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Microstructure Simulation

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  • Microstructure Simulations

    B. Nestler, F. Wendler, A. Choudhury

    December 17, 2011

  • Contents

    1 30.10.10 191.1 Lecture 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    2 1.11.10 442.1 lecture 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    3 1.11.10 553.1 Lecture 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

    4 1.11.10 664.1 lecture 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

    5 1.11.10 745.1 lecture 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    6 1.11.10 796.1 lecture 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.2 Tasks to perform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

  • Introduction to solidification

    Microsstructure simulations

    Content

    Introduction to solidificationTechnical importance of solidificationGeneral terms and basics in solidificationThe role of heat extractionDirectional solidificationSpecial solidification techniquesAim of computational materials scienceDendritic solidificationEutectic solidificationPeritectic solidificationMonotectic solidificationCourse outline

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 2/33

    Introduction to solidification

    Microsstructure simulations

    Literature recommendations

    A large part of this course is treated in [Kurz and Fisher, 1998] and[Porter et al., 2009]. A good german textbook is [Gottstein, 2007].

    Gottstein, G. (2007).

    Physikalische Grundlagen der Materialkunde.

    Springer Verlag Berlin Heidelberg.

    Kurz, W. and Fisher, D. (1998).

    Fundamentals of solidification.

    Trans Tech Publications ltd, Switzerland Germany UK USA.

    Porter, D. A., Easterling, K. E., and Sherif, M. Y. (2009).

    Phase transformations in metals and alloys (third edition).

    CRC Press, Taylor & Francis Group, Boca Raton, London, New York.

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 3/33

  • Introduction to solidification

    Microsstructure simulations

    General problem definition

    During processing of materials an inhomogeneous microstructure evolves,originating from the kinetics of the processes. This may lead to potentially weakpoints and eventually failure.In this lecture, there is a focus on metal solidification. Here crystal nucleation,a necessary prerequisite to solidification, is a ubiquitous event. Glass, ametastable phase, is formed only at extremely high cooling rates.

    Understand microstructure evolution depending on different solidificationconditions. optimize processing parameters.

    Modeling goal:

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 4/33

    Introduction to solidification

    Microsstructure simulations

    Effect of microstructure - example

    Microstructure formed after casting may have severe effects on mechanicalbehaviour.Example: Ingot casting of Al-7%Si alloy with subsequent ECAP processing(severe plastic deformation)

    J.M. Garcia-Infanta et al., Scripta Mater. 58 (2008) 138.

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 5/33

  • Introduction to solidification

    Microsstructure simulations

    Technical importance of solidification

    Solidification is one of the most importantforming processes in materials science,involved in the production of almost alltechnical products. It is a very economicmetal forming process (espec. for complexshaped pieces)Solidification as a phase transition occursduring

    metal casting (ingot casting,continuous casting)

    metal welding, soldering

    polymer injection moulding

    growth of silicon single or poly- crystals

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 6/33

    Introduction to solidification

    Microsstructure simulations

    Technical solidification processes (incomplete)

    Casting continuous castingingot castinginvestment castingprecision castingdie casting

    Welding arc-weldingresistance weldinglaser/electron beam welding

    Soldering/BrazingRapid solidification melt-spinning

    atomisationDirectional solidification Bridgman

    Czochralski

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 7/33

  • Introduction to solidification

    Microsstructure simulations

    Some general terms used in the courseOverview, most of the terms will be filled with live during the following lectures.

    Phase: A phase is a homogeneous part in a possibly heterogeneoussystem (Gibbs1). Here we have solid (s ) and liquid (l ). Can be related tothe local atomic arrangement construction of order parameters.

    Equilibrium: State of minimal free energy (G or F ). Phases in contact dohave enough time (locally) to reach this state.

    Transition: may arise by changing a control parameter (temperature,pressure ...), during which latent heat is released/absorbed.

    1Josiah Willard Gibbs, 1839 - 1903, american physicist, chemist and mathematicianB. Nestler, A. Choudhury, F. Wendler WS 2010-2011 8/33

    Introduction to solidification

    Microsstructure simulations

    Solidification basics - casting

    Casting of a melt of composition C0 andtemperature T into the mold.

