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## MFGT 242 Flow Analysis Chapter 2:Material Properties

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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)

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

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

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

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

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

= µd /dt

Deformed Shape

F

Some Greek Letters

- Nu:
- xi:
- omicron:
- pi:
- rho:
- sigma:
- tau:
- upsilon:
- phi:
- chi:
- psi:
- omega:

- Alpha:
- beta:
- gamma:
- delta:
- epsilon:
- zeta:
- eta:
- theta:
- iota:
- kappa:
- lamda:
- mu:

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

Viscosity

V

Moving, u=V

Y= h

y

Y= 0

x

Stationary, u=0

- 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

P

Viscosity

Ln

0.01

0.1

1

10

100

Ln shear rate,

- 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.

Viscosity

Ln

0.01

0.1

1

10

100

Ln shear rate,

- 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

Viscosity

T=200

T=300

Ln

T=400

0.01

0.1

1

10

100

Ln shear rate,

- 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

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

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

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

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

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.

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

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

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

Extrapolation of Viscosity

Actual crystalline viscosity

Actual amorphous viscosity

Viscosity

Model Extrapolation

Crystalline

No-Flow

Mold

Melt

Temperature

- 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

Moldflow Correction for No-flow

No-flow Temperature

Viscosity

Shear Rate 1

Shear Rate 1

Crystalline

No-Flow

Mold

Melt

Temperature

- 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

Shear Thinning or Pseudoplastic Behavior

Power law

approximation

Actual

Log

viscosity

Log shear rate

- 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

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

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

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

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

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

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

Thermal Conductivity

Q

T+T

T

- 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

Thermal Stability and Induction Time

Temperature (degrees C)

10.

260 240 220 200

HDPE

1

Induction

Time

(min)

EAA

.1

.0018 .0020 .0022

Reciprocal Temp (K-1)

- 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.

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.

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

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

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

PVT Data for Flow Analysis

Polypropylene

Pressure, MPa

1.40

0

20

60

100

Specific

Volume,

cm3/g

160

1.20

1.04

100 200

- 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

PVT Data for Flow Analysis

Polystyrene

Pressure, MPa

1.40

0

20

60

100

Specific

Volume,

cm3/g

160

1.20

1.04

100 200

- 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

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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