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MFGT 242Flow 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)

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• 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

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• 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

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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

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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

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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

FCross SectionalArea A

A

FA

F

Deformed Shape

F

= µd /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

dy

duyx

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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

xy

Y= 0

Y= hP

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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.

dy

duyx

LT

M

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

dy

duyx

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

Tbae ln

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

1 nm

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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

mn lnln1ln

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 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

224

23210 ln)(lnlnln TATAATAAA

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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.

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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

1

2/1

0 1

20

1

2/1

0 __ln

versus

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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

2/)1(2

0

1

n

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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• 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

TemperatureMold Crystalline No-Flow Melt

Actual crystalline viscosity

Actual amorphous viscosity

Model Extrapolation

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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

TemperatureMoldCrystalline No-Flow Melt

Shear Rate 1

No-flow Temperature

Shear Rate 1

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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

Logviscosity

Log shear rate

Power law approximation

Actual

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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

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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

• 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

VV

PP dT

dQC

dT

dQC

;

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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

Material Specific Heat Capacity(J/(kgK))

ABS 1250-1700Acetal 1500PA66 1700PC 1300Polyethylene 2300PP 1900PS 1300PVC 800-1200Steel (AISI1020)

460

Steel (AISIP20)

460

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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

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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

dx

dTkA

dt

dQ

QT+TT

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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

EAAInductionTime(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/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.– 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

0,ˆ, TVpf

TpfV ,ˆ

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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 m2/N

pT

V

V

ˆ1

Tp

V

V

ˆ

ˆ1

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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, C100 200

SpecificVolume,cm3/g

1.04

1.20

1.40Polypropylene

Pressure, MPa020

60100

160

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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

SpecificVolume,cm3/g

1.04

1.20

1.40Polystyrene

Pressure, MPa020

60100

160

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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

paTaeapa

Ta

pa

aV 76

53

2

4

1ˆ

pa

Ta

pa

aV

3

2

4

1ˆ

Tbbp 21