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3.40 Lecture Summary 11/16/09
Better, Faster, Stronger
How to Engineer Metals
With Thermo & Kinetics
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Contributions to Precipitation
Hard Particle Size
Shearablility
Coherency
Ordering
Modulus
Volume Fraction
ening
rrc-b
Cohe
Lattic
Coherent with Strain
Courtesy of DoITPoMS, University of Cambridge.
Used with permission.
rency:Please see Fig. 3.47c in Porter, D.,and K. Easterling.
e strainPhase Transformations in Metals and AlloysBoca Raton, FL: CRC Press, 2009.
coherentincoherent
http://www.matsceng.ohio-state.edu/mse205/lectures/chapter10/index_chap10.htm
D. Porter, K. Easterling. Phase transformations in metals and alloys. CRC Press 2000.
Courtesy of Krystyn Van Vliet. Used with permission.
cutting
bowing
rc-b
rc-i
http://www.matsceng.ohio-state.edu/mse205/lectures/chapter10/index_chap10.htmhttp://www.matsceng.ohio-state.edu/mse205/lectures/chapter10/index_chap10.htm8/13/2019 MIT3_40JF09_lec19
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Contributions to Precipitation
Ha Particle Size
Shearablility
Coherency
Ordering
Modulus
Volume Fraction
rdening
rc-irc-b
How do we engineer metals for maximum strength?
Simple: Large number of particles with r=rc-b
Courtesy of Krystyn Van Vliet. Used with permission.
coherentincoherent
http://www.matsceng.ohio-state.edu/mse205/lectures/chapter10/index_chap10.htm
rc-b
rc-i
http://www.matsceng.ohio-state.edu/mse205/lectures/chapter10/index_chap10.htmhttp://www.matsceng.ohio-state.edu/mse205/lectures/chapter10/index_chap10.htm8/13/2019 MIT3_40JF09_lec19
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Thermodynamics: Phase Diagrams
W. Hosford. Physical Metallurgy CRC Press, 2005
What do we want?Intermetallic:
Ordered phaseLarge Vf
Figure by MIT OpenCourseWare. Adapted from Vol. 3,
449.57oC
410.9oC
326.8oC
924oC
L
Temperatur
eoC
Pb Te
1009080706050403020100
1009080706050403020100
Weight percent tellurium
83.4
Atomic percent tellurium
200
300
400
500
600
327.502oC
700
800
900
1000
PbTe
C0
T1
T2
Alloy Phase Diagrams, ASM Handbook.Materials Park, OH: ASM International, 2009.
Please see "Microstructural Development: Basic Requirements for Aging.
aluMATTER, University of Liverpool."
http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=70&pageid=-1072490953http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=70&pageid=-10724909538/13/2019 MIT3_40JF09_lec19
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iVf i ii
W. Hosford. Physical Metallurgy CRC Press, 2005
Thermodynamics: Phase Diagrams
Figure by MIT OpenCourseWare. Adapted from Vol. 3,
449.57oC
410.9oC
326.8oC
924oC
L
TemperatureoC
Pb Te
1009080706050403020100
1009080706050403020100
Weight percent tellurium
83.4
Atomic percent tellurium
200
300
400
500
600
327.502oC
700
800
900
1000
PbTe
C0
T1
T2 (i) (ii)
Alloy Phase Diagrams, ASM Handbook.Materials Park, OH: ASM International, 2009.
Please see "Microstructural Development: Basic Requirements for Aging. aluMATTER, University of Liverpool."
Tie-Line Construction
http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=70&pageid=-1072490953http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=70&pageid=-10724909538/13/2019 MIT3_40JF09_lec19
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What about particle size: Kinetics
What do we want?
Large Vfof optimum particle size
http://www.uic.edu/classes/cemm/cemm470/Heat%20Treatment%20of%20Steels%20and%20Metallic%20Materials%5B1%5D.pdf
Image removed due to
Please see Fig. 12-7 in
and Pradeep Prabhakar
The Science and Engin
Stamford, CT: Cengag
Temperature
Time
T1
T2
T0
Solution Heat
Treatment
Precipitation Heat
Treatment
Quench
copyright restrictions.
Askeland, Donald R.,
Phul.'
eering of Materials.
e Learning, 2008.
Used with permission. Please also see "Microstructural Development: Stages of Heat Treatment."
aluMATTER, University of Liverpool.
http://www.uic.edu/classes/cemm/cemm470/Heat%20Treatment%20of%20Steels%20and%20Metallic%20Materials%5B1%5D.pdfhttp://aluminium.matter.org.uk/content/html/eng/default.asp?catid=70&pageid=-1542434388http://www.uic.edu/classes/cemm/cemm470/Heat%20Treatment%20of%20Steels%20and%20Metallic%20Materials%5B1%5D.pdfhttp://aluminium.matter.org.uk/content/html/eng/default.asp?catid=70&pageid=-15424343888/13/2019 MIT3_40JF09_lec19
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rc-irc-b
coherentincoherent
Precipitation Hardening: Kinetics
Vf
rave
t
t
Inc.
rnuc
tr
Courtesy of Krystyn Van Vliet. Used with permission.
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rc-irc-b
coherentincoherent
Vf
rave
t
t
Inc. Nuc.
rnuc
Vr
Precipitation Hardening: Kinetics
Courtesy of Krystyn Van Vliet. Used with permission.
