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Retrospective Theses and Dissertations

1998

Laser welding of sheet metals Laser welding of sheet metals

Jian Xie University of Central Florida, jian43026@yahoo.com

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LASER WELDING OF SHEET METALS

by

TIAN XIE B.S. Xi'an Jiaotong University, China, 1983 M.S. Xi'an Jiaotong University, China, 1988

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy

in the Department of Mechanical, Materials and Aerospace Engineering in the College of Engineering and

Center for Research and Education in Optics and Lasers (CREOL) at the University of Central Florida

Orlando, Florida

Spring Term 1998

Major Professor: Aravinda Kar

ABSTRACT

LASER WELDING OF SHEET METALS

Laser welding of sheet metals is an important application of high power lasers,

and has many advantages over conventional welding techniques. Laser welding has a great

potential to replace other welding technique in the car-body manufacturing because of

high laser weld quality and relatively low manufacturing cost associated with the laser

technique. However, a few problems related to the laser welding of sheet metals limit its

applications in industries. To have a better understanding of the welding process, laser

welding experimental studies and theoretical analysis are necessary.

Temperature-dependent absorptivities of various metals are obtained theoretically

for CO2, COIL (Chemical Oxygen-Iodine Laser) and Nd:YAG lasers. It is found that the

absorptivities for COIL and Nd:YAG lasers are 2.84 and 3.16 times higher than for the

CO2 laser, and the absorptivity increases with increasing temperature of the metals.

Surface roughness and oxide films can enhance the absorption significantly. The

reflectivity of as-received steel sheets decreases from 65-80% to 30-40% with surface

oxide films for CO2 lasers. Laser welding experiments show that the tensile strengths of

the weld metals are higher than the base metals. For samples with surface oxide films, the

oxygen concentration in the weld metals is found to be higher than in the specimens

without oxidation, and the toughness of the weld metals is degraded. This new technique

improves the utilization of laser energy with minimal reduction in the weld toughness.

When steel powders are added to bridge the gap between two sheets, the oxygen content

in the weld metals decreases and the toughness increases. Another contribution of this

experiment is a technique for the tensile test of small weldments by introducing notches at

the edges ofweldments.

A mathematical model is developed for the melt depth due to a stationary laser

beam. The model results show that the melt depth increases rapidly with time at the

beginning of laser irradiation and then increases slowly. Also, the melt depth is found to

increase rapidly with laser intensities and then increases slowly for higher intensity. The

average rate of melting and the times to reach the melting and boiling temperatures at the

substrate surface are obtained by using the model. Another mathematical model is

developed for the weld width and weld pool shape due to a moving Gaussian laser beam.

The model predictions compare well with experimental results.

DEDICATION

TO

My parents

Shuxian Xie and Jiquan Lan

For their love, understanding, encouragement and support.

iv

ACKNOWLEDGMENTS

I would like to acknowledge my advisor, Dr. Aravinda Kar, for his support

and guidance throughout my doctoral studies. His encouragement, helpful suggestions

and countless discussions have made this work possible. I have enjoyed working with

him and his deep understanding and wide knowledge have broadened my intellectual

ability in the field of laser materials processing.

I would also like to thank my committee members, Dr. Vimal Desai,

Dr. Antonio Minardi, Dr. Michael Bass and Dr. Lee Chow, for their helpful

comments about my dissertation. My appreciation is extended to other students in

the laser materials processing group at CREOL, for their assistance and useful

discussion. Finally, I wish to thank my wife, Baolan Sun, for her countless support

and understanding.

V

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................... X

LIST OF FIGURES .......................................................................................................... XI

LIST OF SYMBOLS ........................................................................................................ xiv

CHAPTER 1 INTRODUCTION ............................•......................................................... 1 1.1 Laser Welding . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . .. . . . . . . . . . .. . 1 1.2 Physical Proce,ss of Laser Conduction Welding .............................................. 4 1.3 Laser Welding of Steel Sheets in Automobile Bodies ...................................... 7 1.4 Problems in Laser Welding of Sheet Metals .................................................... I 0

1.4.1 High Reflection of Laser Beam by Sheet Metals .............................. 11 1.4.2 Precision Fit-up of Metals Sheets .................................................... 11 1.4.3 Optimization of Process Parameter .................................................. 12 1.4.4 Process Control and Weld Quality Monitoring . ..... .. .. ... . ... .. .. .. ..... ... . 13 1.4.5 Laser Weldability of Sheet Metals .................................................... 14

1.5 Objectives ......................................................................................................... 14

CHAPTER 2 LITERATURE REVIEW ............................................................................ 16 2.1 Absorption of Laser Energy by Sheet Metals ............... ... .... ......... .... .............. I 6 2.2 Laser Welding of Sheets Metals ...... ...... ... ... ...... ...... ...... .. .... ..... .. ... ... .. .. ........... 23

2.2.1 Welding Process Parameter ........................ ....................................... 24 2.2.2 Laser Welding with Filler Materials ......... ...... ............ ............ .. ... ... .. 27 2.2.3 Welding Process Monitoring ............................................................ 31 2.2.4 Laser Weldability of Materials ......................................................... 34

2.3 Mathematical Modeling of Laser Welding ....................................................... 37

CHAPTER 3 ABSORPTION OF LASER ENERGY ...................................................... 43 3.1 Temperature-dependent Absorptivity of Polished Metals ............................. 43

3.1.1 Absorptivity of CO2, COIL (Chemical Oxygen-Iodine Laser) and Nd:YAG lasers ............................................................................ 45

3.1.2 Absorptivity of CO2 for Copper ....................................................... 56 3.2 Reflectivity of Cold-rolled Sheet Metals.......................................................... 59

vi

3.2.1 Experimental Set-up for Reflectivity Measurement ........................... 60 3.2.2 Reflectivity of Sheet Metals ............................................................... 62 3.2.3 Roughness .......................................................................................... 63 3.2.4 Oxide Films and Powder Layer .......................................................... 65

CHAPTER 4 LASER WELDING OF STEEL SHEETS .................................................... 69 4.1 Materials and Laser Welding Experiments ........................................................ 69

4.1.1 Steel Sheets ......................................................................................... 69 4.1.2 Filler Powders ... ..................................................... ....... ... .... .. .. ..... .. .... 71 4.1.3 Laser Welding Conditions .................................................................. 73

4.2 Microstructure of the Weld and Base Metals ................................................... 74 4.2.1 Microstructure of the Base Metals .................................................... 74 4.2.2 Macrostructure of the Weldments ...................................................... 76 4.2.3 Microstructure of the Heat-Affected Zone (HAZ) ............................ 76

4.3 Properties of the Weld and Base Metals ........................................................... 81 4.3.1 Oxygen Content in the Weld Metals .................................................. 81 4.3.2 Tensile Strength of the Base and Weld Metals ................................... 83 4.3.3 Toughness of the Base and Weld Metals ............................................ 86

CHAPTER 5 MATHEMATICAL MODELING OF WELD DEPTH ............................ 90 5.1 Mathematical Model ......................................................................................... 92 5 .2 Method of Solution ......................................................................................... '.. 93 5.3 Results and Discussion ..................................................................................... 96

5 .3 .1 Laser Melting Process ................................................................. ... ... 96 5.3.2 Effect of Laser Power Density on the Melt Depth.......................... 102 5.3.3 Melting and Vaporizing Time........................................................... 111

CHAPTER 6 MATHEMATICAL MODELING OF WELD POOL ............................. 113 6.1 Mathematical Model ....................................................................................... 113 6.2 Method of Solution .. ..... ..... ... .. .................................................................. ........ 115 6.3 Results and Discussion . . .. .. . .. . . . ... ... ... .. . .. . .. .. . . ... .. . .. .. . .. .. . .. .. ... .. . .. .. .. .. ..... ............. 121

6.3.1 Coefficients Ki' and Ki' .................................................................... 122 6.3.2 Weld Pool Shape ................................................................................ 125 6.3.3 Weld Width ........................................................................................ 130 6.3.4 Comparison between the Exact and Approximate Solution .............. 132

CHAPTER 7 CONCLUSIONS .......................................................................................... 136

CHAPTER 8 FUTURE WORK ......................................................................................... 139

Vil

REFERENCES .................................................................................................................... 142

VITA ................................................................................................................................... 157

viii

Table 2.1

Table 2.2

Table 3.1

Table 3.2

Table 3.3

Table 4.1

Table 4.2

Table 4.3

Table 5.1

Table 5.2

Table 6.1

Table 6.2

LIST OF TABLES

Experimental and theoretical values of absorptivity at 10.6 µm ................ 19

Experimental and theoretical values of absorptivity at 1.06 µm ................ 19

Variation of resistivity with temperature, Pnrla8(a+b1), Q-m .............. 46

Absorptivity of metals at room temperature and melting temperatures............................................................................. 47

Reflectivity of as-received cold-rolled sheet metals ................................... 62

Typical chemical composition of AISI 1010 steels ................................... 70

Chemical compositions of A WS classification solid wires for mild steels .. ... . . . . . . . .. . . . . . . . . . . .. .. . .. ... . . . . . . .. .. . . . . . . ... . . .. . . . .. . . . . . . . . . . . . . . . . . . . . . . 72

Chemical compositions of filler powders (wt%,)...................................... 73

Thermophysical properties of metals ........ .. .. .. .. ... ...... ............. .... .... .. ...... .. 97

Times to melt and vaporize at different power densities . ... .......... ............. 112

Variation of coefficients K; and K; with Peclet number P, ....................... 123

Weld width and laser welding conditions................................................... 132

IX

LIST OF FIGURES

Figure I. 1 Fraction of industrial lasers used in automotive industry [Roessler (1996)] ....................................................................... 3

Figure 1.2 General arrangement for laser welding .............................. ....................... 5

Figure 3.1 Absorptivity of CO2, COIL and YAG lasers for aluminum .................... 49

Figure 3.2 Absorptivity of CO2, COIL and YAG lasers for copper ........................ 50

Figure 3.3 Absorptivity of CO2, COIL and YAG lasers for carbon steel................ 51

Figure 3.4 Absorptivity of CO2, COIL and YAG lasers for stainless steels below melting point .................... ........ .......................................... 52

Figure 3.5 Absorptivity of CO2, COIL and YAG l!isers for iron............................. 53

Figure 3.6 Absorptivity of CO2, COIL and YAG lasers for titanium ...................... 54

Figure 3. 7 Temperature-dependent absorptivity of CO2 laser for copper ............... 58

Figure 3.8 Experimental set-up for the measuring of reflectivity of metals .............. 6 I

Figure 3.9 Effect of roughness on the reflectivity for copper and aluminum ............ 64

Figure 3.10 The effect of surface oxidation and steel powder on

Figure 4.1

Figure4.2

reflectivity of steel sheets .......................... ............................ ................... 67

Microstructure of AISI 1010 cold-rolled steel sheets, x500 ..................... 75

Microstructure of the weld for the sample with surface oxide films, x I 00 .. .. .. .. .. .. .... .. .. .. .. .. .... .. .... .. .. .. .. .. .. .. .. .. ...... .. .. .. .... .... .. .. .. .. .. .. . 77

X

Figure 4.3 Laser weldment of cold-rolled steel sheets . ...... ............. .......................... 78

