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    Mechanical Properties and Microstructure of Al–Sc with Rare-Earth Element

    or Al2O3 Additions




    for the degree


    Field of Materials Science and Engineering


    Richard Albert Karnesky, Jr.


    December 2007

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    c© Copyright by Richard Albert Karnesky, Jr. 2007 All Rights Reserved

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    Mechanical Properties and Microstructure of Al–Sc with Rare-Earth Element or Al2O3


    Richard Albert Karnesky, Jr.

    Aluminum alloys strengthened with coherent (L12), nanosize Al3Sc precipitates are structural

    materials that have outstanding strength at ambient and elevated temperatures. They are

    creep resistant at 300 ◦C and exhibit a threshold stress, below which creep is not measurable.

    Introducing ternary alloying additions, such as rare-earth elements (RE=Y, Dy, Er), that

    segregate within Al3Sc precipitates improves this creep resistance by increasing the lattice

    parameter misfit of precipitates with Al. In this thesis, Al–600 Sc–200 RE and Al–900 Sc–300

    Er (at. ppm) are studied. These elements are an order of magnitude less expensive than

    Sc, so reduce alloy costs. As an alternative or supplement to ternary additions, submicron

    (incoherent) Al2O3 dispersoids impart additional strengthening. The dispersion-strengthened

    cast alloys, DSC–Al–1100 Sc and DSC–Al–800 Sc–300 Zr, studied in this thesis contain

    30 vol.% Al2O3.

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    In this thesis, the temporal evolution of Al–Sc–RE and DSC–Al–Sc(–Zr) alloys are measured

    using Local-Electrode Atom-Probe (LEAP) tomography, conventional transmission electron

    microscopy, and electrical conductivity. These techniques measure the changes in precipitate

    number density, size, volume fraction, chemical composition, and interprecipitate distance

    and are compared to models. They are also employed to measure the diffusivity and solid

    solubility of Er in α–Al in Al–300 Er, Al–450 Er, and Al–600 Er.

    The mechanical behavior (microhardness, yield, and creep) of the alloys is studied at 25,

    300, and 350 ◦C. The effect of Al3 �

    Sc1−xErx �

    precipitate size and interprecipitate distance is

    studied by varying isochronal and isothermal aging treatments. Various models and simula-

    tions are compared to experimental data. At ambient temperatures, very small Al3 �

    Sc1−xMx �

    precipitates contribute to order strengthening and larger (unshearable) precipitates are

    bypassed by dislocations through Orowan bowing. Dislocation dynamics simulations allow

    both processes to operate in a glide plane, where precipitate distributions may be gathered

    directly or be informed by LEAP tomography data. At elevated temperatures, the lattice

    parameter and modulus mismatches of Al3 �

    Sc1−xMx �

    oppose both dislocation climb over

    Al3 �

    Sc1−xMx �

    and dislocation detachment from Al2O3.

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    In loving memory of Richard Albert Karnesky Sr.—father, metallurgical engineer, blacksmith,

    and friend.

    This research was only possible through the guidance and support of my thesis advisors,

    Profs. David C. Dunand and David N. Seidman. I’d also like to thank my committee members,

    Profs. Horacio Espinosa and Chris Wolverton for their interest and enthusiasm about this

    work. Prof. Mark Asta (University of California, Davis) gave insight when on my qualifying

    committee. Profs. Georges Martin and Joe Jerome; as well as Drs. Dieter Isheim, Chantal K.

    Sudbrack, Liang Meng, and Volker Mohles are thanked for our rewarding collaborations. Dr.

    Mike Miller and everyone at Imago Scientific deserve appreciation for their willingness to

    share thoughts and code.

    Past and present group members have been nothing but both friendly and helpful. I’d

    especially like to thank Matt Krug and Drs. Keith E. Knipling and Marsha E. van Dalen

    for putting themselves into the same boat as me. Mr. Joe Cabotaje was a hard working

    undergraduate researcher. Thanks also to Drs. Christian B. Fuller and Emmanuelle A.

    Marquis, on whose shoulders I stand. Cheers to Jason, Stephan, Alan, Marcus, John,

    Olivier, Heeman, Erick, and Pow for happy and productive conversations. Research is so

    collaborative, that I can’t help but miss others who have helped me with my graduate studies.

