of a dislocation
How is a slip plane found?
Cross product of the Burgers vector and line direction
Why is there no slip plane in a screw dislocation?
Because the Burgers vector and line direction are parallel
Find the Burgers vector of an edge dislocation
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
What is meant by dislocation loop?
Set up when dislocation doesn’t end at the end of the material
Burgers vector is the same at all points in the loop
How can the Burgers vector and line direction be used to find the type of dislocation?
If B perpendicular to line = pure edge
If B parallel to line = pure screw
If angle in between = mixed edge and screw
What roles are there for dislocations?
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
What is a dislocation node?
Location where dislocation splits/joins with other dislocations
At this point Burgers vectors must be conserved = combine b3= b2 + b1
Describe how dislocation loops are formed
Dislocation pinned between two points, shear applied causing dislocation to lengthen, points still pinned until loop surrounds points and new dislocation forms between points
How can dislocations be seen?
Etching attacks strain field of dislocation or by using TEM
What affect does packing density and atom-atom spacing have on slip?
Plane with highest packing factor will observe slip first (easiest for dislocations to move through), Burgers vector must lie in this plane
Define a slip system
Combination of symmetrically identical slip planes and easiest slip directions
Ie highest packing density planes and shortest atom-atom spacing direction
Describe slip in BCC
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
Describe slip in FCC
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
What is the strain energy causes by a dislocation?
E = 0.5 G.b2
Where G = bulk shear modulus, b = Burgers vector
What are partial dislocations and when might they occur?
When an atom dislocation in two steps rather than one, happens when
Eperfect > Epartial1 + Epartial2 + Estacking
This is energetically favourable, atom displacement is continuous
What are the two changes that occur to a dislocation loop?
Expansion - when shear grows the loop
Contraction - when shear shrinks the loop
What affect does heating have on dislocations
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
What is the force on a dislocation?
Stress x Burgers vector
What affects the critical resolve shear stress?
Made of intrinsic (pierles stress) and extrinsic properties (strengthening mechanisms)
Temperature adds energy to system so reduces the CRSS
What is peierls stress?
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
Describe interstitial strengthening
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
How can there be more than one yield point present in a material?
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
What is Schmidt’s law and the Schmidt factor?
Yield only commences when stress > CRSS
Factor = cosθcosλ
Where θ = angle between force and slip plane, λ = angle between force and slip direction
How can you tell which slip system is active?
The one that requires the least energy = the one with the highest Schmidt factor (sign irrelevant)
Or use OILS rule
Use OILS rule to find the active slip system on a FCC material with tensile axis [123]
[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 for tensile axis [123]
When doesn’t work hardening occur?
When planar slip occurs - this is when only one slip system is active = no dislocation interaction = constant CRSS
Describe stage 2 work hardening
Multiple slip planes are active due to crystals rotating = Schmidt factors becoming equal, this means dislocation stress fields interact with eachother
What is the primary slip system?
The first slip system to move/act
Describe lock and jog formation
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
How many slip systems are needed in polycrystalline materials?
5 active systems for slip to occur
Describe stage 3 work hardening
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
Explain grain size strengthening
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
Explain precipitate hardening
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
How do you calculate the magnitude of a Burgers vector?
Multiply the Burgers vector by a, and then Pythagoras it all (find the magnitude of a vector)
What’s the shortest distance a dislocation can travel?
Always from the edge of a corner of the cube to the centre
b = 0.5 root(2a^2)
How are bulk and Young’s modulus related?
G = E/2+2u
Where u = poisons ratio
How would you work out the stacking fault energy from a micro graph?
Measure the stacking fault length (D)
Then use Estack = Ga2/12D
How can the CRSS of a crystal be calculated?
τ = σy.schmidt factor (cosθcosλ)
σ = yield stress, τ = CRSS
Replace σy with σ to get the shear felt on a crystal
What stress is needed for dislocation generation?
τ = Gb/2r G = shear modulus, b = Burgers vector, r = radius of dislocation
How is yield stress calculated?
σy = 2τmax
Yield stress = 2.max shear
Max shear = G/2π
When working out the number of vacancies in a material, how is N worked out?
Number of sites/molar volume
= avagadros number.density/molar mass
What affect does atom-atom spacing have on slip?
Shortest atom-atom spacing will slip first, means that line direction must be in this direction
