1231 lines
39 KiB
Markdown
Executable File
1231 lines
39 KiB
Markdown
Executable File
---
|
|
author: Alvie Rahman
|
|
date: \today
|
|
title: MMME1029 // Materials
|
|
tags: [ uni, nottingham, mechanical, engineering, mmme1029, materials ]
|
|
---
|
|
|
|
\tableofcontents
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
# Lecture 1 (2021-10-04)
|
|
|
|
</summary>
|
|
|
|
## 1A Reading Notes
|
|
|
|
### Classification of Energy-Related Materials
|
|
|
|
- Passive materials---do not take part in energy conversion e.g. structures in pipelines, turbine
|
|
blades, oil drills
|
|
- Active materials---directly take part in energy conversion e.g. solar cells, batteries, catalysts,
|
|
superconducting magnests
|
|
|
|
- The material and chemical problems for conventional energy systems are mostly well understood and
|
|
usually associated wit structural and mechanical properties or long standing chemical effects like
|
|
corrosion:
|
|
|
|
- fossil fuels
|
|
- hydroelectric
|
|
- oil from shale and tar
|
|
- sands
|
|
- coal gasification
|
|
- liquefaction
|
|
- geothermal energy
|
|
- wind power
|
|
- bomass conversion
|
|
- solar cells
|
|
- nuclear reactors
|
|
|
|
### Applications of Energy-Related Materials
|
|
|
|
#### High Temperature Materials (and Theoretical Thermodynamic Efficiency)
|
|
|
|
- Thermodynamics indicated that the higher the temperature, the greater the efficiency of heat to
|
|
work:
|
|
|
|
$$ \frac{ T_{high} - T_{low} }{ T_{high} } $$ where $T$ is in kelvin
|
|
|
|
- The first steam engines were only 1% efficient, while modern steam engines are 35% efficient
|
|
primarily due to improved high-temperature materials.
|
|
- Early engines made from cast iron while modern engines made from alloys containing nickel,
|
|
molybdenum, chromium, and silicon, which don't fail at temperature above 540 \textdegree{}C
|
|
- Modern combustion engines are nearing the limits of metals so new materials that can function
|
|
at even higher temperatures must be found--- particularly intermetallic compounds and ceramics are
|
|
being developed
|
|
|
|
## Types of Stainless Steel
|
|
|
|
- Type 304---common; iron, carbon, nickel, and chromium
|
|
- Type 316---expensive; iron, carbon, chromium, nickel, molybdenum
|
|
|
|
## Self Quiz 1
|
|
|
|
1. What is made of billion year old carbon + water + sprinkling of stardust?
|
|
|
|
> Me
|
|
|
|
2. What are the main classifications of materials?
|
|
|
|
> Metals, glass and ceramics, ~~plastics, elastomers,~~ polymers, composites, and semiconductors
|
|
|
|
3. [There are] Few Iron Age artefacts left. Why?
|
|
|
|
> They rusted away
|
|
|
|
4. What is maens by 'the micro-structure of a material'?
|
|
|
|
> The very small scale structure of a material which can have strong influence on its physical
|
|
> properties like toughness and ductility and corrosion resistance
|
|
|
|
5. What is a 'micrograph' of a material?
|
|
|
|
> A picture taken through a microscope
|
|
|
|
6. What microscope is used to investage the microstructure of a material down to a 1 micron scale
|
|
resolution?
|
|
|
|
> Optical Microscope
|
|
|
|
7. What microscope is used [to investigate] the microstructure of a material down to a 100 nm scale
|
|
resolution?
|
|
|
|
> Scanning Electron Microscope
|
|
|
|
8. What length scales did you see in the first slide set?
|
|
|
|
> 1 mm, 0.5 mm, 1.5 \textmu{}m
|
|
|
|
9. What material properties were mentioned in the first slide set?
|
|
|
|
> Hardness, brittleness, melting point, corrosion, density, thermal insulation
|
|
|
|
## Self Quiz 2
|
|
|
|
1. What is the effect of lowering the temperature of rubber?
|
|
|
|
> Makes it more brittle, much less elastic and flexible
|
|
|
|
2. What material properties were mentioned in the second slide set?
|
|
|
|
> Young's modulus, specific heat, coefficient of thermal expansion
|
|
|
|
</details>
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
# Lecture 2
|
|
|
|
</summary>
|
|
|
|
## Properties of the Classes
|
|
|
|
### Metals
|
|
|
|
- Ductile (yields before fracture)
|
|
- High UFS (Ultimate Fracture Stress) in tension and compression
|
|
- Hard
|
|
- Tough
|
|
- High melting point
|
|
- High electric and thermal conductivity
|
|
|
|
### Ceramics and Glasses
|
|
|
|
- Brittle --- elastic to failure, no yield
|
|
- Hard (harder than metals)
|
|
- Low UFS under tension
|
|
- High UFS under compression
|
|
- Not tough
|
|
- High melting points
|
|
- Do not burn as oxide ceramics are already oxides
|
|
- Chemically resistant
|
|
- Poor thermal and electric conductivity
|
|
- Wide range of magnetic and dielectric behaviours
|
|
|
|
### Polymers
|
|
|
|
- Organic---as in organic chemistry (i.e. carbon based)
|
|
- Ductile
|
|
- Low UFS in tension and compression
|
|
- Not hard
|
|
- Reasonably tough
|
|
- Low threshold temperature to charring and combustion in air or pure oxygen
|
|
- Low electrical and thermal conductivity
|
|
|
|
- There are some electrically conductive polymers
|
|
|
|
### Composites
|
|
|
|
- Composed of 2 or more materials on any scale from atomic to mm scale to produce properties that
|
|
cannot be obtained in a single material
|
|
|
|
- Larger scale mixes of materials may be called 'multimaterial'
|
|
|
|
- Material propertes depends on what its made of
|
|
|
|
## Terms
|
|
|
|
### Organic vs Inorganic Materials
|
|
|
|
- Organic materials are carbon based
|
|
- From chemistry, organic compounds are ones with a C-H bond
|
|
- Inorganic compounds do not contain the C-H bond
|
|
|
|
### Crystalline vs Non-Crystalline Materials
|
|
|
|
- Most things are crystalline
|
|
|
|
- Ice
|
|
- Sugar
|
|
- Salt
|
|
- Metals
|
|
- Ceramics
|
|
|
|
- Glasses are non-crystalline
|
|
|
|
## Material Properties
|
|
|
|
### Density
|
|
|
|
$$\rho = \frac m v$$
|
|
|
|
- Density if quoted at STP (standard temperature and pressure---$298$ K and $1.013\times 10^5$ Pa)
|
|
- Metals, ceramics, and glasses are high density materials
|
|
- Polymers are low density
|
|
- Composites span a wide range of density as it depends on the materials it is composed of
|
|
|
|
e.g. composites with a metal matrix will have a much higher density than those with a polymer
|
|
matrix
|
|
|
|
### Melting Points
|
|
|
|
- Measured at standard pressure and in an intert atmosphere (e.g. with Nitrogen, Argon, etc)
|
|
|
|
- Diamond and graphite will survive up to 4000 \textdegree{}C in an inert atmosphere but would
|
|
burn at around 1000 \textdegree{}C in oxygen
|
|
|
|
- High melting points -> high chemical bond strength
|
|
|
|
### Corrosion
|
|
|
|
- It's not just metals that corrode
|
|
|
|
- Polymers
|
|
|
|
- UV degradation
|
|
- Water absorption can occur in degraded polymers
|
|
|
|
- Glass
|
|
|
|
- Leaching
|
|
- Sodium ions can leave the glass when covered in water. If the water stays, the high pH water
|
|
can damage the class
|
|
|
|
## Self Quiz
|
|
|
|
### Consolidation Questions 1
|
|
|
|
1.
