1
MFGT 242
Flow Analysis
Chapter 2:Material Properties
Professor Joe Greene
CSU, CHICO
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Types of Polymers
•
Amorphous and Semi

Crystalline Materials
•
Polymers are classified as
–
Thermoplastic
–
Thermoset
•
Thermoplastic polymers are further classified by the
configuration of the polymer chains with
–
random state (amorphous), or
–
ordered state (crystalline)
3
•
Amorphous

Molecular structure is incapable of forming regular order
(crystallizing) with molecules or portions of molecules regularly
stacked in crystal

like fashion.
•
A

morphous (with

out shape)
•
Molecular arrangement is randomly twisted, kinked, and coiled
States of Thermoplastic Polymers
4
•
Crystalline

Molecular structure forms regular order (crystals) with
molecules or portions of molecules regularly stacked in crystal

like
fashion.
•
Very high crystallinity is rarely achieved in bulk polymers
•
Most crystalline polymers are semi

crystalline because regions are
crystalline and regions are amorphous
•
Molecular arrangement is arranged in a ordered state
States of Thermoplastic Polymers
5
Factors Affecting Crystallinity
•
Cooling Rate from mold temperatures
•
Barrel temperatures
•
Injection Pressures
•
Drawing rate and fiber spinning: Manufacturing of
thermoplastic fibers causes Crystallinity
•
Application of tensile stress for crystallization of
rubber
6
Types of Polymers
•
Amorphous and Semi

Crystalline Materials
•
LDPE
Crystalline
•
HDPE
Crystalline
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PP
Crystalline
•
PET
Crystalline
•
PBT
Crystalline
•
Polyamides
Crystalline
•
PMO
Crystalline
•
PEEK
Crystalline
•
PPS
Crystalline
•
PTFE
Crystalline
•
LCP (Kevlar)
Crystalline
•
PVC
Amorphous
•
PS
Amorphous
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Acrylics
Amorphous
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ABS
Amorphous
•
Polycarbonate Amorphous
•
Phenoxy
Amorphous
•
PPO
Amorphous
•
SAN
Amorphous
•
Polyacrylates
Amorphous
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Stresses, Pressure, Velocity, and Basic Laws
•
Stresses: force per unit area
–
Normal Stress: Acts perpendicularly to the surface: F/A
•
Extension
•
Compression
–
Shear Stress,
: Acts tangentially to the surface: F/A
•
Very important when studying viscous fluids
•
For a given rate of deformation, measured by the time derivative d
/dt of a small angle of deformation
, the shear stress is directly
proportional to the viscosity of the fluid
F
Cross Sectional
Area A
A
F
A
F
Deformed Shape
F
= µ
d
/dt
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Some Greek Letters
•
Alpha:
•
beta:
•
gamma:
•
delta:
•
epsilon:
•
zeta:
•
eta:
•
theta:
•
iota:
•
kappa:
•
lamda:
•
mu:
•
Nu:
•
xi:
•
omicron:
•
pi:
•
rho:
•
sigma:
•
tau:
•
upsilon:
•
phi:
•
chi:
•
psi:
•
omega:
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Viscosity, Shear Rate and Shear Stress
•
Fluid mechanics of polymers are modeled as steady flow in shear
flow.
•
Shear flow can be measured with a pressure in the fluid and a
resulting shear stress.
•
Shear flow is defined as flow caused by tangential movement. This
imparts a shear stress,
,
on the fluid.
•
Shear rate is a ratio of velocity and distance and has units sec

1
•
Shear stress is proportional to shear rate with a viscosity constant or
viscosity function
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Viscosity
•
Viscosity is defined as a fluid’s resistance to flow under an applied
shear stress, Fig 2.2
•
The fluid is ideally confined in a small gap of thickness h between one
plate that is stationary and another that is moving at a velocity, V
•
Velocity is u = (y/h)V
•
Shear stress is tangential Force per unit area,
= F/A
Stationary, u=0
Moving, u=V
V
x
y
Y= 0
Y= h
P
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Viscosity
•
For Newtonian fluids, Shear stress is proportional to velocity gradient.
•
The proportional constant,
,
is called viscosity of the fluid and has
dimensions
•
Viscosity has units of Pa

s or poise (lbm/ft hr) or cP
•
Viscosity of a fluid may be determined by observing the pressure drop
of a fluid when it flows at a known rate in a tube.
Ln shear rate,
Ln
0.01
0.1
1
10
100
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Viscosity
•
For non

