634 lines
19 KiB
Markdown
Executable File
634 lines
19 KiB
Markdown
Executable File
---
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author: Alvie Rahman
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date: \today
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title: MMME1029 // Materials
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tags: [ uni, nottingham, mechanical, engineering, mmme1029, materials ]
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---
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\tableofcontents
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# Lecture 1 (2021-10-04)
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## 1A Reading Notes
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### Classification of Energy-Related Materials
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- Passive materials---do not take part in energy conversion e.g. structures in pipelines, turbine
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blades, oil drills
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- Active materials---directly take part in energy conversion e.g. solar cells, batteries, catalysts,
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superconducting magnests
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- The material and chemical problems for conventional energy systems are mostly well understood and
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usually associated wit structural and mechanical properties or long standing chemical effects like
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corrosion:
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- fossil fuels
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- hydroelectric
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- oil from shale and tar
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- sands
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- coal gasification
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- liquefaction
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- geothermal energy
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- wind power
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- bomass conversion
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- solar cells
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- nuclear reactors
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### Applications of Energy-Related Materials
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#### High Temperature Materials (and Theoretical Thermodynamic Efficiency)
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- Thermodynamics indicated that the higher the temperature, the greater the efficiency of heat to
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work:
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$$ \frac{ T_{high} - T_{low} }{ T_{high} } $$ where $T$ is in kelvin
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- The first steam engines were only 1% efficient, while modern steam engines are 35% efficient
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primarily due to improved high-temperature materials.
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- Early engines made from cast iron while modern engines made from alloys containing nickel,
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molybdenum, chromium, and silicon, which don't fail at temperature above 540 \textdegree{}C
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- Modern combustion engines are nearing the limits of metals so new materials that can function
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at even higher temperatures must be found--- particularly intermetallic compounds and ceramics are
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being developed
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## Types of Stainless Steel
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- Type 304---common; iron, carbon, nickel, and chromium
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- Type 316---expensive; iron, carbon, chromium, nickel, molybdenum
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## Self Quiz 1
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1. What is made of billion year old carbon + water + sprinkling of stardust?
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> Me
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2. What are the main classifications of materials?
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> Metals, glass and ceramics, ~~plastics, elastomers,~~ polymers, composites, and semiconductors
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3. [There are] Few Iron Age artefacts left. Why?
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> They rusted away
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4. What is maens by 'the micro-structure of a material'?
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> The very small scale structure of a material which can have strong influence on its physical
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> properties like toughness and ductility and corrosion resistance
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5. What is a 'micrograph' of a material?
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> A picture taken through a microscope
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6. What microscope is used to investage the microstructure of a material down to a 1 micron scale
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resolution?
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> Optical Microscope
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7. What microscope is used [to investigate] the microstructure of a material down to a 100 nm scale
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resolution?
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> Scanning Electron Microscope
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8. What length scales did you see in the first slide set?
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> 1 mm, 0.5 mm, 1.5 \textmu{}m
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9. What material properties were mentioned in the first slide set?
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> Hardness, brittleness, melting point, corrosion, density, thermal insulation
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## Self Quiz 2
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1. What is the effect of lowering the temperature of rubber?
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> Makes it more brittle, much less elastic and flexible
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2. What material properties were mentioned in the second slide set?
