Transport Phenomena in Surface Alloying of Metals ... · Transport Phenomena in Surface Alloying of Metals Irradiated By High ... and heat transfer for pure metals by varying the

Transport Phenomena in Surface Alloying of Metals Irradiated By High Energy Laser Beam

KIRAN BHAT AND PRADIP MAJUMDAR

Department of Mechanical Engineering Northern Illinois University

DeKalb, Illinois 60510 USA

[email protected]

Abstract: - Laser surface alloying has received considerable attention in recent times as it can locally change material properties and retain bulk properties in the interior of the base material. Alloy powder is deposited in a molten pool of substrate material to improve surface properties like hardness resistance to wear and corrosion of a material. The effect of temperature dependent surface tension coefficient is identified as the primary driving force in developing the flow field in a molten pool of metals. This study presents simulation of fluid motion and distribution of alloy element in a molten pool of substrate material subjected to high-energy laser beam. A mathematical model for momentum, energy and concentration is presented and numerical results are obtained using computational code. A parametric study is conducted to analyze the effect of laser beam parameters, and shape and size of molten pool on the surface tension driven flow fields and quality of the alloyed zone in terms of uniform distribution, depth of alloyed zone as well as rate of deposition.

Key-Words: - Surface Alloying, Laser Beam, Transport Phenomena, Computational Model

1 Introduction Laser surface treatment has received considerable attention recently due to the improved surface properties that can be achieved, especially from the point of view of hardness, wear and corrosion resistances. It is of great importance from the manufacturing point of view where one wants to change surface properties of a product, but to retain bulk properties in the interior. Laser surface treatments help in improving the properties like hardness resistance to wear and corrosion of a material thereby producing new materials. Lasers can alter material surface properties of a component to suit a specific industrial application and commonly used for surface engineering. They perform versatile surface treatments with great precision, low heat input and therefore low distortion and fast cycle times. These treatments include non-melting surface treatments like transformation and shock hardening, melting surface treatments

like glazing and cladding. The main advantages of laser surface melting can be summarized as: i. increased productivity; ii. reduced manufacturing costs and ii, improved product quality, iv. increased design and production flexibility, v. new manufacturing opportunities, vi. enhancement of mechanical properties at the surface, and vii. improved resistance to wear and corrosion at specified locations.

Lasers are very efficient in heating localized regions, and hence, they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. A variety of surface treatment processes such as laser cladding, laser surface alloying and laser heat treatment can be achieved by proper combinations of laser power density and interaction time. Laser surface alloying involves melting of the substrate using high energy laser beam to a predetermined

Advances in Modern Mechanical Engineering

ISBN: 978-960-474-307-0 11

mailto:[email protected]

molten pool shape and introducing alloying elements in the molten pool.

Figure 1 shows the schematic diagram of a typical laser installation. The laser beam is transmitted through a focusing lens, which converges near the focal point of the lens. During the heating period, a coaxial assisted gas stream, often oxygen, argon, or nitrogen, is used to achieve higher thermal coupling between the laser beam and the material. The incident laser beam is absorbed by the substrate material and rapidly heats the thin layer of the material surface and forms a thin layer of molten pool in the substrate. A mathematical model and parametric study are essential to analyze the role of fluid flow, transport phenomena and processing condition on the alloy element distribution during laser surface alloying. High precision and control of the alloyed zone in terms of uniform distribution of alloy element, thickness and depth are the major challenges in the development of laser surface alloying process.

Assisted Gas Laser Beam Lens

Nozzle

Lens

Ravindran and Srinivasan. [15] modeled the laser-melting problem by the Galerkin finite element method. Using the apparent capacity method, in which the latent heat is included in the specific heat of the material, they examined the flow field and heat transfer in laser surface melting of an alloy. They neglected the fluid flow in the mushy zone of the solidifying liquid. However, they analyzed the flow field and heat transfer for a typical range of surface tension values of steel.