Newtonian fluids (plastics), Shear stress is proportional to
velocity gradient and the viscosity function.
•
Viscosity has units of Pa

s or poise (lbm/ft hr) or cP
•
Viscosity of a fluid may be determined by observing the pressure drop
of a fluid when it flows at a known rate in a tube. Measured in
–
Cone

and

plate viscometer
–
Capillary viscometer
–
Brookfield viscometer
Ln shear rate,
Ln
0.01
0.1
1
10
100
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Viscosity
•
Kinematic viscosity,
, is the ratio of viscosity and density
•
Viscosities of many liquids vary exponentially with temperature and
are independent of pressure
•
where, T is absolute T, a and b
•
units are in centipoise, cP
Ln shear rate,
Ln
0.01
0.1
1
10
100
T=400
T=300
T=200
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Viscosity Models
•
Models are needed to predict the viscosity over a range of
shear rates.
•
Power Law Models (Moldflow First order)
•
Moldflow second order model
•
Moldflow matrix data
•
Ellis model
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Viscosity Models
•
Models are needed to predict the viscosity over a range of shear rates.
•
Power Law Models (Moldflow First order)
where
m
and
n
are constants.
If m =
, and
n
= 1, for a Newtonian fluid,
you get the Newtonian viscosity,
.
•
For polymer melts
n
is between 0 and 1 and is the slope of the
viscosity shear rate curve.
•
Power Law is the most common and basic form to represent the way
in which viscosity changes with shear rate.
•
Power Law does a good job for shear rates in linear region of curve.
•
Power Law is limited at low shear and high shear rates
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Power Law Viscosity Model
•
To find constants, take logarithms of both sides, and
find slope and intercept of line
•
POLYBANK Software
–
material data bank for storing viscosity model parameters.
–
Linear Regression
http://www.polydynamics.com/polybank.htm
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Moldflow Second Order Model
•
Improves the modeling of viscosity in low shear rate region
•
Where the A
i
are constants that are determined empirically (by
experiments) and the model is curve fitted.
•
Second Order Power Law does well for
–
Temperature effects on viscosity
–
Low shear rate regions
–
High shear rate regions
•
Second Order is limited by:
–
Use of empirical constants rather than rheology theory
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Moldflow Matrix Data Model
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Collection of triples (viscosity, temperature, and shear rate)
obtained by experiment.
•
Viscosity is looked up in a table form based upon the
temperature and shear rate.
•
No regression or curve fitting is used like first and second
order power law.
•
Matrix is suitable for materials with unusual viscosity
characteristics, e.g., LCP
•
Matrix limitations are the large number of experimental data
that is required.
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Ellis Viscosity Model
•
Ellis model expressed viscosity as a function of shear stress,
, and has form
–
where
1/2
is the value of shear stress for which
and is the slope of the graph
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CarreauViscosity Model
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Carreau model expressed viscosity as a function of shear
stress,
, and has form
–
where
is the value of viscosity at infinite shear rate
and n is the power law constant,
is the time constant
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Viscosity Model Requirements
•
Most important requirement of a viscosity model is that it represents
the observed behavior of polymer melts. Models must meet:
–
Viscosity
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Viscosity should decrease with increasing shear rate
•
Curvature of isotherms should be such that the viscoity decreases at a
decreasing rate with increasing shear rate
•
The isotherms should never cross
–
Temperature
•
Viscosity should decrease with increasing temperature
•
Curvature of iso

shear rate curves should be such that the viscoity
decreases at a decreasing rate with increasing temp
•
The iso

shear rate curves should never cross
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Extrapolation of Viscosity
•
Regardless of model, problems occur in flow analysis
–
Due to range of shear rates chosen during data regression is often too low a
range of shear rate than actual molding conditions.
–
Extrapolation (calculation of quantity outside range used for regression) is
necessary due to complex flow and cooling.
–
Materials exhibit a rapid change in viscosity as it passes from melt to solid
plastic.
–
Extrapolation under predicts the actual viscosity
Viscosity
Temperature
Mold
Crystalline
No

