HANDOUT 4 - Dislocations and other stuff

Question 1

How do dislocations move in a material? Give a diagram (atomic level).

Answer 1

Dislocations move by the action of shear stress parallel to the slip plane.

Note that when a dislocation moves:

• no atom moves more than a fraction of the atomic spacing
• the adjacent set of atoms become the “half-plane”

Question 2

Draw the process of a slip step being produced by the passage one dislocation (Burgers vector b).

Answer 2

Dislocations enable incremental slip by extending a few bonds at a time, which is why the stress required is so much less than the ideal strength.

Question 3

Draw, describe and explain edge dislocations.

Answer 3

• shear stress and Burgers vector both at right angles to the dislocation
• dislocation moves in the direction of the stress

Question 4

Draw, describe and explain screw dislocations.

Answer 4

• shear stress and Burgers vector both parallel to the dislocation.
• dislocation moves at right angles to the stress
• same slip step produced as for edge dislocation

Question 5

Draw, describe and explain mixed dislocations.

Answer 5

More generally dislocations are mixed:

• curved, and varying between pure edge and pure screw
• move in a direction normal to the curve under the action of a shear stress (curved sections expand)
• net effect remains a slip step in the direction of the shear stress.

Question 6

Explain why dislocations lead to specimens failing under loads smaller than theoretically calculated?

Answer 6

• crystals contain very man dislocations, with many different planes on which they can glide.
• in (virtually) any stress state, shear stresses exist to move dislocations.

Consider a crystal loaded in tension, with two dislocations crossing at 45^o.

Net effect: crystal becomes longer and thinner by a small increment.

Replicating this increment x 1000s of dislocations on multiple slip planes produces continuum bulk plasticity.

Question 7

Explain why plastic deformation occurs at constant volume.

Answer 7

Blocks of material slip past one another(dislocations) but the crystal packing is unaffected.

Question 8

Give the equation relating the shear stress (tau), movement of dislocation b, and the resitance force f.

Answer 8

tb = f

t= tau

Question 9

Why is the intrinsic lattice resistance to dislocation motion greater in technical ceramics (e.g. diamond) than metals?

Answer 9

Ceramics have covalent bonds which have high intrinsic resitance: high hardness

Metals have metallic bonds which have low intrinsic resistance: annealed pure metals are soft.

Question 10

What is the equation that gives the energy(per unit length) T?

Answer 10

T ≈ Gb²/2

G = shear modulus

b = Burgers vector

Question 11

Explain how dislocation pinning (with diagram) increases resistance to dislocations moving.

Answer 11

• It is pinned by the obstacles, and is forced to bow out between them, increasing the resistance per unit length.
• an additional shear stress ∆t (tau) is needed to overcome this resistance

As the dislocations bows out it applies a force to the obstacle:

force on obstacle = 2Tcos(theta)

dislocation escapes when either:

• force > obstacle strength ( theta > 0^o )
• dislocation forms a semi-circle ( theta = 0^o)

Question 12

Show and explain how dislocation pass through weak obstacles.

Answer 12

Dislocations cut through or pass the obstacle.

Question 13

Show(diagram) and explain how a dislocation passes through a “strong obstacle”.

Answer 13

Dislocations escape by leaving a loop of dislocation round the obstacle.

Question 14

The contribution to the yield stress due to dislocation pinning depends directly on what 2 fixed paramaters and what 2 variable parameters?

Answer 14

Fixed paramaters:

• G: elastic shear modulus
• Burgers vector(atomic spacing)

Can be manipulated by processing parameters:

• L: obstacle spacing
• α: obstacle strength

Question 15

Name the three different methods used on metals to pin dislocations.

Answer 15

• other dislocations: work hardening
• solute atoms: solid solution hardening
• particles of another solid (e.g. a compound): precipitation hardening

Question 16

How does work hardening increase dislocation resistance?

Answer 16

Gliding dislocations on different slip planes interact: pinning occurs due to the additional bond distortion at the intersection.

Strength contribution:

• additional shear stress from dislocation pinning proportional to 1/L
• spacing L depends on the dislocation density, p_d (i.e. total dislocation length per unit volume)

Dislocation density rises with strain - reducing the spacing, L, and increasing the resistance - this is called work hardening.

