Dislocations

define dislocation and types

linear defects in a crystal

• Screw = torsion

• Edge = insertion of plane

process of Dislocation motion

1. Apply an external stress onto crystal

   1. Moving atoms requires a lot of energy, breaking and remaking bonds is less energy

2. When shear stress is high enough = specific bonds along extra plane break and reform

   1. Causes extra plane to "shift" over

   2. Not atoms actually shifting, just the atoms remaking bonds so the defect moves

3. It causes the dislocation to move

   1. Plane doesn't move

   2. The bonds move -> i.e. Bonds are being broken are remade

4. Allows plastic deformation to occur in metals

Edge vs screw dislocation motion

• Dislocation moves along slip plane in slip direction perpendicular to dislocation line

• Burger's vector = slip direction

what is edge dislocation

what is screw dislocation

what is slip + when is it more likely to happen

movement of dislocations

Slip occurs in densely/closely packed planes

I.e. Motion is easier along packed planes

• Lower shear stress required for slip in densely packed planes

  • Slip system = along densest planes -> i.e. along planes with highest densities

  • Slip in direction of highest linear density

• If slip is restricted in closely packed planes = less dense planes slip

• Less energy required to move atoms along denser planes

What are slip systems

combination of slip planes and slip directions

• Different crystals have different linear and planar densities

• Slip systems combine slip planes and slip direction

• Each crystal has a different number of slip systems

  • FCC has 12 slip systems

    • 4 planes {111} = (1,1,1), (-1,1,1), (1,-1,1), (1,1,-1)

    • Three vectors with highest linear density within these planes

    • 4 x 3 = 12 slip systems

  • BCC is material dependant

  • HCP

    • One plane with highest planar density

    • Linear and planar density depends on ratio of lattice parameters: a and b

how does stress impact slip

• Crystals slip due to a resolved shear stress ()

• Applied tension can produce stress

• If I know the force I apply on my material and the tensile stress, then I can fine the shear stress using schmid law

what is schmid’s law

what is Critical resolved shear stress (CRSS)

• A material property telling us how easy it is to move dislocation

• The condition of dislocation movement:

  • If slip direction is perpendicular to direction of force =  = no shear stress = no plastic deformation

  • If slip plane is 45° to force direction =  = shear stress is half of tensile strength

  • If slip plane is parallel to force direction =  = no shear stress

• Crystal orientation can make it easy/hard to move dislocation

how does plastic deformation in single crystals work

• anisotropy

• Plastic deformation of single crystals (anisotropic materials) = creates step markings on surface

  • These markings are called slip bands

  • Slip bands are parallel to each other

• Each crystal has the same λ and ɸ -> same shear stress for each crystal

• Atoms on specific crystallographic planes (slip planes) slip to cause slip bands

how does plastic deformation in polycrystalline materials work

• isotropy

• Polycrystals are stronger

  • Grain boundaries pin deformations

  • Different grains have different orientations

• Dislocations occur on specific planes along specific lines

• Slip planes and directions will be different from one crystal to another

  • λ and ɸ are different

• Shear stress will vary from one crystal to another

• Crystal with the largest shear stress will yield first

• Other, less favourably oriented crystals will yield later

tensile test for polycrystals

1. Etch sample

2. Before deformation = all grains are pretty neat

3. As deformation = grains start to bend from original shape

4. Deformation continues = more slip systems become active, and more plastic deformation

   1. Deformation mot happening uniformly

how to induce anisotropy into polycrystals

By rolling the metal

→ load flattens grains and causes them to align

how do plastic deformation and dislocation motion relate to each other

• Plastic deformation is caused by dislocation motion

• We can increase strength by increasing stress to make deformation moves

• Limiting dislocation = limits plastic deformation

how to prevent dislocations

1. Reduce grain size

2. Solid solutions

3. Precipitation strengthening

4. Cold work (%CW)

impact of reducing grain size on dislocations

Grain boundaries are barriers to slip

• Grain boundaries are a type of deformation

• Mess of atoms

• Least planar or linear density

• Extra energy for slip in grain boundary

Barrier "strength" increases with increasing angle of misorientation

• Atoms are misoriented in grain boundaries

• More misoriented atoms = stronger and more resistant to slip

Smaller grain size = more grain boundaries = more barriers to slip

Follows hall-petch equation → valid until nanograin size

Hall-petch equation

how solid solutions prevent dislocations

INTRODUCE IMPURITIES INTO MATERIAL

Impurity atoms distort lattice and generate stress = reduces dislocations

• This stress is a barrier to dislocation motion

• Requires more energy for dislocation motion

 

We do this be creating an alloy in the metal

• Small impurities tend to concentrate at dislocations

  • Concentrate at vacancies

    • Replaces the number of missing host atoms

  • Small substitutions attract other atoms towards it and increase density = reduces mobility of dislocation = increases material strength

• Large impurities concentrate at dislocations on low density side

  • Concentrate where at vacancies

  • One/two less large substitutional atoms replace three host atoms

  • Causes excess stress = increase material strength

∴ Alloying increases yield stress and tensile strength of the material

-> this reduces ductility

how does Precipitation strengthening reduce dislocations
+ application

Hard precipitates are difficult to shear

• E.g. ceramics in metals

• Large shear stress needed to move dislocation towards precipitate to shear it

• Dislocation moves but precipitates act as "pinning" sites -> prevents slipping in that part of plane

Used in aviation

• Internal wing structure on Boeing 767

• Aluminium is strengthened with precipitates formed by alloying

what is cold work + how it prevents dislocations

Room temperature deformation

• Common forming operations change the cross sectional area

• Through forging, rolling, drawing and extrusion

• Normally two/more of these processes occur

• Compresses microstructure = increases dislocation density = causes dislocation to be harder to move = causes the material to become stronger

Dislocations during cold work

• Dislocations entangle with one another

• Dislocation motion becomes more difficult

• As cold work increases = yield strength increases, tensile strength increases

  • BUT ductility decreases

  • Lower % elongation or % area reduction

  • Maintain ductility by doing heat treatment after cold work

percentage cold work eq

dislocation density eq