Figure 4.4 Grain-refining region in HAZ, x500 ................... ....................... ............... 79

Figure 4.5 Grain-coarsening region in HAZ, x500 ......................... ...... ...................... 80

Figure 4.6 Specimen size for tensile test ..................................................................... 81

Figure 4. 7 Relative oxygen atomic concentration in the base and weld metals .... .... .... 82

Figure 4.8 Typical stress-strain curves for the base and weld metals ........................... 84

Figure 4.9 Ultimate strength of the base and weld metals ............................................ 85

Figure 4.10 Toughness of the base and weld metals ....................................................... 87

Figure 5.1 A semi-infinite slab of!aser irradiation ........................................................ 91

Figure 5.2 Variation of melt depth with laser irradiation time for fused quartz ............ 99

Figure 5.3 Variation of melt depth with laser irradiation time for metals ...................... 100

Figure 5.4 Dynamics of melt depth oflaser irradiation ................................................. 101

Figure 5.5 Variation of melt depth with laser power density·······························:········ 103

Figure 5.6 Variation of melt depth with laser irradiation time for 304 stainless steel ... ................... ...... .. ..... .. ..... ..... ..... .. ... .. ... ......... .... .. ... .. . 106

Figure 5.7 Variation of melt depth with laser irradiation time

Figure 5.8

Figure 6.1

Figure 6.2

for copper and NAR!oy-Z ........................................................................... 107

Variation of melt depth with heat input for copper and stainless steel based on Rosenthal's model, where thermophysical properties of liquid phase are used .... .. ... ........................ ........................... .. 110

A laser beam irradiates on surface of steel sheets to form a weld pool ........ 114

Variation of coefficients K1 • and K/ with Peclet number Pe ....................... 124

xi

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

A laser weld pool after solidification, 40x .................................................... 126

Three-dimensional view of the temperature distribution (T1(x1,y1)) in laser conduction welding of AISI 5130 steels (A=35%, P=!.25 kW, d=0.2 mm, r0=0.31 mm) ........................................... 128

Weld pool shape under the irradiation of a Gaussian laser beam ................. 129

Typical laser weld surface, lO0x .................................................................. 131

Variation of weld width with welding speed ................................................ 133

Error in the approximate temperature compared to the exact temperature

at various location. Y1 is taken equal to x1 for this comparison .................... 135

xii

A

Ac1

Ac3 a b C

Cp

Cp,

Do d E; I Io Jo k Ko x; x; L n p

P, Q r ro T To Ti t fo

V

Vo

V

LIST OF SYMBOLS

Absorptivity, % Ferrite phase transform temperature Austenite phase transform temperature Constant Constant Constant Specific heat, J/kgK Effectjve specifi<; heat, cp,=c.A+,L,,/J'm, J/kgK Diameter of laser beam, m

I • I • • • ~·-•L • Spe_et thickness, in ful\ penetration welding, mm

!, I • l Exponential mtegral taser h1te~ity,'W/m2

Modified Bessel' function of the first kind and zero order Bessel function of the first kind and zero order Thermal Conductivity, W/mK or index of extinction coefficient Modified Bessel function of the second kind and zero order Coefficient

Coe,fficient Latent heat, J/kg Index of refraction coefficient, Laser power, W

Peclet number, P,=vrr/a Power of heat sources, W Radius, m Radius ofl1:!5er beams, m Temperature, K Room temperature, K Dimensionless temperature Laser-materials interaction time, s Laser-materials interaction time, s Scanning speed, mis Welding speed, mis Average melting velocity, mis

XIII

w Whittaker function X Coordinate axis XJ Dimensionless coordinate axis X(t) Melting depth, m y Coordinate axis

Y1 Dimensionless coordinate axis z Coordinate axis Zmax Maximum melting depth, m

Greek symbols

a eo Tl q>

A,

A-1 A-2 µ,.

e p (J'

Vo

m

~

Subscripts

b l m

s V

Thermal diffusivity, m2/s

Permittivity of free space, eo=l/(36m<Irf), Flm

Variable in s -11 cartbsian coordinate

Variable ip p-cp coordinate ' Wavelength oflight, µm

Variably in Fouri~r transfi;>rm

Variable in Fourier transform

Relative permeability

Variable in r-0 cylindrical coordinator

....

Mass density, kg/m3 or variable in p-cp coordinate

DC resistivity of materials, Q-m

Speed of light, mis

Angular frequency of monochromatic radiation, m=2mv').

Variable in s-11 Cartesian coordinate

Boiling point Liquid state Melting point Solid state Vaporization point

xiv

CHAPTER I

INTRODUCTION

I. I Laser Welding

Laser welding is a joining process that produces coalescence of materials with

the heat generated by a laser beam. Laser beams can be focused to a small spot leading

to high energy density. The intensity generated by lasers is greater than I 06 W /cm2

for welding purpose, while the intensity of arc and oxyacety Jene welding are about

5x102-104 W/cm2 and 102-103 W/cm2, respectively [Metzbower (1983) and

Mazumder (1993)]. Numerous experiments have shown that laser permits precision

and high quality weld joints rivaled only by electron beam welding in a vacuum

environment. Compared to the conventional welding processes, laser welding offers

the following advantages:

• High welding speed.

• Less distortion and small heat-affected zone (HAZ).

• High weld depth/width.

• Low heat input.

• Rapid start and stop because lasers are inertialess.

• Joining of some difficult-to-weld materials.

• Used in room atmosphere.

• Good mechanical properties.

• Precision welding.

Therefore, the high power lasers have been widely used in industries such as

automotive, consumer products, aerospace, and electronics industries to join a variety

of materials. Automotive industry, as the biggest user of industrial lasers, takes 30%

of the market share [Irving (1992)] in which more lasers are used for welding purpose

in North America as shown in Fig. I.I [Roessler (1996)]. More production lines are

being added for welded transmissions, mufflers and many other products. One of the

biggest application is tailor-welded blanks in which about 15 million laser welded­

blanks were expected to be produced in 1997 for the automotive industry and the

number will increase to 40 to 60 million by the year 2000 [Irving (1997)]. There is

little doubt that lasers will play a significant role in automotive manufacturing

[Roessler and Uddin (1996)].

Basically, there are two kinds of laser welding modes: deep penetration and

conduction welding. Deep penetration welding is also called "keyhole" welding

because a hole is generated by evaporation of materials due to the sufficient intensity

oflaser beams [Arata (1987)]. This hole is stabilized by a balance of pressures due to

vapor, surface tension and gravity, and the aspect ratio of keyhole is about 10:1. The

2

60

~

,I?. 0 ~

E 50 gj

....l

l I I 1 ■ North America

40 Ill Europe

.s 'E IS 30 .2 .; ,!,! "S. 0.

< 20 ..... 0

" ·fl f! "" 10

0 Cut Weld Mark Drill Other

Fig. I.I Fraction of industrial lasers used in automotive industry [Roessler (1996)]

3

Laser beatn

"tif~·

Workpiece

X-Y stage

Focusing lens

":cs-Shielding gas inlet r---

Fig. 1.2 General arrangement for laser welding

5

I is absorbed and a part is reflected by the surface of the workpiece. Since metals and

many materials are opaque, there is no transmission of the laser beam through the

I

workpiece. Absorptivity, deyined as a ratio of absorbed laser energy divided by the I I

incident laser energy, depends on materials properties, surface conditions, laser

wavelength and the incident angle of the laser beam. In conduction welding, the

multiple-reflection effect of the laser keyhole welding does not exist and therefore, the

absorptivity is not expected to be as high as in the keyhole welding.

The absorbed laser energy is distributed by conduction in the workpiece. This

occurs rapidly over the entire thickness of the workpiece for thin materials, so that

the temperature can be considered uniform in the direction of thickness. The materials

are melted by the absorbed laser heat to form a weld pool and then the molten metals

solidify as a weld after the laser beam moves away. The weld pool has a strong

stirring force driven by Marangoni convection resulting from the variation in surface

tension with temperature. The use of shielding gases is important to protect from

oxidation of molten metals, and the gases could be coaxial with the laser beams or

provided by a side nozzle. The most popular shielding gases are argon and helium,

but use of mixed gases and CO2 as shielding gas have been reported [Abbott and

Albright (1994)].

In laser conduction welding, a few process parameters affect the weld quality.

The primary process parameters include:

6

• Laser and optics: wavelength, power, beam spot size, mode, continuous

wave or pulsed, polarization, focal position, focal length;

• Workpiece: chemical composition, physical properties, thickness, surface

condition;

• Shielding gas: composition, flow rate, pressure, nozzle size and position;

• Welding characteristics: welding speed, joint geometries, gap tolerance.

Laser conduction welding is widely used as a precision joining technology in

many industries such as electronic;;, aerospace and medical facilities. One of the most

important applications of,liiser thin materials welding is for car-body steel sheets.

Most of the car-body sheets used now are low -carbon steels because of its excellent

weldability and formability. To reduce the car weight according to the federal

requirements for fuel economy and e.missions, the thinner gauge high-strength low­

alloy steel sheets will be used in the future [Ashley (1997)]. Actually, the welding of

thin steel sheets is a major job in car-body shops. Since laser :welding has great

potential to replace the current welding techniques in the car-body shops, more

studies on laser conductio.n welding are expected in the near future.

1.3 Laser Welding of Steel Sheets in Automobile Bodies

Despite attempts to find -efficient alternatives, sheet steel is still the material

of choice for car-body structures today and for the foreseeable future because it is the

7

most cost-effective material for car-body [Ashley (1997)]. Typical automobile bodies

contain 1000-4000 resistance spot welds along 40 m of pinch weld flanges and this

welding process employs about 250-300 robots in a modern plant. The laser offers

potential advantages and unique opportunities to improve structural properties and

weld consistency, while reducing weight and costs at the same time. Reducing the

width of pinch weld flanges, for example, could eliminate up to 50 kg of metal­

[DePietro (1989)]. The high welding speeds obtainable with lasers, typically 5

m/min. or more in full penetration lap welds of body sheet metal with a few kilowatts

of laser power~ indicate that one· laset welder can replace several resistance welders

[Roessler (1996)]. Further study shows a 3 kW robotic laser welding at 200 in/min

can replace four resistance welding robots [Keller (1994)]. The benefit of both CO2

and Nd:YAG lasers for welding in the body shop was evaluated by General Motor

[Roessler and-Uddin (1996)]. The overall conclusion was that CO2 laser body shop

would cost about 80% of the traditional shop, while a Nd:YAG laser body shop could

cost less than 70%.

Other benefits include smaller heat-affected zones and less thermal dis(ortion,

single-sided access and good design flexibility. Stretch formability was decreased with

laser welding by 10 to 18% when compared to the base steel, while resistance mash

seam welding decreased it by 29-35%, depending on steel grade, thickness and width

[Baron (1994) and Hallum (1993)]. Fatigue life performance of laser welds was

8

increased by 36 to 126% over resistance welds and the tensile strength increased in

the range of 34-113% [Irving (1994)]. Also, laser welding is several times, even ten

times, faster than the best that can be done with robotic spot welding [Irving (1995)].

The inconsistency in strength of spot welds, which is one of the biggest problem and

has been really brought to the attention of industry, can be avoided by laser welding.

