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Example of solute redistribution calculations for equilibrium and nonequili...
Available to PurchasePublished: 31 October 2011
Fig. 24 Example of solute redistribution calculations for equilibrium and nonequilibrium conditions. (a) Hypothetical phase diagram. (b) Variation in liquid composition for C o = 2 wt%. (c) Variation in liquid composition for C o = 5 wt%. (d) Variation in solid composition for C o = 2
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Volume element for modeling solute redistribution during cellular solidific...
Available to PurchasePublished: 31 October 2011
Fig. 25 Volume element for modeling solute redistribution during cellular solidification. The solidification process can be represented by the enclosed region shown and noting that solidification starts at the cell core (where f s = 0) and finishes at the cell boundary when two cells meet
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Comparison of solute redistribution behavior. (a) Carbon in a nickel-base s...
Available to PurchasePublished: 31 October 2011
Fig. 27 Comparison of solute redistribution behavior. (a) Carbon in a nickel-base superalloy calculated using the lever law, Scheil equation, and Clyne-Kurz model. (b) Titanium in an Fe-10Al-5Cr-1.5Ti-0.4C alloy with varying cooling rates (calculated using the Kobayashi model) compared
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Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005215
EISBN: 978-1-62708-187-0
... Abstract This article discusses the two extremes of solute redistribution, equilibrium solidification and nonequilibrium Gulliver-Scheil solidification, for which solid redistribution of solute within the primary solid phase is the distinguishing parameter. The process and material parameters...
Abstract
This article discusses the two extremes of solute redistribution, equilibrium solidification and nonequilibrium Gulliver-Scheil solidification, for which solid redistribution of solute within the primary solid phase is the distinguishing parameter. The process and material parameters that control microsegregation are discussed in relation to the manifestations of microsegregation in simple and then increasingly complex alloy systems. The measurement and kinetics of microsegregation are discussed for the binary isomorphous systems: titanium-molybdenum; binary eutectic systems: aluminum-copper and aluminum-silicon; binary peritectic systems: copper-zinc; multicomponent eutectic systems: Al-Si-Cu-Mg; and for systems with both eutectic and peritectic reactions: Fe-C-Cr and nickel-base superalloy.
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005609
EISBN: 978-1-62708-174-0
... Abstract This article reviews the fundamental solidification concepts for understanding microstructural evolution in fusion welds. The common concepts, namely, nucleation, competitive grain growth, constitutional supercooling, solute redistribution, and rapid solidification, depend...
Abstract
This article reviews the fundamental solidification concepts for understanding microstructural evolution in fusion welds. The common concepts, namely, nucleation, competitive grain growth, constitutional supercooling, solute redistribution, and rapid solidification, depend on the solidification parameters during welding, are discussed. The article discusses important solidification parameters, including temperature gradient, solid/liquid interface growth rate, and cooling rate.
Book Chapter
Modeling of Microsegregation and Macrosegregation
Available to PurchaseBook: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005237
EISBN: 978-1-62708-187-0
... in Whitehall, Michigan, for performing the simulations of the VAR ingot. References References 1. Beckermann C. , Macrosegregation , Casting , Vol 15 , ASM Handbook , ASM International , 2008 2. Brody H.D. and Flemings M.C. , Solute Redistribution in Dendritic...
Abstract
In order to model macrosegregation, one must consider convection and the partitioning of segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the simulation of macrosegregation and microsegregation.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005210
EISBN: 978-1-62708-187-0
... patterns in which the branched structure evolves with primary, secondary, tertiary, and eventually higher-order branches. Such a branched structure forms because it can effectively allow rapid dissipation of the latent heat of fusion as well as any solute redistribution required for growth due...
Abstract
Nonplanar microstructures form most frequently during the solidification of alloys, and play a crucial role in governing the properties of the solidified material. This article emphasizes the basic ideas, characteristic lengths, and the processing conditions required to control the columnar and equiaxed microstructures. The formation of cellular and dendritic structures in one- and two-phase structures is presented with emphasis on the effect of processing conditions and composition on the selection of microstructure and microstructure scales.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005216
EISBN: 978-1-62708-187-0
... of macrosegregation. Such macrosegregation can be best understood by considering the local solute redistribution equation (LSRE) derived by Flemings and coworkers ( Ref 1 , 2 , 3 ). This equation is based on a solute balance on a lume element inside the mushy zone, as illustrated in Fig. 2 . As in a standard...
Abstract
Macrosegregation refers to spatial compositional variations that occur in metal alloy castings and range in scale from several millimeters to centimeters or even meters. This article presents a derivative approach for understanding the mechanism of macrosegregation induced by flow of the liquid and movement of the solid with examples.
