ELSEVIER Surface and Coatings Technology 79 (1996) 35 49

SOR .COATIJ$

IYEIINOLO T

Laser glazing of vacuum plasma spray coated NARloy-Z

J. S i n g h a, B.N. B h a t b, R. P o o r m a n b, A. K a r °, J. M a z u m d e r d

a Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16804-0030, USA u NASA George C. Marshall Space Flight Center, Huntsville, AL 35812, USA

c Center for Research and Education in Optics and Lasers (CREOL), Mechanical and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32826, USA

a Center for Laser-Aided Materials Processing (CLAMP), Mechanical and Industrial Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Received 9 February 1994; accepted in final form 15 January 1995

Abstract

A C O 2 laser was used to modify the surface layer of vacuum plasma sprayed NARloy-Z (Cu-3 wt.%Ag-0.5 wt.%Zr). The laser glazing dramatically reduced voids and cavities originally present in the alloy matrix. In addition, grain boundary precipitates were eliminated. A highly refined microstructure was obtained with extended solid solubility of solute atoms (Ag and Zr) into the matrix. A theoretical model was developed to predict the melt pool depth that occurred during laser glazing.

Keywords: Laser glazing; Vacuum plasma spray forming

1. Introduction

Vacuum plasma spray (VPS) coatings are widely used to economically fabricate near net-shaped parts with expected properties equivalent to the wrought alloys. However, the VPS coatings contain defects such as micro-porosity, non-bonded interfaces, and grain bound- ary precipitations. These defects in the microstructure may have resulted in lower mechanical properties of VPS coatings such as ductility, resistance to wear, corrosion, oxidation, impact, etc. An improvement in the microstructure and hence in properties is necessary in order to meet requirement of coatings for aerospace applications. There is potential for improving the surface properties of the VPS coatings by laser glazing [ 1-3]. In the laser glazing process, material is rapidly melted and resolidified, resulting in a better microstructure and properties [3].

During the last decade, laser processing of materials has grown dramatically [-1]. However, laser surface treatment of VPS coatings is not as widespread. Iwamoto et al. [-4] have used a CO2 laser to process the plasma sprayed zirconia to improve the surface properties and prevent surface spalling of their coatings from the steel substrate. Ohmori and Kamada [5] have also used a laser beam on the plasma coated Mo surface to modify

0257-8972/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSD1 0257-8972(95)02441-7

surface properties. Refinement of microstructure and dissolution of secondary phases by laser glazing were demonstrated and documented by Breinan and Kear more than a decade ago [6,7].

The objective of this study is to develop the laser glazing process to achieve improved microstructure and properties. This required a combination of theoretical and experimental effort including modeling of laser melting effects and evaluation of the microstructure of laser glazed VPA NARoy-Z (Cu3 wt.%A~0.5 wt.%Zr) coating. Microstructure and properties of the laser glazed alloys are compared with those of wrought alloys to evaluate the effect of the glazing process. The modeling work is for the development of the quantitative relation- ships for process parameters as a function of melt depth. A validated model will be able to provide processing guidelines for laser glazing of other alloys in future.

2. Materials and experimental procedure

NARloy-Z powders of size (10 50 gin) were sprayed on a steel substrate using processing conditions given in Table 1. A schematic of the vacuum plasma spray torch is shown in Fig. 1. A modified Electro-Plasma Inc. 03C

36 J. Singh et al./Surjace and Coatings Technology 79 (1996) 35 49

Cathode

Substrate

Gun Schematic

: i?. !:::.i ?~ii!~ ! i ~ Mollen @ ,,~ . . . . . . . ~: Particle

Solidified Splat t - l - 2 m m

Solldlfylng Splat

Fig. 1. Schematic diagram of vacuum plasma spray torch.

series of 120 kW direct plasma gun was used for the current effort. The VPS process was carried out inside a 60in (1.5 m) diameter vacuum chamber. Vacuum pressure as low as 1.3 x 103 Pa (10 Torr) can be achieved in the chamber. The vacuum chamber was backfilled with Ar gas (pressure 4 40 kPa or 3-300 Tort) to mini- mize the losses of alloying elements present in the powder during the VPS process. The substrate was preheated to a temperature about 930 °C (1200 K) and then the part was cathodically cleaned by transferring reverse polarity/current from the part (negative) to the anode of the plasma gun. After the substrate was pre- heated and cleaned inside the vacuum chamber, high purity powder was injected into the plasma torch. The powder particles were rapidly heated by the arc gener- ated within the plasma torch and accelerated towards the target by the carrier gas. Hot, high velocity powder particles impacted on the substrate surface and rapidly underwent splat quenching, were deformed, and then solidified. It took about 10-15h to coat a 0.5in

(12.7mm) thick coating on a l ft long steel bar of diameter 0.5 in.