The consistency and integrity of the laser weld permitted extensive nondestructive

weld evaluations (via electrical resistivity) and reduced the amount of destructive

testing needed.

Although laser welding was successfully implemented as an alternative to

resistance spot welding, it still represents only a small fraction of over one million spot

welds that are being made every day in US automotive industry. The above advantages

are often offset by the particular problems posed by body sheet metal, such as poor fit­

up or high reflection of the laser beam by the sheet surface. "Lasers are not used in Ford

Motor Co. for body welding because a laser welder becomes a laser cutter, with a little

bit of gap between the sheet metal", said James Hilligoss, chief engineer, stamping and

structures of Ford Motor's Body and Assembly Operations Eirving (1994A)]. A highly

qualified expert queried about this situation of laser welding in US automotive industry

not being as popular as in other countries [Irving (1992)): what happened? Is it the high

initial.cost of the equipment? Is it the perceived fit-up problem? Is it just an awareness

9

I

j,

problem? Is laser welding just another example of a high-tech process that was invented,

but not applied extensively, in the US?

Although some work on laser welding of sheet steels has been done by

researchers and engineers, obviously, this work is insufficient and better

understanding of the process is necessary. Recently, a multi-million dollar research

project was granted to the Precision Lasei: Machining (PLM) center, which has 25

member companies including GE, Ford, GM, Chrysler, Boeing, Caterpillar etc. and led

by TRW Inc., and funded by the Defense Advanced Research Projects Agency

(DARPA) in Washington [Irving (1997)]. In Europe, three automobile manufacturers,

Volvo, BMW, and Rover announced to fund a collaborative program to investigate

high-speed precision welding of sheet-metal car-body panels with support of

$620,000 [Laser Focus World (1996)]. The investigation will be carried out in the

Center for Advanced Joining at Coventry University, Coventry, England, with a 1.2-

kW CO2 and a 2-kW Nd: Y AG laser.

1.4 Problems in Laser Welding of Sheet Metals

As we know, although there are significant potential benefits to be gained in

place of resistance spot welding in automotive body shop, relatively few applications

take advantage oflaser sheet metal welding because there are some problems in

practice to be solved by engineers and scientists. Further applications are limited by

10

these problems and the economy and good quality of the techniques are not realized in

industry. The major problems existed in industrial applications of laser welding of

sheet metals are discussed below.

1.4.1 High Reflection of Laser Beam by Sheet Metals

Most sheet metals are cold-rolled at room temperature, so that the metal

surface is very smooth and there is no oxide film pn it. Laser welding of thin sheets is

a conduction mode welding and there is no multiple-reflection effect as in keyhole

welding. Therefore, the absorptivity of sheet metals is close to polished metals which

is dependent on optical properties of materials and is quite low at room temperature

[Steen (1991)). The high reflection oflaser beams may cause many problems in

production such as damaging other equipment, hurting humans and wasting laser

energy. The use of higher power lasers due to the high reflection will increase the

initial capital cost which is expensive and usually considered as one of the biggest

obstacles to the applications of high power lasers. Unfortunately, this problem has

not brought more attention to people and this may be caused by relative few

applications oflaser welding of metal sheets in industry.

11

1.4.2 Precision Fit-up of Metal Sheets

The maximum acceptable fit-up tolerance in butt joint, usually stated to be

10% of materials thickness, is quite difficult to reach even with machining and good

fixture if the materials thickness is thin or any dimension of the product is more than

about 0.5 m [Salminen and Kujanpiiii (1995)]. In 1974, United Technologies Corp.

delivered a 6-kW CO2 laser to the Ford Motor for underbody welding and the

equipment never went into production because of the fit-up problems experienced

[Irving (1992)]. The persisting problem of poor fitup makes the fixturing and

clamping more extensive and expensive [Roessler and Uddin (1996)]. There is a trend

of adding filler materials to bridge the gap -caused by poor fitup instead of complicated

and expensive fixtures. However, few industrial applications of the technique have

been reported.

1.4.3 Optimization of Process Parameters

Although our knowledge of laser welding has increased and the process has

been applied in industry, we expect more effective use of lasers. Better understanding

of laser-materials interaction and optimized process parameters are important for this

purpose. We still need to learn more about the effects of process parameters such as

the utilization of!aser energy, effect of shielding gases and laser beam shape and

mode. The laser-materials interaction in laser conduction welding is basically a

12

physical process of energy absorption and materials melting, but it is difficult to

observe the melting process experimentally. Some techniques, such as X-ray

transmission in-situ imaging devices and high speed infrared cameras, have been used

to investigate the process, but the knowledge in this area is still limited. An

alternative technique is mathematical modeling of the process which can provide

information on real-time laser-materials interaction and the effects of the process

parameters. The modeling also provides a basis for real-time adaptive process

control.

1.4.4 Process Control and Weld Quality Monitoring

In practice, the sheet metals are punched and formed to special shapes in a die

to meet the requirements of products. In many cases, the sheet edges to be welded are

neither flat nor straight and also there is a size tolerance. It is necessary to have seam

tracking and stand-off height control devices for laser welding process. In addition,

the real-time quality control is also one of the most important aspects in laser welding

to obtain consistent and good welds. An easy way for quality monitoring is to record

primary parameters such as laser power, scanning speed and shielding gas flow and

ensure that these parameters lie within the quality window. Some attempts have also

been made to monitor the laser weld quality based on the secondary signals from the

welding area. The secondary signals include acoustic emission [Gu and Duley

13

(1996A,B, 1997)], plasma emission [Sanders and Leong (1997)], pool oscillation

frequency (Semak, Hopkins and McCay (1997)] and optical emission of the metal

vapor [Beersiek and Poprawe (1997)]. Most of these teclmiques are available only in

the laboratory, and few are put into industrial production.

1.4.5 Laser Weldability of Sheet Metals

Most metals used in auto body are mild steels which have excellent

weldability, but the use of zinc-coated and high-strength low-alloy or high carbon

steels make the laseF weldability worse. The galvanized coatings lead to high porosity

in the weld, especially in the case of lap weld. For alloy or high carbon steels, rapid

changes in temperature induced by laser irradiation will produce hot and cold cracking

and also lead to hard and brittle weld metals.

1.5 Objectives

Generally speaking, laser welding has a great potential to replace conventional

welding processes in industry because of high weld quality and low manufacturing

cost. It is predicated that laser technology will eventually engulf the world of

manufacturing (Irving (1992)].

There are some obstacles in applying the technology and these problems have

been brought to the attention of both scientists and engineers worldwide. The

14

objective of this study is to address some of these problems through laser welding

experimental studies and theoretical analysis. This research includes the following

studies:

• Analysis of theoretical values of temperature-dependent absorptivity;

• Measurement of reflectivity for various sheet metals;

• Investigation of the influence of surface conditions on reflectivity;

• Laser welding of steel sheets with and without surface oxide fihns;

• Laser welding for workpi~ceg with poor fitup by adding filler powder;

• Comparison of physical properties and chemical compositions of the

weldment;

• Mathematical modeling of melt depth in laser conduction welding;

• Mathematical modeling of the weld pool shape in laser conduction

welding.

15

' I

I

I I

II I

. I

CHAPTER2

LITERATURE REVIEW

2.1 Absorption of Laser Energy by Sheet Metals

The efficiency of laser conduction welding depends on the absorption of laser

energy by the workpieces: Only a portion of the laser energy which is absorbed by

the workpieces is utilized for welding, so that absorptivity is one of the most

important parameters in laser conduction welding. However, high absorptivity

achieved in keyhole welding caused by multiple-reflection inside the keyhole is not

expected in laser conduction welding because of the thin sheet metals. Laser welding

experiments of 304 stainless steels showed that the laser energy transfer efficiencies

varied from 0.29 to 0.86 at different penetration depths and decreased significantly at

high travel speeds where the weld penetration depth was as shallow as 0.13 mm

[Fuerschbach and MacCallum O 995)]. :Yhe keyhole welding mode is changed to

conduction mode when welding speed is high. Therefore, the absorption in laser

conduction welding is based on the Fresnel absorption of materials described by the

Drude theory. The absorptivity of metals is very low for CO2 laser irradiation

according to the Drude theory [Steen (1991)]. In the case of highly polished gold, the

16

absorptivity is less than 1 % and it can be used as a reflecting surface film deposited

on the mirror in CO2 laser systems [Arata and Miyamato (1972)).

The absorptivity of metals as estimated based on the Drude theory and the

theoretical results showed that the absorptivity of metals was quite low. Ujihara

(1972) has modified the Drude theory to incorporate a temperature-dependent

absorptivity by taking an average over the photon frequency spectrum and he was

successful in predicting the absorptivity for Cu at 1.06 µm. Weiting and Schriempf

(1976) found that the absorptivity at 10.6 µm for 304 stainless steel and Ti-6Al-4V

alloy were well predicted by such a modified Drude theory. Despite the availability

of Drude theory and the Drude formalism, the best way to obtain the absorptivity of

a metal surface for laser irradiation is to measure it experimentally [Duley (1985)).

In a case of cw CO2 laser, Duley (1985) measured the absorptivity of some

metals and Mineta et al. (1983) presented the experimental values of absorptivity of

carbon and stainless steels at room temperature. Walters et al. (1981) reported their

experimental results for the absorptivity of polished pure iron for the long and short

TEA CO2 laser pulses, respectively. Khan and Debray (1985) showed that the value

of AISI 4340 steels was about 16% under the CO2 pulsed laser irradiation. Chan et al.

( 1977) obtained the reflectivity of copper and aluminum under Ruby laser irradiation

at the wavelength of 0.69 µm. The reflectivity of copper was also obtained

based on the experimental values of optical constants over the temperature range 77-

17

I! r ' I I

920 °c in ultra-high vacuum (10-9 Torr) [Pelis and Shiga (1969)]. A summary of the

absorptivities of various metals for cw CO2.and Nd: YAG lasers is given in Tables 2.1

and 2.2, respectively.

In Table 2.1, the theoretical values exhibit a good agreement with experimental

results for most metals at room and elevated temperatures. For Nd:YAG laser, the

absorptivity for various metals listed in Table 2.2 is higher than that for CO2 laser.

The absorptivity of metals increases at shorter wavelength because the more energetic

photons can be absorbed by a greater number of bound electrons [Steen (1992)].

