MFGT 242
Flow Analysis
Chapter 2:Material Properties
Professor Joe Greene
CSU, CHICO
1
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)
2
States of Thermoplastic Polymers
• 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
3
States of Thermoplastic Polymers
• 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
4
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
5
Types of Polymers
• Amorphous and Semi-Crystalline Materials
•
•
•
•
•
•
•
•
•
PVC
Amorphous
PS
Amorphous
Acrylics
Amorphous
ABS
Amorphous
Polycarbonate Amorphous
Phenoxy
Amorphous
PPO
Amorphous
SAN
Amorphous
Polyacrylates Amorphous
•
•
•
•
•
•
•
•
•
•
•
LDPE
Crystalline
HDPE
Crystalline
PP
Crystalline
PET
Crystalline
PBT
Crystalline
Polyamides
Crystalline
PMO
Crystalline
PEEK
Crystalline
PPS
Crystalline
PTFE Crystalline
LCP (Kevlar) Crystalline
6
Stresses, Pressure, Velocity, and Basic Laws
• Stresses: force per unit area
– Normal Stress: Acts perpendicularly to the surface: F/A
• Extension
• Compression
Cross Sectional A
Area A
A
F
F
– 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

Deformed Shape
F
 = µd /dt
7
Some Greek Letters
•
Alpha: 
•
Nu: 
•
beta: 
•
xi: 
• gamma: 
•
omicron: 
•
delta: 
•
pi: 
•
epsilon: 
•
rho: 
•
zeta: 
•
sigma: 
•
eta: 
•
tau: 
•
theta: 
•
upsilon: 
•
iota:
•
phi:
•
kappa: 
•
chi: 
•
lamda: 
•
psi: 
•
mu: 
•
omega:

8
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
 yx
du

 
dy
9
Viscosity
• Viscosity is defined as a fluid’s resistance to flow under an applied
shear stress, Fig 2.2
Moving, u=V
y
Y= h
V
P
Y= 0
x
Stationary, u=0
• 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
10
Viscosity
• For Newtonian fluids, Shear stress is proportional to velocity gradient.
Ln 
du
 yx  
 
dy , is called viscosity of the fluid and has
• The proportional constant,
0.01
dimensions
 
0.1 1
10
100
Ln shear rate,

M (lbm/ft hr) or cP
• Viscosity has units of Pa-s or poise
LT
• 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.
11
Viscosity
• For non-Newtonian fluids (plastics), Shear stress is proportional to
velocity gradient and the viscosity function.
 yx
du

 
dy
Ln

0.01 (lbm/ft
0.1 1
10 hr)
100or cP
• Viscosity has units of Pa-s or poise
Ln shear rate, 
• 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
12
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
e
T=200
a b lnT
Ln

T=300
T=400
0.01
0.1
1
Ln shear rate,
10

100
13
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
14
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, .
  m
n 1
• 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
15
Power Law Viscosity Model
• To find constants, take logarithms of both sides, and
find slope and intercept of line
• POLYBANK Software

ln   n 1ln   ln m
– material data bank for storing viscosity model parameters.
– Linear Regression
http://www.polydynamics.com/polybank.htm
16
Moldflow Second Order Model
• Improves the modeling of viscosity in low shear rate region
ln   A0  A1 ln   A2T  A3 (ln  ) 2  A4T ln   A2T 2
• Where the Ai 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
17
Moldflow Matrix Data Model
• 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.
18
Ellis Viscosity Model
• Ellis model expressed viscosity as a function of shear stress,
 1
, and has form
  
0



1

 
– where 1/2 is the value of shear stress for which



 1/ 2 
and
is the slope of the graph
2
0
 1
 
  

ln  0  _ versus _ 


 1/ 2 
 
19
CarreauViscosity Model
• Carreau model expressed viscosity as a function of shear
  
stress, , and has form
2 ( n 1) / 2
 1   
0  


– where  is the value of viscosity at infinite shear rate
and n is the power law constant,  is the time constant
20
Viscosity Model Requirements
• Most important requirement of a viscosity model is that it represents
the observed behavior of polymer melts. Models must meet:
– Viscosity
• 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
21
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
Actual crystalline viscosity
Viscosity
Actual amorphous viscosity
Model Extrapolation
Mold Crystalline
No-Flow
22
Melt
Temperature
Moldflow Correction for No-flow
• 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
No-flow Temperature
Viscosity
Shear Rate 1
Shear Rate 1
Mold
Crystalline
No-Flow
Melt
Temperature
23
Shear Thinning or Pseudoplastic Behavior
Power law
approximation
• Viscosity changes when the shear rate changes
Log
viscosity
Actual
– Higher shear rates = lower viscosity
Log shear rate
– 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
24
Effect of Temperature on Viscosity
• 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
25
Temperature
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
26
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
27
Specific Heat and Enthalpy
• Specific Heat
 dQ 
 dQ 
CP  
 ; CV  

dT
dT

P

V
– 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.
– Cp is more common due to high pressures under Cv
28
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
Material
ABS
Acetal
PA66
PC
Polyethylene
PP
PS
PVC
Steel (AISI
1020)
Steel (AISI
P20)
Specific Heat Capacity
(J/(kgK))
1250-1700
1500
1700
1300
2300
1900
1300
800-1200
460
460
29
Thermal Stability and Induction Time
• 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
30
T+T Q
T
Thermal Conductivity
• Most important thermal property
–
–
–
–
 dQ 
 dT 


kA




Ability of material to conduct heat
 dt 
 dx 
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
31
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.
10.
Temperature (degrees C)
260 240 220 200
Induction 1
Time
(min)
.1 .0018
HDPE
EAA
32
.0020 .0022
-1
Density
• Density is mass divided by the volume (g/cc or lb/ft3)
• 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.
33
– At melting point the slope changes abruptly and the volume increases more
slowly.
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
34
Thermodynamic Relationships
• Expansivity and Compressibility


f p, Vˆ , T  0
– 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
Vˆ  f  p, T 
– where g is some function determined experimentally.
• Fig 2.10
35
Thermodynamic Relationships
• Coefficient of volume expansion of material, , is defined
as:   1  Vˆ 
V  T  p
• 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:
1  Vˆ 

   
Vˆ  p 
T
• 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
36
• isothermal compressibility has units m2/N
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
1.40
Specific
Volume,
cm3/g
Polypropylene
0
Pressure, MPa
20
60
100
160
1.20
1.04
100
200
Temperature, C
37
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
1.40
Specific
Volume,
cm3/g
Polystyrene
0
Pressure, MPa
20
60
100
160
1.20
1.04
100
200
38
Temperature, C
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
Vˆ 
a1
aT
 2  a5 e a6T a7 p
a 4  p a3  p
– High Temperature Region
Vˆ 
– Transition Region
a1
a 2T

a 4  p a3  p
p  b1  b2T
39