Plastic Deformation of Materials Flashcards
What convention is used for finding a Burgers vector of a dislocation?
FSRH
Finish, start, right hand.
What direction is the Burgers vector for a screw dislocation?
Parallel or antiparallel to the line direction.
What are screw dislocations defined as either?
Left or right handed screws.
When is a screw dislocation left or right handed?
It is right handed when the line direction and Burgers vector are parallel and left handed when antiparallel.
How can we treat mixed dislocations for stress analysis?
As equivalent to the sum of edge and screw components independently.
Why can we treat mixed dislocations as a sum of edge and screw components?
The stress fields around each are orthogonal (have no components in common).
Sketch a dislocation loop with the Burgers vector in the slip plane (shear loop) and include views down different directions.
Check slide 8
Can dislocations ever terminate in perfect crystals?
No. They will always form closed loops, junctions or terminate at free surfaces or grain boundaries.
Sketch a pure edge dislocation loop.
Check slide 8
How can dislocations be imaged using TEM?
Around the dislocation, the strain field bends the lattice planes which causes them to no longer satisfy Bragg condition, thus they appear dark in a bright fields image
Describe the long range stress field around a dislocation.
Can be modelled using linear elasticity.
Diffuse strain energy stored in a large volume.
No variation with core position relative to atomic structure.
Describe the core structure of a dislocation.
Strains too great to be treated by linear elasticity.
Intense strain energy stored in small volume.
May have large fluctuations of energy with core position.
How does the elastic field around a dislocation affect its interactions within a material?
The elastic field controls how dislocations react to distant microstructure features with their own elastic stress fields such as: Other dislocations Mis-fitting precipitates Mis-fitting solute atoms Twins Applied stresses
Describe how the core structure of a dislocation affects its interactions within a material.
The core structure controls how the dislocation interacts with the crystal lattice and atomic structure:
Dislocation dissociation
Core spreading
Roughly how big is the core of a dislocation considered to be?
The radius is approximately 4 Burgers vectors which is roughly 1nm
States the stresses for the stress tensor in each direction.
Check slide 18
Derive an expression for the stain field of a straight screw dislocation.
Check slide 19
Derive an expression for the stress field of a straight screw dislocation.
Check slide 20
Describe the stress and strain fields around a straight screw dislocation.
Both fields are pure shear.
The fields have radial symmetry
The stresses and strains α 1/r
(Since infinite stresses cannot exist in a real material, the assumption of linear elasticity breakdown at r(0), ≈1nm)
State expressions for the stress field around a straight edge dislocation.
Check slide 21
State how you would derive a set of expressions for the stress field around a straight edge dislocation.
Take a hollow cylinder along the z axis of the dislocation.
Cut on a plane parallel to the z-axis
Displace the free surface LMNO by b in the x-direction
This situation is plane strain so no displacements in the z-direction,
Describe the stress and strain fields around a straight edge dislocation
The stress and strain fields are not pure shear.
The stresses and strains α 1/r
(Since infinite stresses cannot exist in a real material, the assumption of linear elasticity breakdown at r(0), ≈1nm)
Derive an expression for the strain energy around a screw dislocation must know.
Check slide 23
Derive an expression for the strain energy around an edge dislocation.
Check slide 24
Link the expressions for the strain energy around an edge dislocation with that of a screw.
E(edge) = E(screw)/(1-nu) ≈1.4E(screw)
How to find the core energy of a dislocation in its relaxed state.
The vacancy formation energy over the coordination number.
What is Perierls-Nabarro stress?
The minimum stress required to move a dislocation line.
Derive an expression for the approximate elastic energy of a dislocation.
Check slide 25
What energy of a dislocation dominates the total energy of the dislocation motion?
The diffuse elastic energy (energy fluctuations depend on core energy term).
E(el) ≈ 10E(core) so elastic term dominates
Sketch a plot of energy against displacement for a dislocation.
Check slide 25
Under what conditions will an edge dislocation glide?
If there isa shear component of stress in the direction of b.
Under what conditions will an edge dislocation climb?
If there is a dilation stress parallel to b, and if the temperature is high enough for vacancies to diffuse.
What is meant by the “configurational” force on a dislocation?
The rate of change of energy of the system as the dislocation moves.
Why is glide of an edge dislocation conservative motion?
The shape of the material changes but the volume doesn’t. Edge dislocation climb is non-conservative in that the shape and volume both change.
Derive an expression for the force on a dislocation
Check slide 27
State the Peach-Kohler equation
Check slide 27
What do systems want to minimise?
Elastic E.
Show that like dislocations repel and opposite dislocations attract.
Check slide 29
Derive an expression for the force between two screw dislocations.
Check slide 30
Derive an expressions for the forces between two edge dislocations.
Check slide 31
Sketch a plot of F(glide) against ∆x/∆y for like and oppositely signed dislocations stating where each pair have a stable equilibrium.
Check slide 32
What stable arrangement do like dislocations tend to take?
Planar stacks such as a low angle tilt boundary.
What stable arrangement do like dislocations tend to take?
They can form a Taylor lattice or dipole dispersion, both of which have minimal long range stress fields.
What is the traction of a dislocation?
The force per unit area that an dislocation exerts on a surface.
What are image forces?
Image forces are the result of a dislocation near a free surface causing a traction on it. At a free surface there should be no overall forces on the surface a virtual dislocation is introduced as a mirror to the real one.
Derive an expression for dislocation line tension.
Check slide 34
Derive an expression for the critical shear stress required to operate a Frank-Read source.
