Essentials of Polymer Engineering (Introduction to Polymers) Polymers) ChE 197 Mechanical Properties of Polymers
What we have discussed so far •
•
•
•
•
•
•
•
•
•
Introduction Introduction – basic concepts concepts and definitions; definitions; classification of polymers polymers Polymerization Polymerization mechanisms – chain-reaction; chain-reaction; ionic and coordination coordination polymerization; step-growth and ring-opening polymerization Chemical bonding bonding and polymer structure – primary, primary, secondary, secondary, and tertiary structures Thermal Thermal transiti transition on in polymer polymerss – Tg and Tm Tm Polymer modification modification – copolymerization copolymerization;; postpolymerizatio postpolymerization n reactions; functional polymers Condensation (Step-Reaction) (Step-Reaction) polymerizati polymerization on – mechanism; kinetics; kinetics; stoichiometry; molecular weight control and distribution Chain-Reaction (Addition) Polymerization Polymerization Copolymerization Solution properties properties of polymers – solubility parameter, parameter, conformations conformations of polymer chains in solutions, thermodynamics of polymer solutions, solution viscosity Mechanical properties properties of polymers polymers – mechanical tests, stress-str stress-strain ain behavior, behavior, deformation, compression vs tensile tests, effects effects of structural structural and environmental factors
What we have discussed so far •
•
•
•
•
•
•
•
•
•
Introduction Introduction – basic concepts concepts and definitions; definitions; classification of polymers polymers Polymerization Polymerization mechanisms – chain-reaction; chain-reaction; ionic and coordination coordination polymerization; step-growth and ring-opening polymerization Chemical bonding bonding and polymer structure – primary, primary, secondary, secondary, and tertiary structures Thermal Thermal transiti transition on in polymer polymerss – Tg and Tm Tm Polymer modification modification – copolymerization copolymerization;; postpolymerizatio postpolymerization n reactions; functional polymers Condensation (Step-Reaction) (Step-Reaction) polymerizati polymerization on – mechanism; kinetics; kinetics; stoichiometry; molecular weight control and distribution Chain-Reaction (Addition) Polymerization Polymerization Copolymerization Solution properties properties of polymers – solubility parameter, parameter, conformations conformations of polymer chains in solutions, thermodynamics of polymer solutions, solution viscosity Mechanical properties properties of polymers polymers – mechanical tests, stress-str stress-strain ain behavior, behavior, deformation, compression vs tensile tests, effects effects of structural structural and environmental factors
General Outline •
•
•
Mechanical Mechanical tests tests – stress-str stress-strain ain experimen experiments; ts; creep experiments; stress relaxation experiments; experiments; dynamic mechanical experiments; impact experiments Stress-strain Stress-strain behavior behavior – elastic stress-str stress-strain ain relations; relations; deformation of solid polymers; compression vs. tensile tests Effect ffect of structural and environmental environmental factors on mechanical mechanical properties properties – MW MW,, cross-linking, cross-linking, crystallinity crystallinity,, copolymerizatio copolymerization, n, plasticizers, plasticizers, polarity, polarity, streric streric factors, factors, temperature, strain strain rate, pressure
Overview on mechanical properties of polymers •
•
•
•
Mechanical stability stability and durability durability coupled w/ their light light weight weight – pref prefer erable able alternative alternative to to ceramics and metals Mechan Mechanic ical al behav behavior ior – functio function n of microstructure or morphology Strong dependence to temperature and time (visco (viscoela elast stic ic behav behavior ior)) Linear elastic behavior yield phenomena plastic deformation/cold drawing
Mechanical tests Failure of a polymer to perform its function can be due to: Excessive elastic deformation – in structural, load-bearing applications; inadequate rigidity or stiffness; controlling property is the elastic modulus Yielding or excessive plastic deformation – in carrying design loads and occasional accidental overloads; inadequate strength properties; controlling property is the yield strength and corresponding strain Fracture – cracks are regions of material discontinuity; precipitates failure through fracture; fracture can be brittle or through fatigue
Brittle fracture – occurs where the absence of local yielding results in a build-up of localized stresses Fatigue failure - parts are subjected to alternating or repeated loads; no visible signs of yielding since they occur at strengths well below the tensile strength of the material A variety of test methods exist for predicting mechanical performance limits under a variety of loading conditions.
Stress-Strain Experiments
Specimen is deformed (pulled) at a constant rate, and the stress required for this deformation is measured simultaneously This test can be enhanced if they can be carried out over a wide range of temperatures and strain rates
Creep Experiments Specimen is subjected to a constant load, and the strain is measured as a function of time The elongation may be measured at time intervals using a travelling microscope. Measurements may be conducted in an environmental chamber.