|
|
|
|
i. Metal
|
|
ii. Titanium
|
|
|
|
2.
|
|
i. Polymer
|
|
ii. Polyester
|
|
|
|
3.
|
|
|
|
i. Ceramic
|
|
ii. Alumino-silicate
|
|
|
|
4.
|
|
|
|
i. Composite
|
|
ii. GFRP or CFRP
|
|
|
|
5.
|
|
|
|
i. Metal
|
|
ii. Aluiminium alloy
|
|
|
|
6.
|
|
|
|
i. Metal
|
|
ii. Aluiminium alloy
|
|
|
|
7.
|
|
|
|
i. Polymer
|
|
ii. Acrylic
|
|
|
|
8.
|
|
|
|
i. Ceramimc
|
|
ii. Glass
|
|
|
|
9.
|
|
|
|
i. Composite
|
|
ii. Concrete
|
|
|
|
### Consolidation Questions 2
|
|
|
|
> ~~C~~ B
|
|
|
|
</details>
|
|
|
|
# Polymers
|
|
|
|
## Introduction to Polymers
|
|
|
|
There are 3 types of polymers:
|
|
|
|
- thermoplastics
|
|
|
|
![](./images/vimscrot-2021-11-01T11:11:38,143311655+00:00.png)
|
|
|
|
No cross links between chains.
|
|
The lack of cross links allows recycling of polymers by heating it above the glass transition
|
|
material, $T_g$, lowering the viscosity.
|
|
|
|
An example of thermoplastics is PET, used in water bottles
|
|
|
|
- thermosets
|
|
|
|
![](./images/vimscrot-2021-11-01T11:11:59,529214154+00:00.png)
|
|
|
|
has lots of cross-links between chains, making it more rigid.
|
|
Heating does not lower its viscosity making them much harder/impossible to recycle.
|
|
|
|
and example of thermosets is melamine formaldehyde, used on kitchen tabletops
|
|
|
|
- elastomers
|
|
|
|
![](./images/vimscrot-2021-11-01T11:12:28,335292407+00:00.png)
|
|
|
|
has some cross links and a lot of folding of chains
|
|
|
|
Latex is an example of an elastomer
|
|
|
|
Polymers are relatively new materials, lightweight, durable, flammable, and degraded by UV light.
|
|
They are made of long carbon-carbon chains.
|
|
|
|
### Stress-Strain Curve of Polymers
|
|
|
|
![](./images/vimscrot-2021-11-01T11:13:39,370133338+00:00.png)
|
|
|
|
## Industrially Important Polymers
|
|
|
|
The worldwide production of polymers in 2019 was $368\times10^6$ tonnes and the majority is from
|
|
just 5 polymers:
|
|
|
|
- Polyethylene (PE) --- wire insulation, flexible tubing, squeezy bottles
|
|
- Polypropyene (PP) --- carpet fibres, ropes, liquid containers, pipes, chairs in Shoreham Academy
|
|
- Polyvinyl chloride (PVC) --- bottles, hoses, pipes, valves, wire insulation, toys
|
|
- Polystyrene (PS) --- packaging foam, egg cartons, lighting panels
|
|
- Polyethylene terephthalate (PET) --- carbonated drinks bottles
|
|
|
|
All of these materials are low cost.
|
|
|
|
## Thermoplastics
|
|
|
|
The simplest polymer is poly(ethene):
|
|
|
|
![](./images/vimscrot-2021-11-01T11:26:51,027062158+00:00.png)
|
|
|
|
When 2 polymer chains get close together, Van der Waals (vdw) forces keep them together.
|
|
vdw forces are very weak, much weaker than the covalent bonds inside the polymer.
|
|
|
|
### Stress Strain Curve
|
|
|
|
![](./images/vimscrot-2021-11-01T11:33:17,944832427+00:00.png)
|
|
|
|
- During linear deformation, the carbon chains are strethed.
|
|
- At yield stress, the carbon chains get untangled and slide past eache other.
|
|
- Necking initially allows the chains to slide at lower stress.
|
|
- As the chains pull, align, and get closer, the vdw forces get stronger and more stress is required
|
|
to fracture.
|
|
|
|
### Crystalline and Amorphous/Glassy Solids (Heating and Cooling)
|
|
|
|
#### Amorphous Thermoplastics
|
|
|
|
- As you heat above $T_g$, the chains get easier to move past each other.
|
|
- It is known as an *amorphous supercooled liquid*.
