Add notes on composites

mechanical/mmme1029_materials.md

@@ -515,3 +515,119 @@ 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:
+
+  Composite    | Longitudinal UTS | Transverse UTS 
+  ------------ | ---------------- | --------------
+  GF/PET       | 700              | 20
+  CF/Epoxy     | 1000             | 35
+  Kevlar/Epoxy | 1200             | 20
+
+  (All units in MPa)