Mechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.

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1 Mechanical Properties of Polymers Scope MSE 383, Unit 3-1 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Structure - mechanical properties relations Time-dependent mechanical properties Linear viscoelasticity Creep Stress Relaxation Spring and dashpot models Superposition principles Yield and Fracture Yield criteria Necking and cold-drawing Fracture mechanics

2 Why Mechanical Properties? Parameters that determine material response to applied stress Related to molecular structure Facilitates development of materials for specific end-use applications Three Basic Types of Deformation Simple shear Produces a change in shape without a change in volume Bulk compression Produces a change in volume without a change in shape Simple extension Tensile force applied in one direction Material Responses to Applied Stress Apply a FORCE to a material and it will DEFORM Removal of the force yields: ELASTIC recovery VISCOUS flow VISCOELASTIC recovery Polymers are viscoelastic - consequence of long chain nature Definitions of Various Moduli Shear or Rigidity Modulus G F / A F = = = shear stress/shear strain S / D A tanθ S F D F Figure 3.1.1: Shear Modulus Illustration θ

3 Definitions of Various Moduli, Cont d Shear Compliance (J) = 1/G Bulk Compression Bulk modulus e.g., applied pressure to a cube results in V K = bulk stress/bulk strain = P/( V/V 0 ) Bulk compliance B = 1/K B = β (isothermal compressibility) = -1/V(δV/δP) p Extensional or Young s Modulus TensileStress F / A E = = TensileStrain l / l Tensile Compliance D = 1/E Relation Between G, B, & E Only 2 of the 3 moduli are independent for isotropic materials It can be shown that D = J/3 + B/9 Note that B << J for polymers D = J/3 or E = 3G 21 needed for anisotropic materials!! Similar relations involving Poisson's ratio (ν) exist: E = 2G(1+ν) = 3B(1-2ν) ν = [change in width/unit width]/[change in length/unit length] ν = 0.5 (for incompressible materials like rubbers and liquids) E = 3G (for rubbers) no change in volume after deformation

4 Poisson's Ratio Summary of Symbols Deformation Stress Strain Modulus Compliance Tensile σ ε E D Shear f γ G J Bulk p V/V K B SI Units Pa -- Pa 1/Pa Polymer Classifications According to Mechanical Properties Rubbers low stiffness, E = Pa and ε up to high extensions Semi-crystalline polymers intermediate stiffness, E = Pa and typically flexible and tough Glasses high stiffness, E = Pa and typically low ε and brittle Fibers high stiffness, E = Pa and typically tough & strong Note that classification is related to molecular architecture (Unit2)**

5 Tailorable Chemical & Morphological Features to Alter Mechanical Properties MW and MWD affects flow properties during processing and hence ultimate properties Crosslinking and branching vulcanize rubber to raise mechanical properties hardness & E increase with crosslinking Chain branching strongly affects mechanical properties (e.g., LDPE & HDPE) Crystallinity and crystal morphology increasing %C increase mechanical properties size of spherulites affects toughness use nucleating agents to alter size of spherulites Copolymerization and/or Blending used to obtain properties not present in a given polymer (e.g., LIPS & HIPS) Plasticization low MW material blended with polymer (e.g., PVC) to improve processability to produce softer & tougher material Molecular orientation used fibers & biaxial drawn films** undesirable in injection molding & extrusion** Fillers and composites e.g., carbon or glass fibers to increase stiffness and strength (Above can be changed to product polymers for specific engineering applications)!! Influence of Environmental Factors on Mechanical Properties Emphasize importance of ASTM Temperature* Deformation rate, time & frequency* Stress and strain amplitude* Deformation mode (flexure, etc.)* *Will be demonstrated later Heat treatment and thermal history properties depend on process temperatures in particular, rate of cooling from melt reheating produces annealing which modifies properties Surrounding atmosphere water plasticizes nylon, PET petrol/pc helmets lead to fracture