The absorptivityis str;n:giy affected by the temperature of the workpiece and

increases with increasing temperature as shown in Tables 2.1 and 2.2. Konov and

Tokarev (1983) studied the temperature-dependent absorptivity of aluminum

experimentally in the temperature range 20 to 780 °c. An abrupt change of

absorptivity was observed on passing through the melting point and the values for

aluminum varied between 7% at room temperature and 15% at melting point. On the

other hand, Sparks and Loh (1979) gave different values between 1 % and 3% in the

same temperature range. Szil et al. (1985) measured the temperature-dependent

absorptivity of tungsten up to 1800 °c for cw CO2 laser. Arnold (1984) computed

the temperature-dependent absorptivity at I 0.6 µm for silver, aluminum, gold,

copper, lead and tungsten by means of a straightforward application of the Drude

model and experimental de conductivity data over a wide temperature range. The

18

Table 2.1 Experimental and theoretical values of absorptivity at 10.6 µm [Duley (1985)]

Metal Measured(%) Calculated(%) Fe 2.3 2.9

s.3 (soo 0c) s.3 (soo 0c) TI n 8~ Zr IS Cu 1.5 Al 1.9

Mo 5.0 2.7 Ta 10 4.4

304SS 10 10 14 (1000 °C) 14 (1000 °C)

Ti-6Al-4V 13 13 ]4 ~400 °C) 14 ~400 °C)

Table 2.2 Experimental and theoretical values of absorptivity at 1.06 )l,ID

Metal Measured (%) Calculated(%) [Duley (1985)] [Johnson, Christy (1975)]

Ti 39 V 42 Cr Mn Fe

Co

Ni

Cu

Al

1.5 6. 7 (Liquid) 5.6

22 (Liquid)

19

42 35 36 32 (1400 °C) 25 30 (1400 °c) 23 27 (1400 °C)

2.9 3.7 (150 °c)

l

values of absmptivity for gold, silver, aluminum and copper were always less than

5% below their melting temperaturys, Xie and Kar (1995) calculated the temperature­

dependent absorptivity of copper below the boiling point and the absorptivity was

less than 7% at any temperature. Fung et al. (1990) studied the influence of the

temperature, ,shielding gas and gas flow rate on the absorptivity of CO2 for AISI 4340

steels. It was found that the values changed from 6.89% to I 1.7% in the temperature

range of20 to 500 °cat an Ar flow rate of 25 I/min. Stem (1990) investigated

experimentally the absorptivity of35N~D16 aJloyed steels, titanium and titanium

alloy (UT A6V) as a fum;:tion of surface conditipn and temperature at the CO2, CO

and Nd:YAG laser wavelengths. As the.temperature increased from 20 to 800 °c,

polished 35NCDJ6 steel specimens showed that absorptivity increased from 5.2% to

10.5% at the wavelength of 10.6 ~'. from 8.7% to 15.5% at 3.6 µµi (CO laser) and

from 29.6% to 31.2% at 1.06 µm. The absorptivity does not exceed I 5% even at

fusion temperature for most metals under the CO2 laser irradiation [ Arata and

Miyamato (1972)].

The absorptivity in the l~ser-material interaction zone also increases with the

increase in laser intensity [Harth et al. (I 976), Mazumder and Kar (1995)]. Bonch­

Bruevich et al. (1968) first reported that, for incident laser intensity above a threshold •

value which lies between 107 and 109 W/cm2, ;the measured absorptance of a metal

surface increases significantly. Harth (1976) :(ound that the reflectivity of polished

20 ,.

AISI 1045 steels was 90% for the TEA laser intensity less than 3xl04 W/cm2 and

there was a sharp drop in reflectivity to a value of about 50% at 106 W/cm2. Fabbro

et al. ( 1990) studied experimentally the change in reflectivity with CO2 laser intensity

for 35NCD16 steels in solid, liquid, vapor and plasma states. The reflectivity

decreased continuously with the laser irradiation time from 95% in solid state to 85%

in liquid, 70% in vapor and 60% in plasma of polished steels at a laser intensity of 0.1

MW/cm2. When the laser intensity changed from 0.1 MW/cm2 to I MW/cm2, the

reflectivity of the polished steels declined from 95% to 55% in solid state, from 85%

to 52% in liquid and from 70% to 45% in vapor [Fabbro et al. (1990)]. However, this

increase in absorptivity due to high intensity can not be realized in laser conduction

welding because its intensity is about 106 W/cm2.

Surface treatment can improve the absorption of laser energy significantly.

The general methods of surface treatments are surface roughening and coating. Arata

and Miyamoto ( 1972) analyzed the effects of roughness and coating with metallic and

non-metallic layers on the absorptivity of metals for cw CO2 laser. The absorptivity

at room temperature increased from 4% to 12% for iron and from 12% to 17% for

AISI 304 stainless steels, while the grit of sand paper changed from 800 grit to 100

grit. Hopkins et al. (1994) studied the absorptivity with various surface treatments

and the absorptivity of copper increased from 2.7% to 3.9% when the surface was

roughened with 120 grit sand paper. However, Arata and Miyamoto (1972) pointed

21

11

J I

I

out further that, once the ·surface was melted, the absorptivity decreased to a constant

value which was the value of polished metals at fusion temperature, for example, 13%

for AISI 304 stainless steels.

Painted, oxidized and non-metallic layers on the surface can improve the

absorptivity dramatically. The absorptivity of painted copper could be as high as

86.2% and the value of oxidized copper was 21.2% at room temperature [Hopkins et

al. (1994) ]. However, the paint film evaporates completely as soon as the focused

laser beam impinges on the :Surface and has little effect on the increase in absorptivity.

Patel and Brewster (1990) measured the effect of oxide film on the absorptivity of

single-shot Nd:YAG laser pulse irradiation for steel and the absorptivity varied

between 12% and 60% for different thicknesses of the oxide films. fargensen (1980)

reported that the addition of 10% oxygen to the argon shielding gas led to an increase

ofup to 100% in weld depth due to the decrease in reflectivity. Stem (1990) studied

the absorption for milled surface of35NCD16 steels in a temperature range of20 to

800 °c. As the temperature increased from 20 to 800 °c the absorptivity of the

milled surface increased from 12.3 to 21.6% at the wavelength of 10.6 µm and from

19.8 to 33.5% at 5.4 µm. Compared to the polished steels, the increasing factors of

milled surface were 2.4 for both CO2 and CO-laser wavelengths and 1.8 at YAG-laser

wavelength. These results are very useful because milled surfaces are often

encountered in industry instead ·of the "polished surface".

22

In general, much work has been done on the absorption oflaser energy and

many interesting results have been obtained. In many cases, "polished metals" are

used as test samples because the absorptivity is an optical property of materials and

is affected strongly by the surface condition. Since most metals are cold-rolled or

machined in industrial applications, it is necessary to investigate the case of "real

surface metals" such as milled, ground and cold-rolled surfaces. In addition, studies on

the effect of temperature on absorptivity is incomplete [Stem (1990)] and high­

temperature absorptivity-data are still Jacking [Ramanthan and Modest (1994)]

because of the measurement difficulty, especially in the liquid state. In laser welding,

the laser intensity is strong enough to melt the metals· after a little while oflaser

irradiation [Steen (1991), Xie and Kar (1997)]. Therefore, it is also important to

investigate the absorptivity of metals at elevated temperatures for laser materials

processes associated with melting.

2.2 Laser Welding.of Sheet Metals

Since laser welding is an attractive seam welding process due to the high

quality of welds and low manufacturing cost, it has a great potential application in

future car-body manufacturing as well as in other industries [Pecas (1994), Rossler

and Uddin (1996)]. Laser welding of sheet metals is one of major applications in

automotive industries because of increased requirements concerning precision,

23

flexibility and degree of automation which laser welding can meet. However, a number

of problems exist which limit the application as mentioned in Section 1.4, and the

researchers worldwide are making progress gradually. There are still a few problems

to be solved concerning the understanding of process parameters, weldability,

workpiece fit-up, process monitoring and so on.

2.2.1 Welding Process Parameters

It is essential to investigate the influences of process parameters on laser beam

welding when the laser is planned to adapt into an existing manufacturing processes.

The process parameters include the laser beam, materials, shielding gases and welding

characteristics as stated in Section 1.2 and many studies have been carried out for

keyhole welding [Mazumder (1981)]. The process parameters, which are only

sensitive to laser welding of sheet metals, are reviewed here.

For mild steels, it has been known that the optimum focal position is below

the surface [Mazumder (1983)], but the exact distance is dependent on the thickness

of the workpiece and the laser power as well as the welding speed. Betz et al. (1992)

reported that the depth of focus should be in the upper 1/3 in sheet thickness. In

practical welding process, an exact focal position is rather difficult to get because of

tolerance in fixtures, deformation of sheet metals, vibration of!aser and other

equipment. Huang et al. (1991) investigated the effective range of focal position for a

24

laser beam within which a good quality and full penetration weld could be achieved.

Their experiments showed that the effective range decreased with the decrease in laser

power for a given sheet thickness and the increase in thickness of sheet for a given

output power. For example, the effective ranges of focal position were I .5 mm at the

power of 1.4 kW and 5.9 mm at 2.1 kW for 0.9 mm thick steel [Huang et al. (1991)].

For zinc-coated steel sheets, the coating had little effect on the focal position and the

optimum focal position which was under the sheet surfaces depended mainly on the

plate thickness [Pecas (1995)].

Laser power and scaruµng speed are important process parameters in laser

welding of sheet metals. The weld depth always increases with the increase in laser

power and decrease in welding speed in both keyhole and conduction welding [Locke

and Hella (1974), Mannik and Brown (1990)]. Experimental studies showed that, for

a given sheet thickness, there was a minimum laser power which will be required to

penetrate through the sheet fully [Huang et al. (1991), Mazumder (1981)]. When the

laser power was larger than the minimum value, high welding speed could be realized,

but the increase in speed was limited by the required minimum linear energy which

was defined as the ratio of absorbed l~ser power to the welding speed. The weld

depth in keyhole welding was about the laser power raised,to the exponent 0.7

[Mazumder (1983)], but the relationship between weld depth and laser power for

conduction mode is still not clear.

25

Shielding gases are used fo't protecting the molten metal from oxidizing.

Helium and argon were the two most widely used shielding gases because they are

inert and do not react with liquid weld metals [Conway (I 950)], but carbon dioxide

has been proposed as a shielding gas since it is less expensive compared to helium and

argon [Abbott and Albright (1994)]. Of theses three shielding gases, helium provided

the deepest penetration for laser welding, followed by carbon dioxide, and argon

providing the least penetration [Abbott and Albright (1994), Huang et al. (1991)].

The reason for the differences in penetration was attributed to the plume formation

above the weld pool in the direct path of the incident beam [Chiang (1990), Herziger

(1988)]. The major drawback to the use of carbon dioxide as a shielding gas for mild

steel is that it leads to the porosity and other weld discontinuities. The addition of

ferrosilicon powder to the weld pool effectively controlled the formation of carbon

monoxide in these welds and resulted in porosity-free welds with carbon dioxide

shielding [Abbott and Albright (1994)]. Helium was recommended as the best

shielding gas for the welding of zinc-coated steel sheet [Pecas (1995)]. The use of

nitrogen as shielding gas and the effect on porosity, hardness and peel strength was

also presented [Dawes (1986)]. J0rgensen (1980) reported that an addition of 10%

oxygen to argon shielding gas gave an increase ofup to 100% in welding depth for

sheet steels and the gas flow had no significant effect on the weld depth. The increase

in weld depth was associated with a decrease in reflectivity which was achieved by

26

the addition of a small amount of oxygen. Jlllrgensen (1980) pointed out that the

effect of oxygen on the mechanical properties of the weldment had not been

investigated, but it was assumed that the effect would be less than that of nitrogen.

