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Theoretical and experimental investigations of electron beam surface remelting and alloying

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Abstract

A central problem in the numerical treatment of melting and resolidification, as well as alloying processes at metal surfaces, is the coupling of the physical phenomena. Among these phenomena, Marangoni convection, conjugated heat transfer, species transport and free-surface deformation occur simultaneously. The involved transport mechanisms take place at different time scales, which enables the decoupling of the governing equations in the solution process. This decoupling procedure has been proven to be capable of computation of metal-surface remelting and alloying processes. In this article, scaling analysis is presented to determine both the time scales and characteristic velocities. Using this information, two-dimensional transient calculations of velocities, temperatures, and species concentration in both liquid and solid phases have been carried out. These theoretical results have been compared with experiments utilizing the high-speed scan deflection technique in electron-beam (EB) surface remelting and alloying of a Ck45 specimen (AISI 1045) with chromium. It was shown that the shape of the resolidified surface is determined by the fluctuation of the vapor pressure. This fluctuation is due to temperature oscillations induced by the transient behavior of the electron beam.

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Abbreviations

a,b,c,n :

coefficients

A :

surface

C :

mass concentration

c p :

specific heat

D :

mass diffusivity

Δh ev :

enthalpy of evaporation

f :

frequency

g :

earth acceleration

k :

partition coefficient

K :

curvature

l :

length

m :

mass flux

p :

pressure

P :

power

q :

heat flux

S :

free surface location

t :

time

T :

temperature

V :

volume

w :

velocity

x, y, z :

coordinates

β :

volume expansion coefficient

γ :

surface tension

δ :

Kronecker symbol

Δ :

thickness

ɛ :

emissivity

η :

dynamic viscosity

κ :

thermal diffusivity

λ :

wave length

ν :

cinematic viscosity

ϱ :

density

σ :

characteristic radius

τ :

stress tensor

Φ :

dissipation function

ω :

frequency

a :

ambient

d/l/w :

depth/length/width

eff:

effective

ev :

evaporation

lam/turb:

laminar/turbulent

melt/Sol:

melting/solidification

n, t :

normal/tangential

rad:

radiative

Surf:

surface

*:

dimensional

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Author notes

  1. F. Rüdiger (Postdoctoral Fellow, Research Engineer)

    Present address: the Institute for Aerospace Engineering, Dresden University of Technology, 01062, Dresden, Germany

Authors and Affiliations

  1. the Institute for Aerospace Engineering, Dresden University of Technology, 01062, Dresden, Germany

    O. Velde (Research Assistant) & R. Grundmann (Professor)

  2. Schott ML GmbH, 07745, Jena, Germany

    F. Rüdiger (Postdoctoral Fellow, Research Engineer)

Authors
  1. O. Velde
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  2. R. Grundmann
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  3. F. Rüdiger
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Velde, O., Grundmann, R. & Rüdiger, F. Theoretical and experimental investigations of electron beam surface remelting and alloying. Metall Mater Trans B 31, 1405–1417 (2000). https://doi.org/10.1007/s11663-000-0025-z

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  • DOI: https://doi.org/10.1007/s11663-000-0025-z

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