MFGT 242 Flow Analysis Chapter 2:Material Properties

1. MFGT 242Flow 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. 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

4. 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

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 • 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

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   = µd /dt Deformed Shape F

8. 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:

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 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

11. 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.

12. 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

13. 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

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 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

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 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

23. 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

24. 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

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 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

32. 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.

33. 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.

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 m2/N

37. 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

38. 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

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