mechanical)properties)of) polymers) - harvard university · mechanical)properties)of) polymers)...
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Mechanical Properties of Polymers
Kamyar Davoudi
October, 2013
Materials Science Seminar
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Definition of Polymers
• Polymers are materials consisting of very long molecules ,
made up of hundreds or thousands repeating chemical
units (the monomer units), covalently bonded together.
• Organic glasses
• The long molecules are bonded together by
– Ven der Waals
– Hydrogen bonds
– Covalent cross-‐links
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Amorphous & Crystalline
Degree of Polymerization (DP): the number of monomer units in a molecule.
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Classes of Polymers
• Thermoplastics: such as PE. soften on heating
• Thermosets: such as epoxy. Harden when
two components are heated together
• Elastomers or rubbers
• Natural polymers: such as cellulose, lignin,
and protein
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Thermoplastics
• Commonest: Polyethylene (PE)
• Often described as linear polymers (chains are
not cross linked)
• T ñ secondary bonds melt, flow like viscous
liquid
• Polystyrene (PS): amorphous
PE: partly crystalline
• Sub-‐units (monomers) of most of them C C
H
H
H
R
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Thermosets • Are made by mixing two components (resin and
hardener) à react and harden at RT or on heating
• Heavily cross-‐linked à also called network polymers
• T ñ secondary bonds melt, E drops à rubber
• T ññ à decomposes
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Elastomers • Almost linear polymers with occasional cross-‐links
• only in noncrystalline
• the backbone of the chain must be very long and have many kinks and
bends.
• At RT, secondary bonds have already melted
• Vulcanization
• Cross-‐links provide the memory of the material so that it returns to its
original shape
C C
H
H R
C
H
H
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Elastomers • Helical pattern to the chain because of carbon-‐carbon double bonds
• Mechanical Model: a highly coiled skeleton of primary bonds (including cross-‐links) immersed in a viscous like medium.
• During applica,on of a tensile load: coils are unwound to an extent
• Upon unloading, the cross-‐linking atoms act to restore the original dimensions.
• No links, no restora,on
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Elastomers • Elastic behavior of rubbers is different
from that of crystalline material
• Only at extensions where the chains approximately fully extended does the force begin to stretch primary bonds
• decrease in S à Increase in F (free energy)
• Potential energy is unchanged
• No primary bond stretching à small modulus
Source: Courtney, Mechanical Behavior of Materials, 2000
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Elastomers
• Akin to ideal gases (no change in poten,al energy) but …
• Incompressible • Neo-‐Hookean μ=NkBT N : no. polymer chains/V
Source: Courtney, Mechanical Behavior of Materials, 2000
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Glass Transi,on Temperature
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Deforma,on of Polymers
• Elastomers à Always elas,c response • Thermosets à viscoelas,c response • Thermoplas,cs à elas,c or plas,c
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Change of Young’s modulus for linear polymers
Linear-‐amorphous polymers (like PMMA & PS) show five regims of deforma,on
ß Fixed loading ,me
Source: Ashby & Jones, Engineering Materials 2, 1998.
In general
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Glassy Regime and secondary relaxa,ons
• T<<Tg
E1~103 GPa E2~ 1 GPa
Source: Ashby & Jones, Engineering Materials 2, 1998.
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Glass or visco-‐elas,c transi,on
• T>Tg Extra free volume lowers the packing density
• S,ll there are some non-‐sliding parts
• On unloading the elas,c regions pull the polymer to its orgiginal shape
• Modeled by springs and dashpots
Source: Ashby & Jones, Engineering Materials 2, 1998.
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Higher Temperatures • Rubbery behavior
– DP<103 àpolymer becomes s,cky liquid – DP>104àlong molecules intertwined like a jar of very long worms àrubbery behavior
• Viscous flow
• Decomposi,on – the thermal energy exceeds the cohesive energy of some parts of the molecular chain, causing degrada,on or depolymeriza,on.
– PMMA à decomposes into monomer units – PE àrandomly degrade into many products
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Modulus Diagram for Polymers
Source: Ashby & Jones, Engineering Materials 2, 1998.
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The influence of Cross-‐linking on a contour of the modulus diagram for polyisoprene
Source: Ashby & Jones, Engineering Materials 2, 1998.
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The effect of Temperature on Deformation
Source: Gibson & Ashby, Cellular solids-‐structure & proper,es, Pergamon Press, Oxford, 1988
PMMA Strength decreases and elonga,on increases with higher temperature
Source:Carswell & Nason, ASTM Symposium on Plas,cs, Philadelphia, 1944
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Briile Fracture • Polymers are briile at T<~0.75 Tg
• Pre exis,ng cracks lel by machining or abrasion or caused by environmental aiack
• Fracture toughness KIC ~ 1 MPa m ½
• Crack size a ~ O(μm) • σ ~ 1 MPa
Source: Ashby & Jones, Engineering Materials 2, 1998.
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Cold Drawing
At ε ~ 0.1 The chains unfold (if folded) or draw out of the amorphous tangle (if glassy)
For λ sufficient enough (2-‐4) (ε=100-‐300%) : alignment of molecules à neck propagates until it is all drawn
Source: Ashby & Jones, Engineering Materials 2, 1998.
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Crazing • Craze || maximum stress
• Propagates along a direc,on perpendicular to the principle axis
• Depends on T (PE & PP draw at RT, PS does not, but it crazes)
• No crazing in compression
• Precursor to fracture
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Shear Banding Highly localized In the direc,on of maximum shear stresses More easily formed in tension Crazing and shear banding compete with each other
Source:McClintock & Ashby, Mechanical Behavior of Materials, 1966
Source: Ashby & Jones, Engineering Materials 2, 1998.
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Glassy Polymers: Thermoplas,cs
Micro-‐shear bands At-‐Polystyrene at 22° C under compression (Op,cal Microscopy w/ Polarized Light)
Crazes At-‐Polystyrene in tension
(TEM) Source: hip://www.files.chem.vt.edu/chem-‐dept/marand/Lecture23.pdf
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Source: Ashby & Jones, Engineering Materials 2, 1998.
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Deforma,on of Crystalline Polymers • Crystalline polymers always contain some remnant non-‐
crystalline material.
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Crystallization
Crystallization increases the modulus too
Source: Courtney, Mechanical Behavior of Materials, 1998
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Summary • Polymers may be amorphous or semi-‐crystalline • Deforma,on of polymers is highly affected by temperature,
,me, DP, etc. • Elastomers deform elas,cally over a long range of
temperature • Linear polymers may be glassy, leathery, rubbery or viscous
flow • Plas,c behavior of linear polymers may cause by cold
drawing, crazing or shear banding • Crystalline polymers always have remnants of amorphous
polymers • The tension and compression behavior of polymers can be
quite different
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Glass Transi,on Temperature