In practical laser welding of sheet metals, it is difficult to ensure vertical

incidence of the laser beam and constant stand-off of focusing lens because of the

deformation of sheets and unstable movement, especially in the case of robotic laser

welding. Huang et al. (1991) investigated the effect of the deviations oflaser beam on

the weld quality and geometry. Their study showed that the permissible variation in

the incident-angle increased:with-increasing the laser power and the fluctuation of the

laser beam affected the weldin~ process and resulted in different weld geometry. One

of the interesting experiments was laser welding of steel sheet as thin as 0.15 mm

[Minamida (1992)]. A·rippled mode Nd:YAG laser was used and the waveform of

rippled mode laser output looked like "ramp down".

2.2.2 Laser Welding with Filler>Materials

In the practical laser. welding of sheet metals, precise part fit-up and alignment

are much more critical in laser welding than in ordinary arc welding because of the

small focal spot diameter in the range of0.1-1 mm typically [Mazumder (1981)]. The

maximum acceptable air gap in buttjoint, usually stated to be 10% of the workpiece

thickness, is quite difficult to reach even with machining and good fixture if the thin

27

sheet metals are welded or any dimension of the product is more than about 0.5 m

[Salminen and Kujanplili (1995)]. According to the most stringent requirements, the

air gap should be as narrow as 0.09 mm for the workpiece thickness of 3 mm, and

0.13 mm for the workpiece thickness of 6 mm [Salminen et al. (1994)]. As the gap

increases, the amount oflaser beam leaving through the bottom of the weld zone

increases, and there is a critical gap in size at which the available melt cannot bridge it

and the welding process fails.

Wire and powder were two types of materials available as the filler metal in laser

welding with gap [Phillips andMetzbower (1992), Salminen et al. (1994)]. Wire

addition appeared to hold the best potential because it was similar to TIG welding with

feeding wire which was one of the most popular welding technique, so that most research

was carried out on the laser welding with feeding wire. The ability to fill opening gaps

between the workpieces with filler wire offered new prospects for laser welding [Dilthey

et al. (1995)].

Salminen et al. (! 994) indicated that filler wire was suitable for enlarging

tolerances of laser welding and the addition. of filler wire allowed an air gap up to 1.6

mm for a 3 mm plate thickness and 2.5 mm for 6 mm thick plate. The filler wire

addition increased the tolerances of a butt joint by about 10 times in comparison with

autogenous laser welding. In the welding process with filler wire, shielding gas was

introduced coaxially with the vertical laser beam, and plasma control gas at a 45° angel

28

to the laser beam, directed towards the beam-wire interaction point. The laser beam

was focused on the surface of the workpiece, in the middle of the joint gap, and filler

wire was fed to the leading edge of the keyhole wall at the interaction point of the

focal point of the laser beam and the workpiece with a 45° angle to the beam axis.

Filler wire should be fed towards the focal point of the laser beam [Panten et

al. (1990)]. Feeding was performed parallel to the welding seam at the trailing or

leading edge of the weld pool. When the laser beam impinged on the filler wire, a part

of the beam was absorbed in the wire, a part reflected by the wire and a part

penetrated though the wire [Arata et al. (1986)]. The fraction ofreflected beam

depends on the beam power, the wire feed rate and wire-beam interaction point and

up to 57% of the incoming laser power might be reflected [Salminen (1996)]. The

fraction of the beam reflected by the filler metal wire increased with an increase in the

filler metal feed rate, a decrease in the laser power, or an increase in the focal length of

the focusing mirror [Salminen (1996)]. The laser beam melted the wire, which flowed

into the gap and filled it. The molten materials, which flew into the gap, melted the

walls of the joint together with the portion of the beam reflected into the groove. The

fraction of power used to melt the base fnaterials was constant, whereas the part of

the power used for wire melting and the part of the beam which passed through the

keyhole increased with air gap [Carlson and Gregson (1986)].

29

When the wire was fed to the trailing edge of weld pool, it might be aimed at

the melt pool such that the heat of the molten metal could be used to melt the filler

wire. This feeding direction suffered from the risk of the wire sticking in the

solidifying melt pool and disturbing the process [Panten et al. (1990)]. The most

often used technique was to feed wire to the leading edge of the molten pool. The

melting efficiency was reduced if the wire was fed at higher or lower position of the

focal point [Panten et al. (1990)]. An offset from the focal point of2 mm reduced

the efficiency by 35 %, and an offset of 4 mm produced a reduction of 50 % in

efficiency [Arata et al. (1986)]. With an 8 mm thick workpiece, the optimum feeding

position was 2 mm in front of the molten pool when feeding to the leading edge, and

the feeding angle relative to the laser beam should be 30-60° [Salminen et al. (1994)].

Most of the work was focused on filler wire, although both wire and powder

were considered as potential types of filler materials in laser welding [Phillips and

Metzbower (1992), Salminen et al. (1994)). A few applications of filler powder have

been reported. Ferravante et al. (1994) reported their initial experiment in applying

the powder as filler material and satisfactory seam joints were achieved by the laser

welding with filler powder sprayed with a coaxial nozzle. Shannon and Steen (1996)

presented the feasibility of laser welding with a coaxial powder feeding nozzle for

sheet and thick welding. The use of powder as filler was also investigated recently in

Dynamic Metal Products Co., Connecticut [Irving (1997)]. Actually, the use of filler

30

r

powder provided a few advantages over wire feeding such as improvement in laser

energy absorption due to the high absorptivity of powder, flexible alloy design for

high carbon or alloy steel welding and less sensitive to process parameters. This

application will provide the precise amount of additional materials for thin sheet

welding because the commercial welding wires are usually too large in diameter for the

process.

2.2.3 Welding Process Monitoring

In practical industrial applications, laser weld quality and performance are

critical and the flaws and inconsistent of quality are not acceptable in the final

products, so in-process quality control or monitoring systems are being developed to

avoid defects in the weld and ensure consistent quality. The systems can detect

abnormal conditions and autonomously prevent defective parts in the mass

production.

The in•process monitoring methods are basically dependent on a relation of

the signals from the welding, area with'the weld quality. More attention was paid to

weld quality monitoring studies in keyhole welding. The monitoring signals used in

keyhole welding were usually based on the plasma plume above the workpiece surface

generated by vaporization and ionization, for example, the optical spectrum [Muller

and Duley (1997)), luminosity of plasma [Griebsch (1994)), plume temperature and

31

species concentration [Muller (1996)], acoustic emission [Gu and Duley (1996A),

Farson et al. (1994)], infrared emissions [Leong (1997)], velocity of the vaporized

metal atoms ejected from the metal surface[Essien and Keicher (1997)] and ultrasonic

signals [Parthasarathi (1992)]. The optical radiation was also another issue for quality

monitoring in which the signals were picked up by direct photo-diodes, optical fibers,

or they were the returned lights [Hand et al. (1997)]. Relatively few studies have

been reported for in-process monitoring of the conduction mode welding of sheet

metals. For CO2 laser weldipg of aluminum sheets, Gu and Duley (1995) investigated

the reflected laser radiation, from the weld pool by a pyroelectric detector. Based on

the radiation signals processed by fast-Fourier transform, the component in a low

frequency region represented good welds and the signal could be used to monitor the

welding process. Kim et al. (1996) measured the thermal radiation signals to detect

the weld pool depth and width during Nd: YAG pulsed laser welding of steam

generator heat exchanges tubes in nuclear power plants.

Highly precise.positioning of the workpieces is required in laser welding of

sheet metals, especially in roboticJaser welding. It is difficult for sheets to meet the

requirement due to the large size and less stiffness of sheets which results in the

misalignment-by tolerance and thermal deformation. There are two types of

positioning to be corrected in practical industrial applications, seam tracking and

stand-off height adjustment. Juptner and !i'alldorf(l991) developed a seam tracking

32

system by utilizing real-tim,e processing of a camera image from the workpiece

surface. The seam position and the stand-off height between the workpiece and

nozzle could be detected by the imaging technique and compared to the progranuned

values, and then the deviation would be compensated by actuators internal to the

welding head. In laser welding with filler wire, the vertical distance variation between

the wire tip and weld pool were not permissible as this caused globular metal transfer

and accordingly resulted in strongly rippled and unclean welds [Dilthey et al. (1995)],

so that an automatic tracking system of the vertical wire position was developed by

recording a process-internal signal. This controlled positioning of the wire tip

guaranteed high process stability and simultaneously homogeneous dilution of the

molten pool [Dilthey et al. (1995), Dilthey and Schneegans (1995)]. Kropla (1994)

reported a system to measure the gap position and the joint gap width based upon an

optical stereo sensor. The measured width was used to control the filler wire speed

and the sensor system was integrated into the work table control system thus

allowing seam tracking based on the measured joint width.

Moreover, it was also of fundamental importance to ensure stable operation of

the laser machine which was necessary for optimal processing. Steen and

Weerasinghe (1986) discussed the use oflaser beam analyzer for feedback control of

the laser itself and the use of acoustic mirror-for monitoring either a laser parameter or

a process parameter. Hoffmann and Geiger (1995) proposed a method to stabilize the

33

laser power by a closed loop control and optimize the laser beam quality by

transmitting through adaptive optics.

2.2.4 Laser Weldability of Materials

Sheet steel is still a major material in automotive industry due to excellent

weldability and formability, but there is a trend to reduce the car weight by the use of

aluminum and to improve the corrosion resistance by the use of zinc-coated steels.

Aluminum and some of its alloys are very difficult to join by laser welding because of

their properties such as high reflectivity and thermal conductivity [Mazumder

(1983)]. In addition, the level of welding defects, porosity, hot cracking and other

discontinuities, strongly depend on the material composition. In the early stage of

laser welding of aluminum, successful results were obtained for thick materials and

attention was paid to the welding metallurgy to avoid welding defects [Mazumder

(1981)]. Various types of aluminum alloys have been investigated such as aluminum

lithium alloy [Calder et al. (1992)], Al-Mg, Al-Mg-Si and Al-Zn alloys [Sakamoto et

al. (1992)], and A2219, A5083 and A6063 aluminum alloys [Kutsuna (1993)]. Hilton

(1995) reviewed laser weldability and weld mechanical properties for several

aluminum alloys.

Leong (1997 B) studied the process parameters needed to obtain consistent

laser welds for 5000 series aluminum alloys. Hugel et al. (1996) reviewed the laser

34

welding process of alumimim and indicated that high quality welds could be achieved

by a proper choice of parameters. A few critical parameters were discussed such as

the beam irradiance requirement, the effect of plasma, shielding gases and process

monitoring technique. One of the main problems in laser welding of aluminum was

inconsistency in the process that was sensitive to some unknown factors. A number

of models were developed to address these factors such as the plasma interaction,

melt pool dynamics and melt flow caused by surface tension [Hugel et al. (1996)).

Leong (1997 B) explained that the variation in absorptivity might result in

inconsistent welds for insufficient beam irradiance because the joint fitup and surface

conditions can vary from day to day or from one batch of components to another.

Therefore, it was important to study the absorptivity of aluminum in the as-received

or machined state.

Zinc-coated sheet steels were used extensively in auto body components for

· corrosion resistance and laser welding was being evaluated as an alternative joining

technique. The well-known problem with welding these materials was related to the

low boiling point of zinc (906 °c) compared with the melting temperature of steel

(-1550 °C). Pecas (1995) investigated the effects of process parameters and

proposed a clamping fixture for laser butt welding of zinc-cerated steel sheets. Xiao et

al. (1991) investigated .the laser welding of food cans made of sheet steel coated by tin.

