Transcript MFGT 242 Flow Analysis Chapter 2:Material Properties Professor Joe Greene
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 PS Acrylics ABS Amorphous Amorphous Amorphous Amorphous Polycarbonate Amorphous Phenoxy PPO Amorphous Amorphous SAN Polyacrylates Amorphous Amorphous • • • • • • • • • • • LDPE HDPE PP PET PBT Polyamides PMO Crystalline Crystalline Crystalline Crystalline Crystalline Crystalline Crystalline PEEK PPS Crystalline 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 Area A 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
= µd
/dt
7 F
• • • • • • • • • • Alpha: • beta: • gamma: delta: epsilon: zeta: eta: theta: iota: kappa: lamda: mu:
Some Greek Letters
• Nu: • • • • • • • • • • • xi: omicron: pi: rho: sigma: tau: upsilon: phi: chi: psi: 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 V Y= h y P x Stationary, u=0 Y= 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.
du dy
Ln
yx
• The proportional constant, , is called viscosity of the fluid and has dimensions 0.01
0.1 1 10 100 Ln shear rate,
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 • Viscosity has units of Pa-s or poise (lbm/ft hr) or cP 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 a
b
ln
T
Ln T=200 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, • For polymer melts
n
viscosity shear rate curve.
.
m
n
1 • 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 – material data bank for storing viscosity model parameters.
ln – Linear Regression http://www.polydynamics.com/polybank.htm
16
Moldflow Second Order Model
• Improves the modeling of viscosity in low shear rate region ln
A
0
A
1 ln
A
2
T
A
3 (ln ) 2
A
4
T
ln
A
2
T
2 • 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 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, , and has form – where 1/2 1 is the value of shear stress for which ln 0 _
versus
_ 1 / 2 2 0 0 1 1 / 2 1 19
CarreauViscosity Model
• Carreau model expressed viscosity as a function of shear stress, , and has form – where 0 is the value of viscosity at infinite shear rate 1 2 (
n
1 ) and n is the power law constant, is the time constant / 2 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 Viscosity Actual crystalline viscosity Actual amorphous viscosity Model Extrapolation 22 Mold Crystalline No-Flow 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 Viscosity No-flow Temperature 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 – Higher shear rates = lower viscosity – Results in shear thinning behavior Log viscosity Actual Log shear rate – 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 Temperature 25
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
C P
dQ dT P
;
C V
dQ dT
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
Thermal Conductivity
T • Most important thermal property – Ability of material to conduct heat
dQ dt
– Plastics have low thermal conductivity = insulators
kA
dT dx
– 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 Time (min) 1 HDPE EAA .1
.0018 .0020 .0022
Reciprocal Temp (K -1 ) 32
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.
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
,
V
ˆ ,
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
V
ˆ
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
V
V
ˆ
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
V
ˆ
V
ˆ
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 • isothermal compressibility has units m 2 /N 36
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
Specific Volume, cm 3 /g 1.40
1.20
Polypropylene 0 Pressure, MPa 20 60 100 160 37 1.04
100 200 Temperature, C
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 1.40
Polystyrene • Fig 2.12
Specific Volume, cm 3 /g 1.20
0 Pressure, MPa 20 60 100 160 1.04
100 200 Temperature, C 38
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
V
ˆ
a
4
a
1
p
a
3
a
2
T
p
a
5
e a
6
T
a
7
p
– High Temperature Region
V
ˆ
a
4
a
1
p
a
3
a
2
T
p
– Transition Region
p
b
1
b
2
T
39