Molten Pool

Work Piece

Figure 1 Schematic representation of laser heated molten pool A considerable amount of research has been conducted in the past in dealing with the role of fluid flow in the formation of the molten pool and distribution of alloy elements. Most of there work showed the dominance of Marangoni convection driven force in the molten pool. Anthony and Cline [1] developed the first one-dimensional model for molten fluid flow during laser melting and found

that the flow in the molten pool is created by the surface tension gradient with temperature. Chan et al. [7] proposed the first two-dimensional transient model for convective heat transfer and surface tension driven fluid flow. They examined the effects of different process parameters, such as beam power density, beam radius, surface tension, and additional material properties, on free surface velocity, surface temperature, pool shape, and cooling rate. In their subsequent work, Chan et al. [8] analyzed the steady state laser-melting problem within the power range of 107-109 Wm-2. They found that the scanning velocity plays an insignificant role because of the higher magnitude of the surface tension velocity. Basu and Srinivasan [2] confirmed the work carried on by Chan et al and also examined the flow pattern in a laser-melted pool under steady state conditions. They assumed a top-hat heat flux distribution and used the vorticity-stream function method for solving the momentum equation in the molten region. They have shown the existence of two contra-rotating cells in the flow pattern. Basu and Date [3] investigated the steady state and transient laser-melting problems for an axisymetric model. Using a Gaussian distribution of input heat flux, they presented a detailed analysis of the flow field and heat transfer for pure metals by varying the beam power density and the beam radius

Kim and Sim [11] presented a detailed transient and steady state analysis of the flow field and heat transfer, including fluid flow in the mushy zone for an alloy. They compared the geometry of the pool, the free surface velocity, and the surface temperature with and without convection in the mushy zone. Morvan et al. [12] presented a numerical model of the


ISBN: 978-960-474-307-0 12

thermocapillary flow in a melted pool created by a scanning CW laser. They also analyzed the effects of scanning velocity and beam dimension upon thermocapillary flow intensity, dimensions and the shape of the melted zone. Basu and Date [5] studied the effect of various solidification parameters and pool characteristics on rapid solidification following laser melting of aluminum and steel. Pericleous and Bailey [13] presented numerically the role of surface tension in the dynamics of the melt pool including post solidification stress history using a control volume approach. Kar and Majumder [9] determined the metastable alloy composition and various process parameter effects on the composition of binary alloy system. They also modeled heat conduction through the pool and the substrate. Basu and Date [4] presented a parametric study of laser melting problems for varying beam radius and beam power using steel and aluminum. They also analyzed the effect of convection on the overall heat transfer. Ravindran et al. [14] simulated the surface-tension-driven convection in the laser melting by Galerkin finite element method and showed the dependence of flow pattern on surface tension temperature gradient. Ravindran et al. [15] modeled the surface melting by a stationary, pulsed laser using finite element model and presented the role of surface tension driven convection in detail. Basu et al. [6] studied the flow field and its effect on the depth and width of the steady state pool based on numerical and analytical methods. They validated their results by carrying out an experimental study using surface melting of Al-4.5%Cu alloy with an electron beam. Dharani and Majumdar [16] developed an enthalpy-based computational model for analyzing laser heating and melting of metals. She developed a solution algorithm and a code to estimate the temperature distribution, solid- liquid interface location, and shape and size of the molten pool. Kasula and Majumdar [10] based their study on the resulting temperature and stress distribution, the width and depth of the molten pool formed with the application of a high energy Gaussian laser beam. The mathematical model developed was based on

multidimensional transient heat and mass transfer equations, and the numerical solution obtained was based on a three-dimensional finite element model.

The objective of this work is to study the fluid motion and distribution of alloy element in a predetermined molten pool of substrate material subjected to high-energy laser beam. A computational model is developed to understand the role of different governing physical phenomena including fluid flow, heat transfer and mass transfer with operating process parameters. A parametric study will be conducted to analyze the effect of operating material and laser beam parameter on the quality of the alloyed zone in terms of uniform distribution, thickness and depth of alloyed zone.

2. Mathematical Formulation The physical processes involved in laser surface treatment are basically thermal in nature, which involves creating a molten pool of substrate and distributing alloy element or solute in the pool subjected to an approximately selected laser beam parameters. A mathematical model is developed based on three-dimensional and transient transport of heat and mass in the presence of a fluid flow in a predetermined molten pool of substrate subjected to a high energy laser beam. A predetermined molten pool of substrate is coated with a thin layer of alloy element, deposited by a nozzle spray, and continued to be subjected to a high-energy laser beam. As laser beam of constant power with Gaussian heat flux distribution strikes the surface of the cavity, the incident radiation is transmitted in the semi-transparent liquid pool as well as volumetrically absorbed based on the optical properties of the material. Figure 2 shows the schematic representation of the physical model.