A radio-frequency excited 6kW CO2 laser was employed for the surface glazing of the VPS coated NARloy-Z. The laser glazing parameters are given in Table 2. Inert He gas shielding was maintained during laser glazing.

Metallographic samples were prepared by chemical etching using an ammonium persulphate etchant (10 g ( N H 4 ) 2 8 2 0 8 per 100ml H 2 0 ). A scanning electron microscope (SEM) was used to examine the metallo- graphic samples. Ag-rich and Zr-rich precipitates were identified through carbon tape extraction in which the precipitates were pulled out of the matrix for subsequent analysis using energy dispersive spectrometry (EDS). The extraction technique allowed precise determination of precipitate composition without background inter- ference from the Cu matrix. An Hitachi SEM S-5000 field emission tip equipped with EDS analysis was also used for the present investigation.

Table 1 Process parameters of VPS coatings

Arc gas pressure (argon/hydrogen) (lbfin-2(kg cm-2)) 50 (3.52) Arc current (A) 1000 Arc voltage (V) 54 Stand off spray distance (in (cm)) 10 (25.4) Preheat stand off distance (in (cm)) 10 (25.4) Gun type 03 CK Powder size (mesh) 325 Preheat substrate temperature (°C(K)) ~ 930 (1200) Powder feel rate/feeder (g s - l ) 0.766 Traverse speed of gun (in rain l(cm s 1) 300 (12.7)

3. Theoretical modeling for melt depth

Besides experimental studies on laser glazing of VPS NARloy-Z, a mathematical model has also been

Table 2 Laser process parameters for glazing of VPS coated substrate

Laser power (kW) Spot size (mm) Traverse speed (in min l(cm s 1)) He shielding gas (1 atm at substrate surface)

3-6 0.5 1.5 15 400 (0.64 17) 15 400 (0.64 171

J. Singh et al./Surfitce and Coatings Technology 79 (1996) 35 49 37

developed to understand the effects of various process parameters on the depth of glazing. This will enable the glazing process to be optimized and controlled in order to glaze the substrate precisely to any predetermined depth. The model is based on the three-dimensional transient heat conduction equation which is solved ana- lytically by using an integral transform technique [8]. The thermal conductivity, density, and specific heat of the substrate are taken to be temperature dependent; however, the thermal diffusivity is considered constant because it only varies slowly with temperature for many materials. The geometry used for this model is given in Fig. 2, where the laser beam moves in the x-direction at a constant velocity U. The mathematical model used to determine the temperature field is discussed below.

3.1. Governing equation and initial and boundary conditions

A list of symbols is provided in Appendix A for all the symbols used in the following expressions.

The following equation

~T p(T)Cp(T) ~ - (x, y, z, t) = V[k(T) V T(x, y, z, t)]

is solved to satisfy the initial boundary conditions at the surfaces of the slab described below. Both convective and radiative heat losses through the boundary surfaces of the substrate are considered in this analysis.

Initial condition

T(x, y, z, O) = Ti

Boundary conditions

OT k(T) ~ = h ~ o ( T - T.) + o'g(T 4 - - T 4) at x = 0

~T - k ( T ) ~ x x = h~,~(T- T~) + a~(T 4 - T 2) at x = L

OT k(T) ~ = h y o ( T - 7".) + ae(T 4 - T 4)

uy

OT - k ( T ) ~ z " = h y . , ( T - Ta)+ a e ( T 4 - T 4)

c,y

0T k(T) ~xx = h ~ o ( T - Ta) + Ge(T 4 -- Ta 4)

at y = 0

a t y = W

at z = 0

k(T) ~?T 2 P ( 1 - R ) Oz - rcr 2 e x p ( - 2r2/r 2) - h~h ( T - Ta)

Solution The solution of the above problem yields the following

expression for the temperature distribution [8]

1 T * - (1 - T*°+l + (c7 + 1)T'*) + T * (1) (4 + 1)7"*~

The expressions for various terms in Eq. (1) are given in Appendix B. Eq. (1) is used to determine the temper- ature distribution in the substrate during laser glazing.

