Metals and Alloys

Question 1

List some Physical Properties

Answer 1

density, mass, melting/ boiling point, conductivity

Question 2

List some Mechanical Properties

Answer 2

stiffness, yield stress, ductility, strength

Question 3

What are structural property (S-P) relations?

Answer 3

Mathematical expressions that embody the functional dependence of properties for a material.

Question 4

What are constitutive relations?

Answer 4

Mathematical description of the response of a material to some applied stimuli. Such relations are dependent. e.g. electromagnetic, kinematic, chemical.

Question 5

What is this expression: σ(y) ≈ σ(0,y) + 1/(d)^0.5

Answer 5

Hall-Petch Effect
σ(y) = yield stress
σ(0,y) = Peierls stress
d = grain size

Question 6

What is this expression : σ(y) ≈ (2/3)^0.5 * Gb/λ

Answer 6

Orowan-by Pass Mechanism
σ(y) = yield stress
G = shear modulus
b = magnitude of Burgers vector
λ = mean precipitate spacing

Question 7

How would you construct a Total Stress/ Strain Tensor?

Answer 7

σ = S + Pm*I
S = deviatoric stress tensor
Pm*I = hydrostatic stress tensor
I = identity matrix
Pm = 1/3 * (σ(11) + σ(22) + σ(33))

Question 8

How would you determine the Yield Surface, F(σ) for a given material?

Answer 8

Load a material multiaxially with σ(11) along X1 and σ(22) along X2. Suppose σ(11) and σ(22) are increased proportionally to each other (σ(11) = k*σ(22)). During loading record whether response is elastic or plastic. By connecting all loci of points that first cause plasticity, we identify the elastic, plastic transition.

Question 9

What is the Von Mises yield function?

Answer 9

F(σ) = 1/(2^0.5) * ((σ1-σ2)^2 + (σ2-σ3)^2 + (σ3-σ1)^2)^0.5
It converts any stress state tensor σ in stress space to an effective stress.
F(σ) >= σ(y) plastic yield
F(σ) < σ(y) elastic behaviour

Question 10

Describe a polycrystalline structure

Answer 10

Polycrystals are a collection of crystals, called grains, that are arranged into long-range patterns, a crystal lattice.
e.g. steels, aluminium, titanium alloys.

Question 11

What are the three main Crystalline Structures?

Answer 11

Hexagonal Close Packed (HCP): titanium(α), zinc, zirconium
Face-Centred Cubic (FCC): nickel, aluminium, iron(γ)
Body-Centred Cubic (BCC): chromium, titanium(β), iron(α,δ)

Question 12

List the types of Crystal Defects

Answer 12

Point defects- vacancies, interstitial and substitutional atoms
Line defects- dislocations
Surface defects- twins, staking faults, grain boundaries
Volume defects- voids, cracks, foreign inclusion

Question 13

What is the maximum size of a solute atom for it to occupy an interstitial site?

Answer 13

r(solute) < 0.85 * r(host)

Question 14

Define a dislocation

Answer 14

crystal defect characterised by a chain of atoms that are incorrectly placed in the lattice. Types of dislocation include edge, screw or mixed.

Question 15

Define a Burgers Vector

Answer 15

-Choose a positive direction of dislocation line.
-describe the right handed closed circuit in a perfect crystal.
-repeat around dislocation, S and F no longer coincide. burgers vector is whats needed to connect S and F.
b = FS

Question 16

How do you measure the energy of a dislocation per unit length (Line Tension)?

Answer 16

T = 0.5 * G * b^2
G - shear modulus
b - magnitude of burgers vector

Question 17

How do you calculate the magnitude of the Burgers vector?

Answer 17

say b = (b1, b2, b3)

b^2 = b1^2 + b2^2 + b3^2

Question 18

How do you calculate dislocation density?

Answer 18

ρ = (number of dislocations) / (area)
ρ = N / L^2
L - grain size

Question 19

How do you calculate the plastic shear strain due to a dislocation in motion?

Answer 19

γ^p = b / L = N * b / L = b * ρ * L
plastic strain ≈ 10^-5
If dislocations advance by increment δx ...
δγ^p = b * ρ * δx
If the glide velocity is vg ...
δγ^p = b * ρ * vg * δt

Question 20

What influences velocity of dislocations?

Answer 20

Point defects, pinning by precipitates/ grain boundaries, lattice friction, dissociation of the dislocation.

