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Determination of elastic parameters of cross-linked rubber

A sample of an ideal crosslinked rubber has a number average molecular weight between crosslinks of 5000 and a density of 900kg/m3. A block of this rubber, a cube of sides 100mm, is tested at a temperature of 300K.

a). What is its tensile modulus?

b). What is its shear modulus?

Axes X, Y, and Z are chosen parallel to the edges of the cube. A compressive force FX is applied in the X-direction, to reduce the X-dimension from 100mm to 50mm.

c). Calculate FX

A further compressive force is applied in the Y-direction to reduce the Y-dimension to 75mm, the X-direction remaining at 50mm.

d). What now are the magnitude of FX and FY?

e). What has the Z-direction now become?

f). How much strain energy is now stored in the block?

Assume the rubber obeys Gaussian statistics and make all other necessary (or usual) assumptions to solve this problem.


Solution Preview

We consider some limitations like : only works for small strains - and use Stirling's approximation; also we assume that bond distortion is ignored.
<br>In our case,
<br>Rho=900 kg/m^2, T=300 K, Mx= 5000 (given). Let R=molar gas const.
<br>(b) Then the shear modulus is given by the expression,
<br> G=( Rho * R * T)/Mx
<br>(a) The tensile modulus is given by the ...

Solution Summary

A cubic Cross-linked rubber sample having an average molecular weight and density is tested at 300 K. Tensile modulus, shear modulus are computed. Now compressive force along X and Y dircetion is given such that we have measured values of strains. Stress components in different directions are then computed along with strain energy from those data.