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    Many thanks to all family and friends! Beverly put up with living in the midwest so that she

    could share her love and support. Warm wishes to my mother, grandparents, and brothers;

    none of whom I see often enough. Thanks also to my “second family,” the Watrouses and to

    David Olver and others at IL–855. Seth, Sue, Clayton, Cev, Ersan, Dinkar, and many others

    are thanked for long-time encouragement in my career path.

    This research was supported by the United States Department of Energy, Basic Sciences

    Division, under contract DE–FG02–98ER45721. Financial support was also provided by a

    Walter P. Murphy Fellowship at Northwestern University.

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    This thesis examines the improvement of the mechanical properties of Al–Sc by adding rare-

    earth elements (RE=Y, Dy, and particularly Er (which is fully soluble in Al3Sc)) and Al2O3

    dispersoids. Novel strengthening models and atom-probe tomographic analysis techniques

    are presented.

    Chapter 1 provides a short background about this study. Because the literature data for

    kinetic and thermodynamic variables (particularly the (temperature-dependent) diffusivity

    in α–Al and the solid solubility in α–Al) are missing, we measure these for the Al–Er binary

    system in chapter 2. Chapter 3 applies this to study the temporal evolution of the Al–Sc–RE

    ternary alloys. In chapter 4, a novel algorithm to measure the edge-to-edge interprecipitate

    distance distributions is presented and applied to Al–Sc–Er and simulated datasets. This

    quantity is important in predicting the time to reach stationary-state coarsening, as is

    shown in chapter 5 and in predicting alloy strength or validating the statistical accuracy

    of simulated obstacle fields, as in chapter 6. This latter chapter compares experimental

    yield measurements with dislocation dynamics simulations that have been informed by

    atom-probe tomography data. The study of Al–Sc–RE alloys is concluded in chapter 7, which

    presents the creep properties of these alloys at 300 ◦C. Chapter 8 discusses the strengthening

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    mechanisms at work in alloys that contain two populations of strengtheners: nanometer-

    sized, coherent Al3 �

    Sc1−xZrx �

    and submicron, incoherent Al2O3. The work is summarized

    and possible further research is discussed in chapter 9.

    The appendices cover:

    A: The methodology of the best-fit ellipsoid method, which is used in Chapter 4, and

    its use in studying preferred orientation of coalesced/coagulated precipitates in


    B: Quantification and propagation of error

    C: Source code for chapter 4, the interprecipitate distance algorithm

    D: Source code for chapter 8, the dual-strengthening creep model for dislocation

    detachment from an incoherent particle that is hindered by the additional back-

    stress due to coherent precipitates

    E: The computing facilities that the author setup for the Northwestern University

    Center for Atom-Probe Tomography

    F: The use of the SUBVERSION version control software and GNU BUILD SYSTEM

    G: The details of the preparation of this thesis

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    α linear thermal expansion coefficient

    αβ parameter describing the geometry of a trailing dislocation, Eq. 6.2 (page 112)

    R̄ mean planar radius, Eq. 4.3 (page 86)

    ∆Ci difference in the equilibrium solubility of i in the precipitate and matrix phases

    ∆Cαi supersaturation of component i in phase α

    "̇ strain rate, Eq. 1.1 (page 39)

    γα/β interfacial free energy

    γAPB anti-phase boundary energy

    καi,KV coarsening rate constant for ∆C α i (t) from KV model, Eq. 3.7 (page 73)

    καi,LSW coarsening rate constant for ∆C α i (t) from LSW model, Eq. 2.2 (page 53)

    Λ coarsening coefficient from KV model, Eq. 3.4 (page 72)

    〈R〉 mean radius λ2De−e edge-to-edge interprecipitate spacing in a plane, Eq. 4.2 (page 86)

    λ3De−e edge-to-edge interprecipitate spacing in three dimensions, Eq. 4.1 (page 85)

    µ shear modulus

    ν Poisson’s ratio

    ωi i th moment of the precipitate size distribution

    σ applied stress

    σD detachment stress for a dislocation to overcome an attractive interface

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    σOr Orowan stress increment, Eq. 6.1 (page 111)

    σOS long-range-order stress increment, Eq. 6.2 (page 112)

    σth threshold stress, Eq. 1.3 (page 40)

    τ" lattice misfit stress, Eq. 8.5 (page 160)

    τB back stress that an array of precipitates exerts onto a dislocatio