Can be done in tension, shear, torsion, flexure, or compression Usually measures compliance
Stress Relaxation Experiments Specimen is rapidly (ideally, instantaneously) extended a given amount, and the stress required to maintain this constant strain is measured as a function of time
Stress that is required to maintain the strain constant decays with time
Usually measures the relaxation modulus Er(t ,T ) = time-varying stress over constant strain
Dynamic Mechanical Experiments
Response of a material to periodic stress is measured Torsion pendulum - a polymer sample is clamped at one end, and the other end is attached to a disk that is free to oscillate Provide useful information about the viscoelastic nature of a polymer
Dynamic Mechanical Experiments Assume we impose a sinusoidal strain to two types of materials (extreme): 1) elastic and 2) viscous
Stress response if material is purely elastic, by Hooke’s law: Stress and strain are in phase!
ε0 – amplitude ω – frequency (rad/s; = 2πf)
G – shear modulus
Stress response if material is purely viscous, by Newton’s law of viscosity: Stress and strain are 90 0 out of phase!
In case of polymers (viscoelastic materials), response falls between the two extremes. Sinusoidal stress and strain are out of phase by an angle δ
Dynamic Mechanical Experiments
Phase relation is shown between dynamic strain and stress for viscous, elastic, and viscoelastic materials.
Dynamic Mechanical Experiments Lag angle between stress and strain is defined by the dissipation factor or tan δ Denotes material damping characteristics Ratio of energy viscously dissipated as heat G” over the maximum energy stored in the material G’ during one cycle of oscillation
Complex modulus G = G’ + iG”
We can measure damping from experiments: A1 and A2 are the amplitudes of two consecutive peaks
This may be expressed in terms of log decrement (Δ) for free vibration instruments like the torsional pendulum
Impact Experiments Prediction of failure due to rapid stress loading (impact load) Measurement of the area under the stress strain curve in the high-speed (rapid) tensile test Falling ball or dart test - measurement of the energy required to break a specimen by a ball of known weight released from a predetermined height Izod test - measurement of the energy required to break a H × H in. notched cantilever specimen that is clamped rigidly at one end and then struck at the other end by a pendulum weight Brittle polymers (e.g. PS) – low impact resistance Engineering thermoplastics (e.g. PA, PC) – high impact resistance/impact strength
Charpy test - hammerlike weight strikes a notched specimen that is rigidly held at both ends
Stress-Strain Behaviors of Polymers
Typical polymer specimen for the tensile test L0 – initial gauge length Dog bone shape – encourages failure at the thinner middle portion It is clamped at both ends and pulled at one of the clamped ends (usually downward) at constant elongation Engineering (nominal) stress
Engineering (nominal) strain
Stress-Strain Behaviors of Polymers Engineering stress–strain curves generally depend on the shape of the specimen Plot of true stress vs true strain - more accurate measure of intrinsic material performance Ratio of the measured force (F) to the instantaneous cross-sectional area (A) at a given elongation Sum of all the instantaneous length changes, dL, divided by the instantaneous length L
True strain and engineering strain
σt = σ ⋅
L L0
True stress and engineering stress Note: AL = A0L0 since plastic deformation is a constant volume process up to the onset of necking
= σ ⋅ (1 + ε )
For small deformations true stress ≈ engineering stress
Elastic Stress-Strain Relations When a material is subjected to small stresses, it responds elastically
Since stress may act on a plane in different ways, this constant is defined in different ways depending on the applied force and the resultant strain
τ = Gγ τ – shear stress G – shear modulus
Elastic shear strain = tangent of angle of deformation
Elastic Stress-Strain Relations D
=
∆V V
Dilatation strain
σ = KD Majority of cases – mixture of shear and dilatation (tensile and compressive tests)
K – bulk modulus E – Young’s modulus (or modulus of elasticity)
For most polymers, there is a change in volume Poisson’s ratio v = 0.5 (incompressible materials; constant volume deformation) Axial elongation accompanied by transverse contractions
For isotropic materials w/ elastic deformations:
Example 1 In a tension test, a brittle polymer experienced an elastic engineering strain of 2% at a stress level of 35 MN/m2. Calculate: a) True stress; b) True strain; and c) fractional change in crosssectional area
Example 2 Polypropylene has an elastic modulus of 2 × 105 psi and Poisson’s ratio of 0.32. For a strain of 0.05, calculate the shear stress and the percentage change in volume.