Discussion of the model It can be seen from the above-mentioned governing

equation and the initial and boundary conditions that this model takes into account the variations of various thermophysical properties with temperature. However, the thermal diffusivity is considered to be constant because it varies slowly with temperature for most metals.

The governing equation is solved using an integral transform technique [8] instead of a finite difference approximation because the latter usually takes a longer computational time than an analytic solution for the nonlinear problem considered in this paper. For the present glazing problem, the temperature is required to be determined only at one point to calculate the maxi- mum melt depth. This can be done more conveniently using an analytic solution than a finite difference method. An analytic solution allows one to determine the temper- ature at any one point without computing temperatures at other points. In the finite difference approximation, one has to compute the temperatures at all of the mesh points. For all these reasons, an analytic technique is used in this study instead of a numerical technique to solve the above-mentioned problem.

However, the integral transform techniques are suit- able for linear problems. For this reason, the nonlinear governing equation is linearized using the Kirchofftrans- form, and the boundary conditions are linearized using the Kirchoff transformation and Taylor series expansion [-8]. The Kirchoff transformation linearizes the conduc- tion terms in the governing equations and boundary conditions involving the temperature gradients, and the Taylor series expansion linearizes the radiation heat loss terms in the boundary conditions involving the T 4 terms.

........ ~G-"

Hi re r ~'- x (o,o,o) L

-- o'e(T 4 -- T 4) at z = H Fig. 2. Geometry of the substrate and the path of the laser beam.

38 J. Singh et al./Surface and Coatings Technology 79 (1996) 35-49

Fig. 3. Optical micrograph of the wrought alloy showing uniform distribution of second phase {Zr203) in the matrix, as marked by arrows.

It should be noted that the heat source term appears in the boundary condition at z = H instead of the governing equation because the laser beam is considered to deposit its energy at the substrate surface. This is a reasonable assumption because the penetration depth of CO 2 lasers is very small for metals.

Melt depth estimation

The melt depth can be determined from Eq. (1) by obtaining the isotherm that correspoonds to the melting temperature Tm of the substrate. For this study, the melt pool is considered to be the deepest along the axis of the laser beam, and the maximum melt depth is com- puted by determining the coordinates of a point on this axis where the temperature is Tin- When a point reaches Tm, it absorbs the latent heat of fusion in order to melt. Since the latent heat of fusion is neglected in this model, the maximum melt depth is expected to be overestimated as discussed in Section 4.6.

(a) (b)

(c)

Fig. 4. Optical (a) and SEM (b) and (c) micrographs of the NARloy-Z powder showing two phase microstructure with Ag segregation at grain boundaries.

J. Singh et al./Surface and Coatings Technology 79 (1996) 35 49 39

2 0 - J u 1 - 1 9 9 2 1 2 : 4 8 : 3 7

#1, RSP PONDER

C u

A9

• • 8 9 ~

4- O . O O O Ran ._qe= 1 0 . 2 3 8 ke'v' I B . 1 1 8 - ~ I n t e~3ral 0 = 125850

(:: U

(a)

20-.Tu 1-1992 1 2 : 4 3 : 0 1

#1, HATRIX OF RSP

4-

(b)

C u

C u

A ~ C u

Zr

0 . 0 0 0 Range= 1 0 . 2 3 0 key I n t e g r a l 12

Fig. 5. SEM-EDS spectra showing composition variation of Ag and Zr from two regions: (a) grain boundary precipitate and (b) matrix precipitate.

40 J. Singh et al./Surface and Coatings Technology 79 (1996) 35 49

4. Results and discussion

4.1. Microstructure of wrought NARloy-Z

An optical micrograph of the wrought NARloy-Z is shown in Fig. 3. The microstructure consisted of two phases, i.e. Zr was uniformly dispersed as second phase (Zr203) in the Cu rich matrix. The average size of the Zr-rich second phase was 10-12 ~tm. No grain boundary precipitation was observed. The average matrix grain size was about 75 gin.

