Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Summary

In this TLP we have:

1. Learned how the Young's modulus of a material may be determined using the relationship between the deflection of a cantilever beam δ and the load P applied to it, given by

$\delta = \frac{1}{3}\frac{{P{L^3}}}{{EI}}$

where L is the distance from support to point of load application, I is the second moment of area of the beam's cross section, and E is the Young's modulus of the beam's material.

2. Used measurements of the deflection and load of a steel cantilever beam to determine the Young's modulus of steel as 210 GPa.

3. Looked at how the asymmetry in the energy-separation graph for atoms in a solid gives rise to an increase in the average interatomic spacing of vibrations as the temperature is increased, the origin of thermal expansion.

4. Derived a formula relating curvature κ to the length x and deflection δ of a bi-material strip:

$\kappa = \frac{{2\sin \left[ {{{\tan }^{ - 1}}\left( {\delta }/{x} \right)} \right]}}{{\sqrt {\left( {{x^2} + {\delta ^2}} \right)} }}$

5. Defined the misfit strain Δε for the two components of a bi-material strip as

Δε  = (αA - αBΔT

and quoted a formula relating the curvature κ to the misfit strain, the thickness of the strips h (of equal thickness) and the ratio of the Young's moduli E*

$\kappa = \frac{{12 \Delta \varepsilon }}{{{h_{}}\left( {{E_*} + 14 + 1 / {E_*}} \right)}}$

6. Used measurements of the change in shape of a steel-aluminium bi-material strip immersed in liquid nitrogen to estimate the boiling temperature of nitrogen as -193ºC.

7. Used measurements of the change in shape of an aluminium-polycarbonate bi-material strip immersed in liquid nitrogen to estimate the thermal expansivity of the polycarbonate as 4.5 x 10-K-1.