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steady-state nucleation rate

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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
... 25 ) allows the definition of a steady-state nucleation rate, J st , and an incubation time, t inc . Fig. 6 Possible shapes of a nucleus in heterogeneous nucleation. (a) Cap shape. (b) Lens shape Fig. 8 Parallel tangent construction leading to the maximal nucleation driving...
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
... by the solid common tangent. 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...
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
... during steady-state discontinuous dynamic recrystallization. Data pertaining to 304 steel were used at 1050 °C and two strain rates ( Table 4 ). Fig. 8 Schematic representation of a grain in the aggregate, which grows when (a) ρ i ≤ ρ ¯ and shrinks when (b) ρ i > ρ...
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
..., 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 is balanced by dislocation annihilation due to the nucleation and growth of new grains...
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
... temperature. The value of Q is typically determined from the steady-state flow stress, σ s , and the expression: (Eq 2) σ s = k Z m in which k is a constant for a given material, and m is the strain-rate sensitivity of the fully recrystallized material. The Zener-Hollomon...
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
..., 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 the stress is changing), and time to failure (often referred to as rupture life). This latter measurement...
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
... of constant interface temperature and composition. He showed that a parabolic dendrite 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...
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
... interlayers, compared with those utilizing electrodeposition or brazed-silver alloy, are discussed in the section “Effect of Interlayer Fabrication Method” in this article. The change in steady-state strain-rate (or time-to-rupture, according to the Monkman-Grant relationship) with applied stress...
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
... resistant to plasticity than other regions. The heterogeneities 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...
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
... centered at 35° to the rolling plane. By ε m , the onset of a steady-state flow stress, the substructure has frequently become equiaxed ( Fig. 3b ) and remains equiaxed with increasing strain because the dynamic balance of work hardening and recovery continually regenerates constant mean values...
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
... independent of the Norton creep exponent ( n ). R o , outside radius of tube Fig. 2 Distribution of normalized elastic stresses in a pressurized tube with a ratio of inner radius, R i , to outer radius, R o , of 0.6 Fig. 1 Distribution of normalized steady-state creep stresses...
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
... 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 conditions on Earth, because...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005227
EISBN: 978-1-62708-187-0
... model of pushing. The model considers acceleration of an initially stationary particle by the front to a steady state at which a thin film is retained. The critical velocity is the limiting velocity at steady state. Sasikumar et al. Approach is similar to Chernov et al. but a more rigorous numerical...
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
... blanket. The high agitation rates inherent in a spray quench also accelerate cooling in the nucleate boiling and convective cooling portions of the quench. Based on the mathematics needed to describe the spray systems, one author has stated that “spray cooling is also a sort of turbulent flow cooling...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003545
EISBN: 978-1-62708-180-1
... at a minimum rate, generally known as the minimum creep rate. The stage of secondary creep is sometimes referred to as the region of steady-state creep, because the creep rate is often nominally constant for some period of time. Finally, there is a region of drastically increased strain rate with rapid...
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006314
EISBN: 978-1-62708-179-5
.... ( Ref 7 ). The developments on the theory of dendritic growth occurred in a similar fashion. A shape-preserving solution for the steady-state dendritic growth was first obtained by Ivantsov in 1947 ( Ref 8 ). Because Ivantsov’s solution could only predict the product between the growth velocity...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0003995
EISBN: 978-1-62708-185-6
... mechanisms. Dynamic recovery is signified, in the flow curve, by the appearance of a steady-state stress after an initial stage of work hardening ( Fig. 5a ). This steady state is basically an indication that the work hardening is being removed by recovery mechanisms. Dynamic recrystallization ( Fig. 5b...
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
... of this plot yields the value of the strain-rate 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...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006780
EISBN: 978-1-62708-295-2
... materials is sufficiently constant to be considered as a steady-state creep rate. For these materials, the minimum creep rate is a steady-state value that can be empirically related to rupture life and is widely used in research and engineering studies. However, the concept of a steady creep rate during...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005518
EISBN: 978-1-62708-197-9
... described in Ref 32 . The interfaces of the grains are mapped with a large number of facets. Each grain is described by a series of variables that include the position of the r, the radius, and facet states indicating whether a given facet is still in contact with the liquid. The growth rate is calculated...