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rc-irc-b
coherentincoheren
Vf
rave
t
t
rc-b
r~t1/2
Inc. Nuc. Growth
rnuc
tVrVr
Vf,eq
Precipitation Hardening: Kinetics
Large contribution to strengthening:Volume fraction and radius increasing
Courtesy of Krystyn Van Vliet. Used with permission.
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Vf
rave
t
t
rc-b
rc-i
r~t1/2
r~t1/3
Inc. Nuc. Growth Ostwald ripening
rnuc
Via Thermo.
tie lineNot impingement!
tVrV rr
rc-irc-b
coherentincoherent
Precipitation Hardening: Kinetics
Vf,eq
Sweet Spot for Max Strengthening:
rc-b & Vf,,eq
Courtesy of Krystyn Van Vliet. Used with permission.
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Gibbs-Thompson Effect: Ostwald
ripening
Curvature affects free energy diagram solubility in smaller particles
Established concentration gradient Large grow, small shrink
R. Balluffi, S. Allen, C. Carter. Kinetics of Materials. Hoboken, NJ: J. Wiley & sons. 2005 W. Hosford. Physical Metallurgy CRC Press, 2005
Images removed due to copyright restrictions.
Please see: Fig. 15.1c in Balluffi, Robert W., et al.Kinetics of Materials.
Hoboken, NJ: Wiley-Interscience, 2005.
Fig. 10.20 in Hosford, William F.Physical Metallurgy. Boca Raton, FL: CRC Press, 2005.
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Time-Temperature-Transformation
Diagram (TTT)
Plots representing the level of transformation (in
%) during an isothermal process from non-equilibrium conditions to equilibrium vs. time
TTT diagram
Please see "Underlying Metallurgy: Transformation Diagrams(CCT & TTT)."SteelMATTER. University of Liverpool, 2000.
http://www.matter.org.uk/steelmatter/metallurgy/7_1_2.htmlhttp://www.matter.org.uk/steelmatter/metallurgy/7_1_2.htmlhttp://www.matter.org.uk/steelmatter/metallurgy/7_1_2.htmlhttp://www.matter.org.uk/steelmatter/metallurgy/7_1_2.htmlhttp://www.matter.org.uk/steelmatter/metallurgy/7_1_2.htmlhttp://www.matter.org.uk/steelmatter/metallurgy/7_1_2.html8/13/2019 MIT3_40JF09_lec19
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TTT i d
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TTT continued
Image from Wikimedia Commons,http://commons.wikimedia.org.
Growth dominated
Nucleation dominated
http://commons.wikimedia.org/http://commons.wikimedia.org/http://commons.wikimedia.org/8/13/2019 MIT3_40JF09_lec19
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How does strength evolves with time at
constant T?
1) Bell-shape curve
2) Fastest at Tnose
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Strength vs. time
Tnose= T3
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How does strength evolves with time at
constant T?
1) Bell-shape curve
2) Fastest at Tnose
3) If T is high, Vf is getting smaller (lever rule) >few precipitates + before coarsening > rc/b
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http://www.doitpoms.ac.uk/tlplib/phase-diagrams/lever.php
Temperatu
re(C)
Composition (%)
Phase Diagram
Courtesy of DoITPoMS, University of Cambridge. Used with permission.
http://www.doitpoms.ac.uk/tlplib/phase-diagrams/lever.phphttp://www.doitpoms.ac.uk/tlplib/phase-diagrams/lever.php8/13/2019 MIT3_40JF09_lec19
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http://upload.wikimedia.org/wikipedia/en/6/63/Strengtheningg.png
if T is high, at
the end of growth
http://upload.wikimedia.org/wikipedia/en/6/63/Strengtheningg.pnghttp://upload.wikimedia.org/wikipedia/en/6/63/Strengtheningg.png8/13/2019 MIT3_40JF09_lec19
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Strength vs. time
Tnose= T3
T4 >T3T4 > Tnose
Tnose= T3
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How does strength evolves with time at
constant T?
1) Bell-shape curve
2) Fastest at Tnose
3) If T is high, Vf is getting smaller (lever rule) >few grain + before coarsening > rc/b
4) If T is low, nucleation is dominating, lots of
small grain: < rc/b
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http://upload.wikimedia.org/wikipedia/en/6/63/Strengtheningg.png
if T is low, at
the end of growth
http://upload.wikimedia.org/wikipedia/en/6/63/Strengtheningg.pnghttp://upload.wikimedia.org/wikipedia/en/6/63/Strengtheningg.png8/13/2019 MIT3_40JF09_lec19
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Strength vs. time
Tnose= T3
T1 < T3RT=T1
T4 >T3
T2: optimal for strengthening,experimentally a little above
Tnose
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Refinements Take into account aging during service
Non metallic precipitates e.g. VC in Fe-V-C
Core-shell e.g. Zr around Al3Sc
Particle alignment (coherency stress) e.g. Ni3Al inNi-Al
Extrinsic nanoparticles seeding > no growth, noshear
Zr shell impedes diffusion thus growth
Al3Sc precipitate
Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.
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MIT OpenCourseWarehttp://ocw.mit.edu
3.40J / 22.71J / 3.14 Physical Metallurgy
Fall 2009
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