35

Graham et al. (1994) worked on the weldability of coated steel sheets for the

lap-joint with no clearance,between the sheets using a 2-kW Nd:YAG laser capable of

cw and sine or square wave modulated output. The results showed that good quality

welds could not be produced when there was no joint clearance between the two steel

sheets. The welds displayed excessive porosity or complete weld metal expulsion

due to the zinc vapor created at the interface between the two sheets during welding.

Williams et al . (1993) reported that good quality laser beam welds could be achieved

when the zinc coating in the wel(,iing area was removed. By introducing a small joint

clearance between the sheets using preplaced shims, good quality welds have been

produced using cw CO2, YAG and·pulsed YAG lasers [Aknter and Steen (1990)]. It

was shown that clearances were in the range of0.04 mm to 0.3 mm and dependent on

a number of variables including the coating type and thickness, sheet thickness, laser

type and beam diameter, and welding speed. A controlled joint clearance between two

sheets was produced by rolling or prestamping stand-off projections into the top

steel sheet. Graham et al. (1996).welded successfully 0.75 mm thick galvanized and

galvannealed sheet steels by using a modified lap-joint consisting of a groove-shaped

projection in the top sheet of the joint.

Mazumder (1983) reviewed the application oflaser welding to other materials

such as high alloy and high carbon steels, titanium, iridium and its alloys. Daurelio

and Giorleo (1991) reviewed the CO2 laser welding and cutting of copper sheets of

36

thicknesses ranging from 0.2 to 4 mm. The laser welding of copper sheets was

possible by overlapping layers of cupric oxide, CuO, with a small quantity of cuprous

oxide in order to improve the absorptivity of the copper surface. Xie and Kar (1995)

investigated temperature-dependent absorptivity and Semak et al. (1994) studied the

effect of surface condition on the absorptivity of copper.

2.3 Mathematical Modeling of Laser Welding

Laser welding is basically a process of energy transfer from the laser beam to the

workpiece. The temperature of the workpiece increases up to the melting or

vaporization point of the material under the laser beam irradiation. Therefore, the laser

welding process can be described by mathematical expressions of mass, momentum and

energy transfer. By solving these governing equations with the boundary conditions of

laser irradiation, the information on the temperature and mass flow in the welding area

can be obtained and the dynamics oflaser welding can be described.

When a high intensity laser beam is irradiated on the substrate's surface, a

cavity called a keyhole may be formed. Much work has been done on the mechanism

of keyhole welding and only a concise description of this large volume ofliterature is

attempted here. Andrews eta!. (1976) investigated the formation of keyhole and

Klemens (1976) studied the energy and pressure balance for a long thin keyhole. The

shape and location of keyhole were also investigated [Trappe et al. (1994), Kroos et

37

'

al. (1993)]. Metzbower (1995) calculated the size and temperature of the keyhole and

melt pool on the top surface of the workpiece based on the laser power loss due to

evaporation and a minimum laser power density required to generate a keyhole. Tix

and Simon (1993) examined the transport of electrons, ions, and neutrals in the

partially ionized vapor formed in the keyhole. Kar and Mazumder (1995) presented a

model of keyhole welding by considering the surface forces and the energy balance at

the liquid-vapor and solid-liquid interfaces.

The conduction heat transfer was dominated in laser welding at low laser

intensities. Conduction mode has been applied to other processes such as surface

transformation hardening, laser chemical vapor deposition, cutting and ablation.

Rosenthal (1941) presented a model for moving point heat sources and obtained an

exact solution for, the temperature distribution in both semi-infinite and finite bodies.

For the Gaussian circular moving heat source, the temperature profiles have been

determined by many researchers. Cline and Anthony (1977) derived a temperature

field in semi-infinite solid for Gaussian beam. Chen and Lee (1983) took into account

the effects of the scanning velocity, beam radius and beam shape on the temperature

profiles. Sanders (1984)l)resented a general solution for the temperature profile as a

function of normalized velocity. Nissim et al. ( 1980) presented an analytical solution

for a moving elliptical Gaussian heat source. Pittaway (1964) solved the temperature

distribution in an adiabatic thin plate with either a stationary or a moving circular

38

Gaussian heat source. Lolov (1987) obtained the solution to the three-dimensional

linear problem for a finite depth and indefinite width adiabatic substrate. Kar and

Mazumder (1989) determined the transient three-dimensional temperature

distribution in a solid where the thermophysical properties were temperature­

dependent. Manca et al. (1995) derived a solution for substrates of finite depth and

width with a circular Gaussian moving heat source. Most of the solutions were

approximate and very complicated. Based on the temperature distributions obtained

by both analytical and numerical solutions, the melting pool could be described by the

isothermal boundary defined by the melting point of the workpiece.

Although much work has been done on the temperature distribution and the

shape of the molten pool, very few researchers considered the case of the phase

change at the pool boundary. In most cases, they neglected the phase change and

considered only one governing equation for the substrate. If both solid and liquid

phases are considered as the regions with different thermophysical properties, two

governing equations should be used to describe the problem. In addition, a Stefen

condition which takes the latent heat of melting into account, should be satisfied at the

solid-liquid interface. The latent heat of solidification determines the solidification

rate and weld cooling curve, which significantly affect the qualities of the welded joint.

In the case of steels, the latent heat of melting could be as high as 30% of the energy

required to raise the temperature of the substrate to its melting point and the

39

corresponding value for vaporization might be ten times higher [Malmuth et al.

(1974)].

The heat conduction problems with phase change have received a great deal of

attention, but there have been only a few analytical solutions for Stefan problems due to

the nonlinearity of this problem that makes it more complicated and more difficult to

solve.

Several mathematical models for laser materials processing with phase change

were developed. Rogerson and Chayt (1971) calculated the total melting time for one­

dimensional ablating slabs subjected to a constant heat flux with complete removal of

the melt. Dabby and Paek (1972) solved for the temperature profile inside a

stationary semi-infinite solid that was vaporizing at its free surface by considering

laser penetration into the solid. Allmen (1976) considered drilling processes with

material expulsion due to pressure gradient caused by evaporation by assuming

reflection losses and negligible vapor absorption. For moving irradiation sources,

further complication of the problem arises. Gonsalves and Duley (1972) found the

melting isotherm by assuming uniform disk source and no interaction between the

solid and melt. Modest and Abakians (1986) modeled the formation of deep grooves.

by considering evaporation of a moving semi-infinite substrate.

The laser melting process could be simplified as one-dimensional heat flow

problem [Ready (1965)] with the assumption that the diameter of the laser beam is

40

large enough compared to the regions of interest. To simplify the analysis for the heat

transfer problem, it is also necessary to assume that the radiation emitted by the

surface is negligible and that the thermophysical properties of the material are

independent of temperature [EI-Adawi (1986), Lax (1977) and Ready (1965)].

Carslaw and Jaeger (1959) discussed the melting of a semi-infinite; body with

constant thermophysical properties, and obtained an analytic solution for Dirichlet

boundary conditions. They also presented an approximate series solution for the

melting of a semi-infinitely large substrate that was initially at its melting temperature

and whose surface was exposeq,to a uniform heat flux. Lax (1977) studied the

temperature rise under a steady-state c;ondition due to a stationary Gaussian beam in a

semi-infinite cylindrical medium. Bell (1979) developed a one-dimensional thermal

model for laser annealing over a wide range of laser pulse duration and absorption.

Ready (1965) computed the temperature rise with no liquid phase change, and the

depth of heat-affected zone due to pulsed-laser irradiation. El-Adawi (1986)

presented results concerning the thickness of the melted layer and the rate of melting

for very short irradiation times.

The approximate series solution for the melting of a semi-infinitely large

substrate given by Carslaw and Jaeger (1959) can be applied to low intensity

irradiation. The solutions to the one-dimensional heat conduction problem with phase

change in the case of laser irradiation were given by a few researchers. Cohen and

41

Epperson (1968) solved the problem with an assumption that the thermal

conductivity and diffusitivity in the solid and liquid phases were the same and the

location of the melt front was given by

X(t) = 0-;:I (t- tm) (2.1)

where tm was the time to start melting at the substrate surface, which was found to be

[Cohen and Epperson(l968)]

mc2,T~ t - --2-m - 4a.) (2.2)

Another solution to the phase change problem in spherical coordinates due to a point

source was obtained under the assumptions of constant thermophysical properties

and a Stefan number less than unity [Shannon et al. (1994)], and the quasi-steady

state location of the solid-liquid interface was

X(t) = ( 3Qt )½ 21tpL

42

(2.3)

1-

I i'

CHAPTER 3

ABSORPTION OF LASER ENERGY

3.1 Temperature-dependent Absorptivity of Polished Metals

The efficiency of laser welding depends on the absorption of laser energy by the

workpiece. Only a portion of the incident laser energy is utilized for welding and the

rest of laser energy is reflected away by the substrate surface. The absorption is

basically a process of laser-materials interactions and the process is usually called

Fresnel Absorption. According to the classical theory of electrodynamics, the

components of the electric field of lasers interact with the electric dipole moments of

the metal atoms. The infrared absorption of metals largely depends on conductive

absorption by free electrons. The energy of these energetic electrons is transferred to

the vibrating lattice by collisions which heat up the material. Therefore, the absorption

of metals largely depends on conductive absorption by free electrons and the

absorptivity is a function of the electrical resistivity of the substrate.

The absorptivity increases with increasing temperature because the electrons of

metals transfer energy to the lattice more rapidly at higher temperatures than at lower

43

temperatures [Mazumder and Kar (1995)]. The effect of temperature on absorptivity can

be explained by noting that (i) the electrons move faster and transfer energy to the lattice

more rapidly by more electron-lattice collisions, (ii) the electrons can absorb the radiation

to undergo interband transitions which leads to an enhancement of the absorptivity of the

materials, (iii) the chemical reaction between the surrounding gas and the hot metal surface

can increase the absorption of energy, (iv) the increase in the phonon population causing

more phonon-electron energy exchanges.

Experimental data for the absorptivity of many materials at high temperatures

are lacking due to the difficulty of measurement. Arata and Miyamoto ( 1972)

calculated the absorptivity of metals for Fresnel absorption of CO2 laser by using the

following relation

Aco, = 112. 2,,/p,;; (3.1)

where Aco2 is the absorptivity of metals for CO2 laser and PDc is the direct current (DC)

resistivity in n-m. Their experimental results showed that this expression was valid for the

"polished" metals at room and melting temperatures [Arata and Miyamoto (1972)]. Xie and

Kar (1995) calculated the absorptivity of copper as a function of temperature ranging from

room to nearly boiling temperature, and compared with other theoretical and experimental

results below the melting temperature and found that the results obtained from Eq. (3.1)

were in good agreement with others' data. Here, a general expression of the temperature­

dependent absorptivities is derived from Drude theory which is valid for polished metals.

44

3.1.1 Absorptivity of CO2: COIL (Chemical Oxygen-Iodine Laser) and Nd:YAG Lasers

Fresnel relation for absorptivity at normal incidence is given as [Sokolov (1967)]

A (n-lj +k' (n+lj +k'

For long wavelengths, the coefficients are approximated as

n~k~ µ, 2e0roPvc

Eq. (3.2) can then be simplified as

( 2 1 ) A =1- 1-;;+ ,i + ...