|
|
- There is not really a melting point are there are no crystals, but $T_m$ is the point where the
|
|
chains are easy to move
|
|
|
|
#### Crystalline Polymers
|
|
|
|
- The glass transition point does not exist for crystalline polymers
|
|
- The solid is difficult to deform below $T_m$ and is not ductile
|
|
- Above $T_m$ the chains are very easy to move past each other
|
|
|
|
#### Semi-Crystalline
|
|
|
|
- Below $T_g$, only local movements in chains are possible, so the material is less ductile.
|
|
The solid crystalline regions makes it difficult to move the chains.
|
|
- Between $T_g$ and $T_m$, the glassy chains are easier to move but the crystalline regions remain
|
|
difficult
|
|
- Above $T_m$ the chains easily move past each other
|
|
|
|
### Specific Volume vs Temperature
|
|
|
|
![](./images/vimscrot-2021-11-01T12:56:40,483489005+00:00.png)
|
|
|
|
#### Path ABCD
|
|
|
|
- a-b --- Start cooling the true liquid
|
|
- b-c --- At the freezing point, $T_m$, the true liquid freezes diretly to a crystalline solid
|
|
- c-d --- The crystalline solid cools t room temperature as the temperature is lowered
|
|
|
|
#### Path ABEF
|
|
|
|
- a-b --- start cooling the true liquid
|
|
- b --- at the freezing point nothing freezes
|
|
- b-e --- the liquid becomes *supercooled* and contracts and becomes more viscous as the temperature
|
|
decreases.
|
|
|
|
The supercooled liquid region is between $T_g$ and $T_m$
|
|
|
|
Supercooling requires you to cool the sample quicker than you would for path ABCD
|
|
|
|
- e --- $T_g$ is reached and the supercooled liquid sets to a amorphous solid
|
|
- e-f --- the amorphous solid cools from room temperature and contract as the temperature is lowered
|
|
|
|
## Relative Molar Mass and Degree of Polymerisation
|
|
|
|
- Number Average RMM --- $\bar M_n = \sum x_iM_i$
|
|
- Weight Average RMM --- $\bar M_w = \sum w_iM_i$
|
|
- Degree of polymerisation --- $n_n = \frac {\bar M_n} m$ and $n_w = \frac {\bar M_w} m$
|
|
|
|
where
|
|
|
|
- $M_i$ is the RMM of the chain
|
|
- $x_i$ is the fraction of the polymer that is composed of that chain by number/quantity
|
|
- $w_i$ is the fraction of the polymer that is composed of that chain by mass/weight
|
|
- $m$ is the RMM of the monomer from which the polymer was made
|
|
|
|
## Making Polymers
|
|
|
|
There are two ways to make polymers:
|
|
|
|
- [Addition Poymerisation](http://www.chemguide.co.uk/14to16/organic/addpolymers.html)
|
|
- [Condensation Polymerisation](https://www.chemguide.uk/14to16/organic/condpolymers.html)
|
|
|
|
# Elastic Deformaion
|
|
|
|
Elastic deformation is deformation where the material will return to original shape after the
|
|
applied stresses are removed.
|
|
|
|
Elastic deformation is the first type of deformation that happens when stresses are applied to
|
|
a material and is represented by the straight line at the beginning of a stress-strain curve.
|
|
|
|
## Modulus of Resillience ($E_r$)
|
|
|
|
This is the area under the elastic portion of a stress-strain graph of a material.
|
|
|
|
# Plastic Deformation
|
|
|
|
## Toughness (Absorbing Energy Through Plastic Deformation)
|
|
|
|
- The toughness of a material is its ability to absorb energy through plastic deformation
|
|
without fracturing
|
|
- The material toughness of a ductile material can be determined by finding the area under its
|
|
stress-strain curve (e.g. by integrating the graph)
|
|
- Brittle materials like ceramics and glasses exhibit no material toughness
|
|
- Ductile materials have a possibility of achieving large material toughness
|
|
|
|
Ductility measures how much something deforms plastically before fracture, but just because a
|
|
material is ductile does not make it tough.
|
|
|
|
*The key to high material toughness is a good combination of large ultimate fracture stress and
|
|
large ductility*.
|
|
|
|
- The unit of toughness is energy per unit volume as toughness can be mathematically expressed as:
|
|
|
|
$$toughness = \int^{\varepsilon_f}_0\! \sigma \,\mathrm{d}\varepsilon
|
|
= \frac{\text{Energy}}{\text{Volume}} $$
|
|
|
|
- A metal may have satisfactory toughness under static loads but fail under dynamic loads or impact
|
|
|
|
This may be caused by the fact that ductility and toughness usually decrease as rate of loading
|
|
increases.
|
|
- Ductility and toughness decreasee with temperature
|
|
- Notches in the material affect the distribution of stress in the material, potentially changing
|
|
it from a uniaxial stress to multiaxial stress
|
|
|
|
### Charpy Impact Test
|
|
|
|
Measures material toughness by determining the amount of energy absorbed during fracture.
|
|
|
|
It works by essentially dropping a hammer into a sample whose dimensions are standardized
|
|
(usually either by BSI or ISO) and measuring how high the hammer goes up on the other side,
|
|
after it breaks the material
|
|
|
|
The height of the hammer after impact will tell you how much enery is left in it, and therefore
|
|
how much has been aborbed by the now broken sample.
|
|
|
|
Under a microscope, more ductile fractures appear fibrous or dull, whereas less ductile surfaces
|
|
have granular or shiny surface texture.A
|
|
|
|
The charpy test has a couple issues:
|
|
|
|
- Results are prone to scatter as it is difficult to achieve a perfectly shaped notch
|
|
- Temperature has to be strictly controlled since it affects a material's ductility
|
|
|
|
#### The setup of a charpy impact test
|
|
|
|
1. Sample is made to standardized dimensions, with a notch
|
|
2. Sample is placed on support
|
|
3. A very heavy hammer pendulum of mass $m$ is dropped from rest at $h_0$ to swing about a pivot,
|
|
reaching $E_{kmax}$ vertically below the pivot.
|
|
4.
|
|
|
|
a. If no sample is in place then the hammer will swing back up on the other side to a height of
|
|
$h_h$ where theoretically $h_h = h_0$
|
|
b. With a sample placed vertically below, some of the $E_k$ is transferred to the sample to bend
|
|
and (usually) break the sample.