4.2. Microstructure of NARloy-Z powder

The optical and SEM microstructure of the rapidly solidified NARloy powder revealed a two phase microstructure (Figs. 4(a) and 4(b) respectively). The powder size ranged from 50 to 200 lain. The small powder particles (about 50 Jam) were showing dendrites in the matrix while large particles (greater than 200 gin) were showing grain boundaries in addition to the dendrites (Fig. 4(c)). Some segregation of solute atoms (Ag) was observed at the grain boundaries (Fig. 4(c)). The varia- tion of Ag in the matrix and at the grain boundaries was determined by the SEM-EDS analysis (Figs. 5(a) and 5(b)).

4.3. Microstructure of" VPS coatings

The optical microstructure of VPS coated NARloy-Z is shown in Fig. 6. The microstructure of the unetched surface clearly revealed presence of micro-voids at grain boundaries. In addition, large voids (about 10-30 ~tm) were also often observed, as shown by arrows in Fig. 6. Three different types of precipitation were observed in

the VPS coated NARloy-Z; (a) grain boundary precipi- tations, (b) Ag-rich and (c) Zr-rich precipitates in the matrix as marked by arrows in Fig. 7. The grain bound- ary precipitates were identified as Ag-rich phases that were segregated as individual grains, as marked in Figs. 7(a) and 7(c). The Ag-rich phase segregation was predominantly observed at large angle boundaries with only a relatively small volume fraction of Ag-rich phase segregation observed at low angle boundaries (see Fig. 7(d)). An extensive grain boundary separation was observed in the large angle grain boundary region, where Ag-rich phases had precipitated out. Corresponding SEM-EDS analysis from the precipitates in the matrix (as marked 1 in Fig. 7(a)), grain boundary precipitates (as marked 2 in Figs. 7(b) and 7(c)) and matrix (as marked 3 in Fig. 7(c)) are shown in Figs. 8(a) 8(c) respec- tively. The electron probe microanalysis (EPMA) across the grain boundary precipitate is shown in Fig. 9. The EPMA revealed that the composition of matrix in the wrought alloy was uniform where as segregation of Ag and Zr (in the form of oxide) was observed at the grain boundaries.

There was a loss of Ag in the VPS coatings which resulted in compositional variation of alloying elements within each grain. In addition, a long VPS process cycle (930 °C for 15 h) and compositional variation of alloying elements within each grain contributed to precipitation of second phases in the matrix and grain boundaries. It was not possible to redissolve the precipitates or to obtain a single phase microstructure of the VPS coating by homogenizing at high temper- atures. Furthermore, the homogenization heat treat- ment did not have any influence on the grain growth of the VPS coatin~ as the second phases acted as

Fig. 6. Optical micrographs of the VPS coated sample showing the presence of voids and grain boundary precipitates: (a) unetched surface, (b) etched surface.

J. Singh et al./Surface and Coatings Technology 79 (1996) 35-49 41

(a) (b)

(c) (d)

Fig. 7. SEM micrographs of the VPS coated surface showing the precipitation of Ag rich phases at high angle boundaries: (a) low magnification, (b) and (c) show grain boundary separation and segregated individual Ag particles (as marked by arrows), (d) shows small volume fraction of segregated individual Ag particles at low angle boundaries.

anchors at the grain boundaries and restricted the grain boundary migration.

4.4. Microstructure of HIPPed VPS coated NARloy-Z

To reduce voids present in the VPS coated substrate, samples were hot isostatic pressed (HIPPed) at a high pressure (2.21 x 105 Pa) and temperature (930 °C) for 3 h. The optical microstructure of the HIPPed sample (unetched and etched) is shown in Fig. 10; the volume fraction of voids and grain boundary precipitates still appeared to be about the same as coated specimens (Fig. 6). This suggest that the voids could not be com- pletely removed from the material by HIPPing process.

4.5. Microstructure of laser glazed VPS coated NARloy-Z

Laser glazing was carried out on the VPS NARloy-Z substrate containing voids (about 30% by volume),

unmelted particles and Ag-rich precipitates at grain boundaries as well as in the matrix. The depths and widths of the glazed zone as a function of various laser processing parameters are provided in Tables 3 and 4.

