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steady-state nucleation rate

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Published: 01 December 2008
Fig. 6 Steady-state nucleation rate as a function of undercooling below the melting point. At low undercooling, the nucleation rate is primarily controlled by driving free energy; at high undercooling, as the temperature approaches the glass transition temperature, T g , nucleation More
Image
Published: 01 December 2009
Fig. 7 Variation with quenching temperature of steady-state nucleation rate in the case of solidification ( Eq 31 ). T m , melting temperature More
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005410
EISBN: 978-1-62708-196-2
... Abstract This article describes the results obtained by Volmer, Weber, Farkas, Becker, and Doring, which constitute the classical nucleation theory. These results are the predictions of the precipitate size distribution, steady-state nucleation rate, and incubation time. The article reviews...
Image
Published: 01 December 2009
Fig. 5 Precipitate density as a function of aging time for an aluminum solid solution containing 0.18 at.% Sc aged at 300 °C. The time evolution obtained from cluster dynamics simulations ( Ref 25 ) allows the definition of a steady-state nucleation rate, J st , and an incubation time, t More
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005207
EISBN: 978-1-62708-187-0
... ) is the concentration of critical clusters. The full expression for the steady-state nucleation rate is then: (Eq 16) I = ( D L a 2 ) ( 4 π r cr 2 a 2 ) Z C ℓ exp ( − Δ G cr k T ) For typical metals, C ℓ ∼ 10 28...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005403
EISBN: 978-1-62708-196-2
... of a grain during steady-state discontinuous dynamic recrystallization. Data pertaining to 304 steel were used at 1050 °C and two strain rates ( Table 4 ). Parameters used in <xref rid="a0005403-f11" ref-type="fig">Fig. 11</xref> Table 4 Parameters used in Fig. 11 Strain-hardening...
Image
Published: 01 November 2010
of the set of axes). (c) Steady-state velocity of a dendrite tip growing along a boundary reported to the growth rate in the bulk as a function of the incidence angle, α. Source: Ref 150 More
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
... re-crystallized structure is obtained. However, even at this stage, recrystallized grains are being further strained and thus undergo additional cycles of dynamic recrystallization. Nevertheless, a steady state is reached in which the rate of dislocation input due to the imposed deformation...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005459
EISBN: 978-1-62708-196-2
... is the strain-rate sensitivity of the fully recrystallized material. The Zener-Hollomon parameter is extremely important, inasmuch as it describes well the dependence of numerous parameters on strain rate and temperature. For example, the recrystallized grain size during steady-state flow, d s , can...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002472
EISBN: 978-1-62708-194-8
... concentrated on generating long-time creep data on engineering materials. The testing was invariably at constant load, and data extracted included times for specific creep strains, minimum creep rates (although the term steady state was often used despite the fact that constant rates cannot be expected when...
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
... satisfies the steady-state shape-preserving constraint in that the entire interface will not change shape during growth. However, the solution gave a relationship between the growth rate, tip radius, and tip composition (or the tip undercooling). Thus, for a known V , the model predicts an infinite number...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005556
EISBN: 978-1-62708-174-0
... by the macroscopic plastic strain rate. Therefore, the static (or creep) and dynamic (or quasi-static) failures of the thin interlayer welds should be, according to cavity-growth-based theories, related to the macroscopic strain in the interlayer. If steady-state plasticity is achieved throughout the silver...
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001352
EISBN: 978-1-62708-173-3
... at the solid-state-welded silver interface may be less significant in increasing the nucleation and coalescence rate of cavities in specimens utilizing plastic base metals than those utilizing elastic base metals, where the strain is indigenous to the interlayer, rather than being imposed by base-metal...
Series: ASM Handbook
Volume: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.a0006964
EISBN: 978-1-62708-439-0
.... Due to this characteristic grain structure, it is normally observed that the creep performance normal to the building direction is inferior to that along the building direction. For example, the steady-state creep rate of AM IN718 was reported to be 2 × 10 −8 along the building direction, while...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003291
EISBN: 978-1-62708-176-4
... Abstract This article presents effective stress equations that are based on the von Mises criterion, the Tresca criterion, and the Huddleston criterion. It describes the calculation of effective stresses for different cases: elastic stresses, steady-state creep stresses, stresses in a fully...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004027
EISBN: 978-1-62708-185-6
... for the strain rates of industrial hot working, because the dynamically recrystallized grain size is small compared with the original grain size, and lead to the fall in flow stress from a peak value soon after recrystallization starts to a steady-state value at strains greater than ε s in Fig. 2(b) , when...
Book Chapter

Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005816
EISBN: 978-1-62708-165-8
... studied the variations in the cooling rate due to the different boiling regimes. Steady-State Investigations of Jet Cooling Wolf et al. ( Ref 50 ) carried out steady-state experiments using a 10 mm (0.4 in.) wide water jet kept at 50 °C (120 °F) of subcooling impinging on a horizontal flat surface...
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
.... Three samples, which differed in indium content, were processed at the same growth rate to permit comparison of their microstructures and to determine how indium was distributed during freezing in the aluminum matrix. Two of these alloys had compositions that could not be processed under steady-state...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003292
EISBN: 978-1-62708-176-4
... sensitivity, m . In the second type of presentation, the data are plotted logarithmically as strain rate against stress. The slope of such a plot represents the stress exponent, n . Under steady-state conditions, n is equal to 1/ m . In early work on the mechanical behavior of superplastic alloys...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005224
EISBN: 978-1-62708-187-0
... is based on the fact that under steady-state conditions, the semisolid slurry behaves as a shear-thinning (pseudoplastic) fluid, wherein the effective viscosity decreases with increasing shear rate. However, under rapid transient conditions, the semisolid slurry behaves as a shear-thickening fluid...