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> Young's modulus, specific heat, coefficient of thermal expansion
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# Lecture 2
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## Properties of the Classes
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### Metals
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- Ductile (yields before fracture)
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- High UFS (Ultimate Fracture Stress) in tension and compression
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- Hard
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- Tough
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- High melting point
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- High electric and thermal conductivity
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### Ceramics and Glasses
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- Brittle --- elastic to failure, no yield
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- Hard (harder than metals)
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- Low UFS under tension
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- High UFS under compression
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- Not tough
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- High melting points
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- Do not burn as oxide ceramics are already oxides
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- Chemically resistant
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- Poor thermal and electric conductivity
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- Wide range of magnetic and dielectric behaviours
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### Polymers
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- Organic---as in organic chemistry (i.e. carbon based)
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- Ductile
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- Low UFS in tension and compression
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- Not hard
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- Reasonably tough
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- Low threshold temperature to charring and combustion in air or pure oxygen
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- Low electrical and thermal conductivity
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- There are some electrically conductive polymers
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### Composites
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- Composed of 2 or more materials on any scale from atomic to mm scale to produce properties that
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cannot be obtained in a single material
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- Larger scale mixes of materials may be called 'multimaterial'
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- Material propertes depends on what its made of
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## Terms
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### Organic vs Inorganic Materials
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- Organic materials are carbon based
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- From chemistry, organic compounds are ones with a C-H bond
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- Inorganic compounds do not contain the C-H bond
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### Crystalline vs Non-Crystalline Materials
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- Most things are crystalline
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- Ice
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- Sugar
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- Salt
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- Metals
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- Ceramics
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- Glasses are non-crystalline
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## Material Properties
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### Density
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$$\rho = \frac m v$$
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- Density if quoted at STP (standard temperature and pressure---$298$ K and $1.013\times 10^5$ Pa)
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- Metals, ceramics, and glasses are high density materials
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- Polymers are low density
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- Composites span a wide range of density as it depends on the materials it is composed of
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e.g. composites with a metal matrix will have a much higher density than those with a polymer
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matrix
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### Melting Points
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- Measured at standard pressure and in an intert atmosphere (e.g. with Nitrogen, Argon, etc)
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- Diamond and graphite will survive up to 4000 \textdegree{}C in an inert atmosphere but would
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burn at around 1000 \textdegree{}C in oxygen
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- High melting points -> high chemical bond strength
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### Corrosion
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- It's not just metals that corrode
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- Polymers
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- UV degradation
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- Water absorption can occur in degraded polymers
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- Glass
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- Leaching
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- Sodium ions can leave the glass when covered in water. If the water stays, the high pH water
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can damage the class
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## Self Quiz
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### Consolidation Questions 1
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1.
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i. Metal
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ii. Titanium
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2.
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i. Polymer
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ii. Polyester
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3.
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i. Ceramic
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ii. Alumino-silicate
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4.
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i. Composite
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ii. GFRP or CFRP
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5.
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i. Metal
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ii. Aluiminium alloy
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6.
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i. Metal
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ii. Aluiminium alloy
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7.
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i. Polymer
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ii. Acrylic
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8.
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i. Ceramimc
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ii. Glass
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9.
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i. Composite
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ii. Concrete
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### Consolidation Questions 2
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> ~~C~~ B
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# Polymers
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## Introduction to Polymers
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There are 3 types of polymers:
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- thermoplastics
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No cross links between chains.
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The lack of cross links allows recycling of polymers by heating it above the glass transition
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material, $T_g$, lowering the viscosity.
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An example of thermoplastics is PET, used in water bottles
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- thermosets
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has lots of cross-links between chains, making it more rigid.
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Heating does not lower its viscosity making them much harder/impossible to recycle.
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and example of thermosets is melamine formaldehyde, used on kitchen tabletops
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- elastomers
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has some cross links and a lot of folding of chains
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Latex is an example of an elastomer
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Polymers are relatively new materials, lightweight, durable, flammable, and degraded by UV light.
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They are made of long carbon-carbon chains.
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### Stress-Strain Curve of Polymers
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## Thermoplastics
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The simplest polymer is poly(ethene):
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When 2 polymer chains get close together, Van der Waals (vdw) forces keep them together.
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vdw forces are very weak, much weaker than the covalent bonds inside the polymer.
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### Stress Strain Curve
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- During linear deformation, the carbon chains are strethed.
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- At yield stress, the carbon chains get untangled and slide past eache other.
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- Necking initially allows the chains to slide at lower stress.
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- As the chains pull, align, and get closer, the vdw forces get stronger and more stress is required
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to fracture.
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### Crystalline and Amorphous/Glassy Solids (Heating and Cooling)
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#### Amorphous Thermoplastics
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- As you heat above $T_g$, the chains get easier to move past each other.
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- It is known as an *amorphous supercooled liquid*.
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- There is not really a melting point are there are no crystals, but $T_m$ is the point where the
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chains are easy to move
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#### Crystalline Polymers
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- The glass transition point does not exist for crystalline polymers
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- The solid is difficult to deform below $T_m$ and is not ductile
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- Above $T_m$ the chains are very easy to move past each other
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#### Semi-Crystalline
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- Below $T_g$, only local movements in chains are possible, so the material is less ductile.
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The solid crystalline regions makes it difficult to move the chains.
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- Between $T_g$ and $T_m$, the glassy chains are easier to move but the crystalline regions remain
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difficult
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- Above $T_m$ the chains easily move past each other
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### Specific Volume vs Temperature
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#### Path ABCD
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- a-b --- Start cooling the true liquid
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- b-c --- At the freezing point, $T_m$, the true liquid freezes diretly to a crystalline solid
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- c-d --- The crystalline solid cools t room temperature as the temperature is lowered
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#### Path ABEF
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- a-b --- start cooling the true liquid
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- b --- at the freezing point nothing freezes
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- b-e --- the liquid becomes *supercooled* and contracts and becomes more viscous as the temperature
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decreases.