Deformation of Solid Polymers To relieve stress, all materials under the influence of external load undergo some deformation. Elastic deformation - up to a certain limiting load, a solid will recover its original dimensions on the removal of the applied loads; ability of deformed bodies to recover their original dimensions Plastic deformation - beyond the limit of elastic behavior (elastic limit); a material will experience a permanent set or deformation even when the load is removed
Deformation of Solid Polymers Gradient of the initial linear portion of the curve, within which Hooke’s law is obeyed, gives the elastic, or Young’s, modulus Maximum on the curve denotes the yield strength marks the limit of usable elastic behavior or the onset of plastic deformation Stress at which fracture occurs (material breaks apart) = ultimate tensile strength or, simply, tensile strength σB
Deformation of Solid Polymers – Physical Significance of Measured Parameters •
•
•
•
•
Stiffness — ability to carry stress without changing dimension; magnitude of the modulus of elasticity is a measure of this ability or property Elasticity — ability to undergo reversible deformation or carry stress without suffering a permanent deformation; elastic limit or yield point Resilience — ability to absorb energy without suffering permanent deformation; area under the elastic portion of the stress-strain curve gives the resilient energy Strength — ability to sustain dead load; tensile strength or stress at which the specimen ruptures σ B. Toughness — ability to absorb energy and undergo extensive plastic deformation without rupturing; area under the stress-strain curve
Deformation of Solid Polymers Brittle polymers - fail with little or no plastic deformation; no ability for local yielding; local stresses build up around inherent flaws, reaching a critical level at which abrupt failure occurs Ductile polymers - ability to undergo plastic deformation; this property assists in the redistribution of localized stresses
Deformation of Solid Polymers At small strains, polymers (both amorphous and crystalline) linear elastic behavior; from bond angle deformation and bond stretching Further increase in strain straininduced softening ; reduction of the instantaneous modulus; uncoiling and straightening of chains Onset of necking increase in the local stress at the necked region due to the reduction in the load-bearing cross-sectional area (cold drawing) Schematic representation of macroscopic changes in Polymer chains in the amorphous tensile specimen shape during cold drawing regions undergo conformational changes; become oriented in the direction of the applied tensile stress
Example 3 The mechanical properties of nylon 6,6 vary with its moisture content. A nylon specimen with a moisture content (MC) of 2.5% has an elastic modulus of 1.2 GN/m2, while that for a sample of moisture content of 0.2% is 2.8 GN/m2. Calculate the elastic energy or work per unit volume in each sample subjected to a tensile strain of 10%. In the elastic region:
Example 4 Two nylon samples of moisture contents 2.5% and 0.2% have ε B of 300% and 60%, respectively. Calculate the toughness of each sample if the stress-strain curve of nylon for plastic deformation is given by:
Compression versus Tensile Tests Normal stresses can be either tensile or compressive
Compressive stress–strain data for two amorphous polymers: polyvinyl chloride (PVC) and cellulose acetate (CA)
Compressive stress–strain data for two crystalline polymers: polytetrafluoroethylene (PTFE) and polychlorotrifluoroethylene (PCTFE)
Stress–strain curves for the amorphous polymers are characteristic of the yield behavior of polymers; no clearly defined yield points for the crystalline polymers
Compression versus Tensile Tests In tension polystyrene exhibited brittle failure In compression behaved as a ductile polymer Strength and yield stress are generally higher in compression than in tension
Tensile properties of brittle materials depend to a considerable extent on the cracks and other flaws inherent in the material; brittle fracture occurs by propagation of these cracks
Stress–strain behavior of a normally brittle polymer, polystyrene, under tension and compression.
Compressive stresses close open cracks; enhances strength
Criterion for plastic deformation to occur during application of tensile stress Shear stress on A’
Max shear stress at φ = π/4 Plastic deformation occurs when τmax is at least equal to the yield strength of the material
Generation of shear stress due to uniaxial loading
for plastic deformation to occur, the imposed tensile stress must be at least twice the magnitude of the shear stresses generated; the tensile strength must be at least twice the shear strength (theoretical only)
Effects of Structural and Environmental Factors on Mechanical Properties – Molecular Weight T < Tg – glassy region T = Tg – transition from glassy to rubbery T > Tg – rubbery region T = Tfl – transition from rubbery to melt flow If Tg >
room temp, polymer is rigid at room
temp If Tg < room temp, polymer is rubbery or viscous at room temp
Schematic representation of the effect of molecular weight on shear modulus temperature curve. Tg is the glass transition temperature while T fl is the flow temperature. Tfl , Tfl , Tfl”’ - represent low-, medium-, and high-molecular-weight materials, respectively ′
″
MW has practically no effect on the modulus in the glassy region; also in location of Tg and modulus drop High MW high number of entanglements high T at which viscous flow becomes predominant over rubbery behavior; longer rubber plateau
Effects of Structural and Environmental Factors on Mechanical Properties – Cross-Linking Glassy region increase in modulus due to cross-linking is relatively small Increase in modulus in the rubbery region and the disappearance of the flow regions Cross-linking raises the glass transition temperature at high values of cross-link density Cross-linking increases polymer ability to resist deformation under load increases its modulus Effect of cross-linking on shear modulus of natural rubber; mean number of chain atoms between successive cross-links is indicated (Mc); low Mc, high cross-link density
Example 5 The densities of hard and soft rubbers are 1.19 and 0.90 g/cm3, respectively. Estimate the average molecular weight between cross-links for both materials if their respective moduli at room temperature are 106 and 108 dynes/cm2. average molecular weight between cross-links ρ = density, R = gas constant, T = absolute temperature, and G = shear modulus
Hard rubber
Soft rubber
Effects of Structural and Environmental Factors on Mechanical Properties – Crystallinity Crystallinity has only a small effect on modulus below the Tg but has a pronounced effect above the Tg Intensity of modulus drop at the Tg decreases with increasing degree of crystallinity
Sharper drop at the melting point
Effect of crystallinity on the modulus temperature curve. The numbers of the curves are rough approximations of the percentage of crystallinity
Melting temperature generally increases with increasing degree of crystallinity
Effects of Structural and Environmental Factors on Mechanical Properties – Copolymerization
Random and alternating copolymers are homogeneous; block and graft copolymers with sufficiently long sequences exhibit phase separation Random and alternating copolymers single transition that is intermediate between those of the two homopolymers of A and B; shifts the the modulus–temperature curve
Effect of plasticization or copolymerization on the modulus–temperature curve. The curves correspond to different copolymer compositions. (B) Unplasticized homopolymer; (A) either a second homopolymer or plasticized B.