|
|
|
|
If breaks the sample, it will swing up to the other side, where its max height, $h_f$ can be
|
|
used to calculate how much energy was used to break the sample:
|
|
|
|
$$E = mg(h_h-h_f)$$
|
|
|
|
Where $g$ is acceleration due to gravity.
|
|
|
|
# Ductility
|
|
|
|
Ductility is the plastic deformation a material withstands before fracture.
|
|
|
|
# Griffith Surface Flaws
|
|
|
|
These flaws vary in size and shape.
|
|
They limit the ability of any material, brittle or ductile, to withstand tensile stresses as they
|
|
concentrate the tensile forces applied to a smaller area.
|
|
|
|
The stress at the tip of the flaw:
|
|
|
|
$$\sigma_{actual} = 2\sigma\sqrt{\frac a r}$$
|
|
|
|
For deep ($a$ is large) or thin ($r$ is small) the stress is magnified and, if it exceeds the UFS
|
|
in a brittle material, the flaw will grow into a crack, resulting in the brittle material
|
|
fracturing.
|
|
|
|
However in a ductile material, the tip of the flaw can heal, reducing $a$ and increasing $r$.
|
|
This is due to the chemical structure of ductile materials like metals.
|
|
|
|
![](./images/vimscrot-2021-11-08T13:51:17,152036728+00:00.png)
|
|
|
|
## Stress Intensity Factor
|
|
|
|
Stress Intesity Factor, $K$:
|
|
|
|
$$K = f\sigma\sqrt{\pi a}$$
|
|
|
|
where:
|
|
|
|
- $f$ is the geometry factor (1 would represent an infinite width sample, and 0 a 0 width sample)
|
|
- $\sigma$ is applied tensile strength
|
|
- $a$ is flaw depth
|
|
|
|
## Fracture Toughness
|
|
|
|
![An example sample for testing fracture toughenss. From: <https://www.researchgate.net/figure/Compact-tension-sample-geometry-used-for-fracture-toughness-measurement_fig2_340037774> [accessed 8 Nov, 2021]](./images/Compact-tension-sample-geometry-used-for-fracture-toughness-measurement.png)
|
|
|
|
The value of $K$ that causes the notch to grow and cause fractures.
|
|
This is value is known as the fracture toughness, $K_c$.
|
|
|
|
At low thicknesses fracture toughness depends on thickness but as thickness increases, $K_c$
|
|
decreases to the constant value, the plane strain fracture toughness, $K_{1c}$.
|
|
|
|
# Composites
|
|
|
|
Composites are made of two or more materials, which when combined together, at up to a milimetre
|
|
scale, have superior properties to their parent materials.
|
|
|
|
Composites tend to be 2-phase: a dispersed phase in a matrix.
|
|
The disepersed phase tends to be fibres (large aspect ratio) or particles (low aspect ratio) which
|
|
are embedded in a matrix, which are often resins.
|
|
|
|
Composite properites are affected by the dispersed phase geometry:
|
|
|
|
- Shape
|
|
- Size
|
|
- Distribution
|
|
- Relative orientation (for fibres)
|
|
|
|
## Rule of Mixtures
|
|
|
|
$E_c$ lies between the arithmetic mean (upper limit):
|
|
|
|
$$V_mE_m + E_pV_p$$
|
|
|
|
and the geometric mean (lower limit):
|
|
|
|
$$\frac{V_mE_mE_pV_p}{V_mE_m + E_pV_p}$$
|
|
|
|
Where $E_c$, $E_m$, $E_p$ are the Young's moduluses of the composite, matrix, and particles,
|
|
respectively, and $V_m$ and $V_p$ are the volume of the matrix and particles, respectively.
|
|
|
|
## Particle Reinforced Composites
|
|
|
|
### Applications of Composites
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
#### Tungsten Carbide Cobalt for Cutting Tools
|
|
|
|
</summary>
|
|
|
|
The Tungest Carbide (WC) particle are a truly brittle ceramic.
|
|
They are very hard but the brittleness means they are easy to break.
|
|
|
|
The solution is to hold small WC particles in a ducitle metal matrix.
|
|
In this case it is Cobalt (Co).
|
|
|
|
This way, crack in one WC particle does not necessarily mean other particles are broken,
|
|
meaning the cutting tool overall still works.
|
|
|
|
Another advantage of this composite is that WC is not very thermally conductive and has a high
|
|
melting point, which allows it to work well the environment it's in.
|
|
|
|
</details>
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
#### Resin Bonded Alumina for Sanding Disks
|
|
|
|
</summary>
|
|
|
|
This is another example of brittle but hard ceramics being put in a ductile matrix.
|
|
In this case it's a resin.
|
|
|
|
It follows the same idea---separating the ceramics into small particles means the particles can
|
|
break and the product still works overall, as there are thousands of particles which are not broken.
|
|
</details>
|
|
|
|
## Fibre Reinforced Composites
|
|
|
|
### Specific Property
|
|
|
|
Specific Property of a composite is a property divided by density of composite.
|
|
Here are some examples of specific properties:
|
|
|
|
- Specific ultimate tensile stress $= \frac{\sigma_{UTS}}{\rho_c}$
|
|
- Specific Young's modulus/stiffness $= \frac{E_c}{\rho_c}$
|
|
|
|
### Influence of the Fibres
|
|
|
|
Depends on:
|
|
|
|
- Fibre type
|
|
- Fibre length and diameter
|
|
- Fibre orientation
|
|
- Strength of bond between fibre and matrix
|
|
|
|
### Stress Strain Graph of a Fibre Reinforced Composite
|
|
|
|
![Under uniaxial, longitudinal loading in tension](./images/vimscrot-2021-11-12T19:16:58,443814950+00:00.png)
|
|
|
|
Note that the composite fails at the same strain as the fibres but yields at the same strain as
|
|
the polymer matrix.
|
|
|
|
The elastic behaviour of the composite before yielding is dependent on the strength of the chemical
|
|
bonds between the surface of the fibre and matrix.
|
|
|
|
### Mechanical Performance of a Fibre Reinforced Composite
|
|
|
|
- Stress/strain behaviour of fibre
|
|
- Stress/strain behaviour of matrix
|
|
- Fibre volume fraction
|
|
- Applied stress direction
|
|
|
|
Longitudinal is along direction of fibres, transverse is 90\textdegree to direction.