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Figure 2 Schematic representation of a molten metal pool created by laser melting.

A laser beam having a constant power distribution strikes the surface of the material. Heat generated due to the absorbed incident laser beam radiation develops a molten pool. The heat energy generated is partly convected to the surroundings and mostly dissipated to the cooler regions of the material by conduction. The flow in this molten pool is mainly due to the surface tension gradient produced by the temperature gradient at the free surface. This surface tension gradient acts as a shear stress at the free surface thereby inducing convective flow within the molten pool as depicted in .the Figure 2. Laser beam characteristics

The intensity of the laser beam that is incident on the work piece is expressed as

(1) (1) Continuity Equation The intensity of the laser beam that is absorbed

in the molten pool is expressed as

(2)

2y2xaz

o e*a*IIa = absorption coefficient

Io = laser beam density at the centre (W/m2)

The beam intensity distribution and the value of

Io is assumed such that

Po = (3) oR

AdAxI )(

Po = laser power (W) Ro = effective radius of the laser beam (mm) A = area (mm2)

Mathematical Model

A transient heat flux is applied at the centre of the top surface thereby creating a molten metal pool with associated temperature distribution. Heat is lost from all sides of the plate by convection.

The following assumptions are made with the formulation of the combined heat and mass transfer model: 1. All properties of the material are independent of temperature except surface tension, 2. The free surface of the melt is assumed to be flat, 3. The laser beam is stationary, 4. The buoyancy force is of negligible order of magnitude compared to marangoni force, 5. The flow is assumed to be laminar and Newtonian, 6. The secondary effects like thermo-diffusion or sorret effect are neglected, 7. Alloying element is assumed to be melted instantaneously and secondary effect such as absorption of injected particle or shadow effect is neglected as a first approximation.

The non-dimensionalized three-dimensional governing equations of continuity, momentum and energy mass transport in the x-y-z plane is as follows:

Governing equations

0*

*

*

*

*

*

*

z

w

y

v

x

u

t

(4)

2

22

* oR

yx

o eII


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X-Momentum Equation

*

**

*

**

*

**

z

uw

y

uv

x

uu

t

u

2*

*2

2*

*2

2*

*2

*

*

z

u

y

u

x

u

R

1

x

p (5)

Y-Momentum Equation

*

*

*

*

*

**

z

vw

y

vv

x

vu

t

v

(6)

2*

*2

2*

*2

2*

*2

*

*

z

v

y

v

x

v

R

1

y

p

M Z- Momentum Equation

*

*

*

*

*

**

z

ww

y

wv

x

wu

t

w

2*

*2

2*

*2

2*

*2

*

*

z

w

y

w

x

w

R

1

y

p

(7)

Energy Equation

) (8

Mass Concentration Equation

*

**

*

**

*

**

*

*

z

Cw

y

Cv

x

Cu

t

C

2*

*2

2*

*2

2*

*2

D z

C

y

C

x

C

Ma

1

Boundary conditions

The molten metal pool is divided into two regions. The region on the top is the free surface and the region surrounding the metal pool is the solid-liquid interface. Figure 3 shows a three-dimensional heat transfer model with specified boundary conditions.

w

(9)

y Th,

z

b T T

2oR

2y2x

o e*II

Solid/liquid

Figure 3 Three-dimensional schematic of the molten metal pool.

Velocity boundary condition Shear force balance at the free surface gives

xz

uzx

(10)

yz

zy

v (11) *

**

*

**

*

**

*

*

z

Tw

y

Tv

x

Tu

t

T

These expressions can be written in non-dimensional form as

q

z

T

y

T

x

T

Ma

12*

*2

2*

*2

2*

*2

T

x

TC

z

u p

*

(12)

y

TC

z

v p

*

(13)


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At solid/liquid interface (no slip condition)

(14) 0),,( zyxV

Temperature boundary condition

Energy Balance at the free surface gives

)(* )0,,()0,,(

TThz

TK yx

yx

(15)

Energy Balance at the solid/liquid interface gives

)TT(*hqz

TK )0,y,x(c

''s

)0,y,x(

(16) )TT(*h )0,y,x(r

Concentration boundary condition At the free surface (17) 10,, yxC

At solid/liquid interface

0

n

C (18)

