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FE-2: Continuation of part 1Polymers, phase diagrams, steel
• Carbon-based of concern here.• One or more monomers joined to form giant molecules.• The bonding within a molecule is primarily covalent.• Polymer solids held together by:
– Entanglement of the polymer chains.
– Van der Waals forces.
– Cross linking between polymer chains by chemical reactions, often at elevated temperature (thermoset). For rubber, called vulcanization, typically by sulfur. Cross-linked polymers can't be heated and reshaped as can thermoplastics.
• May have partial crystallization, with molecule chains folded within small crystals and going between crystals. Crystals have higher density (g/cc)– Crystallization favored by polymer molecules having the same shape, and
without cross linking. For example, polyethylene.
– Another example: isotactic polyvinyl chloride rather than syndiotactic or atactic chains.
Last revised January 11, 2014 by W.R.Wilcox at Clarkson University.
Mechanical behavior of polymers• Plastic deformation of polymers usually involves the movement of polymer
molecules past one another.• In addition to brittle and plastic
behavior, can also be highly elastic (elastomeric).
brittle
elastomeric
ductile
• An amorphous polymer may behave like a brittle glass below a glass transition temperature and a rubbery solid at intermediate temperatures.
• For small deformations, the behavior depends on how quickly the stress is applied and released. If this is fast, the material behaves elastically. If very slow, it flows and takes a new permanent shape. (Think silly putty.)
• For intermediate rates, the deformation is viscoelastic, so that only part of the strain is recovered when the stress is removed.
• Tg is the glass-transition T, below which it's brittle.
• Tm is the melting T, above which it flows when stressed and can be formed into shapes. (But it's not a usual liquid.)
• Notice that these are not sharp transitions like the melting point of non-polymers.
From the FE exam handbook
Conditions favoring solubility in solid metals
Substitutional impurities: Hume-Rothery rules1)Atomic size: The closer the atomic radii the greater the solubility.
2)Electronegativity: The closer the electronegativities, the greater the solubility. True when metals are near one another in the periodic table. If not near, formation of an intermetallic compound is favored. •For complete solid solubility, the pure components must have the same crystal structure, i.e. "isomorphous." Uncommon.•The electronegativities must be near and the atomic radii close.•Most often get limited solubility with formation of other phase(s). The solubility usually depends strongly on temperature.•Example of complete solid solubility: Ni-Cu
Interstitial impurities• Atomic radius of impurity must be much smaller than host, e.g. C (0.071nm)
in Fe (0.1241nm).
CrystalStructure
electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278
Nickel-copper binary phase diagram at 1 atm• Only melt
above the liquidus.
• Only solid below the solidus.
• Both in between• Isotherm shows
composition of the liquid and solid in equil.
• Called a tie line
At B: T = __oC?Solid = __%Ni?Liquid = __%Cu?
1
1. Melting point pure B
2. Solubility of B
3. Melting point pure A
4. Solubility of A
5. Eutectic point2
3
4
5
Solid A and solid B in equilibrium with one another
T
A BFraction of B
Binary phase diagram with no solid solubility – simple eutectic
Liquid
Solution 2 and solid B
A + 4
When two phases are in equilibrium with one another they are at the same temperature.
Find compositions in equilibrium with one another by drawing an isotherm, called a “tie line.” For example:
Eutectic with some solubility,
e.g.Pb-Sn
Greek letters
and used for solid
solutions.
Metallurgists call eutectic liquid going
to solid the “eutectic
reaction” L +
Compound formation, e.g. Mg-Pb
Two eutectics
Intermetallic compound
Mg2Pb shown at
exact comp’n, but would exist over small
comp’n range.
Some compounds decompose
before melting
Peritectic
S1 + L S2
cool
heat
• At the peritectic point, when heated a solid goes to another solid and a melt. Vice versa when cooled.
• Metallurgists call this the “peritectic reaction” and write it:
• At 184oC, 27wt%Bi goes from to + L.
• Where’s the eutectic point?
• What phases can be in equilibrium at the peritectic point?
• At A?
BiPb
A
Eutectoid points• A eutectoid point is where a solid dissociates to two solids when cooled.
Analogous to a eutectic point, at which a liquid dissociates to two solids when cooled. For example, V-Zr phase diagram:
• Eutectoid point:
• Zr V2Zr + Zr
• What is sequence of phases as A is cooled ?
• L• L + Zr• Zr• Zr + Zr
• V2Zr + Zr
A
Liquid immiscibility and monotectic points
• Sometimes melts separate into two liquids below a certain temperature,e.g. Pb & Zn:
• At the monotectic point, a liquid separates into a solid and the other liquid.
• Here liquid A Zn + liquid B• What happens as we cool from the
blue dot?• What do we have at the red oval?
Zn Pb
Another viewpoint
Cmix
Distance to opposite phase
Total distance
For example: simple eutectic with no
solid solubility.
the total distance between phases A & B
Check: the closer the mixture composition is to a phase the more of that phase must be present, in the limit 100%!
Fraction of A equals the distance from the mixture composition to the opposite phase (B)
divided by
Fraction of grains with eutectic structure
• Consider the red point.• Rather than asking how
much of A and B are present, we can ask what weight fraction of the grains is eutectic and what fraction is primary B.
• To do this, treat the eutectic as a compound.
• Then use the lever rule in the usual way to calculate the weight fraction of grains that have the eutectic microstructure.
• The fraction of eutectic is opposite/total.
T
A BWeight fraction of B
Liquid
B + L
A + L
opposite
total
Fe – Fe3C (cementite): C steels and cast iron
Eutectoid reaction to form pearlite• When slowly cool eutectic or eutectoid compositions get a lamellar structure.• For example, 0.76 wt% C austenite gives pearlite, which consists of
alternating layers of ferrite and cementite.
To left of eutectoid, get pearlite + ferrite steel. To right, brittle pearlite+Fe3C.
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