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ChE 671Final Examination
Prof. Dilhan M. KalyonSpring 2010, May 7, 2010, 12:30 to 3:00
p.m.Please start open book section upon turning
in your closed book section of the
exam______________________________
Closed Book and Notes -The time allotment suggested for each
question is included as a guide.
Good luck!
1. (10 points 10 minutes) Your company is manufacturing blown
film, which is generallyused for pharmaceutical packaging. In film
blowing the film needs to be stretched in the
axial direction and also needs to be expanded in the radial
direction by air pressure acting
inside the film bubble. The bubble breaks frequently and you are
suspecting that the
manufacturer of the polymer being used is selling your company
off-spec resin, which
varies from day to day but the manufacturer is denying it. You
are asked to establish a
quality control program. Select one piece of equipment to
purchase and identify which
experiment you would carry out with this instrument. Justify by
writing a few sentences
(an executive summary to your CEO) on why the instrument
selected is the proper one.
2. (10 points 10 minutes) You are given a PVC suspension for a
medical grade applicationthat you suspect is degrading possibly
through oxidative crosslinking during extrusion
processing. What type of equipment and procedures would you use
to study and
document the degradation of the suspension in your lab?
3. (10 points 5 minutes) What are the typical error sources in
step strain flow for thecharacterization of the relaxation
modulus?
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Open book section:
6. (15 points 10 minutes) The following damping function has
been suggested for integral
type non-linear viscoelastic constitutive equations:
h(I1, I2) = f expn1 3 (1 f ) exp n2 3
where I= I1 + (1-) I2, i.e., weighted average of the invariants
I1 and I2 of theFinger strain tensor. Show that the damping
function, h(I1, I2), for simple shear flow isindependent of
parameter , whereas h(I1, I2) for uniaxial extensional flow is a
functionof the parameter .
7. (35 points 45 minutes) Consider the following constitutive
equation:
(t) =
')]2/()2/1([)1(11/)'(2
21
0dtCCeII
ttt
where C-1
and C are the Finger and Cauchy strain tensors and 1, 2, , 0are
parameters andII is the second invariant of the rate of deformation
tensor.
a. Derive and expression for the growth of the shear stress,
i.e, + (t, shear rate)b. Is the shear stress overshoot possible? Is
so, at what time does the stress reach its
maximum value?
c. What is the shear viscosity? Is it realistic?