The governing equations are nondimensionalized with the following non-dimensional variables:

or

xx

*

; or

yy

*

; or

zz

*

; kqr

TTT

o

a

/

** ;

cU

uu

*

; cU

vv

*

; cU

ww

*

; 2

*

cU

pp

2

*

or

tt

; Dqr

CCC

o

a

/

** and

pc CdT

dU

*

Governing Parameters

Reynolds number is defined based on surface tension force as

oooc r

k

qr

dT

drUR

*

Marangoni number based on energy is defined as

ooTT

r

k

qr

dT

dRMa

*Pr

Marangoni number based on diffusion is defined as

D

r

k

qr

dT

dRMa oo

DD

*Pr

3. Computational Model A computational model related to the

mathematical model presented is developed using FLUENT 6.0 commercial software and using GAMBIT graphical user interface (GUI) for building, meshing and assigning zone types to the model. The geometry of the molten pool is imported from the previous finite-element solution laser heat and formation of molten pool for a pure metal [16]. The geometry of the melt pool is shown in Figure 4a.

The meshing is done using Tet/Hybrid model and the mesh is composed primarily of tetrahedral mesh elements but also includes hexahedral, pyramidal, and wedge elements where appropriate.

(a) Geometry of the model


ISBN: 978-960-474-307-0 16

4. Results and Discussion

(b) Computational mesh

Figure 4 Geometry of the model and computational mesh

The mesh elements used for generating the mesh

is 8-node hexahedron volume element, 6-node wedge volume element, 4-node tetrahedron volume element, and 5-node pyramid volume element. The meshing is uniform throughout the model. The model consists of two volumes: solid cylinder and a hollow cone. The total number of cells in the model is 45821, faces are 94902, nodes are 9329, cell zones are 2, and face zones are 7. Figure 4b shows a typical mesh of the model. The input for heat source and marangoni stress are applied as a source term using a user defined macro written in C-code composed of number variable such as the index for cell number with heat source, an array of derivative of the source term with respect to dependent variable of the transport, and time value. These derivatives may be used to linearize the source term if they enhance the stability of the solver.

Solver used for the computational study is segregated solver that requires less memory compared to the other solvers. The governing equations in the solver are solved sequentially (i.e., segregated from one another). Several iterations of the solution loop are performed before a converged solution is obtained because of the non-linearity of governing equations. A point implicit linear equation solver is used in conjunction with an algebraic multigrid (AMG) method to solve the resultant scalar system of equations for the dependent variable in each cell. The discretization is based on second-order upwind scheme for the convective terms and the pressure-velocity coupling is based on PISO algorithm for transient calculations.

The finest mesh for accurate evaluation of the numerical model is selected based on the mesh refinement study. In the parametric study, the temperature and velocity distribution when subjected to varying time steps, varying lengths of time, varying power densities of the beam, varying laser beam diameter, and varying aspect ratio’s (ratio of the width to the depth of the pool) are studied. Aluminum alloy Al-4.5%Cu is used as the base material and Nickel (Ni) as the alloy element material. The parameters and operating conditions for the study are: Aspect ratio, AR = 2.0, Laser beam power intensity, I = 4e8W/m2, Molten pool dimensions (10 x 5mm, 5 x 2.5mm, and 3 x 1.5mm), and Laser beam diameter, d= 3mm.

Mesh refinement study The basic model has a mesh with an interval

size of 0.026 and a total number of elements of 45832. The mesh intensity is varied from an interval size of 0.04 to 0.026 to improve the convergence of the solution so as to reduce the percentage relative error. Results for the variation of temperature at different x locations and the corresponding percentage relative error at the midsection of the model are presented in Figures 5. It can be seen from the results that as the mesh size decreases, the percentage relative error in the temperature decreases. Strong dependence on the mesh size can be noticed through the percentage relative error in Figure 5a. Results show continuous convergence of temperature profile to =0.026. The maximum percentage relative error is below 0.0015%. The mesh with an interval size of 0.026 gives the least percentage error and hence it is taken as the final mesh to obtain the desired results. Results for the variation of temperature at different z-locations and the corresponding percentage relative error at the mid-section of the model are given in Figures 6. For mesh refinement in z-direction, results also show convergence of temperature profile along z-direction towards

x

x

z = 0.026 with maximum percentage relative error less than 0.001%.


