$1-($a$)$ Spring and dashpot amangements are offes esed so represent the mechanical behaviour of polymen.

Analyse Be mathematical stress surain relaticenthip for the Mexwell and Kelvin$-$Voigt models under condlitions of

$($i$)$ constant atresk, $($ii$)$ constant utrain, $($iii$)$ recovery, and draw the appropriase strain$-$time, strest$-$time diagrama,

commenting upon their suitahility to predict behaviour of real polymen.

$($b$)$ Maxwell and Kelvin$-$Voigt models are to be set up to simulate the behaviour of a plastic. The elastic

and viscous constants for the Kelvia$-$Voigt model are $2{10}^9\frac{N}{m^2}$ and $100{10}^{9}N\frac{s}{m^2}$ respectively and the

viscous constant for the Maxwell model is $272{10}^{9}N{s}^2.$ Calculate a value for the elastic constant for the

Maxwell model if both models are to peredict the same strain after $100$ seconds when subjected so the same stress.

$15\mathrm{.}45{10}^6\frac{N}{m^2{?}^2}$

$2-$ the model shows in Fig. $12$:$21$ is trequently wsed to sumuiate the mechanical behaviour of polymen:

ing $12\mathrm{.}41-$

$($a$)$ With reference to Figure $12\mathrm{.}21,$ state what components of botal strain the elements $A,B$ and $C$ represeat.

$($b$)$ Sketch a typical strain$-$time graph for the model when the load $F$ is applied and then removed. Clearly label

those parts of the graph corresponding to the strain composests $lo{n}_1,lo{n}_2$ and $lo{n}_3.$

$($c$)$ A certain polymer may be modelied on such a system by using the following constants for the elements:

Dashpot A:

Dashper B:

Spring A:

Spring B:

This polymer is subjectod to a direct stress of $6{10}^3\frac{N}{m^2}$ for $30$ seconds ONLY.

Determine the strain in the polymer after $30$ seconds, $60$ seconds and $2000$ seconds.

$3\mathrm{.}17{10}^{-2},0\mathrm{.}75{10}^{-2},0\mathrm{.}06{10}^{-2}$

$3-$A $)$ what do we meant by : strain rate, creep test and

relaxation test in viscoelastic materials

B$)$ Derive the standard equation of stress and strain for the

following viscoelastic models

$3\mathrm{.}17{10}^{-2}\mathrm{.}0\mathrm{.}75{10}^{-2}\mathrm{.}0\mathrm{.}06{10}^{-2}$