Flow
Melt
Actual crystalline viscosity
Actual amorphous viscosity
Model Extrapolation
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Moldflow Correction for No

flow
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No

Flow Temperature to overcome this problem
–
the temperature below which the material can be considered solid.
–
The viscosity is infinite at temperatures below No

flow
Temperature
Viscosity
Temperature
Mold
Crystalline
No

Flow
Melt
Shear Rate 1
No

flow Temperature
Shear Rate 1
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Shear Thinning or Pseudoplastic Behavior
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Viscosity changes when the shear rate changes
–
Higher shear rates = lower viscosity
–
Results in shear thinning behavior
–
Behavior results from polymers made up of long entangles chains. The degree
of entanglement determines the viscosity
–
High shear rates reduce the number of entanglements and reduce the viscosity.
–
Power Law fluid: viscosity is a straight line in log

log scale.
•
Consistency index: viscosity at shear rate = 1.0
•
Power law index, n: slope of log viscosity and log shear rate
–
Newtonian fluid (water) has constant viscosity
•
Consistency index = 1
•
Power law index, n =0
Log
viscosity
Log shear rate
Power law
approximation
Actual
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Effect of Temperature on Viscosity
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When temperature increases = viscosity reduces
•
Temperature varies from one plastic to another
–
Amorphous plastics melt easier with temperature.
•
Temperature coefficient ranges from 5 to 20%,
•
Viscosity changes 5 to 20% for each degree C change in Temp
•
Barrel changes in Temperature has larger effects
–
Semicrystalline plastics melts slower due to molecular structure
•
Temperature coefficient ranges from 2 to 3%
Viscosity
Temperature
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Viscous Heat Generation
•
When a plastic is sheared, heat is generated.
–
Amount of viscous heat generation is determined by product of
viscosity and shear rate squared.
–
Higher the viscosity = higher viscous heat generation
–
Higher the shear rate = higher viscous heat generation
–
Shear rate is a stronger source of heat generation
–
Care should be taken for most plastics not to heat the barrel too hot
due to viscous heat generation
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Thermal Properties
•
Important is determining how a plastic behaves in an
injection molder. Allows for
–
selection of appropriate machine selection
–
setting correct process conditions
–
analysis of process problems
•
Important thermal properties
–
thermal conductivity
–
specific heat
–
thermal stability and induction time
–
density
–
melting point and glass transition
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Specific Heat and Enthalpy
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Specific Heat
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The amount of heat necessary to increase the temperature of a material by one
degree.
–
Most cases, the specific heat of semi

crystalline plastics are higher than
amorphous plastics.
–
If an amount of heat is added
Q, to bring about an increase in temperature,
T.
–
Determines the amount of heat required to melt a material and thus the amount
that has to be removed during injection molding.
•
The specific heat capacity is the heat capacity per unit mass of
material.
–
Measured under constant pressure, Cp, or constant volume, Cv.
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Cp is more common due to high pressures under Cv
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Specific Heat and Enthalpy
•
Specific Heat Capacity
–
Heat capacity per unit mass of material
–
Cp is more common than Cv due to excessive pressures for Cv
–
Specific Heat of plastics is higher than that of metals
–
Table 2.1
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Thermal Stability and Induction Time
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Plastics degrade in plastic processing.
–
Variables are:
•
temperature
•
length of time plastic is exposed to heat (residence time)
–
Plastics degrade when exposed to high temperatures
•
high temperature = more degradation
•
degradation results in loss of mechanical and optical properties
•
oxygen presence can cause further degradation
–
Induction time is a measure of thermal stability.
•
Time at elevated temperature that a plastic can survive without
measurable degradation.
•
Longer induction time = better thermal stability
•
Measured with TGA (thermogravimetric analyzer), TMA
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Thermal Conductivity
•
Most important thermal property
–
Ability of material to conduct heat
–
Plastics have low thermal conductivity = insulators
–
Thermal conductivity determines how fast a plastic can be
processed.
–
Non

