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Effect of Fluid Convection on Dendrite Arm Spacing in Laser Deposition

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Abstract

Ni superalloys are widely used for hot section components in jet engines because they are very resistant to corrosion and maintain reasonably high strength at elevated temperature. However, the repair cost of the parts is high, partly due to the complexities of process variable optimization and control in laser cladding. In particular, optimizing the process parameters by experiments is time-consuming and costly. The microstructure and properties of the metal deposit are significantly influenced by values temperature gradient G and solidification rate R at the weld pool solidification boundary. Optimized values can help to reduce defects and improve properties of laser deposits. Optimization is hindered by the fact that the clad melt pool is hot and small, making in situ measurement of such solidification conditions difficult. Numerical simulation of the laser deposition process is a possible alternative to experimental measurement to obtain values of clad solidification parameters. In this investigation, G and R values at the weld pool solidification boundary were obtained from a three dimensional numerical simulation of laser deposition process and melt pool. The primary dendrite arm spacing and cooling rate of the deposited material were then correlated to these solidification conditions.

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Abbreviations

ρ :

fluid density (g/cm3)

t :

time (s)

\( \vec{v} \) :

molten metal velocity (cm/s)

\( \dot{m}_{\text{s}} \) :

mass source rate (g/s)

H :

enthalpy (g cm2/s2)

\( \dot{h}_{\text{s}} \) :

enthalpy source rate (g/s3)

σ :

thermal conductivity (g cm/s3/K)

P :

hydrodynamic pressure (g/cm/s2)

μ :

viscosity (g/cm/s)

g :

gravitational acceleration (m/s2)

β :

constant of thermal expansion (K−1)

T m :

melting temperature (K)

\( \vec{p}_{\text{s}} \) :

momentum source rate (g/cm2 s2)

F :

volume fraction of fluid in a cell (0 to 1)

\( \dot{F} \) :

change in F

A :

absorptance

ε 0 :

permittivity of free space (F/m)

ω :

angular frequency of laser radiation (rad/s)

ρ e :

electrical resistivity (Ω cm)

ϕ :

powder catchment efficiency, ratio of S m and S jet

S m :

area of molten pool (cm2)

S jet :

area of substrate struck by powder jet (cm2)

γ o :

surface tension in pure metal (g/s2)

T r :

reference temperature (K)

K s :

surface tension temperature coefficient (g/s2 K)

R g :

gas constant (g cm2/s2 mol K)

S e :

surface excess at saturation (g mol/cm2)

a m :

activity of species m in solution

E :

entropy segregation constant

ΔH 0 :

segregation in enthalpy (kJ/kg mol)

T i :

surface tension transition temperature (K)

T :

temperature (K)

ΔT :

undercooling (K)

ΔT S :

solidus and liquidus temperature difference (K)

ΔT n :

non-equilibrium solidification range (K)

ΔT 0 :

equilibrium solidification range (K)

G :

three dimensional temperature gradient normal to solid–liquid interface (K/cm)

G L :

temperature gradient in liquid region (K/cm)

G x :

x-component of G

G y :

y-component of G

G z :

z-component of G

R :

solidification rate at solid–liquid interface (cm/s)

R b :

laser beam travel speed (cm/s)

Θ:

angle between solid–liquid interface normal and beam travel direction (deg)

L :

constant of harmonic perturbation

D L :

diffusion coefficient in liquid region (m2/s)

Γ:

Gibbs–Thomson coefficient (K m)

K :

partition coefficient

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Acknowledgments

The authors would like to thank Rolls-Royce Corporation for the funding support and providing laser cladding samples in this work. They also appreciate NSF-I/UCRC: Center for Integrative Materials Joining Science for Energy Applications. The authors express their thanks to J.S. Bader for helpful suggestions and interest in this project.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Welding Engineering Program, The Ohio State University, Columbus, OH, 43221, USA

    Yousub Lee (Ph.D. Candidate) & Dave F. Farson (Professor)

  2. Rolls Royce Corp., Indianapolis, IN, 46206, USA

    Mark Nordin (Senior Welding Engineer)

  3. Department of Mechanical, Aerospace, and Biomedical Engineering, The University of Tennessee, Knoxville, TN, 37996, USA

    Sudarsanam Suresh Babu (Professor)

Authors
  1. Yousub Lee
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  2. Mark Nordin
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  4. Dave F. Farson
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Corresponding author

Correspondence to Dave F. Farson.

Additional information

Manuscript submitted October 17, 2013.

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Lee, Y., Nordin, M., Babu, S.S. et al. Effect of Fluid Convection on Dendrite Arm Spacing in Laser Deposition. Metall Mater Trans B 45, 1520–1529 (2014). https://doi.org/10.1007/s11663-014-0054-7

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