|
|
|
|
Fibre composites tend to be much much weaker in transverse direction:
|
|
|
|
<div class="tableWrapper">
|
|
|
|
Composite | Longitudinal UTS | Transverse UTS
|
|
------------ | ---------------- | --------------
|
|
GF/PET | 700 | 20
|
|
CF/Epoxy | 1000 | 35
|
|
Kevlar/Epoxy | 1200 | 20
|
|
|
|
</div>
|
|
|
|
(All units in MPa)
|
|
|
|
# Thermal Properties of Materials
|
|
|
|
## Specific Heat Capacity
|
|
|
|
How much heat energy is required to raise the temperature of a body by one unit:
|
|
|
|
$$ C_p = \frac{\Delta E}{m\Delta T} $$
|
|
|
|
where $c$ is specific heat capacity.
|
|
|
|
It is measured at a constant pressure, usually $1.013\times 10^5$ Pa.
|
|
|
|
## Molar Heat Capacity
|
|
|
|
$$C_pm = \frac{\Delta E}{n\Delta T}$$
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
#### What is a mole?
|
|
|
|
</summary>
|
|
|
|
> The mole (symbol: mol) is the base unit of amount of substance in the International System of
|
|
> Units (SI).
|
|
> It is defined as exactly $6.02214076\times 10^{23}$ elementary entities ("particles")
|
|
|
|
~ [Wikipedia: Mole (unit)](https://en.wikipedia.org/wiki/Mole_(unit))
|
|
|
|
</details>
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
#### How Much Does a mol of Something weigh?
|
|
|
|
</summary>
|
|
|
|
A mol of an element weighs its relative atomic mass ($A_r$) but in grams.
|
|
For example, Carbon-12 has an $A_r$ of 12 (as it's made of 6 neutrons, 6 protons, and 6 electrons
|
|
which have negligible mass) so a mol of Carbon-12 has a mass of 12 g.
|
|
|
|
</details>
|
|
|
|
## Thermal Expansion
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
### Origin of Thermal Expansion
|
|
|
|
</summary>
|
|
|
|
All atomic bonds vibrate, on the magnitude of gigahertz.
|
|
The bonds vibrate about a mean positoin and the vibration is a simple harmonic motion.
|
|
|
|
From the graph below you can see that as energy (in the form of heat) is supplied to the bonds,
|
|
the amplitude of the vibrations get larger and larger.
|
|
You can also see the mean position of the bond gets further and further away, meaning the volume
|
|
of the material also is increasing.
|
|
The mean position of the bond is what dictates the volume, as this means the inter-atomic
|
|
separation increases.
|
|
|
|
![Morse Potential Graph](./images/vimscrot-2021-12-21T19:51:58,667328620+00:00.png)
|
|
|
|
Morse potential is the energy well between 2 bonded atoms.
|
|
The graph is asymmetric due to the repulsion experienced by atoms as they apporach.
|
|
|
|
</details>
|
|
|
|
### Linear Coefficient of Thermal Expansion
|
|
|
|
$$\alpha_L = \frac{\Delta L}{L_0 \Delta T}$$
|
|
|
|
where $L$ is the sample length.
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
#### Example 1
|
|
|
|
A 1 m long bar of aluminium metal cools in the solid state from 660 \textdegree{}C to
|
|
25 \textdegree{}C.
|
|
Calculate the length of the bar after it cools down, given $\alpha_L = 25\times10^{-6}$ K$^{-1}$.
|
|
|
|
</summary>
|
|
|
|
\begin{align*}
|
|
l_0 &= 1 \\
|
|
\Delta T &= T_f - T_0 = 25 - 660 = -635 \\
|
|
\\
|
|
\alpha_L &= \frac{l_f - l_0}{l_0 \Delta T} \\
|
|
\alpha_L l_0 \Delta T &= l_f - l_0 \\
|
|
l_f &= \alpha_L l_0 \Delta T + l_0 = 0.984
|
|
\end{align*}
|
|
|
|
</details>
|
|
|
|
### Linear Thermal Expansion and Isotropism
|
|
|
|
Since isotropic solids have the same properties in all directions, you can say that for an
|
|
isotropic solid:
|
|
|
|
$$\alpha_V = 3\alpha_L = \frac{\Delta V}{V_0 \Delta T}$$
|
|
|
|
### Reasons to Care About Thermal Expansion
|
|
|
|
- A coating on a material may fail if the thermal expansion coefficients do not match
|
|
- A brittle material may thermally shock and fracture due to thermal expansion mismatch between
|
|
the ouside and inside, especially if the material is not very thermally conductive
|
|
|
|
## Thermal Conductivity
|
|
|
|
Thermal conductivity is the rate at which heat power is transferred through a material.
|
|
|
|
$$\frac{Q}{A} = k \frac{\Delta T}{\Delta x}$$
|
|
|
|
where $Q$ is heat power, $A$ is area of the surface, $\frac{\Delta T}{\Delta x}$ is the
|
|
temperature gradient, and $k$ is the thermal conductivity constant.
|
|
|
|
<details>
|
|
<summary>
|
|
|
|
### Origin of Thermal Conductivity
|
|
|
|
</summary>
|
|
|
|
Heat is transferred through materials by electrons (and partially by atomic vibrations)
|
|
|
|
Metals have high thermal conductivity as their delocalised 'sea' electrons are about to move about
|
|
easily.
|
|
This makes them excellent conductors of heat and electricity.
|
|
|
|
Ceramics, glasses, and polymers do not have delocalised electrons and are therefore poor conductors
|
|
of heat and electricity (they are insulators).
|
|
|
|
Polymer foams are even better insulators because they have holes which lowers their density.
|
|
|
|
</details>
|
|
|
|
# Chemical Bonding of Materials
|
|
|
|
Chemical bonds are what holds a material together in solid state.
|
|
There are 5 main types of bonds:
|
|
|
|
Type | Dissociation energy
|
|
-------- | -------------------
|
|
Ionic | 600 to 1500
|
|
Covalent | 300 to 1200
|
|
Metallic | 100 to 800
|
|
Hydrogen | 4 to 23
|
|
vdw | 0.4 to 4
|
|
|
|
The dissociation energy is the energy required to break the bond, or the strength of the bond.