Effects of Structural and Environmental Factors on Mechanical Properties – Copolymerization
Block and graft copolymers, which exist as a two-phase system, have two distinct glass transitions, one for each of the homopolymers modulus–temperature curve shows two steep drops (Tg of poly butadiene = -800C; Tg of postyrene = 100oC) Behaves like a polybutadiene (rubber) matrix reinforced with polystyrene (hard) phase Shear modulus as a function of temperature for styrene–butadiene–styrene block copolymers. Wt.% styrene is indicated on each curve
Effects of Structural and Environmental Factors on Mechanical Properties - Plasticizers
Effect of plasticization or copolymerization on the modulus–temperature curve. The curves correspond to different copolymer compositions. (B) Unplasticized homopolymer; (A) either a second homopolymer or plasticized B.
Effects of Structural and Environmental Factors on Mechanical Properties - Polarity
Tg of polar poly(vinyl chloride) is about 90°C higher than that of the nonpolar polypropylene.
Effect of the substitution of the chlorine atom for the methyl group depends on the molecular environment of the chlorine atom.
Shear modulus (a) and damping (b) as a function of temperature: solid line is PVC; dashed line is PP
Effects of Structural and Environmental Factors on Mechanical Properties - Polarity
Tg of poly(2-chloroethyl methacrylate) is only 20°C higher than that of poly(n propyl methacrylate) Shear modulus (a) and damping (b) at 1 Hz as a function of temperature: (———) poly(2-chloroethyl methacrylate); (––––) poly(n-propyl methacrylate
Effects of Structural and Environmental Factors on Mechanical Properties – Steric Factors Long, flexible side chains reduce Tg, while stiff side chains increase Tg Long, flexible side chains increase the free volume and ease the steric hindrance from neighboring chains and as such facilitate the movement of the main chain Increase in modulus in the glassy region with increase in length of the alkyl group for poly(n-alkyl methacrylate). Shear modulus (a) and damping (b) at 1 Hz as a function of temperature for poly(n-alkyl methacrylate): (––––) Polymethyl methacrylate; (– – –) polyethyl methacrylate; (— — —) poly(n-propyl methacrylate); (· · · ·) poly(n-butyl methacrylate)
Effects of Structural and Environmental Factors on Mechanical Properties – Steric Factors
Brittleness temperatures for polyacrylates as a function of the total length of the side chain
Softening temperature of polyolefins with branched side chains
Effects of Structural and Environmental Factors on Mechanical Properties – Steric Factors
Effects of the Introduction of Rings into the Main Chain of Some Polyamides
Effects of Structural and Environmental Factors on Mechanical Properties – Steric Factors
Polymer Stiffening Due to the Introduction of Rings into the Main Chain
Effects of Structural and Environmental Factors on Mechanical Properties – Temperature
Modulus of a polymer decreases with increasing temperature
Below the Tg, the modulus is high; no yield point,brittle polymer
As the temperature is increased, the modulus and yield strength decrease and the polymer becomes more ductile
Stress–strain behavior of cellulose acetate at different temperatures
Effects of Structural and Environmental Factors on Mechanical Properties – Strain Rate Polymers are very sensitive to the rate of testing
As the strain rate increases, polymers in general show a decrease in ductility while the modulus and the yield or tensile strength increase
Effect of decreasing temperature is equivalent to that of increasing the strain rate
Schematic illustration of the effect of strain rate on polymers