Question 17

What methods are used to work harden metals?

Answer 17

Alloys may be hardened by deformation processing (e.g. rolling, wire drawing), to increase the dislocation density while shaping the product.

Question 18

What is solid solution hardening? What strength contribution does it have? how are metals made this way?

Answer 18

Intersitial solid solutions provide hardening, by displacing host atoms from their equilibrium positions - same effect on the slip plane

Solid solutions provide a weak obstacle to dislocations, which bow out until the line tension pulls the dislocation past the solute atom.

Casting is used to mix elements together in the liquid state, enabling solid solutions to be manufactured.

Strength contribution:

• additional shear stress from dislocation pinning proportional to 1/L
• spacing L of solute atoms scales with solute concentration C as 1/C^0.5.
• Hence additional shear stress from solid solution is proportional to C^0.5.

Question 19

What is precipitation hardening? what is its strength contribution?

Answer 19

Alloying elements also forms compounds. When distributed as small particles within a lattice, they provide pinning points for dislocations.

Particles provide strong obstacles: the dislocation cannot pass over them, and (usually) the precipitate lattice is unrelated to the surrounding lattice.

Strength contribution:

• maximum shear stress required to pass (strong) particles is when the dislocation bows out into a semi-circle, leaving a dislocation loop behind it.

Additional shear stress from precipitation hardening: ∆t_ppt = Gb/L

Question 20

Explain how grains are formed in metals?

Answer 20

Casting: solidification occurs by nucleation and growth of tiny solid crystals - these grow randomly until they impinge, forming grains;

Question 21

How do grains effect the hardening of a metal?

Answer 21

The lattice orientation changes at a grain boundary. As a result:

• dislocations cannot slip directly from grain to grain.
• dislocation pile-ups occur at the boundaries
• additional stress from pile-up nucleates dislocations in the adjoining grain.

The finer the grain size d, the more often boundaries obstruct dislocations.

Question 22

Why isn’t it that increasing grade boundaries is an effective hardening mechanism?

Answer 22

It is a weak hardening mechanism - grain boundaries are much further apart than dislocations, solute or precipitates. It is useful as a strengthening mechanism for pure metals or dilute alloys.

Question 23

What particle spacing in Al alloy gives a yield stress increment (∆σ_y)_ppt of 400 MPa?

Answer 23

Question 24

How many atoms are in a precipitate cluster ( the ones used precipitation hardening ) ?

Answer 24

Practical precipitates vary in size from clusters of 10 or so atoms, to compounds containing 10⁶ or more atoms. ( i.e diameters 0.5 - 200 nm )

Question 25

How do amorphous thermoplastics behave and fail when T < 0.8 T_g ( draw stress-strain )?

How do they behave at 0.8 T_g < T < 1.2 T_g?

Answer 25

T < 0.8 Tg : elastic-brittle (PMMA)

• chain sliding limited
• brittle fracture from inherent flaws in the material
• little or no ductility

(2) 0.8 Tg < T < 1.2 Tg : elastic-plastic

• chain mobility increases around Tg as van der Waals bonds melt
• yielding takes place by crazing, shear yielding or cold drawing.

Question 26

What is crazing? ( in polymers )

Answer 26

Microcracks open in tension, bridged by stiff fibres of material with aligned molecules, preventing immediate fracture.

Question 27

What is shear yielding? ( in polymers )

Answer 27

Shear bands form, and are stabilised by alignment of molecules; multiple bands form, giving greater ductility.

Question 28

What is cold drawing? ( in polymers )

Answer 28

Polymers which do not craze can often be cold drawn. Necking occurs, but the neck is stable: the molecules align in the neck and strengthen it, so the neck spreads along the specimen.

Question 29

what performance indices do these represent?

(σ_f/p) = constant

(σ_f^0.5/p) = constant

(σ_f²/2E) = constant

Answer 29

Minimum mass under tensile stress(pg 20)

Minimum mass under bending(pg 21)

Maximum elastic stored energy per unit volume

Question 30

From page 20-21, there are no flashcards, it is better to read the notes.

Answer 30

:)