|
|
|
|
## Materials and their Properties and Bonding
|
|
|
|
### Ceramics and Glasses
|
|
|
|
Ceramics and glasses are composed of mixed ionic and covalent bonding.
|
|
Their strong and rigid bonds have no ability to slide past each other.
|
|
This makes the materials brittle.
|
|
|
|
### Metals
|
|
|
|
Metals are based on metallic bonding (woah).
|
|
This type of bonding *does* allow for ions to slide past each other, making metals ductile.
|
|
|
|
### Polymers
|
|
|
|
Polymer chains made of C-C covalent bonds are strong, like those found in ceramics.
|
|
|
|
However, in thermoplastics polymers, the materials can yield by having the chains untangle and
|
|
then align, as the chains slide past each other.
|
|
This means that **stronger bonds between polymer chains means a higher yield stress in thermoplastic
|
|
polymers**.
|
|
|
|
# Crystallisation of Materials
|
|
|
|
## Atomic Arrangement
|
|
|
|
- No order
|
|
- Short range order
|
|
|
|
Silica glasses have short range order on the atomic scale.
|
|
They are composed of regular SiO$_4$ units which all have the same bond length and bond angles.
|
|
|
|
However, these units bond together irregularly, which results in different length chemical bonds
|
|
and angles between the units, meaning they do not have any long range order.
|
|
|
|
- Long range order
|
|
|
|
## Cubic Unit Cells
|
|
|
|
- Lattice Parameter --- One side of a unit cell
|
|
|
|
The lattice parameter can be different for each side of a cell.
|
|
|
|
- Simple cubic unit (SC):
|
|
|
|
![](./images/vimscrot-2021-12-21T21:28:34,863875469+00:00.png)
|
|
|
|
Lattice Parameter = 2r
|
|
|
|
- Face centred cubic (FCC)
|
|
|
|
![](./images/vimscrot-2021-12-21T21:44:21,618384089+00:00.png)
|
|
|
|
- Body centred cubic (BCC)
|
|
|
|
![](./images/vimscrot-2021-12-21T21:44:40,816535537+00:00.png)
|
|
|
|
### Packing Factor
|
|
|
|
$$\text{packing factor} = \frac{\text{ions per unit cell} \times V_{ion}}{V_{cell}}$$
|
|
|
|
### Theoretical Density
|
|
|
|
$$\text{theoretical density} = \frac{\text{ions per unit cell} \times m_{ion}}{V_{cell}}$$
|
|
|
|
### Polymorphism
|
|
|
|
Example of a polymorphic solid-state phase transfomration of iron at 1185 K and 1 atm:
|
|
|
|
$$\text{Fe}_{\text{BCC}} \longleftrightarrow \text{Fe}_{\text{FCC}}$$
|
|
|
|
Below 1185 K and at 1 atm, only BCC exists. Above 1185 K and at 1 atm, only FCC exists.
|
|
|
|
### Points, Directions, Planes in a Cubic Unit Cell
|
|
|
|
![](./images/vimscrot-2021-12-21T22:33:35,491930818+00:00.png)
|
|
|
|
### Slip Systems in Metals
|
|
|
|
Metal ions lying in close-packed planes and directions move more easily, increasing ductility.
|
|
The combination of a close packed plane and direction is called a *slip system*.
|
|
|
|
A close packed direction is where ions touch all the way along the direction.
|
|
|
|
A close packed plane is where ions touch all the way on a plane.
|
|
|
|
FCC metal ductility is mainly controlled by the *(111) slip plane*
|
|
|
|
![](./images/vimscrot-2021-12-21T22:40:37,978916142+00:00.png)
|
|
|
|
|
|
## X-Ray Diffraction (Bragg's Law)
|
|
|
|
The wavelength of x-rays, $\lambda$, is roughly equal to the distance, $d$, between atom/ion layers.
|
|
This allows x-rays to probe for $d$ via Bragg's Equation:
|
|
|
|
![](./images/vimscrot-2021-12-21T22:44:15,147729727+00:00.png)
|
|
|
|
Requirements for the x-rays:
|
|
|
|
- Monochromatic
|
|
- Coherent (phase difference of $2\pi n$ where n is any integer)
|
|
- Parallel with each other
|
|
|
|
|
|
The incoming x-rays 1 and 2 strike the rows of ions in the crystal and are diffracted, which can be
|
|
considered reflection at the atomic level.
|
|
The angle of incidence equals the angle of reflection.
|
|
|
|
The outgoing x-rays 1 and 2 are coherent only if the extra path travelled by ray 2, $2d\sin\theta$
|
|
is any multiple, $n$, of $\lambda$. Or:
|
|
|
|
$$n\lambda = 2d\sin\theta$$
|
|
|
|
This is Bragg's Law.
|
|
|
|
# Metals
|
|
|
|
## Defects on the Atomic Scale
|
|
|
|
Defects on the atomic scale have a significant effect on yield stress, ultimate tensile stress, and
|
|
ultimate fracture stress.
|
|
|
|
The yield stress of a real metal(-alloy) is much lower than the theoretical yield stress for
|
|
the perfect metal(-alloy) crystal.
|
|
This difference is because of the defects in the metal, particularly dislocations, as the
|
|
dislocations allow the ions to slide past each other at much lower yield stresses.
|
|
|
|
The 5 types of defects are:
|
|
|
|
- Grain boundaries
|
|
- Vacancies (missing ion)
|
|
- Dislocations (missing row of ions)
|
|
- Impurity ions
|
|
- Crystalline includison
|
|
|
|
![](./images/vimscrot-2021-12-22T13:02:28,180694109+00:00.png)
|
|
|
|
### Dislocation Movement vs. Simple Sliding
|
|
|
|
The layers of ions in a crystalline metal could simply over each other:
|
|
|
|
![](./images/vimscrot-2021-12-22T13:16:39,506214227+00:00.png)
|
|
|
|
However, the stress required for simple sliding is much higher than the stress required to move a
|
|
dislocation.
|
|
This is because dislocation motion is successive sliding of the partial plane of ions under applied
|
|
shear stress (black arrow).
|
|
The vacancy in the slip plane (yellow arrow) moves in steps in sequence from left to right.
