Chapter 2:Material Properties

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Oct 30, 2013 (3 years and 11 months ago)

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1

MFGT 242

Flow Analysis

Chapter 2:Material Properties

Professor Joe Greene

CSU, CHICO

2

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



PP


Crystalline



PET


Crystalline



PBT


Crystalline


Polyamides

Crystalline


PMO


Crystalline


PEEK

Crystalline


PPS


Crystalline


PTFE

Crystalline


LCP (Kevlar)

Crystalline















PVC


Amorphous



PS


Amorphous



Acrylics

Amorphous


ABS


Amorphous


Polycarbonate Amorphous


Phenoxy

Amorphous


PPO


Amorphous


SAN


Amorphous



Polyacrylates

Amorphous














7

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


8

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:


9

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

10

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

11

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

12

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

13

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

14

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

15

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

16

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

17

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


18

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.


19

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



20

CarreauViscosity Model


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



21

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


22

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

23

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

Viscosity

Temperature

Mold

Crystalline

No
-
Flow

Melt

Shear Rate 1

No
-
flow Temperature

Shear Rate 1

24

Shear Thinning or Pseudoplastic Behavior


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

25

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

Temperature

26

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

27

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

28

Specific Heat and Enthalpy


Specific Heat


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


29

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

30

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

31

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

32

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

33

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.

34

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

35

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