Check slide 36
Sketch a plot of curvature against line length for the operation of a Frank-Read source.
Check slide 36
Describe how slip bands can widen by multiple cross-slip.
Screw dislocations have a high enough resolved shear stress for glide on more than one slip plane.
Cross slip can occur which leaves segments of the dislocation on the primary slip plane.
The dislocation can then cross slip back onto a parallel slip plane to the primary slip plane where it forms a new dislocation source as it has pinned ends.
This repeats when new dislocations are produced, resulting in the widening of the slip band.
Derive an expression for the strain rate from the motion of dislocations.
Check slide 47
What affect does dislocation core width have on the mobility of dislocations?
Wider cores need lower force to move dislocation.
Derive an expression for the Peierls stress of a dislocation.
Check slide 54
Why do kinks in dislocations form and what limits their formation?
Dislocation kinks form when parts of the dislocation line fall into different Peierls valleys. This is opposed by the line tension and mutual attraction of opposite kinks.
How can a kink form when two dislocations intersect?
When an edge and a screw intersect.
For the screw the kink is effectively an atomic length section of edge.
On same glide plane as rest of dislocation
Acts as a “secondary dislocation”
Sideways motion of kink can act as glide mechanism for main screw.
Diagram on slide 58
When can jogs form?
When 2 screws intersect or an edge and a screw intersect.
What is the difference between a kink and a jog forming?
A kink forms on the same slip plane as the main dislocation whereas a jog forms on a new slip plane.
Describe how a jog forms when a screw and edge intersect.
The jog forms on a new slip plane than the edge dislocation and can move with the dislocation it is attached to for glide.
Diagram slide 59
Describe how a jog forms when 2 screws intersect.
The 2 screws intersect as in the diagram on slide 60
The jog acts as a piece of edge in each dislocation.
The edge dislocation is likely to be on a non-glide plane.
This means can only move this part of the dislocation by climb.
Which dislocations can climb?
Only edge
Which dislocations can cross slip?
Only screw
Will an edge dislocation climb if vacancy diffusion is great enough?
Yes but without a driving force there will be no net climb.
What driving forces can cause climb of an edge dislocation?
Mechanical driving force - stress applied.
Chemical driving force - excess vacancy conc in the crystal (dislocation core can act as a vacancy sink).
Does climb occur uniformly along the length of an edge dislocation?
No, each vacancy that “lands” creates a pair of unit height jogs (diagram on slide 62).
What is the primary slip system in ccp?
{111}
<110>
Describe what happens in dislocation dissociation in cap metals.
The perfect a/2<110) Burgers vector forms 2 partials of a/6<211> Burgers vector. This is not a whole lattice vector and creates an intrinsic stacking fault.
Why do dislocations dissociate?
The two partial dislocations that form have a combined energy lower than that of the perfect dislocation. This is due to their shorter Burgers vector.
Describe the energetics of a stacking fault that results from dislocation dissociation.
As the stacking fault width increases (and it’s energy as it is has an excess energy) the dislocation energy decreases from Ga^2/4 to Ga^2/6 (perfect to partials).
Why do ccp metals have dislocations that dissociate but bcc not?
ccp metals meet the following criteria:
A stacking fault structure of low energy
Partial dislocations with a lower combined energy than the perfect.
bcc metals have a high stacking fault energy.
Sketch a plot of dislocation energy, fault energy and total energy for the dissociation of perfect dislocations into partials.
Check slide 69
Sketch the geometry of a perfect cap dislocation and its partials.
Check slide 69
Derive an expression for the equilibrium spacing of the stacking fault when a perfect dislocation dissociates in a cup metal.
Check slide 70
What is Thompson Tetrahedron used for?
To visualise the order in which a perfect dislocation will dissociate to creak an intrinsic stacking fault.
What phrase to remember for Thompson Tetrahedron?
Look down line of dislocation. Greek-Roman on left, Roman-Greek on right. Greek-Roman always first partial, Roman-Greek always second.
What is a Lomer-Cottrell lock?
When the first dislocation in two sets of partial dislocations on different slip systems meet and form a new full dislocation in a non-primary slip system which causes it to be locked along with the second partials behind them.
In order for a screw dislocation to cross slip in a ccp metal, what must first happen?
The partials must recombine in order for the whole dislocation to cross slip.
What is constriction in the sense of cross slip in ccp metals?
It is the force to recombine the dissociated dislocations. The constriction can be assisted by the stacking fault energy and materials with higher stacking fault energies recombine more easily. This means materials with lower stacking fault energies require more energy to recombine the dislocations and cross slip.
How does cross slip affect monotonic loading?
In early work hardening it causes glide band spreading, formational of new dislocation sources and can by pass precipitates.
In later work hardening it also bypasses locks and dislocation tangles.
How is cross slip important in fatigue?
Irreversible slip in cyclic loading.
Stability of persistent slip band structures.
When vacancies collect to form an intrinsic stacking fault, what else forms?
A loop bound by pure edge dislocation.
The loop must have Burgers vector of a/3<111> in ccp
This is normal to the {111} plane.
This is a Frank loop
How can a Frank loop be removed from a material?
The loop is sessile so can only grow or be removed by addition of vacancies (by climb).
It could also be removed by a dislocation reaction. If it combines with the right Schockley partial a prefect dislocation forms.
Describe how a Frank loop be converted to a prismatic loop.
A Schockley partial nucleates within the Frank loop.
The partial traverse the loop and converts it to a perfect dislocation loop.
This loop can glide, but not in its own loop plane.
This is a prismatic dislocation loop.