ISBN: 978-960-474-307-0 17

820.75

821

821.25

821.5

821.75

822

822.25

822.5

822.75

823

823.25

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m )

Tem

pera

ture

(k)

0 .05

0.04

0.035

0.03

0.028

0.027

0.026

(a) Temperature distribution along x-axis at the top surface

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m)

Per

cen

tag

e re

lati

ve e

rro

r(%

)

0.04 & 0.035

0.05 & 0.04

0.03 & 0.028

0.035 & 0.03

0.028 & 0.027

0.027 & 0.026

(b) Percentage relative error at the top surface of the mid-section

Figure 5. Percentage relative error for different mesh interval size

820.75

821

821.25821.5

821.75

822

822.25

822.5

822.75823

823.25

823.5

-0.005 -0.004 -0.003 -0.002 -0.001 0

Z ( m)

0.05

0.04

0.035

0.03

0.028

0.027

0.026

(a) Temperature distribution along the mid- section

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

-0.005 -0.004 -0.003 -0.002 -0.001 0

Z ( m)

Per

cen

tag

e re

lati

ve e

rro

r(%

)

0.04 & 0.035

0.05 & 0.04

0.03 & 0.028

0.035 & 0.03

0.027 & 0.026

(b) Percentage relative error along the depth of the mid-section

Figure 6 Mesh refinements in z-direction for different mesh sizes

In order to check the sensitivity of the time step on the convergence, simulation is performed with decrease in time steps: Δt = 0.05, Δt = 0.02, Δt = 0.01, Δt = 0.005, and Δt = 0.002 sec . It was observed that the least percentage error occurs for time step size between Δt = 0.005 sec and Δt = 0.002 sec. It is observed that the temperature distribution is invariable for time step size Δt = 0.005 sec and Δt = 0.002 sec.

Effect of laser beam and surface tension gradient

This section mainly presents the effect of including a laser beam and surface tension gradient in the alloy particle distribution in molten pool. Results presented in this section include the contour plots of temperature and concentration, vector plots depicting the flow field and the corresponding numerical data. Figure 7 present the contour plots for temperature and the velocity vectors for the model with and without the inclusion of laser beam and surface tension gradient. It can be observed from the plots that the temperature in molten pool decreases away from the centre of the laser beam with the application of laser beam and Marangoni stress whereas the temperature increases away from the centre of the pool when the effect of laser beam and Marangoni stress is neglected.

The velocity vector plots shown in Figure 7b show that when the laser beam and marangoni stress is applied, the flow field takes a predefined direction


ISBN: 978-960-474-307-0 18

of flow that flows away from the centre of the laser beam because of surface tension gradient. Two recirculating eddies are visible near the top on both left and tight sides of the pool. When the laser beam and marangoni stress is neglected, the flow is from within the pool towards its free surface mainly because of the buoyancy force acting in the upward direction and due to the decrease in the temperature from inside the pool towards its free surface. The line plots of temperature distribution along a line near the top surface and along the vertical line at the center of the pool are shown for both cases in Figure 8. As expected temperature distribution follows a Gaussian distribution with peak temperature below the beam center. Temperature distribution along the vertical line shows a peak temperature underneath the free surface and reduced temperature toward the bottom. In case with no laser beam and shear stress, heat pool was primarily called by dissipating heat from the curved bottom surface by natural convection. In Figure 9, the velocity distribution near the top surface shows the strong convective velocities with peak velocities near the center of two circulating eddies, induced by the surface tension forces.

Figure 7 Effect laser beam and surface tension on temperature contour plots and velocity vectors in the pool

820.5

821

821.5

822

822.5

823

823.5

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m)

Tem

pe

ratu

re (

k)

with HF & ST without HF & ST

(a) Distribution of temperature at the top surface of the pool

820.5

821

821.5

822

822.5

823

823.5

824

-0.006 -0.005 - 0.004 -0.003 -0.002 -0.001 0

Z (m)

Tem

pera

ture

(k)


(b) Distribution of temperature along the depth of the pool

Figure 8 Distribution of temperature in the molten pool

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m)

Vel

oci

ty (

m/s

)


(a) Distribution of velocity near the top surface of the pool


ISBN: 978-960-474-307-0 19

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

Z (m)

Ve

loci

ty (

m/s

)


(b) Distribution of velocity along the depth of the pool

Figure 9. Distribution of velocity in the molten pool

Figures 10 show the variation of Ni alloy distribution within pool for the above-discussed cases for time steps 0.5 sec to 6.5 sec. In the case with laser beam power and surface tension driven flow, the Ni-alloy element transports towards the two side walls of the pool driven by the strong surface tension driven by the two recirculating eddies. Results show, in 6.5 second, the Ni-alloy has penetrated also most entire depth of the pool. However, there is considerable non uniform distribution of the Ni-alloy with in the pool. In case - II with the absence of the laser beam power and marangoni stress, the transport of Ni-allow with the substrate is primarily by diffusion and the penetration is at a slower rate, but maintains a uniform concentration distribution of ally element within a thin layer at the free surface.