Question 21

What is a phase diagram?

Answer 21

collection of solubility limit curves, mapping equilibrium states of matter. shows the chemical composition at each phase

Question 22

How do you calculate phase fractions from a phase diagram?

Answer 22

draw a line through the point that intersects the liquidus and solidus at compositions CL and Cα. Use lever rule to calculate mass fractions
WL = S / (R+S) = (Cα-C0) / (Cα-CL)
Wα = R / (R+S) = (C0-CL) / (Cα-CL)

Question 23

What is a Eutectic and Eutectoid reaction?

Answer 23

Eutectic: a phase change from single liquid solution into two solid phases. L <=> S1 + S2
Eutectoid: involves the transformation of a solid solution into two phases. S3 <=> S1 + S2

Question 24

What is a yield Surface?

Answer 24

the yield surface is a surface in stress space that separates stress states that result in elastic behaviour from those leading to plastic deformation. Points on the yield surface result in plastic deformation

Question 25

What is the normality condition?

Answer 25

dε^p ∝ n. Specifies that the plastic strain increment ‘dε^p’ for a stress state on the yield surface is given by a normal vector ‘n’ to the surface at that point.

Question 26

Explain the difference between an edge, screw and mixed dislocation

Answer 26

Edge: burgers vector and tangent vector to dislocation line are perpendicular.
Screw: burgers vector and tangent vector to dislocation line are parallel.
Mixed: burgers vector and tangent vector to dislocation line are arbitrarily oriented at angle θ (not parallel or perpendicular)

Question 27

Why can dislocations not terminate within a crystal?

Answer 27

Would require the non-closure of a burgers vector, as measured by the burgers circuit around a dislocation. this is not physically possible.

Question 28

How does dislocation motion result in plastic strains?

Answer 28

For a crystal size ‘L’, movement across it results in shear displacement equal to the burgers vector. This results in shear plastic strain γ given by γ=b/L, where b is magnitude of burgers vector.

Question 29

What are liquidus and solidus lines?

Answer 29

The liquidus is the solubility limit separating liquid phase and liquid+α phase. The solidus is the solubility limit separating the liquid+α phase and the α phase field.

Question 30

What are hypoeutectoid and hypereutectoid alloys?

Answer 30

Hypoeutectoid: alloy with composition to the left of the eutectoid composition.
Hypereutectoid: alloy with composition to the right of the eutectoid composition.

Question 31

Describe the two categories for phase transformations

Answer 31

Diffusion dependent transforms:
-no change in number of composition phases
-changes to actual composition and number of phases
Diffusionless transformations:
-formation of metastable phase
-martensitic transformation is an example

Question 32

How can homogeneous and heterogeneous nucleation of a phase occur?

Answer 32

Homogeneous nucleation- nuclei of new phase form uniformly from parent phase.
Heterogeneous nucleation- nuclei form on solid impurity or container walls. Growth of the nucleated phase occurs when the size of the nuclei exceeds a critical value. Nuclei less than this are unstable and will dissolve.

Question 33

What two contributions are associated with the change in free energy during homogenous nucleation of a solid particle from liquid?

Answer 33

1) the formation of a volume solid ΔGn1

2) the formation of interface separating the solid and liquid phase ΔGn2

Question 34

What are the four scaling laws for strengthening mechanisms?

Answer 34

1) Frank-Read: dislocation generation, σy ∝ (Lfr)^-1
2) Solid solution hardening: Interstitial and Substitutional atoms, σy ∝ (C)^1/2
3) Work hardening: dislocation density, σy ∝ (ρ)^1/2
4) Hall-Petch effect: dislocation density, σy ∝ (d)^-1/2

Question 35

From a temp-nucleation rate schematic, explain how coarse and fine microstructures may be
generated

Answer 35

we can see that at high temps we have a low nucleation rate and high growth rate. This will result in a low density of solid nuclei that can grow fast. In this case we generate course microstructure. At low temps, we have the opposite, high nucleation rate and low growth rates, resulting in a fine microstructure.

Question 36

Give two reasons for why are material constitutive relations important in design?

Answer 36

Constitutive relations provide information on:

1) how a material deforms (stress-strain curve)
2) causal link between a material microstructure and its mechanical properties

Question 37

What is recrystallisation?

Answer 37

Nucleation of new grains