Book Chapter
Modeling of Transport Phenomena during Solidification Processes
Available to PurchaseSeries: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005525
EISBN: 978-1-62708-197-9
... the redistribution of solute by interacting with the flow in the mushy zone and carrying the free-floating solid grains, is only weakly controlled by the ingot size or the superheat ( Ref 54 ): (Eq 45) u b ~ R 2 7 Δ T 3 7 Because u b is such a weak function of R and Δ T...
Abstract
This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during solidification processing. It presents transport equations and several examples of their applications to illustrate the physics present in alloy solidification. The examples demonstrate the utility of scaling analysis to explain the fundamental physics in a process and to demonstrate the limitations of simplifying assumptions. The article concludes with information on the solidification behavior of alloys as predicted by full numerical solutions of the transport equations.
Book Chapter
Solidification and Castability of Foundry Alloys
Available to PurchaseSeries: ASM Handbook
Volume: 2A
Publisher: ASM International
Published: 30 November 2018
DOI: 10.31399/asm.hb.v02a.a0006496
EISBN: 978-1-62708-207-5
... in commercial aluminum casting processes, and the B-F model for segregation and diffusion of solute in the solid describes the microsegregation. Macrosegregation Macrosegregation is the redistribution of solute elements on a larger scale. In net shape aluminum alloy castings, this is caused by the motion...
Abstract
Castability is a complex characteristic that depends on both the intrinsic fluid properties of the molten metal and the manner in which the particular alloy solidifies. This article discusses the practical aspects of solidification important to aluminum foundrymen. The primary focus is on the chemical segregation that occurs during freezing, because it determines the castability of the alloy. The article describes the two types of segregation, namely, microsegregation and macrosegregation. It discusses the effect of freezing range on castability of an alloy. The article lists the freezing range of a number of important alloys. It concludes with a discussion on castability of 2xx, 3xx, 4xx, 5xx, and 7xx alloys.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005228
EISBN: 978-1-62708-187-0
... obtained with MEPHISTO allowed specific evaluation of the effects of convection on solute redistribution during the directional solidification of alloys and the observation of transitions in interface morphology from planar to cellular. By using three identical samples that were alternately melted...
Abstract
Gravity has profound influences on most solidification and crystal growth processes. Modification of gravity over practical time scales for the purposes of modifying or controlling solidification proves to be a far more daunting and expensive technological challenge. This article discusses various microgravity solidification experiments that involve pure metals, alloys, and semiconductors and presents the official NASA acronyms for them. MEPHISTO, TEMPUS, the isothermal dendritic growth experiment, and advanced gradient heating facility, are also discussed.
Book Chapter
X-Ray Imaging of Solidification Processes and Microstructure Evolution
Available to PurchaseBook: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005218
EISBN: 978-1-62708-187-0
... of solute redistribution and boundary layer propagation ( Ref 8 , 9 ). The spatial resolutions available, Δ r ∼100 μm, prevented detailed studies of solid-liquid interface morphologies, but the resolution in x-ray absorption contrast was adequate to verify proximity to Scheil-Gulliver conditions as well...
Abstract
Metal transparency and interaction with X-rays have been recognized as obvious candidate principles from which methods for in situ monitoring of solidification processes could be developed. This article describes the use of X-ray imaging-based techniques to investigate interface morphology evolution, solute transport, and various process phenomena at spatiotemporal resolutions. It discusses the three viable imaging techniques made available by synchrotron radiation for the real-time investigation of solidification microstructures in alloys. These include two-dimensional X-ray topography, two-dimensional X-ray radiography, and ultra-fast three-dimensional X-ray tomography.
Book Chapter
Computer Modeling of Solidification Microstructures
Available to PurchaseSeries: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003729
EISBN: 978-1-62708-177-1
.... A more fundamental approach ( Ref 20 ) includes time-dependent calculations for temperature distribution, solute redistribution in the liquid and solid phases, curvature, and growth anisotropy. Solidification velocity is calculated from the transport equations and not with analytical models...
Abstract
Computational modeling assists in addressing the issues of solid/liquid interface dynamics at the microlevel. It also helps to visualize the grain length scale, fraction of phases, or even microstructure transitions through microstructure maps. This article provides a detailed account of the general capabilities of the various models that can generate microstructure maps and thus transform the computer into a dynamic microscope. These include standard transport models, phase-field models, Monte Carlo models, and cellular automaton models.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005229
EISBN: 978-1-62708-187-0
... HOMOGENIZATION, in a broad sense, refers to processes designed to achieve uniform distribution of solutes or phases in a given matrix. During solidification of a melt, microsegregation occurs due to the redistribution of solutes as solute is rejected into the liquid. Uniform distribution of the solute elements...
