Calculate the stress developed inside a tooth


Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57oC is drunk. You can take body temperature to be 37oC and α = 1.7 × 10-5oC, bulk modulus for copper = 140 × 109 N/m2.


Decrease in temperature, ∆t = 57 – 37 = 20oC

Coefficient of linear expansion, α = 1.7 × 10-5oC

Bulk modulus for copper, B = 140 × 109 N/m2

Coefficient of cubical expansion, γ = 3α = 5.1 × 10-5oC

Increase in volume with increase in temperature is given as

$\Delta V=\gamma V \Delta t \Rightarrow \frac{\Delta V}{V}=\gamma \Delta t$

Thermal stress = B(γ∆t) = 1.428 × 108 N/m2

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