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The supercooled liquid region is between $T_g$ and $T_m$
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Supercooling requires you to cool the sample quicker than you would for path ABCD
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- e --- $T_g$ is reached and the supercooled liquid sets to a amorphous solid
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- e-f --- the amorphous solid cools from room temperature and contract as the temperature is lowered
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## Relative Molar Mass and Degree of Polymerisation
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- Number Average RMM --- $\bar M_n = \sum x_iM_i$
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- Weight Average RMM --- $\bar M_w = \sum w_iM_i$
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- Degree of polymerisation --- $n_n = \frac {\bar M_n} m$ and $n_w = \frac {\bar M_w} m$
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where
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- $M_i$ is the RMM of the chain
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- $x_i$ is the fraction of the polymer that is composed of that chain by number/quantity
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- $w_i$ is the fraction of the polymer that is composed of that chain by mass/weight
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- $m$ is the RMM of the monomer from which the polymer was made
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## Making Polymers
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There are two ways to make polymers:
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- [Addition Poymerisation](http://www.chemguide.co.uk/14to16/organic/addpolymers.html)
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- [Condensation Polymerisation](https://www.chemguide.uk/14to16/organic/condpolymers.html)
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# Elastic Deformaion
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Elastic deformation is deformation where the material will return to original shape after the
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applied stresses are removed.
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Elastic deformation is the first type of deformation that happens when stresses are applied to
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a material and is represented by the straight line at the beginning of a stress-strain curve.
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## Modulus of Resillience ($E_r$)
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This is the area under the elastic portion of a stress-strain graph of a material.
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# Plastic Deformation
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## Toughness (Absorbing Energy Through Plastic Deformation)
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- The toughness of a material is its ability to absorb energy through plastic deformation
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without fracturing
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- The material toughness of a ductile material can be determined by finding the area under its
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stress-strain curve (e.g. by integrating the graph)
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- Brittle materials like ceramics and glasses exhibit no material toughness
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- Ductile materials have a possibility of achieving large material toughness
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Ductility measures how much something deforms plastically before fracture, but just because a
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material is ductile does not make it tough.
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*The key to high material toughness is a good combination of large ultimate fracture stress and
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large ductility*.
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- The unit of toughness is energy per unit volume as toughness can be mathematically expressed as:
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$$toughness = \int^{\varepsilon_f}_0\! \sigma \,\mathrm{d}\varepsilon
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= \frac{\text{Energy}}{\text{Volume}} $$
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- A metal may have satisfactory toughness under static loads but fail under dynamic loads or impact
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This may be caused by the fact that ductility and toughness usually decrease as rate of loading
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increases.
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- Ductility and toughness decreasee with temperature
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- Notches in the material affect the distribution of stress in the material, potentially changing
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it from a uniaxial stress to multiaxial stress
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### Charpy Impact Test
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Measures material toughness by determining the amount of energy absorbed during fracture.
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It works by essentially dropping a hammer into a sample whose dimensions are standardized
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(usually either by BSI or ISO) and measuring how high the hammer goes up on the other side,
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after it breaks the material
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The height of the hammer after impact will tell you how much enery is left in it, and therefore
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how much has been aborbed by the now broken sample.
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Under a microscope, more ductile fractures appear fibrous or dull, whereas less ductile surfaces
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have granular or shiny surface texture.A
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The charpy test has a couple issues:
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- Results are prone to scatter as it is difficult to achieve a perfectly shaped notch
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- Temperature has to be strictly controlled since it affects a material's ductility
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#### The setup of a charpy impact test
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1. Sample is made to standardized dimensions, with a notch
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2. Sample is placed on support
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3. A very heavy hammer pendulum of mass $m$ is dropped from rest at $h_0$ to swing about a pivot,
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reaching $E_{kmax}$ vertically below the pivot.
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4.
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a. If no sample is in place then the hammer will swing back up on the other side to a height of
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$h_h$ where theoretically $h_h = h_0$
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b. With a sample placed vertically below, some of the $E_k$ is transferred to the sample to bend
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and (usually) break the sample.
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If breaks the sample, it will swing up to the other side, where its max height, $h_f$ can be
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used to calculate how much energy was used to break the sample:
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$$E = mg(h_h-h_f)$$
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Where $g$ is acceleration due to gravity.
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# Ductility
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Ductility is the plastic deformation a material withstands before fracture.
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# Griffith Surface Flaws
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These flaws vary in size and shape.