6 Influence of Environmental Factors on Mechanical Properties Types of Mechanical Properties E(t,T) for polymers (cf. metals) therefore, need to measure E(t,T) to characterize bulk behavior F F Effect of Temperature Rigid Log (E) Leathery Rubbery Viscous T G Temperature T Tensile Stress - Strain Behavior Figure 3.3.3: Effect of Temperature on Polymers Stress Linear Elastic Deformation Strain Figure 3.3.4: Stress - Strain Curve

7 Instron Tensile Testing of Nylon Creep Behavior variation of deformation with time of a material subjected to constant loading very important in structural applications ε 1 2& Time 1 - instantaneous elastic deformation due to bond orientations 2 - delayed elastic deformation (1 o creep) due to segmental motion and chain uncoiling 3 - viscous flow (2 o creep) due to molecular slippage 4 - instantaneous elastic recovery due to bond recovery 5 - delayed elastic recovery due to segmental motion returning molecule to original configuration 6 - irreversible plastic deformation due to viscous flow D (t) = creep strain/creep stress Linear viscoelasticity at low strains {D = f (t)} Non-linear viscoelasticity at high strains {D = f (ε,t)}

8 Creep Behavior in Metals (ε versus time) Strain Time Stress Relaxation Behavior Stress A stress is applied to cause a fixed strain in a polymer Time Stress relaxation modulus = f (t) Dynamic Mechanical Behavior Measures material response to periodic or varying forces Applied force and resulting strain both vary sinusoidally with time Very useful for studying transition phenomena in polymers (TBD) Note: Creep & SRM give long - time behavior and DMA can give short - time behavior

9 Linear Viscoelasticity Ideal HOOKEAN response σ = E ε (uniaxial extension) Ideal NEWTONIAN response τ = η a λ & (Newtonian fluid) Viscoelastic response σ = f (ε, t) - Nonlinear viscoelasticity σ = ε f (t) - Linear viscoelasticity σ ε - for fixed elapsed time t 1, t 2 linear visc. t 1 t 2 σ t 2 t 1 nonlinear visc. ε Typical σ - ε Plot for a Ductile Polymer σ strain hardening ε

10 Practical Demonstration of Strain Hardening Typical σ - ε Plot for Typical Polymers at 20 o C and low rates PMMA; PS E ~ 2-3 GPa ε = 3% xtalline polymer E ~ 100 MPa ε = % σ ε Rubber E ~ 2 MPa ε = 600 %

11 Time & Temperature Effects on σ - ε Behavior speed of testing σ ε σ T > Tg Temp Temperature Effect on Modulus of a Typical Polymer ε Rigid 1 Log (E) Leathery 2 3 Rubbery 4 Viscous 5 T G Temperature Region 1 - (T < 90 C - glassy region) 10 9 < E < Pa. Polymer is glassy, hard, brittle; main-chain segments frozen-in; no rotational motion Region 2 - ( C - transition region) < E < 10 9 Pa. Polymer is leathery and T-dependent, hard, brittle; main-chain segments begin to undergo rotational and shortrange motions T M

12 Temperature Effect on Modulus of a Typical Polymer, Cont d Region 3 - ( C - rubber plateau) < E < Pa. Polymer is rubbery short-range chain motions are now extremely rapid; long-range motions are retarded Region 4 - ( C - rubbery flow region) < E < Pa. Polymer is elastic, rubber and liquid-like long-range molecular motions set in Region 5 (T > 180 C - liquid flow region) E < Pa whole scale motion of molecules with no elastic recovery (Above regions present in polymers to greater or lesser extent) Recap Polymers exhibit unique mechanical properties Mechanical properties related to molecular structure can be tailored!! Polymers are viscoelastic Time & temperature effects important Five regions discernible in E vs. T plot Creep & SR more important in polymers relative to other materials End of Lecture Read Class text, Ch.4 Optional additional reading Nielsen and Landel (1994) Ward and Hadley (1993)