# Thermoforming the question that why we use this

Thermoforming

A/C Taimoor, A/C Salman, A/C
Waqar

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Theoretical Background:

First
of all, thermoforming is a process in which a sheet is first heated and then
molded into a required mold shape. Here we will see what is the background
process, means that how certain inputs are varying and how are they changing,
because in software (Ansys) we are just giving the inputs not the formulas or
the relations by which they are varying.

·
Before
polydata there is geometry as well as meshing, but these donot involve any
formulas.

·
In
polydata we create some tasks as well as their sub tasks and we have to create
mold as well

Velocity or Force Driven:

In polyflow, when we define a
contact we do it with the help of penalty technique. In this way we define the
fluid velocity and wall velocity are related by the condition (in normal
direction) which involves the penalty co-efficient k, i-e,

fn=-k(v-vwall).n

Similarly, we can use this equation
for the tangential direction but we have to take the slip co-efficient into
account, i-e

fs=-Fslip(vs-vs,wall)

We have
seen how the contact force is applied, now here we have some selection of
whether we want our problem to be velocity imposed or force driven. If our
problem is velocity imposed we can use the above mentioned equations but if it
is force driven then we have to solve the corresponding momentum equation,

Fm+Ff =Ma

·
Fm
= force applied on mold

·
Ff  = resistance from the fluid

·
a = acceleration of the mold

·
M=mass
of the moving part

Now here
is the question that why we use this equation? It is because we want to define
a limit for the maximum displacement, because when the deformation increases
shear force and hence the motion of the mold is decreased. So if displacement
tends to increase beyond its limit its motion is stopped. That’s why maximum
displacement is calculated.

Isothermal or non-isothermal:

If our simulation is isothermal then
the conditions (thermal boundary conditions) are same before and after the
contact but if our simulation is non-isothermal then the flow conditions are
not the same before and after the contact,i-e

Q=a(T-Tmold)

where ‘a’ is convective co-efficient

·
similarly
the viscosity changes with change in temperature as shown by the following
graph.

Constant viscosity and strain
dependent viscosity:

Most of the times we take constant
viscosity for shell models but sometimes it is more desirable to take viscosity
in terms of local strain. For this case the fluid constitutive equation is
written as follows:

T=2?(?)D

In
simple traction experiment, we, at constant stretching velocity, stretch the
sample of initial length L0 and record the tensile stress as a
function of deformation. After some manipulation we can take viscosity as a
ratio of stress to strain rate.

?*
= V0/(L0+?L)

?
=exp(?*0t)

?(?)=
?0+a ?2+bexp(-((?-
?p)/ ?w)2)

Typical Viscosity Curve Exhibiting Strain
Hardening

Typical
Viscosity Curve Described with the Smooth Ramp Function

·
Now
how postprocessor things are calculated.

Mass of the blown
product:

mblown=?A?hdA

·
?=density
of the parison

·
h=layer
thickness

·
A=surface
area

Permeability of the
blown product:

Permeability is important to be calculated in the
packing of pharmaceuticals where moisture content is important.

p= ? /h

·
?
is permeability co-efficient

·
h
is local thickness

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