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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
The contents of this lecture are protected under U.S. copyright law and should not be duplicated or redistributed for commercial purposes.
MATSE 259
Lecture 3: Phase Diagrams and Deformation of Materials
Christopher L. Muhlstein, Ph.D.
Department of Materials Science and EngineeringThe Pennsylvania State University
University Park, PA
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Last Lecture
• Aluminum alloy designations
• Microstructures
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Lecture 3: Key Concepts and References
• Reading binary phase diagrams• Introduction to age hardening• Elastic deformation of materials
• Reference: Callister, Chapter 9
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Gibbs Phase Rule
• Relationship between components, phases, state variables, and degrees of freedom
• Gibbs phase rule
P-T diagram for water2 PCFSchaffer et al., The Science and Design of Engineering Materials (1999)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Phase Diagrams
• Binary phase diagram– phases present– composition of
phases– relative amount of
phases• Solid solutions
Callister, Materials Science and Engineering: An Introduction (2003)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Dispersion Strengthening and Precipitation Hardening
• Mechanism: small particles in a metal can impede deformation
• Dispersion strengthening– Particulates added to the (usually liquid) material– Material added should not react with base metal– Composite
• Precipitation Hardening– “Age hardening”– Particulates created in material by heat treatment– Nucleation and growth process– Phase diagram used to identify amenable alloy systems
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Precipitation Hardening
• Phase diagram features– “Appreciable” solid
solubility of one component
– Solubility limit that decreases rapidly
– Alloy composition less than solubility limit
– Necessary, but not sufficient, condition for precipitation-hardenable alloy
Hypothetical phase diagram of precipitation-hardenable alloy.
Callister, Materials Science and Engineering: An Introduction (2003)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Precipitation Hardening
• Two-stage heat treatment– Solution heat
treatment and quench
– Precipitation heat treatment in + phase field (“aging”)
Callister, Materials Science and Engineering: An Introduction (2003)
Schematic of precipitation hardening heat treatment.
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Precipitation Hardening
Underaged
Peak Aged
Overaged
Aging behavior of a hypothetical aluminum alloy.
Callister, Materials Science and Engineering: An Introduction (2003)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Heat Treatment of Aluminum Alloys
• Under, peak, and overaged aluminum alloys
Precipitation hardened 7150-T651 alloy.Callister, Materials Science and Engineering: An Introduction (2003)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Linear Elastic Behavior of Materials
• Engineering stress, , and strain,
• Hooke’s law• Poisson’s Ratio, • Stiffness and
compliance
Schematic of tensile, shear, and torsion in elastic solids.
Callister, Materials Science and Engineering: An Introduction (2003)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Measuring Tensile Behavior
Schematic of tensile test.Schematic of tensile specimen.
• Specimen geometry• Experimental setup• ASTM Standards E8
and E9
Callister, Materials Science and Engineering: An Introduction (2003)
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Room Temperature Elastic Moduli of Materials
• Compare– Polymers– Metals– Ceramics
Ashby, Materials Selection in Mechanical Design (1999)
A material property chart of Young’s modulus and density.
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MATSE 259 Spring 2007, C. Muhlstein© C. Muhlstein, 2007
Elastic Behavior of Al, Fe, and Ti Alloys
Alloy Young’s Modulus, E (GPa)
Poisson’s Ratio, v
Al 69 0.33
Ti 107 0.34
Steel 207 0.30
• Room temperature behavior
• Elevated temperature behavior
Temperature dependence of elastic modulus of metals.
Callister, Materials Science and Engineering: An Introduction (2003)
Room temperature elastic properties.
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