(a) time steps 0.5 sec and 1 sec

(a) time steps 4 sec and 6.5 sec

Figure 10 Ni-allow concentration distribution within the molten pool with time.

Alloy distribution is more uniform when laser beam and marangoni stress are neglected and diffusion is the only mode for transport of helps and penetration of alloy particles, However, faster alloy penetration takes place when laser beam and marangoni stress are present, which leads to a strong flow field that enhances alloy transport by diffusion and convection in the substrate molten pool.

Figures 11-13 show the distribution of Ni alloy at various depth of the molten pool and at different time steps. Results in Figure 10 show that right beneath the surface (Z = -0.05) of the pool, alloy distribution is more uniform when laser beam and marangoni stress is neglected. In fact at this location there is considerable concentration


ISBN: 978-960-474-307-0 20

variation with pool with low concentration in the mid-section and high concentration near the edge for the case with laser beam and marangoni stress. Apparently, just near the surface with pure diffusion mode helps to maintain uniform ally element concentration. But if we take into consideration of the alloy penetration higher depth of the pool (Figure 12-13), the effect of laser beam plays a major role. It not only helps in attaining the desired thickness of alloy deposition uniformly but also helps in attaining it at a faster rate. For example, Ni alloy concentration at a depth of -1 mm from the free surface attains a concentration value of 0.18 in 4 sec and 0.29 in 6.5 sec when laser beam and marangoni stress is used as compared to a no alloy concentration when these parameters are not used.

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

- 0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m )

Ni

Con

cent

ratio

n

w ith HF & ST without HF & ST

(a) Ni concentration at -0.05 mm from the top surface at time step 0.5 sec

0

0.2

0.4

0.6

0.8

1

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m)

Ni C

once

ntra

tion

w ith HF & S T without HF & S T

(b) Distribution of Ni concentration at -0.05 mm from the top surface at time step 4s

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

X (m)

Ni C

on

cent

ratio

n


(c) Distribution of Ni concentration at -0.05 mm from the top surface at time step 6.5s

Figure 11 Variation of distribution of Ni concentration at -0.05 mm from the top surface with time

0

0.005

0.01

0.015

0.02

0.0250.03

0.035

0.04

0.045

0.05

-0.004 -0.002 0 0.002 0.004

X (m)

Ni C

on

cent

ratio

n


(a) Ni concentration at -0.1 mm from the top surface at time step 0.5s

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.004 -0.002 0 0.002 0.004

X (m)

Ni C

on

cent

ratio

n

wi th HF & ST without HF & ST

(b) Ni concentration at -0.1 mm from the top surface at time step 4s


ISBN: 978-960-474-307-0 21

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.004 -0.002 0 0.002 0.004

X (m)

Ni C

onc

entr

atio

n


(c) Ni concentration at -0.1 mm from the top surface at time step 6.5s

Figure 12 Variation of Ni concentration within the pool with time at a depth of -0.1 mm from the top surface with time.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

X (m)

Ni C

onc

entr

atio

n


(a) Ni concentration at -0.2 mm from the top surface at time step 0.5s

0

0.05

0.1

0.15

0.2

0.25

-0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

X (m )

Ni C

on

cent

ratio

n


(b) Ni concentration at -0.2 mm from the top surface at time 4 sec

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

X (m)

Ni C

onc

entr

atio

n


(c) Ni concentration at -0.2 mm from the top surface at time step 6.5 sec Figure 13 Variation of Ni concentration within the pool with time at a depth of -0.2 mm from the top surface with time.

5. Conclusions A three-dimensional mathematical model has been presented to study the fluid flow, heat transfer, and alloy element concentration distribution in a molten pool created in a metallic substrate irradiated by high energy laser beam. The material was characterized with respect to temperature dependent surface tension force as primary force in developing flow field and transport of alloy element. Computational analysis is performed to study the flow patterns, temperature and concentration distributions in the molten pool. Results show strong dependence of laser beam power and Marangoni stress on the effective transport and distribution of alloy element in the substrate metal. The model is suitable for developing laser surface alloying process for any combination of alloy and substrate material combinations in terms of creating a uniform distribution of alloy element over a desired thickness of the surface layer.