The optical micrograph of the planar view of the laser glazed area is shown in Fig. 11 and cross-sectional view is shown in Fig. 12. The voids were dramatically reduced (from 30 vol.% to 1 vol.%) after laser glazing as observed in the unetched and etched sample (Figs. 12(a) and 12(b) respectively). In addition, segregation of solute atoms (Ag- and Zr-rich phases) was not observed at grain boundaries and uniform distribution of undis- solved phases was observed in the matrix (Fig. 12(b)). The average size of the second phases was about 1 gin. At low magnification, it was difficult to resolve the presence of voids in the matrix. Small voids were observed on examination in the SEM; these may be due to pull-out of Ag particles during polishing and etching (Fig. 12(c)). The volume fraction of voids was further reduced or eliminated by having two passes of the laser

42 3] Singh et aL/Surface and Coatings Technology 79 (1996) 35 49

28-Jui-1992 15:12:58

Q-II, PPT IN HATRIX

C u

t -

(a)

A9

I ,2 13 ,4 ,6 ,7 ,8

I n t e g r a l 0 i

ZS-Jul-1992 14:57:18

Q-II, FROM GRAIDI BOUHDQRY PPT

C U

A9

C u

27 I1 [2 I 3 14 I 5 16 17 18 [9

i - ~.~80 R a n g e = I0,230 key 9.958 -~ Integral 8 188185

(b)

Fig. 8. SEM-EDS spectra showing composition variation of Ag and Zr from three regions: (a) matrix precipitate from the region as marked by arrow 1, (b) grain boundary precipitate from the region as marked by arrow 2, and (c) matrix.

beam on the same area (Fig. 12(d)). There was no loss of any element from the laser glazed region as determined by the EPMA. The average composit ions of the VPS

coated substrate and the laser glazed region are shown in the form of a bar chart (along with the standard deviation) in Figs. 13 and 14 respectively. The standard

J. Singh et al./Surface and Coatings Technology 79 (1996) 35 49 43

28-Ju 1-1992 15"84:82

Q-f1, M~TRIX

Cu

Cu ~ u

J I 1 12 13 I 4 15 16 [ 7 18 19

4- 13.080 Range= 10.230 ke"¢' 113.110 -t' It~te~r'a 1 8 194914

(c)

deviation of the Ag and Zr in the laser glazed region was relatively small, indicating high solid solubility of alloying elements (especially Zr) in the matrix; this uniform Cu matrix contained only a small volume fraction of second phases. However, the standard devia- tion in the VPS area is significantly larger than in the laser glazed area, indicating a nonuniform matrix with more precipitation of second phases (Fig. 14). As men- tioned above, the VPS region contained voids, unmelted particles, grain boundary precipitation, etc., which result in the large standard deviation of Ag and Zr in the VPS coatings.

4.6. Model predictions

Eq. (1) is used to study the effects of various process parameters on the melt pool depth which is obtained by

Table 3 Key hole formation (focused beam)

Traverse speed Laser power Z' Glazed zone (gm) (in min-l(cm s 1)) (kW)

Depth Width

200 (8.4) 6 0 166 160 300 (12.7) 6 0 130 126 400 (16.9) 6 0 124 140

Z' = distance of the substrate from the focal plane.

Table 4 Glazed parameters (defocused beam)

Traverse speed Laser power Z ' Glazed zone (gm) (in rain l(cm s-i)) (kW)

Depth Width

25 (1.06) 6 1.0 90 370 20 (0.850) 6 1.0 96 376 15 (0.635) 6 1.0 96 360 15 (0.635) 6 1.3 96 366 15 (0.635) 6 1.6 150 490

Z' = distance of the substrate from the focal plane.

determining the location of the isotherm that corres- ponds to the T m of the substrate. It should be noted that the latent heat of fusion is not taken into account in the energy balance of this model, and due to this, the melt pool depth predicted by this model is higher than the experimental result. Since the NARloy-Z (Cu-3wt .%Ag-0.5wt .%Zr) alloy is mostly Cu, the thermophysical properties of this alloy are taken to be the same as those of Cu. The thermophysical data used in this study are given in Table 5. Figs. 15 and 16 show the comparison between the theoretical and experimental results, where the maximum melt pool depth refers to the vertical distance of the T m isotherm from the laser beam center located at the substrate surface. Both figures indicate that the model predicts the correct trend and

