diff --git a/mechanical/mmme1029_materials.md b/mechanical/mmme1029_materials.md index 215b6e0..9c5a414 100755 --- a/mechanical/mmme1029_materials.md +++ b/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 + +
+ + +#### Tungsten Carbide Cobalt for Cutting Tools + + + +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. + +
+ +
+ + +#### Resin Bonded Alumina for Sanding Disks + + + +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. +
+ +## 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)