Abstract
Homogenization, in a broad sense, refers to the processes designed to achieve uniform distribution of solutes or phases in a given matrix. This article addresses the root cause for inhomogeneities in cast components. It is nearly a standard industrial practice to homogenize alloys before thermomechanical processing. The article lists the objectives of homogenization and benefits of homogenization treatments. The benefits include increased resistance to pitting corrosion, increased resistance to stress-corrosion cracking, improved ductility, and uniform precipitate distribution during subsequent aging. The article provides a schematic illustration of an energy-dispersive X-ray spectroscope (EDS) scattered data of solute distributions across a dendrite due to microsegregation of chromium and molybdenum. It concludes with information on the computational modeling for simulation of microsegregation of chromium and molybdenum.
Book Chapter
The Austenite-to-Pearlite/Ferrite Transformation
Available to PurchaseSeries: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006300
EISBN: 978-1-62708-179-5
... the atomic distance. This leads to the conclusion that austenite transformation proceeds without redistribution of substitutional solutes—in other words, that ferrite inherits the solute content of the parent austenite. These so-called para-equilibrium conditions have been well studied in steels ( Ref 12...
Abstract
This article discusses the stable and metastable three-phase fields in the binary Fe-C phase diagram. It schematically illustrates that austenite decomposition requires accounting for nucleation and growth of ferrite and then nucleation and growth of pearlite in the remaining untransformed volume. The article describes the austenite decomposition to ferrite and pearlite in spheroidal graphite irons and lamellar graphite irons. It provides a discussion on modeling austenite decomposition to ferrite and pearlite.
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003735
EISBN: 978-1-62708-177-1
... and solute redistribution. Fig. 1 Growth of massive ferrite in pure iron, illustrating the crossing of prior-γ/γ grain boundaries outlined by surface grooving. Reprinted with permission from Ref 3 Fig. 2 The two-plateau behavior of the transformation temperature as a function...
Abstract
Massive transformations are thermally activated phenomena and exhibit nucleation and growth characteristics primarily controlled by the interface between parent and product phases that is generally considered incoherent. This article focuses on the nucleation and growth kinetics involved in massive transformations and illustrates the resulting phases and structures in ferrous and nonferrous metals and alloys.
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005786
EISBN: 978-1-62708-165-8
... with coarse alloy-enriched carbides represent the most sluggish austenitization kinetics, because the formation of homogeneous austenite requires dissolution of coarse carbides, involving redistribution of substitutional solutes, and carbon transport into the large volume previously consisting of carbon...
Abstract
Austenitization refers to heating into the austenite phase field, during which the austenite structure is formed. This article highlights the purpose of austenitization, and reviews the mechanism and importance of thermodynamics and kinetics of austenite structure using an iron-carbon binary phase diagram. It also describes the effects of austenite grain size, and provides useful information on controlling the austenite grain size using the thermomechanical process.
Book Chapter
Modeling of Casting and Solidification Processes
Available to PurchaseSeries: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005501
EISBN: 978-1-62708-197-9
... a large number of prototype binary phase diagrams with different topological features using ideal and regular solution models. Since then, many researchers began to incorporate phase equilibrium data to evaluate the thermodynamic properties of alloys. It was not until the late 1980s that a number of phase...
Abstract
This article reviews the topic of computational thermodynamics and introduces the calculation of solidification paths for casting alloys. It discusses the calculation of thermophysical properties and the fundamentals of the modeling of solidification processes. The article describes several commonly used microstructure simulation methods and presents ductile iron casting as an example to demonstrate the ability of microstructure simulation. The predictions for the major defects of casting, such as porosity, hot tearing, and macrosegregation, are highlighted. Finally, several industry applications are presented.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005208
EISBN: 978-1-62708-187-0
... of Solidification Phenomena in Al-Cu Alloys , Mater. Sci. Forum , Vol 508 , 2006 , p 69 – 75 6. Bower T.F. , Brody H.D. , and Flemings M.C. , Measurements of Solute Redistribution in Dendritic Solidification , Trans. AIME , Vol 236 , 1966 , p 624 7. Kurz W.F. and Fisher...
Abstract
This article begins with balance equations for mass, momentum, energy, and solute and the necessary boundary conditions for solving problems of interest in casting and solidification. The transport phenomena cover a vast range of length and time scales, from atomic dimensions up to macroscopic casting size and from nanoseconds for interface attachment kinetics to hours for casting solidification. The article describes how to determine which phenomena are most important at the particular length and time scale for the problem. It concludes with several examples of the application of transport phenomena in solidification, focusing on microstructure formation.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005437
EISBN: 978-1-62708-196-2
... Phenomena in Al-Cu Alloys , Mater. Sci. Forum , Vol 508 , 2006 , p 69 – 75 6. Bower T.F. , Brody H.D. , and Flemings M.C. , Measurements of Solute Redistribution in Dendritic Solidification , Trans. AIME , Vol 236 , 1966 , p 624 7. Kurz W.F. and Fisher D.J...
Abstract
This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example problems that illustrate how the hierarchy of time and length scales associated with transport leads to the important features of cast microstructures. It includes equations for estimating microsegregation in cast alloys.
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