|
|
|
|
![](./images/vimscrot-2021-12-22T13:19:51,513367988+00:00.png)
|
|
|
|
If there are no dislocations then plastic deformation is delayed to a higher applied stress,
|
|
meaning the yield stress of the metal would be much higher.
|
|
|
|
Dislocations move more easily on specific planes and in specific directions called the
|
|
slip planes and slip directions which make up what is known as the
|
|
[slip system](#slip-systems-in-metals).
|
|
|
|
There are a very large amount of dislocations in metals and alloys.
|
|
Dislocation density is expressed as total length of dislocations per unit volume.
|
|
|
|
## Single Crystal Metals
|
|
|
|
![](./images/vimscrot-2021-12-22T12:58:16,773351925+00:00.png)
|
|
|
|
Normally when a molten metal is cooled to a solid, then lots of tiny crystals (grains) grow in
|
|
different directions until they impinge.
|
|
The grain boundaries are a source of mechanical weakness.
|
|
|
|
A single crystal metal is one for which the casting is cooled to form just one giant crystal:
|
|
|
|
1. The molten metal is cast into a mould
|
|
2. At the very base of the mould, the temperature is dropped and the alloy crystallises into many
|
|
little crystals
|
|
3. The crystals grow upwars through the liquid and meet a spiral tube and are constricted
|
|
4. This tube only allows one crystal to grow through the spiral and then into the main mould
|
|
|
|
## Polycrystalline Metals
|
|
|
|
Most normal metals you see everyday are polycrystalline.
|
|
|
|
![](./images/vimscrot-2021-12-22T12:58:38,918714742+00:00.png)
|
|
|
|
![Acid etched surface of a polycrystalline metal](./images/vimscrot-2021-12-22T12:59:11,940527867+00:00.png)
|
|
|
|
## Elastic and Plastic Strain in Metals
|
|
|
|
When you apply a tensile stress to a mteal, this will produce a shear stress in any part of the
|
|
metallic lattice that is not parallel or perpendicular to the applied stress.
|
|
Under the action of shear stress, the metallic lattice will tend to experience a combination of
|
|
elastic strain and plastic strain:
|
|
|
|
![](./images/vimscrot-2021-12-22T13:46:45,608572706+00:00.png)
|
|
|
|
## Raising the Yield Stress of a Metal
|
|
|
|
There are 4 main ways to raise the yield stress of a metal:
|
|
|
|
- Make a solid-solution---by metal alloying or atomic addition
|
|
- Precipitate crystalline inclusions---by metal alloying or atomic additions and then heat treatment
|
|
- Work-harden --- by processing and/or cold-working
|
|
- Decrease the grain size --- by processing and/or heat-treatment
|
|
|
|
### Make a Solid-Solution
|
|
|
|
Adding an alloying element, B, to the host, A, forms a solid-solution as the ions or atoms of B
|
|
dissolve in A.
|
|
|
|
The impurity particles of B are a different size from the particles of A, distorting the metal
|
|
lattice.
|
|
The larger the difference in radii of the particles, the bigger the distortion.
|
|
|
|
![Substitutional addition replaces ions in the host](./images/vimscrot-2021-12-22T14:21:25,321894455+00:00.png)
|
|
|
|
![Interstitial addition adds particles between the ions in the host](./images/vimscrot-2021-12-22T14:21:32,009562988+00:00.png)
|
|
|
|
The particles of B tend to diffuse to dislocations and immobilise them.
|
|
This is why alloying increases the yield stress.
|
|
|
|
Impurity particles generate lattice strain in the structure too:
|
|
|
|
- Smaller particles introduce a compressive strain in the surrounding lattice
|
|
- Larger particles introduce a tensile strain in the surrounding lattice
|
|
|
|
![How Ni content in Cu affects Yield and Ultimate Tensile Stress](./images/vimscrot-2021-12-22T14:25:58,567632767+00:00.png)
|
|
|
|
### Precipitating Crystalline Inclusions
|
|
|
|
When adding an element, B, to a host, A, exceeds the solubility, the result is the formation of a
|
|
solid-solution with a fixed ratio of B to A, but also precipitated crystals of a different ratio of
|
|
B to A.
|
|
|
|
![](./images/vimscrot-2021-12-22T14:30:14,141230179+00:00.png)
|
|
|
|
Crystalline inclusions are really difficult to shear, especially if they are small, numerous, and
|
|
have high Vickers' hardness.
|
|
This slows down dislocation movement, increasing yield stress.
|
|
|
|
### Work-Hardening and Cold Working
|
|
|
|
We can use room temperature deformation to increase the number of dislocations present in a metal.
|
|
As the % cold-work (%CW) is increased, the number of dislocations present also increases:
|
|
|
|
$$\% CW = \frac{A_0 - A_d}{A_0} \times 100\%$$
|
|
|
|
where $A_0$ is the initial cross sectional area and $A_d$ is the final cross sectional area.
|
|
|
|
A carefully prepared sample has a dislocation density, $\rho_d$ of around $10^3$ mm mm$3$,
|
|
whereas for a heavily deformed sample it is around $10^{10}$.
|
|
|
|
A high density of dislocations means they are more likely to get entangled with each other,
|
|
making it harder for dislocations to move.
|
|
Therefore as $\rho_d$ increases, yield stress does too.
|
|
|
|
### Decreasing the Grain Size
|
|
|
|
- Most metals are polycrystalline with many grains.
|
|
- Different grains will have a different crystal orientation.
|
|
- Grains impede dislocation motion
|
|
|
|
As you decrease grain size, you get more grain boundaries which basically creates more barriers
|
|
to prevent slip.
|
|
|
|
This is because a dislocation would have to change orientation across a grain boundary and "ionic
|
|
disorder in the grain boundary results in discontinuity of slip" (A.B Seddon University of
|
|
Nottingham 2020) (I think that's repeating it but it said it on the slideshow sooo...).
|
|
|
|
So for any given metal, the fine grained is harder and has greater yield stress than the coarse
|
|
grained version of it.
|
|
|
|
#### Hall Petch Equation
|
|
|
|
$$\sigma_{yield} = \sigma_0 + k_yd^{-0.5}$$
|
|
|
|
where $d$ is the grain size and $\sigma_0$ and $k_y$ are material constants.
