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MFGT 242 Flow Analysis Chapter 2:Material Properties. Professor Joe Greene CSU, CHICO. Types of Polymers. Amorphous and Semi-Crystalline Materials Polymers are classified as Thermoplastic Thermoset

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types of polymers
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
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 polymers4
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
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 polymers6
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, 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
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
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
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

viscosity11
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.
viscosity12
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
viscosity13
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
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 models15
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
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
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
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 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
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
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
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
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
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
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
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
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 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 enthalpy29
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
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
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 time32
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
  • 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
  • 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
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 relationships36
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
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 analysis38
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 analysis39
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