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They limit the ability of any material, brittle or ductile, to withstand tensile stresses as they
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concentrate the tensile forces applied to a smaller area.
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The stress at the tip of the flaw:
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$$\sigma_{actual} = 2\sigma\sqrt{\frac a r}$$
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For deep ($a$ is large) or thin ($r$ is small) the stress is magnified and, if it exceeds the UFS
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in a brittle material, the flaw will grow into a crack, resulting in the brittle material
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fracturing.
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However in a ductile material, the tip of the flaw can heal, reducing $a$ and increasing $r$.
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This is due to the chemical structure of ductile materials like metals.
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## Stress Intensity Factor
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Stress Intesity Factor, $K$:
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$$K = f\sigma\sqrt{\pi a}$$
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where:
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- $f$ is the geometry factor (1 would represent an infinite width sample, and 0 a 0 width sample)
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- $\sigma$ is applied tensile strength
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- $a$ is flaw depth
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## Fracture Toughness
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![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)
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The value of $K$ that causes the notch to grow and cause fractures.
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This is value is known as the fracture toughness, $K_c$.
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At low thicknesses fracture toughness depends on thickness but as thickness increases, $K_c$
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decreases to the constant value, the plane strain fracture toughness, $K_{1c}$.
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# Composites
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Composites are made of two or more materials, which when combined together, at up to a milimetre
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scale, have superior properties to their parent materials.
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Composites tend to be 2-phase: a dispersed phase in a matrix.
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The disepersed phase tends to be fibres (large aspect ratio) or particles (low aspect ratio) which
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are embedded in a matrix, which are often resins.
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Composite properites are affected by the dispersed phase geometry:
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- Shape
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- Size
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- Distribution
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- Relative orientation (for fibres)
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## Rule of Mixtures
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$E_c$ lies between the arithmetic mean (upper limit):
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$$V_mE_m + E_pV_p$$
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and the geometric mean (lower limit):
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$$\frac{V_mE_mE_pV_p}{V_mE_m + E_pV_p}$$
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Where $E_c$, $E_m$, $E_p$ are the Young's moduluses of the composite, matrix, and particles,
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respectively, and $V_m$ and $V_p$ are the volume of the matrix and particles, respectively.
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## Particle Reinforced Composites
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### Applications of Composites
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<details>
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<summary>
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#### Tungsten Carbide Cobalt for Cutting Tools
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</summary>
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The Tungest Carbide (WC) particle are a truly brittle ceramic.
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They are very hard but the brittleness means they are easy to break.
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The solution is to hold small WC particles in a ducitle metal matrix.
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In this case it is Cobalt (Co).
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This way, crack in one WC particle does not necessarily mean other particles are broken,
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meaning the cutting tool overall still works.
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Another advantage of this composite is that WC is not very thermally conductive and has a high
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melting point, which allows it to work well the environment it's in.
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</details>
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<details>
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<summary>
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#### Resin Bonded Alumina for Sanding Disks
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</summary>
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This is another example of brittle but hard ceramics being put in a ductile matrix.
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In this case it's a resin.
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It follows the same idea---separating the ceramics into small particles means the particles can
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break and the product still works overall, as there are thousands of particles which are not broken.
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</details>
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## Fibre Reinforced Composites
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### Specific Property
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Specific Property of a composite is a property divided by density of composite.
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Here are some examples of specific properties:
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- Specific ultimate tensile stress $= \frac{\sigma_{UTS}}{\rho_c}$
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- Specific Young's modulus/stiffness $= \frac{E_c}{\rho_c}$
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### Influence of the Fibres
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Depends on:
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- Fibre type
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- Fibre length and diameter
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- Fibre orientation
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- Strength of bond between fibre and matrix
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### Stress Strain Graph of a Fibre Reinforced Composite
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Note that the composite fails at the same strain as the fibres but yields at the same strain as
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the polymer matrix.
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The elastic behaviour of the composite before yielding is dependent on the strength of the chemical
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bonds between the surface of the fibre and matrix.
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### Mechanical Performance of a Fibre Reinforced Composite
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- Stress/strain behaviour of fibre
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- Stress/strain behaviour of matrix
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- Fibre volume fraction
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- Applied stress direction
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Longitudinal is along direction of fibres, transverse is 90\textdegree to direction.
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Fibre composites tend to be much much weaker in transverse direction:
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Composite | Longitudinal UTS | Transverse UTS
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------------ | ---------------- | --------------
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GF/PET | 700 | 20
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CF/Epoxy | 1000 | 35
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Kevlar/Epoxy | 1200 | 20
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(All units in MPa)
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