    Cooling: A heat flux q depending on heatdiffusivity k gives rise to undercooling Tof melt.

    Then, due to the difference of chemicalpotentials between s - l crystallizationstarts, the speed of which is given by T .

    For the (macro) flow of melt the viscosity and liquid-vapour surface tension maybe important.

    Kurz, Fisher, Fig. 0B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 9/33

  • Introduction to solidification

    Microsstructure simulations

    Solidified ingots - morphology

    Melt is usually cooled from thecrucible wall

    This results in growth, beingfastest parallel to the temperaturegradient G.

    Mushy zone: the solid/liquidcontact region, in which all growthdetermining kinetic processes takeplace evolution of complicateinterface structure.

    Density changes givr rise toshrinkage and porosity.

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 10/33

    Introduction to solidification

    Microsstructure simulations

    Solidified ingots - morphology IIMicrostructure zones in cast ingot,schematicKurz and Fisher, Fig. 1.6

    Aluminum ingot (5 cm)H. K. D. H. Bhadeshia, University of Cambridge

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 11/33

  • Introduction to solidification

    Microsstructure simulations

    The role of heat extraction

    After casting the liquid metal, heat of different physicalorigin must be extracted:

    Heat related to the specific heat capacity of onephase: enthalphy decrease H =

    T2T1

    CdT

    Latent heat of fusion, released in the phasetransition: Hf

    Later, we will use the specific latent heat hf = Hf/Vm (Vm: molar volume)and specific heat capacity c = C/Vm.

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 12/33

    Introduction to solidification

    Microsstructure simulations

    Solidification stages

    After casting, three different steps in thesolidification can be observed in the coolingcurve:

    1. Cooling from pouring temperature,nucleation starts after falling belowmelting temperature Tm

    2. Reheating to Tm (recalescence) due torelease of latent heat

    3. After complete transformation to solid,continued cooling sets on.

    Figure: Quasi 1-D experiment,P. Thevoz et al., Metal Transact. 20 A (1989) 311

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 13/33

  • Introduction to solidification

    Microsstructure simulations

    Directional solidification - experimentsExperimental setup: Controlled solidification using optical microscopywith transparent binary analog substances.

    2D:

    3D:Figure: Eutectic growth in SCN - DC,[Akamatsu et al., Journal of Crystal Growth 299 (2007) 418]

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 14/33

    Introduction to solidification

    Microsstructure simulations

    Directional solidification - principlesSteady heat extraction at pulling velocities v small enough to reach steady state.Growth rate (= v ) and temperature gradient G can be separately controlled. Ifheat flux qext and temperature gradient are parallel:

    Ts+z =Tz z

    ts+z = G v

    s+z

    But: due to different heat conductivity in solid/liquid and release of latent heat:

    Gsolid 6= Gliquid

    Experimental setup foralloys:

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 15/33

  • Introduction to solidification

    Microsstructure simulations

    Directional solidification - technical applicationsProduction setup (schematic): Adjust(and move) temperature field bycontrolling current in electric coils.

    Figure: Al alloy - polycrystal [Tom Quested,Microstructural kinetics group - Univ. of Cambridge.]

    Figure: Solar grade silicon, directionallysolidified using the Bridgman method [B. Ryningen].

    B. Nestler, A. Choudhury, F. Wendler WS 2010-2011 16/33

    Introduction to solidification

    Microsstructure simulations

    Special solidification methods - metal matrix composites

    Gas pressure infiltration of melt into fibre matrix to produce compositematerials:

    Figure: Steps of gas pressure infiltration: a)porous preform preheating; b) immersion ofporous preform into the melt and inlet ofpressurized gas; c) infiltrated sample inmolten matrix and d) withdrawal ofinfiltrated sample from melt.[Institute of materials & machine mechanics, Slovakian academy ofsciences]

    Figure: Pure Al matrix reinforcedby unidirectional carbon fibres (65vol %)[G. Requena et al., Composites: Part A, 40 (2009) 152.]

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