Tutorial question was given.....
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The Creep response of a polymer corresponding to a load application for 100s can be described by a Voight Model where the Elastic element = 2GPa, and the Viscous element = 100 x10^09 Ns/m^2. If the Maxwell model has viscous element = 200 x10^09 Ns/m^2
Find the value of the Maxwell elastic element.
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I have the solution below.....but I'm not sure that I'm correct. I have, for Maxwell, Epsilon = (sigma / E) + (sigma / Viscosity).
I think it should be Epsilon = (sigma / E) + (sigma^dot / Viscosity). where sigma^dot is 'stress rate' rather than stress..?
can anyone clarify for me?? If it is 'stress rate' rather than stress' how do I calculate this - is it as a function of the time period??)
my working is this:
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Strain Rate for the Voight model is found from:
Epsilon = (Sigma / E) (1- exp (-E * t)/Viscosity))
Epsilon = (Sigma / 2 x10^9) (0.864)
Epsilon = Sigma * 0.432 x 10^-9 [eqn 1]
For the Maxwell model
Epsilon = (sigma / E) + (sigma / Viscosity)
Substituting eqn 1 gives
Sigma * 0.432 x 10^-9 = (sigma / E) + (sigma / Viscosity)
Div thru by Sigma to give
0.432 x 10^-9 = (1 / E) + (1 / Viscosity)0.432 x 10^-9 = (1 / E) + (1 / 200 x10^9)
0.432 x 10^-9 = (1 / E) + (5 x10^-12)1 / (0.432 x 10^-9 - 5 x10^-12) = E
E = 2.34 x10^9 Pa
E = 2.34 GPa