44 J. Singh et aL/Surface and Coatings Tec/mology 79 (1996) 35-49

From Intermetallic Phase Camebax-SX- Beam scanning

Vertical Linear scale SPI: 0 SP2: Ag SP3: Zr

w .

e

i

e 0

0

Max: 2082 Max: 2918 Max: 3756

Vertical scale: 140 counts/cm Vertical scale: 200 counts/cm Vertical scale: 250 counts/cm

0 2 Q

w

0

o B ~ ~ $ - ° ° ' ~ . ° t Q ' ~ o ° ° ° ° ° ° ° e ° ' ~ •

,= i=.o%

_ _

Zr

Beam Current: 14.96 nA High Voltage: 20.00 kV Counting Time: 10,000 mS

N , , / ' ' \ \

^d A

t / - I o I | I - | ! I I / \

I ..'-. . . . . . . | : . 't" - . . . . " " " " "

' Q O l i Q ~ IQq 'Q i

I - t :"--'. ... I 1 " '"

4

_l I I

I I I \

. . . - ,..., 1 " 7 , . . . . , . " ~ , ~ , . ~ , I . . . . I . . . . I . . . . I . . . . I . . . . t . . . . I . . . . I ' ' '

0 2 4 6 8 10 12 14 16 18 20

Distance (gin)

Fig. 9. Electron microprobe analysis across the grain boundary precipitates showing concentration gradient across the grain boundary Peaks representing segregation of solute atoms (Ag and Zr) in the form of oxide at the grain boundary.

U N E T C H E D . . . . E T C H E D

Fig. 10. Optical micrographs of the VPS coated sample which has been HIPed and vacuum annealed, still showing the existence of voids and grain boundary precipitation: (a) unetched, (b) etched.

J. Singh et aL/Surfitce and Coatings Technology 79 (1996) 35-49 45

Fig. 1l. Optical micrograph showing the tracks of the laser glazed regions (A and C) on the VPS coated region (B). The VPS region shows nonuniform microstructure (with voids, unmelted particles, grain boundary precipitates, etc.), whereas laser glazed region shows uniform microstructure.

L G S

• . V P S . , . . , - . . . . . '

(a) (b)

(e) (d)

Fig. 12. Optical and SEM micrographs of the cross-section of the laser glazed area showing the uniform distribution of second phases and the reduction in voids and cavities as a function of multiple laser beam passes: (a) low magnification, unetched surface; (b) low magnification, etched surface; (c) high magnification, negligible voids in matrix after single laser beam pass; (d) high magnification, uniform microstructure and elimination of voids after two laser beam passes.

46 J. Singh et al./Surface and Coatings Technology 79 (1996) 35 49

100,

A

-,..-, 10

0 . m

o " 1 o (3

• Concentration

[ ] Standard Deviation

Cu Ag Zr

Fig. 13. Bar chart of the average composition of each alloying element present in the VPS substrate along with their standard deviations.

100

t - O

O= l b .

C ~0 0 C O ¢.9

10

• Concentration

[] Standard Deviation

Cu Ag Zr

Fig. 14. Bar chart of the average composition of each alloying element present in the laser glazed area along with their standard deviations.

the model accuracy is within the range 10%-20%. Improved data on temperature dependent thermophysi- cal properties and incorporation of latent heat of fusion should improve the accuracy of the prediction. However, once the correct trend is established by the model, a few calibrating experiments can be made to optimize the process parameters and thus reduce expensive trial and error experiments for the determination of derived process parameters.

5. Summary

Laser glazing is a promising method to refine and improve the microstructure of the VPS coated NARloy-Z alloy. The VPS coated substrate microstruc- tural inhomogeneities such as unmelted powder particles, voids and cavities were eliminated by laser glazing. In addition to the refined microstructure, extended solid solubility of the Zr in the matrix was achieved. The

J. Singh et al./Surface and Coatings Technology 79 (1996) 35 49 47

Table 5 Thermophysical properties of NARloy-Z (Cu 3 wt.%Ag-0.5 wt.%Zr) substrate used in this study