(3.2)

(3.3)

(3.4)

Substituting Eq. (3.3) into Eq. (3.4), Hagen-Ruben's relation can be obtained as below

A= .jse0ropoc (3.5)

where m = 21ee/ A. In terms of wavelength, Eq. (3.5) can be written as

A= 365 15✓Poc . A, (3.6)

whereA is the laser wavelength in µm. Substituting A-=10.6 µm for CO2 laser, A=l.315

µm for COIL, and A=l .06 µm for YAG laser into Eq. (3.6), the absorptivities for CO2,

COIL and Nd:YAG lasers are respectively found to be

Aco, = 112.2.jp,;;

AcoJL = 318. 43.jp,;;

45

(3.7)

(3.8)

ArAo = 354.67~ (3.9)

The resistivity of metals is linearly proportional to the temperature, so that the variation

of absorptivity can be expressed as a function of temperature. It should be noted that

expression (3. 7), which provides the absorptivity of metals for CO2 laser, was the same

as that derived by Arata et al., Eq. (3.1) [Arata and Miyamato (1972)]. Although Eq.

(3. 7) is obtained in the case of long wavelength, experimental data showed that it was

valid for many metals at }.,=J0.6 µm [Arata and Miyamato (1972)]. The resistivity of

metals, which is a function of temperature, can be found in handbooks [Brandes (1983),

Touloukian et al. (1970) and (1977)] as shown in Table 3.1.

Table 3.1 Variation of resistivity with temperature, PDc=Jo-8 (a+bT), (Q-m)

Solid Liquid

Tm Tb a bxl02 Temperature a bx!01 Temperature

Metals (K) Range (K) Range (K)

Aluminum 933 2723 -1.0 1.25 273-933 10.7 1.45 933-1473

Copper 1358 2833 -0.125 0.675 273-1358 6.2 1.02 1358-1873

Iron 1810 3273 -80.0 I 7.5 273-1060

69.5 3.5 !060-1808 50 3.3 1808-1973

Nickel 1728 3180 6.8 3.6 273-1726 63 1.27 1726-1973

Titanium 1953 3533 3.2 15.2 273-1150

50 0.0 1150-1953

Carbon Steel 1800 3273 -37.2 0.144 273-1000

76 0.04 1000-1300

Stainless Steel 1700 3273 60 0.05 273-1700

46

Determining cr from the data given in Table 3.1, and using Eqs. (3.7-3.9), the

variation of the absorptivity of metals with temperature can be computed for CO2, ,.

Nd:YAG and COIL lasers. The values of absorptivity at room and melting

temperature (liquid phase) are listed in Table 3 .2.

Table 3.2 Absorptivity of metals at the room and melting temperatures

Room Temperature Melting Temperature (liquid phase)

CO2 Laser COIL YAG Laser CO2 Laser COIL YAGLaser

Aluminum 1.86 5.28 5.88 6.4 18.2 20.2

Copper 1.55 4.39 4.89 5.1 14.5 16.1

Iron 3.07 8.72 9.71 13.0 36.9 41.1

Nickel 4.70 13 .36 14.88 10.3 29.2 32.6

Titanium 8.13 23.07 25.70 13.7 38.9 43.3b

Carbon Steel 2.75 7.80 8.69 12.1 34.1 38.2'

Stainless Steel 9.72 27.57 30.72 14.0 39.7 44.2b

a Values in 13 phase

by alues at the temperature just below melting point

According to Eqs. (3.7-3.9), the absorptivities of COIL and Nd:YAG lasers

are respectively 2.84 and 3.16 times higher than that of CO2 laser. For this reason,

short-wavelength lasers have better penetration ability than CO2 laser, and deeper

47

penetration depth can be achieved in Nd:YAG laser welding. In general, CO2 lasers

can generate higher power than a Nd:YAG laser. However, the Nd:YAG laser berun

can be transmitted by flexible optical fibers and a small runount of optical energy is

lost during transmission. COIL has the advantage of both the high power of CO2 laser

and short wavelength of Nd: YAG laser. COIL can generate power as high as a CO2

laser and its wavelength (1.315 µm) is close to the Nd:YAG laser. Since COIL and

CO2 are flowing gas lasers, they can have near diffraction-limited optical quality at

very high powers. They are not limited by thermal defocusing as the power increases.

Due to shorter wavelength, the absorptivity of materials at the wavelength of COIL is

higher than at the wavelength of CO2 laser. In comparison to a Nd:YAG laser, the

absorptivity of materials for COIL is slightly less than for the Nd:YAG laser due to

the shorter wavelength of Nd: YAG.

Figures 3.1-3.6 show the increase in absorptivity of various metals for the

CO2, COIL and Nd:YAG lasers. There is a jump in absorptivity at the melting point

because of the abrupt change in resistivity when melting occurs. Aluminum and

copper have the lower absorptivities and stainless steel has the highest absorptivity

runong commercial metals. The absorptivity of aluminum has a bigger jump at the

melting temperature than other metals. Although the absorptivities of carbon steel

and stainless steel are different at room temperature, they are almost equal at high

temperatures, especially after the melting point is reached. In most laser

48

~ ~

c :i 0

"' J:,

<

25

20

15

10

~ I /

5

0

0

~~

500

I

1000

Temperature [Kl

YAG

COIL

co 2

1500

Fig. 3.1 Absorptivity of CO, COIL and YAG lasers for aluminum. 2

49

2000

20 ~

YAG

COIL r r

-------15

~ e....

.f 10 ·i

0 ~

..0

< r .// COIL co, -, -5

0 0 500 1000 1500 2000 2500

Temperature [KJ

Fig. 3.2 Absorptivity of CO2

, COIL and Y AG lasers for copper.

50

50

YAG 40

r COIL :r--~

~ 30

-f .,, 0. ~ 0 "' 20 .0 .,:

t // co

2 -IO

0 200 400 600 800 1000 1200 1400

Temperature [KJ

Fig. 3.3 Absorptivity of CO2, COIL and YAG lasers for carbon steel.

51

45

40

35

~ e.... 30

~ ·;;: ·;:: 25 e-0 ~

..0

< 20

15

IO

5 0 500 1000 1500

Temperature [Kl

YAG

COIL

co 2

2000 2500

Fig. 3.4 Absorptivity of CO , COIi and YAG lasers for stainless steel below meting point. 2

52

50

40

~ 30 -~ ·E: e-0 ~ .0 20 <

~ 10

0

0

'• i

YAG

~COIL

f co

2 • ~

500 1000 1500 2000 2500 3000 3500

Temperature [Kl

Fig. 3.5 Absorptivity of CO , COIL and Y AG lasers for iron. 2

53

I I

11

i ! I 11

45

40

35

~

:R e.... 30

:t 25 -0 ~

..0

< 20

15

IO

5 0 500 1000

.,..------YA

__.,.----- COIL

1500

co 2

2000

Temperature [K]

2500

Fig. 3.6 Absoiptivity of CO , COIL and Y AG lasers for titanium. 2

54

materials processing, the absorptivities of metals above the melting temperature are of

interest since the surface of the workpiece melts in a very short time after high power

laser irradiation begins [Xie and Kar (1997)].

Generally, the absorptivity of COIL and Nd:YAG laser is 2.84 and 3.16 times

higher than for CO2 laser according to Eqs. (3.7-3.9). This is based on the assumption

that the incident laser beam is normal to the substrate surface and is reflected by the

flat surface. However, it should be noted that the total absorption of laser energy by

the workpiece depends on (i) the absorptivity at normal incidence, and (ii) the effect

of the geometry around the cutting or welding region. For thick-section workpieces,

the total absorption of laser energy will increase due to multiple reflections of the

incident beam in the kerf. For example, the absorption can be very high (almost

100%) in laser key-hole welding irrespective of the thermophysical and optical

properties of the workpiece. For thick-section cutting, the increase in the absorption

of laser energy may improve the cutting capability of a CO2 laser more than that for

COIL and Nd:YAG lasers. This is because the absorption will become almost 100%

for all lasers and for thick-section due to multiple reflections of the laser beam around

the cut or welding region. Therefore, the absorptivity of COIL and Nd:YAG laser is

expected to be smaller than 2.84 and 3.16 times the absorptivity of CO2 laser

respectively in the case of thick-section workpiece.

55

3 .1.2 Absorptivity of CO2 Laser for Copper

Special attention is paid to the absorptivity of copper because it is difficult to

welded by arc welding and a CO2 laser has the potential to be an ideal heat source for this

work. Also, in order to verify the accuracy, the absorptivities of copper as a function of

temperature ranging from room to nearly boiling temperature are computed and

compared with other theoretical and experimental results below the melting temperature.

The temperature-dependent electric resistivity of solid [Khanna and Jain (1974)]

and liquid copper [Iida and Guthrie (1988)] are given by

Poc., = 6. 75 X 10-nT-J.25 x 10-9 273K<T<1358K

Poc, = J.02x 10-10T +6.2xJ0--a 1358K<T<1873K

(3.10)

(3.11)

where Poc.s and Poc.1 are electric resistivities of solid and liquid copper respectively, in

0-m. Substituting Eqs. (3.10) and (3.11) into Eq. (3.7), we obtain

A.,= l.122xl0-2✓6. 75 xJ0-3T-0.125 273K<T<1358K

A, =l.122xl0-2✓1.02x10-2T+6.2 1358K<T<1873K

(3.12)

(3.13)

where A, and Ar are the absorptivities of solid and liquid copper respectively.

Simple expressions for the temperature-dependent absorptivity at 10.6 µm have

been computed using the room temperature value of plasma frequency and the electron

relaxation time of the materials [Arnold (1984)]. For solid copper, there were significant

differences between the two sets of results as shown below.

56

A, = 3.88 X 10-s T + 1.92 X 10-3 (3.14)

A, = 2.59 X 10-s T - 2.83 X l o-s (3.15)

We note that the resistivity of liquid copper in Eq. (3 .11) was obtained

experimentally below the temperature 1873K [Iida and Guthrie (1988)). For any

temperature below boiling point (2833K), the Wiedemann-Franz-Lorenz law [Iida and

Guthrie (1988), Kittel (1996)] is used

2.45Xl0-sT Poc = k

(3.16)

For copper below boiling point, the thermal conductivity is given by [Touloukian et al.

(1970)]

k, = -6.3x 10·2T+ 419 273K< T< 1358K

k,=2XJ0-2 T+J40 1358K<T<2833K

(3.17)

(3.18)

Combining Eqs. (3 .17), (3 .18), (3 .I 6) and (3. 7), the absorptivities are found to be

2.45T A,= 1.122x10·

2J _6_3 x10

-2r+ 419

2.45T A,= J.122X 10·\/ 2x Jo·2T+ 140

273K < T < 1358K (3.19)

1358K < T < 2833K (3.20)

The values of absorptivity obtained from Eqs. (3.12-3.15), (3.19) and (3.20), and

experimental data [Hopkins et al. (1994)) are shown in Fig. 3.7.

57

7

6

5

~

~ 4

.i l 3 0 ~

.0

< 2

0

I ,.