|
|
|
|
Therefore a plot of $\sigma_{yield}$ against $d^{-0.5}$ would results in a straight line.
|
|
|
|
# Diffusion
|
|
|
|
Diffusion is atomic or ionic movement down a concentration gradient.
|
|
|
|
## Solid State Diffusion
|
|
|
|
![](./images/vimscrot-2021-12-22T13:54:09,340198890+00:00.png)
|
|
|
|
Solid state diffusion is the stepwise migration (*march*) of atoms or ions through a lattice, from
|
|
site to site.
|
|
|
|
In order for this to happen, there must an adjacent vacant site.
|
|
The diffusion particle must also have sufficient thermal energy to 'jump' to the new site.
|
|
|
|
### Vacancy Diffusion (Diffusion of Metal Ions)
|
|
|
|
![](./images/vimscrot-2021-12-22T13:59:03,553059517+00:00.png)
|
|
|
|
### Interstitial DIffusion (Diffusion of Small, Non-Metallic Particles)
|
|
|
|
![](./images/vimscrot-2021-12-22T13:59:53,080635889+00:00.png)
|
|
|
|
## The Math(s) of Diffusion
|
|
|
|
Diffusion is time dependent.
|
|
|
|
For steady state diffusion, Fick's 1st Law holds:
|
|
|
|
$$J = -D \frac{\mathrm{d}C}{\mathrm{d}x}$$
|
|
|
|
where $J$ is the *flux*, $\frac{\mathrm{d}C}{\mathrm dx}$ is the concentration gradient, and $D$ is
|
|
the constant of proportionality known as the *diffusion coefficient*.
|
|
|
|
$D$ is constant for a particular metal at a particular temperature.
|
|
The *flux*is the number of atoms or ions moving per second through a cross sectional area.
|
|
|
|
### Things that Affect the Speed of Diffusion
|
|
|
|
- size of the diffusion species --- smaller species results in faster diffusion
|
|
- temperature --- more thermal energy allows more particles to have enough energy to make the 'jump'
|
|
- host lattice
|
|
|
|
- simple cubic --- 52% occupancy of ions
|
|
- body centered cubic --- 68% occupancy of ions
|
|
- face centered cubic --- 74% occupancy of ions
|
|
|
|
Diffusion is faster in a BCC host than in an FCC host for iron ions in an iron host and also for
|
|
carbon atoms diffusing into an iron host.
|
|
However this is not always the case.
|
|
|
|
### Influence of Temperature on Diffusion (Arrhenius Equation)
|
|
|
|
You can apply the Arrhenius equation for all thermally activated diffusion:
|
|
|
|
$$D = D_0 \exp{\left( - \frac{Q}{RT} \right)}$$
|
|
|
|
where $D$ is the diffusion coefficient, $D_0$ is the frequency factor, $Q$ is the activation energy,
|
|
$R$ is the ideal gas constant (8.31 J k$^{-1}$ mol$^{-1}$).
|
|
|
|
You can find the diffusion distance, $x$, with the following equation:
|
|
|
|
$$x ~ \sqrt{Dt}$$
|
|
|
|
![](./images/vimscrot-2022-02-28T20:31:12,395307966+00:00.png)
|
|
|
|
|
|
# Materials in Sustainable Transport
|
|
|
|
- Concerns over use of fossil fuels, climate change
|
|
- Const of energy
|
|
- Energy use in making and moving vehicles
|
|
- Rising energy prices mean cost of fuel is comparable to cost of car
|
|
- 1/4 of energy used in UK is to transport goods and people
|
|
- Legislation and voluntary targets set by EU to improve fuel efficiency
|
|
- In 2015 average CO2 emmisions as 130 g / km
|
|
- Engine powerhas gone up significantly from 2001 to 2018 (~30%) yet engine displracement has gone
|
|
down ~10% and CO2 emissions down ~18% while weight has gone up ~10%
|
|
|
|
## Is the car emissions reduction target significant?
|
|
|
|
Overall CO2 emissions in 2016 is 466 Megatonnes.
|
|
|
|
Does a reduction from 130 g / km to 95 g / km (a 35 g/km reduction) make a significant difference?
|
|
|
|
There are 33 million registered cars in the uk.
|
|
|
|
If they average around 8000 miles each (~13000 km) per year that's a ~15 Megatonne reduction,
|
|
or about 3% of the annual C02 emmissions, a significant reduction.
|
|
|
|
## Materials in Cars
|
|
|
|
- Most of the energy used by cars is during driving (71%)
|
|
- This means the mass of the vehicle has a great effect on its emmissions across a lifetime
|
|
- The body, suspension, drivetrain, and interior all contribute roughly a quarter to the mass of the
|
|
car
|
|
- However, the mass of cars are increasing
|
|
|
|
### Material Substitution
|
|
|
|
- The material will likely have performance requirements:
|
|
|
|
- It may need to be a physical size
|
|
- It may need to operate at certain temperatures
|
|
- It may need to bear a certain load
|
|
|
|
- The component mustalso be designed for convenient manufacturing, assembly, servicing, disposal,
|
|
remanufacturing and/or disassembly
|
|
|
|
#### Case Study --- 2012 Honda Accord
|
|
|
|
- Body --- opted to stay with steel --- aluminium intense and multi-material approaches were both
|
|
rejected due to higher costs and limitations in manufacturing and assembly.
|
|
Recyclability was also noted as an issue due to different grades of aluminium needing to be
|
|
separated at end of life.
|
|
- Doors and bonnets --- move to aluminium from steel --- more costly but the mass savings made this
|
|
option worth it
|
|
- Wiring --- aluminium to copper --- lower mass for same conductivity, copper is more expensive
|
|
(I think)
|
|
- Seats --- steel to composites or magnesium structural components --- very high weight savings
|
|
|
|
## Choosing a Material
|
|
|
|
|
|
|
|
|
|
# Glossary
|
|
|
|
- liquidus - for a system of more than one component, the liquidus is the lowest temperature at
|
|
which the whole system is all in the liquid state.
|
|
- solidus - for a system of more than one component, the solidus is the highest temperature at which
|
|
the whole system is still in the solid state
|