Properties Values

Density (kg m -3) 8955 Thermal diffusivity (m 2 s 1) 0.934 x 10 -4 Melting temperature (K) 1356 Temperature (K) 296 373 473 573 673 k(T) 1 348.2 347.8 343.5 352.5 347.9

773 873 923 344.1 347.5 345.6

1 k(T) is the temperature dependent thermal conductivity (W m-1 K 1).

g e~

0 0

1.30

1.25

1.20

1.15

1.10

1.05

1 . 0 0

0.95

0.90 0.6

o Theoretical Results I • Experimental Results I

Laser Intensity = 190.99 kW/crn 2

~ T , I i t f , I , f i , I , i i I ] i i i f

0.7 0.8 0.9 1 1.1

Scan Rate (era/s)

Fig. 15. Comparison of experimental and theoretical results for laser glazed NARloy-Z at a fixed laser intensity.

o

1.30

1.25

1.20

1.15

1.10 -

1.05

1.00 "•

0.95 r r 187

, t i i i ~ J

o Theoretical Results I • Experimental Results

Scan Rate = 0.635 crrds

i , I r r r , I i s i i I u i r , I t I , I

188 189 190 191 192

Laser Intensity (kW/em ~)

Fig. 16. Comparison of experimental and theoretical results for laser glazed NARIoy-Z at a fixed scan rate.

mechanical properties of the laser glazed VPS coated NARloy-Z are expected to improve significantly. The mathematical model developed indicates the correct trends and, therefore, with the help of a few calibrating

experiments optimum process parameters can be established.

Acknowledgment

This work was made possible by a grant from NASA Marshall (Grant #NASA-NAG-8-934).

Appendix A: Nomenclature

a

A Cp(T) D

Fo h hi, h2

h3, h4

hs, h6

Hi

H k(T) k*(T*) L

P

~o to* ro

R S

aspect ratio, L/W absorptivity of the substrate heat capacity (J kg - t K - t ) transverse position of the center of the laser beam on the top surface of the substrate (m) nondimensional variable D/W Fourier number, Ig'c/L 2 heat transfer coefficient ( W m -2 K-1) heat transfer coefficient at x = 0 and x = L respectively heat transfer coefficient at y = 0 and y = W respectively heat transfer coefficient at z = 0 and z = H respectively nondimensional heat transfer coefficient at the ith surface thickness of substrate (m) thermal conductivity (W m - t K - l ) nondimensional thermal conductivity length of the substrate (m) slope of the log k(T) vs. T graph total power from laser (W) radial distance from the center of the laser beam on the top surface of the substrate (m) laser spot radius at 1/e 2 point (m) nondimensional variable, foiL radius of laser beam (m) reflectivity slenderness ratio, L/H

48 J. Singh et al./Surface and Coatings Technology 79 (1996) 35-49

t t* T T. Tm T'*

T* T*

L

T*

U

W X

X*

Y y*

Z

Z*

V

time variable 6) normalized time variable temperature (K) ambient temperature (K) substrate melting temperature (K) nondimensional temperature in Kirchoff's transformation nondimensional temperature field nondimensional ambient temperature nondimensional temperature for linearization by Taylor series expension temperature for linearization by Taylor series expansion (K) dimensionless initial temperature of the sub- strate translational speed of the substrate with respect to the laser beam (m s -~) width of the substrate (m) longitudinal position (m) normalized longitudinal position transversal position (m) normalized transversal position elevation (m) normalized elevation the three-dimensional Del operator (m -2)

Greek letters

K

p(T)

emissivity thermal diffusivity (m 2 s-1) density (kg m a) Stefan-Boltzmann constant (W m - 2 K - 4) laser-substrate interaction time (s)

Appendix B: Expressions for terms in Eq. 1

T'*(x*, y*, z*, t*)

= ~ KI~(X*) { ~ K,,r(y*) 1=0 Nix m=O Nmy

n=O

K.:(z*)q) × iOl t0 t e x p l - # o . t * l + -

"Fiv(21x, "~my, Z*, t* ) = flm( t* )(ZoZ* + 1)/A z

A~ = Zo( 1 - Zn) - Zn

ftm(t*) is the source integral which is given by

flm(t*)=folfo~dX*dyKl~(X*)Kmy(y*)p *

x exp(- r*~)(x *, '* y , t*)