Nomenclature I Laser beam intensity

oI Laser beam intensity

P Laser beam power Ro Laser beam radius d Laser beam diameter x Global x-coordinate y Global y-coordinate


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z Global z-coordinate T Temperature Tm Melting temperature T Ambient temperature h Enthalpy hc Convection film coefficient hr Radiation film coefficient k Thermal conductivity

sq Surface heat flux q volume heat generation due to laser beam Vr Radial velocity Vz Axial velocity R Surface tension Reynolds number p Pressure Cp Specific heat t Time step MaT Marangoni number based on energy MaD Marangoni number based on diffusion D Diffusion coefficient C Concentration of the alloy element a absorption coefficient HF Heat flux ST Surface tension Greek Symbol Latent heat of fusion dynamic viscosity kinematic viscosity Density 6. References [1] Anthony, T. R., and Cline, H. F. (1977). Surface rippling induced by surface-tension gradients during laser surface melting and alloying. Journal of Applied Physics, 48, 3888-3894. [2] Basu, B., and Srinivasan, J. (1988). Numerical study of steady state laser melting problem. International journal of Heat Mass transfer, 31, 2331-2338. [3] Basu, B., and Date, A. W. (1990). Numerical study of steady state and transient laser melting problems-I. Characteristics of flow field and heat transfer. International Journal of Heat Mass transfer, 33, 1149-1163.

[4] Basu, B., and Date, A.W. (1990). Numerical study of steady state and transient laser melting problems-II. Effect of the process parameters. International journal of Heat Mass transfer, 33, 1165-1175. [5] Basu, B., and Date, A.W. (1992). Rapid solidification following laser melting of pure metals-II. Study of pool and solidification characteristics. International journal of Heat Mass transfer, 35, 1059-1067. [6] Basu, B., Sekhar, J.A., Schaefer., & Mehrabian, R. (1991). Analysis of the steady state molten pool obtained by heating a substrate with an electron beam. Acta metal. mater, 39, 725-733. [7] Chan, C., Mazumdar, J., and Chen, M. M. (1984). Two-dimensional transient model for convection in laser melted pool. Metal. Trans., 15A, 2175-2184. [8] Chan, C., Mazumdar, J., and Chen, M. M. (1985). Three-dimensional model for convection in laser melted pool. Paper presented at ICALEO-85. [9] Kar, A., and Majumder, J. (1988). One-dimensional Finite-Medium diffusion model for extended solid solution in laser cladding of Hf on nickel. Acta metal, 36, 701- 712. [10] Kasula Bhavani and Pradip Majumdar, Three-Dimensional Finite Element Analysis of Melting in an Alloy Irradiated with a High Energy Laser Beam, Proceedings of the 2003 International Mechanical Engineering Congress and R& D Expo, Paper NO: IMECE2003-43688, pp. 1-8, 2003

[11] Kim, W. S., and Sim, B. C. (1997). Study of thermal behavior and fluid flow during laser surface heating of alloys. Numerical Heat Transfer. Part A, applications, 31, 703-723. [12] Morvan, D., Cipriani, F.D., Dufrescne, D., & Garino, A. (1990). Thermocapillary effects in a melted pool during laser surface treatment.


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Eighth International Symposium on Gas Flow and Chemical Lasers, SPIE 1397. [13] Pericleous, K.A., & Bailey, C. (1995). Study of Marangoni phenomena in laser-melted pools. Modelling the casting process and predicting residual stresses. Paper presented at Numiform’95. [14] Ravindran, K., Srinivasan, J., & Marathe, A. G. (1994). Finite element study on the role of convection in laser surface melting. International journal of numerical hear transfer, 26A, 601-618. [15] Ravindran, K., Srinivasan, J., & Marathe, A.G. (1994). Role of surface tension driven convection in pulsed laser melting and solidification. Proc Instn Mech Engrs, 209. 75-82. [16] Sowdari, Dharani and P. Majumdar, Finite element analysis of laser irradiated metal heating and melting processes, Journal of Optics & Technology, 42, pp. 855- 865, 2010.


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