Presentation on theme: "Day 29: Mechanical Behavior of Polymers Review How are Properties Defined Introduction to Viscoelasticity Simple Material Models Strain Rate and Temperature."— Presentation transcript:
Day 29: Mechanical Behavior of Polymers Review How are Properties Defined Introduction to Viscoelasticity Simple Material Models Strain Rate and Temperature Effects
Review Basic definitions: thermoplastic, thermoset, elastomer. Let’s talk about the kind of mechanical behavior seen in polymers. 1.Stiffness, E 2.Strength 3.Ductility Factors which can determine the strength of a polymer.
Let’s remember some particular polymers PolymerPlusDeltaPolymerPlusDelta PEPC PSTeflon PPPI PVCPB NylonSBS KevlarABS PMMAEpoxy Importance of fiber. What does it take for a polymer to form fiber?
Different Types of Mechanical Behaviors in Polymers A=brittle B=elastic/plastic C=elastomeri c Focus on this one today
Mechanical Properties i.e. stress-strain behavior of polymers 5 brittle polymer plastic elastomer FS of polymer ca. 10% that of metals Strains – deformations > 1000% possible (for metals, maximum strain ca. 10% or less) elastic modulus – less than metal Adapted from Fig. 15.1, Callister 7e.
7 T and Strain Rate: Thermoplastics Decreasing T... -- increases E -- increases TS -- decreases %EL Increasing strain rate... -- same effects as decreasing T. Adapted from Fig. 15.3, Callister 7e. (Fig. 15.3 is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.) 20 40 60 80 0 00.10.20.3 4°C 20°C 40°C 60°C to 1.3 (MPa) Data for the semicrystalline polymer: PMMA (Plexiglas)
Effects of Strain Rate and Temperature stress strain Increasing temp Increasing strain rate
Time Temp for Delrin (Strain Rate) http://www2.dupont.com/Plasti cs/en_US/assets/downloads/d esign/230323c.pdf
Time Temp for Delrin (Strain Rate and Temp) http://www2.dupont.com/Plasti cs/en_US/assets/downloads/d esign/230323c.pdf
Time Temp Dependence Plastic deformation of polymers involves chain uncoiling and chain sliding Increasing temperature increases relative space between chains and makes uncoiling easier. Slowing the strain rate means there is more time for chain reconfiguration.
Introduction to Viscoelasticity Some features that are observed in polymeric materials that do not seem to be noticeable in metals or ceramics 1.Mechanical properties depend on Temperature 2.Mechanical properties depend on Strain Rate 3.Creep (noticed in metals at high temperatures) 4.Stress Relaxation 5.Hysteresis
Creep Take a tension specimen made from a polymer and and put on a series of constant stresses on it. We observe Creep: Progressive strain (deformation) over time at constant stress (load), usually at high temperatures
Creep Test We instantly load with constant stress for a certain time, and instantly unload. Note that both linear elastic and viscous fluid behaviors are present. Note that there seems to be some residual strain at the end, i.e. the material does not completely recover. There is both elasticity and plasticity.
Write down two examples of parts that see constant tensile or bending load.
Stress Relaxation Think of a polymer specimen loaded with a constant strain. Note that both linear elastic and viscous fluid behaviors are present. Note that there seems to be some residual stress at the end, i.e. the material does not completely recover. There is both elasticity and plasticity. Stress Relaxation: Progressive loss of stress (load) over time under constant strain (deformation), usually at high temperatures
Stress Relaxation of Delrin http://www2.dupont.com/Plasti cs/en_US/assets/downloads/d esign/230323c.pdf
Write down two examples of parts that see constant strain.
20 Time Dependent Deformation Stress relaxation test: -- strain to and hold. -- observe decrease in stress with time. Relaxation modulus: Sample T g ( C) values: PE (low density) PE (high density) PVC PS PC - 110 - 90 + 87 +100 +150 Selected values from Table 15.2, Callister 7e. time strain tensile test oo (t)(t) Data: Large drop in E r for T > T g. (amorphous polystyrene) Adapted from Fig. 15.7, Callister 7e. (Fig. 15.7 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) 10 3 1 10 -3 10 5 60100140180 rigid solid (small relax) transition region T(°C) TgTg E r (10s) in MPa viscous liquid (large relax)
Effect of Temperature: Glass Transition Temperature Or why does Garden Hose behave the way it does?