2PAH p* -= rcL2r.2k(Tm)Tm

r*~ = r~- (x* - r* - + (y* - D*) 2

01(0)=TI sin 2,: + - - ( 1 - cos 2..) t~nz

[ O,lcOS l )] T~ = T~ sin .)qx -~-

x s in2mr+~(1- -COS2my)

T *°+1 -- 1 TI= T~+

c7+1

1 - ~ , . + 1 ~ T~ = T*o (T* - T* + (~+ 1-~,~ j

IP2(t* ) = @ l ( t * ) - - O ( t * )

(J~(t*) = exp(-22,.,t *) Fo s22.z~O(f *)

x exp(2~, f*) dr* - O(t*)

O ( t * ) - f l ~ ( t * ) I Z ° J A~ ~ ( 1 - cos £.:) + sin 2.:

I cos)...) ZoJi.,(t* ) (sin 2.z + ~ . Zo ~ U

[cos 2,: - 1 sin 2,_ +

2~2 2-2 +s,~._) 22. = Fo(2~:, + a Zmy

The kernels Klx(X*), Kmy(y*), and K.=(z*), the character- istic equations for the eigenvalues £1x, 2,.y, and 2.z, and the normalization constants Nix, Nmy, and N.z for the finite Fourier integral transform are defined as follows.

For the x-direction

Klx(X* ) = X o sin(21~x*) + ,i1~ COS(21xX*)

;~(Xo - X~) tan )~1~ = 2~ + XoXL

1 x ~

J. Singh et al./Surface and Coatings Technology 79 (1996) 35 49 49

For the y-direction

Kmy(y*) = Yo sin(2myy*) + 2my cos(2myy*)

,L~(ro- Yw) tan Amy -- 2

2my "~ YoYw

N m y = ~ Ilo+(22~y+Y2) 1 ,2 'troy + Y

For the z-direction

K,~(z*) = Zo sin(2,~z*) + 2,~ cos(2,~z*)

~ n z ( Z o - ZH) tan 2,z = 22: + ZoZH

~2--- 2 N.~ = Z o + G L + z 2) 1

H I L H 2 L

Xo- k(Tm)7~,q XL- k(Tm)~.q

H 3 W H 4 W I1o- k(Tm)~,.r~ Yw = -- k(Tm)~,.q

H5 H H 6 H Z o - k(Tm)~,. ~ Z n - k(Tm)~.0

The effective heat transfer coefficient Hi at the boundary surface of the substrate is given by

,2 --, Hi = hi + aeT[(T*2,..--a ." T a )(T a + T*)

where i = 1, 2, 3, 4, 5 and 6 which denote the x = 0 , x = L, y = 0, y = W, z = 0 and z = H planes respectively.

x* = x / L y* = y / W z* = z / H t* = t/z

where z = L / U

T* = T I T m T* = T,~/T m T* =- Ta/T m

T~ is the dimensional temperature a round which T 4 (see the boundary conditions in Section 3) is expanded in Taylor series to linearize them in order to apply integral transform. In the present study, 7", is taken to be equal to Tm because the laser irradiated spot is expected to be at about the melting temperature during laser glazing.

References

[-1] J. Singh, J. Met. September (1992) 8. [2] F.H. Stott, P.K.N. Bartlett and G.C. Wood, Oxid. Met. 112(27)

(1987) 37. [3] N. Iwamoto, Surf. Coat. Technol., 34 (1988) 59. [-4] N. Iwamoto, N, Umesaki, Y. Katayama and H. Kuroki, Surf.

Coat. Technol., 34 (1988) 59. [5] A. Ohmori and K. Kamada, Trans. Jpn. Weld. Res. Inst., 20

(1991) 26. [-6] E.M. Breinan and B.H. Kear, Proc. Conf. on Rapid Solidification

Processing, Reston, VA, Claitor, Baton Rouge, LA, 1978, p. 87. [7] E.M. Breinan and B.H. Kear, in M. Bass (ed.), Laser Materials

Processing, North-Holland, Amsterdam, 1983, pp. 237-294. [-8] A. Kar and J. Mazumder, Three-dimensional transient thermal

analysis for laser chemical vapor deposition of uniformly moving finite slabs, J. Appl. Phys., 65 (1989) 2923 2934.