Mechanical models are often used to describe the viscoelastic behavior of polymers. The Maxwell model, which consists of a spring and dashpot in series, predicts that the variation of strain, e, with time, t, for a viscoelastic material can be described by an equation of the form

de 1 do dt E dt + | 9E= modulus of spring, \eta = viscosity of dashpot, where \sigma is the applied stress. The Voigt model, which consists of a spring and dashpot in parallel, leads to an equation of the form

\frac{de}{dt} = \frac{\sigma }{\eta } - \frac{Ee}{\eta }

(a) Derive equations describing the variation of strain with time for both models subjected to a constant stressing-rate (i. e. \frac{d\sigma }{dt } = constant).

(b) Derive equations describing the variation of stress with time when both models are subjected to a constant strain-rate (i. e. \frac{de}{dt} = constant).

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?