Applied Mathematics in Plastic Industry — Winter 2018

Define: Newtonian fluid, Shear stress and Shear Strain

Give detail classification of Non Newtonian fluids along with example.

Explain the mathematical model using Maxwell model for Viscoelastic behavior.

Discuss short term test methods for Plastics.

Write a note on: Swelling ratios due to Shear Stresses.

Explain cone and plate viscometer to obtain flow data on polymer melts.

In a particular extruder screw the channel depth is 2.4 mm, the screw diameter is 50mm, the screw speed is 100 rev/min, the flight angle is 17o42' and the pressure varies linearly over the screw length of 1000 mm from zero at entry to 20 MN/m2 at the die entry. Estimate (a) the drag flow (b) the pressure flow (c) the total flow. the plastic has a viscosity of 210Ns/m2

Discuss forms of Fiber reinforcement in composites.

With neat diagram explain Ram extruder to obtain flow data on polymer melt.

Explain: Iso thermal flow in channels: Non Newtonian fluids -flow of power law fluid along a channel of uniform circular cross-section.

The output of polythene from an extruder is 30 x10-6 m3/s. If the breaker plate in this extruder has 80 holes, each being 4 mm diameter and 12 mm long, estimate the pressure drop across the plate assuming the material temperature is 170°Cat this point. The shear stress is 1.2 x 105 N/m2

Draw the creep curve and explain its various stages.

Explain concentric cylinder viscometer to obtain flow data on polymer melts.

Draw graphs for Hooke model, Newton Model and Voigt model showing Elongation –Time and Stress-strain behaviour.

The density of a composite made from unidirectional glass fibers in an epoxy matrix is 1950 kg/m3. If the densities of the glass and epoxy are known to be 2540 kg/m3 and 1300 kg/m3, calculate the weight fraction of fibers in the composite

Discuss Residence Time and Relaxation Time.1

Discuss about Melt fracture and Sharksin flow defects in polymer melt.

Write a short note on strength of composites for Fiber reinforced materials.

Explain the analysis of heat transfer during polymer processing.

Define drag flow, pressure flow, leakage flow

Applying the Carreau model to PP, the following constants are known at 190ºC. Ƞ =2250 Ns/m2 , A =0.05, n=0.33, Estimate the viscosity of 0 T PP at 230 ºC and a shear rate of 1000 s-1 . The glass transition temperature for the PP is -10 ºC.

Explain the analysis of continuous fiber composite having the longitudinal properties.

PEEK is to be reinforced with 20% by volume of unidirectional carbon fibers and the properties of the individual materials are given below. Calculate the density, modulus and strength of the composite in the fiber direction. Material Density Tensile Strength Modulus (kg/cm3) (GN/m2) (GN/m2) PEEK 1300 0.058 3.8 Carbon Fiber 1800 2.1 400

Derive Rheological models for Polymer melt flow.

Explain the radius of gyration of an ideal branched polymer using Kramers Theorem.