uniform plastic temperatures are likely to occur.
•
Where, k is the thermal conductivity of a material at temperature T.
•
K is a function of temperature, degree of crystallinity, and level of
orientation
–
Amorphous materials have k values from 0.13 to 0.26 J/(msK)
–
Semi

crystalline can have higher values
Q
T+
T
T
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Thermal Stability and Induction Time
•
Plastics degrade in plastic processing.
–
Induction time measured at several temperatures, it can be plotted
against temperature. Fig 4.13
•
The induction time decreases exponentially with temperature
•
The induction time for HDPE is much longer than EAA
–
Thermal stability can be improved by adding stabilizers
•
All plastics, especially PVC which could be otherwise made.
HDPE
EAA
Induction
Time
(min)
Temperature (degrees C)
Reciprocal Temp (K

1
)
.1
1
10.
260 240 220 200
.0018 .0020 .0022
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Density
•
Density is mass divided by the volume (g/cc or lb/ft
3
)
•
Density of most plastics are from 0.9 g/cc to 1.4 g/cc_
•
Table 4.2
•
Specific volume is volume per unit mass or (density)

1
•
Density or specific volume is affected by temperature and pressure.
–
The mobility of the plastic molecules increases with higher temperatures (Fig
4.14) for HDPE.
PVT diagram very important!!
–
Specific volume increases with increasing temperature
–
Specific volume decrease with increasing pressure.
–
Specific volume increases rapidly as plastic approaches the melt T.
–
At melting point the slope changes abruptly and the volume increases more
slowly.
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Melting Point
•
Melting point is the temperature at which the crystallites
melt.
–
Amorphous plastics do not have crystallites and thus do not have a
melting point.
–
Semi

crystalline plastics have a melting point and are processed 50
C above their melting points. Table 4.3
•
Glass Transition Point
–
Point between the glassy state (hard) of plastics and the rubbery
state (soft and ductile).
•
When the Tg is above room temperature the plastic is hard and brittle
at room temperature, e.g., PS
•
When the Tg is below room temperature, the plastic is soft and
flexible at room temperature, e.g., HDPE
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Thermodynamic Relationships
•
Expansivity and Compressibility
–
Equation of state relates the three important process variables, PVT
•
Pressure, Temperature, and Specific Volume.
•
A Change in one variable affects the other two
•
Given any two variables, the third can be determined
–
where g is some function determined experimentally.
•
Fig 2.10
36
Thermodynamic Relationships
•
Coefficient of volume expansion of material,
, is defined
as:
•
where the partial differential expression is the instantaneous change
in volume with a change in Temperature at constant pressure
•
Expansivity of the material with units K

1
•
Isothermal Compressibility,
,
is defined as:
•
where the partial differential expression is the instantaneous change
in volume with a change in pressure at constant temperature
•
negative sign indicated that the volume decreases with increasing
pressure
•
isothermal compressibility has units m
2
/N
37
PVT Data for Flow Analysis
•
PVT data is essential for
–
packing phase and the filling phase.
–
Warpage and shrinkage calculations
•
Data is obtained experimentally and curve fit to get
regression parameters
•
For semi

crystalline materials the data falls into three area;
–
Low temperature
–
Transition
–
High temperature
•
Fig 2.11
Temperature, C
100 200
Specific
Volume,
cm
3
/g
1.04
1.20
1.40
Polypropylene
Pressure, MPa
0
20
60
100
160
38
PVT Data for Flow Analysis
•
Data is obtained experimentally and curve fit to get
regression parameters
•
For amorphous there is not a sudden transition region from
melt to solid. There are three general regions
–
Low temperature
–
Transition
–
High temperature
•
Fig 2.12
Temperature, C
100 200
Specific
Volume,
cm
3
/g
1.04
1.20
1.40
Polystyrene
Pressure, MPa
0
20
60
100
160
39
PVT Data for Flow Analysis
•
The equations fitted to experimental data in Figures 2.11
and 2.12 are:
–
Note: All coefficients are found with regression analysis
–
Low Temperature region
–
High Temperature Region
–
Transition Region
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