Melting vs. Glass Transition Temp. What factors affect T m and T g ? Both T m and T g increase with increasing chain stiffness Chain stiffness increased by 1.Bulky sidegroups 2.Polar groups or sidegroups 3.Double bonds or aromatic chain groups Regularity – effects T m only 22 Adapted from Fig. 15.18, Callister 7e.
Hysteresis Polymers often don’t load and unload on the same line on the stress-strain curve. The difference in areas under those curves represents energy loss (often to heat). This means that polymers can have inherent energy damping. This means plastic springs may not be as good an idea as plastic dampers.
Sinusoidal Response Tests We have a polymer specimen experiencing a sinusoidal loading. Note that there is a phase shift, and that there is also hysteresis indicating that energy is being dissipated cyclically. This all suggests some simple material models.
Takeaways Yield and Ultimate Strength are defined differently for polymers. Polymers have time and temperature dependent properties (viscoelasticity) Creep Stress Relaxation T g, T m Hysteresis
Maxwell Model Here is an alternative to the simple spring model of linear elasticity. Add a damper. This gives what is called as the Maxwell model. strain time stress time Creep not too good! Stress relaxation is not bad In the limit, it’s a fluid!
Kelvin-Voigt Model Try putting the spring and damper in series! This gives the Kelvin-Voigt model. In the limit, it’s a solid! strainstress time Doesn’t really show stress relaxation!
Standard Linear Solid Further improvement is possible. stress time Shows both creep and stress relaxation! strain
Stress Strain Relationships We can get stress from strain history and strain form stress history through the following heriditary relationships. K is creep modulus, and F is the relaxation modulus.
Examples of These Time Dependent Moduli MaterialCreep ModulusRelaxation Modulus Maxwell Kelvin Voigt Standard Linear Solid H(t) is the unit step function. (t) is the Dirac delta function
More on the material models Testing needs to be done to fit the parameters of the model to the behavior of an actual material. Note the fact that the history of the material must be recorded to be able to complete the calculations. Some additional complexity. The parameters in the creep modulus and relaxation modulus are 1.Temperature Dependent 2.Strain Rate Dependent
Summary Very complex behavior! Difficult to model. Great sensitivity to temperature. Great sensitivity to strain rate.
Tensile Response: Brittle & Plastic 36 brittle failure plastic failure (MPa) x x crystalline regions slide fibrillar structure near failure crystalline regions align onset of necking Initial Near Failure semi- crystalline case aligned, cross- linked case networked case amorphous regions elongate unload/reload Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along plastic response curve adapted from Figs. 15.12 & 15.13, Callister 7e. (Figs. 15.12 & 15.13 are from J.M. Schultz, Polymer Materials Science, Prentice- Hall, Inc., 1974, pp. 500-501.)
37 Tensile Response: Elastomer Case Compare to responses of other polymers: -- brittle response (aligned, crosslinked & networked polymer) -- plastic response (semi-crystalline polymers) Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along elastomer curve (green) adapted from Fig. 15.15, Callister 7e. (Fig. 15.15 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) (MPa) initial: amorphous chains are kinked, cross-linked. x final: chains are straight, still cross-linked elastomer Deformation is reversible! brittle failure plastic failure x x
38 Thermoplastics vs. Thermosets Thermoplastics: -- little crosslinking -- ductile -- soften w/heating -- polyethylene polypropylene polycarbonate polystyrene Thermosets: -- large crosslinking (10 to 50% of mers) -- hard and brittle -- do NOT soften w/heating -- vulcanized rubber, epoxies, polyester resin, phenolic resin Adapted from Fig. 15.19, Callister 7e. (Fig. 15.19 is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.) Callister, Fig. 16.9 T Molecular weight TgTg TmTm mobile liquid viscous liquid rubber tough plastic partially crystalline solid crystalline solid
Predeformation by Drawing 39 Drawing…(ex: monofilament fishline) -- stretches the polymer prior to use -- aligns chains in the stretching direction Results of drawing: -- increases the elastic modulus (E) in the stretching direction -- increases the tensile strength (TS) in the stretching direction -- decreases ductility (%EL) Annealing after drawing... -- decreases alignment -- reverses effects of drawing. Compare to cold working in metals! Adapted from Fig. 15.13, Callister 7e. (Fig. 15.13 is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.)