0

, ,

I /

I

, , ,

500

I I

/

1000

I

.-------p·······

--Eqs. (3.12) and (3.13) - - • Eq. (3.14) - - - - · Eq. (3.15) ··•·•••·· Eq. (3.19) and (3.20)

o Experiment [Hopkins (1994)]

1500 2000 2500

Temperature, [K]

Fig. 3.7 Temperature-dependent absorptivity of CO2

laser for copper

58

3000

According to the data in Fig. 3.7, the absorptivity of copper, even liquid copper,

is less than 7%. Early experiments have showed the absorptivity of CO2 lasers for

copper was less than I% [Bass and Liou (1984)]. Therefore, the increase in absorbed

laser energy is not expected during laser welding of copper without surface treatment.

Since the solid copper begins to melt within a short time of laser irradiation, an average

absorptivity of liquid copper is chosen to be the absorptivity during laser welding of

copper and it is taken as 5. 8%. In addition, it is found that the absorptivity obtained

from Hugen-Ruben's relation is in good agreement with others' data.

3.2 Reflectivity of Cold-rolled Sheet Metals

The theoretical values of absorptivity of metals discussed above are applicable

to polished metals. In practice, the real metal surfaces used in industry are machined

or rolled and their surfaces are different from the polished surface of metals. Most

sheet metals are cold-rolled at room temperature and their absorptivity is expected to

be higher than the polished metal surface, so that it is important to understand how

much laser energy will be absorbed by the cold-rolled sheet metals and the influence of

surface conditions on absorption.

The laser energy is partially absorbed and the rest is reflected or transmitted.

The relationships among absorption, refl~ction and transmission are different for

opaque and transparent materials.

59

For opaque materials the reflectivity= I - absorptivity, and

for transparent materials the reflectivity = I - (transmissivity + absorptivity).

Metals can be considered opaque for I 0.6 µm wavelength and the reflectivity

can be converted to absorptivity easily. In this section, measured reflectivity of cold­

rolled metals is presented and the effect of surface conditions on the absorption of

laser energy is discussed.

3.2.1 Experimental Set-up for Reflectivity Measurement

The CO2 laser beam came out from a nozzle at an angle of75° with respect to

the surface of the sheet metal workpiece. The incident laser beam irradiated the

surface and the reflected beam went into a detector head where reflected laser power

was read by a laser power meter, as shown in Fig. 3.8. The sheet metal was mounted

on a linear translation stage and the reflectivity could be measured in moving and

stationary conditions. The reflectivity was calculated as the ratio of the reflected and

incident laser powers.

The experimental set-up for reflectivity measurement was simple and the

scattering of the beam by the substrate surface was not considered. It was found that

the reflectivity of copper measured by the experimental set-up was as high as 0.92.

The absorptivity could be considered as (I - reflectivity) approximately by neglecting

the scattering effect of the surface. No reflected beam was detected by the detector

60

CO2 laser

machine

Shielding gas

Mirror Energy meter

C:::)

□ □ □□

Cold-rolled steel sh~ I? ? ? ? l l l l ;J(, ,:: ~e2fl;:t:d,b;7;. Moving

1vel~ v

I Translation stage

Fig. 3.8 Experimental set-up for the measuring of reflectivity of metals

61

-----

when the metal vapor or plasma above the metal surface was very strong because of

the scattering and absorption of the incident laser beam by the vapor or plasma.

3.2.2 Reflectivity of Sheet Metals

The reflectivity of CO2 laser was measured for cold-rolled sheet metals and the

results are listed in Table 3.3.

Table 3.3 Reflectivity of as-received cold-rolled sheet metals for A.=10.6 µm

Materials .. -Reflectivity (%) Surface Melting Focused Beam

Aluminum 79-90 Yes Yes

Copper 80-92 No Yes

Mild Steel 65-80 Yes Yes

Stainless Steel (304) -33 Yes No

Titanium 46-50 Yes Yes

Inconel 44-64 No No

Inconel 36-51 Yes Yes

For sheet metals, the reflectivities have the same trend as polished metals as

shown in Table 3.2. Aluminum and copper sheets have the highest reflectivities and

the value of mild steels (65-80%) is also very large. The high reflectivity oflow

carbon steels will make the steel sheets more difficult to be laser-welded. However,

the reflectivity of cold-rolled sheet metals is different from polished metals and it is

62

expected to be lower than polished metals because the cold-rolled surface of metals is

not as smooth as the polished surface. The surface of cold-rolled sheet metals is fresh

metal without any oxide films, but the presence of oil or water film on the surface can

enhance the absorption of!aser energy. The surface roughness and the oil or water

film are major reasons for the difference in reflectivity of cold-rolled sheet metals and

polished metals.

3.2.3 Roughness

The surface roughness has a strong influence on the absorption oflaser energy.

The absorption is enhanced by the irregular reflections of!aser beams on the rough

surface, so that the reflectivity decreases with increasing roughness. The change in

reflectivity with roughness for copper and aluminum is shown in Fig. 3.9. The metal

surface was roughened by sand papers of various grits.

As can be seen in Fig. 3.9, the reflectivity for stationary samples decreases

from 84% with a 600-grit roughening to 66% with a 240-grit for copper sheets, and

from 63% with a 600-grit roughening to 51 % with a 240-grit for aluminum sheets.

Experiments also show that there is no difference in reflectivity at various abrasive

directions for both copper and aluminum.

63

~ 0

.?? > -~ "' ~

100 -

90 -

80 -

70 -

" 60 r

" " 50 I-

" 40 r

30

. ' . ' ' .

0 • • 0 6

i

" 6

" 6

Cold-rolled sheets Ar shielding gas CO

2 laser power: 360 W

' As-received

• I •• . ' 600 400

Roughness, Grit

' ' ' I

0 Cu, stationary • Cu, moving 6 Al, stationary

" .AI,moving

0

• i

" 6

" 6

' ' 320 200

Fig. 3.9 Effect of roughness on the reflectivity for copper and aluminum.

64

-

-.

-.

-

.

-

.

I

11

! i I

I ' I •

I I

I

The reflectivity of sl4tionary aluminum samples is a little lower than for

moving samples due to the melting of stationary aluminum workpieces with longer

laser-interaction time. For copper, the reflectivities of moving and stationary samples

are almost the same because the laser power used in the experiments was insufficient

to melt the copper sheets. For short laser irradiation time or insufficient laser power

to melt the workpiece, the reflectivity is dependent on the optical properties and

surface conditions of the material. If the laser power is strong enough, the metal

surface will melt, even vaporize to fopn a metal vapor or plasma plume which will

absorb the laser energy. Small plasma plume will sometimes enhance the absorption

oflaser energy by reducing the surface reflection, but it will block the propagation of

the laser beam to the workpiece in many cases. However, when a strong vapor or

plasma plume is generated on the material surface, the laser-plasma interaction

dominates the absorption process instead of the Fresnel absorption.

3.2.4 Oxide Films and Powder Layer

The reflectivity at the room temperature is higher than at the melting

temperature because of the higher resistivity of metals. However, the reflectivity is

more than 85% even at the melting temperature [Arata and Miyamoto (1972)] and most

of the laser energy is reflected away by metal surfaces. In the case of cold-rolled steel

65

'

11

sheets, the surface is also very smooth after several times of rolling at room temperature

and the reflection of CO2 laser is as high as 65-80%. The absorption of laser energy can

be improved significantly by surface coatings such as oxide films and paints. Coatings

usually worsen the laser weldability of metals and mechanical properties of welds are

degraded. So care must be taken to select coatings for improving absorption in laser

welding. Oxide films can enhance the absorption of laser energy because of the low

resistivity of steel oxides. The reflectivities of cold-rolled steel sheets with oxide films

and deposited powder layers were measured for CO2 lasers. Surface oxide films were

obtained by heat treating the steel sheet substrates at I 000 °C for 20 and 40 seconds. A

thin steel powder layer with the mesh size of 80-100 was deposited on steel sheets for

measuring reflectivity. The experimental results are shown in Fig. 3.10.

The results show that the reflectivity of oxidized samples treated at I 000 °c for

40 seconds is in the range of 30-40% which is much lower than the as-received steel

sheets. This means that the surface oxide film can significantly improve the absorption

of laser energy because the electrical DC resistivity (poc) of oxide films is much higher

than steels. The samples with steel powder layers on the surface has the lowest

reflectivity in the range of20-35% because of the irregular reflection of!aser beams by

the fine steel powder. The use of steel powder as an additional material to bridge big

gaps between the sheets to be welded has been reported recently [Irving (1997)]. In

66

100 • I ' 7 '

r . ' '

• v=40 mm/min., Argon

L ♦ v=l50 mm/min.,Argon

80 0 v=40 mm/min., Helium

' i v=!50 mm/min., Helium -◊ L

◊ ,, Powder, Argon • • • • ~ 60 ~

L

1 -

8 ~

:f 0:: 40 ~

L As-received f e

L 20 secJI 000 °c

-

• ' Surface oxidation

f ' 20

L Cold-rolled steel: IO I 0 40secJI000°c

-

~ Sheet thickness: 0.6 mm Surface oxidation CO laser Power: 360 W Powder 2

' ' ' ' 0

Fig. 3 .10 The effect of surface oxidation and steel powder on reflectivity of steel sheets

67

I I I f •

this case, the absorption of laser energy is expected to increase significantly compared

to other filler materials such as wires for which the reflectivity may be as high as 57%

[Salminen et al. (I 996)].

68

CHAPTER4

LASER WELDING OF STEEL SHEETS

4.1 Materials and Laser Welding Experiments

Laser welding experiments are carried out for steel sheets with or without

surface oxide films. Filler powder is also used for a group of samples to relax the

strict requirement of sheet fit-up, which is usually I 0% of the sheet thickness, and to

improve the mechanical properties of the weld metals. The mechanical properties of

the weldment produced under various processing conditions are investigated.

4.1.1 Steel Sheets

The steel sheets used for laser welding were AISI 1010 mild steel of thickness

0.6 mm. The cold-rolled sheets are produced from rimming steels, and are intended

for parts involving severe forming, drawing or welding. Sheets have a great degree of

ductility and are consistent in performance because of higher standards in production,

selection, and processing of the steel. The typical chemical composition of this kind

of mild steel is listed in Table 4.1. The weldability and formability of AISI 1010

69

steels are excellent and it is widely used in industries as structural materials such as

car-body, machine and instrument covers.

Table 4.1 Typical chemical composition of AISI 1010 steels (wt%)

C Mn S P ~

0.10 0.50 0.035 0.025 Balance

As discussed in Chapter 3, the reflectivity of steel sheets is in the range of 65%

-80%. Surface oxidation can improve the absorption of CO2 laser energy significantly

and the reflectivity is reduced to 30-40%. Several welding samples were oxidized first

by placing them in a furnace for 40 seconds at 1000 °C. The surfaces were degreased by

washing them with acetone before oxidizing. The oxygen content in the weld metal is

expected to be higher for samples with oxide films than for samples without oxide films.

Oxygen contamination can deteriorate the mechanical properties of the weld metal.

Experiments showed that the strength, toughness, and ductility of mild steel welds

decrease with increasing oxygen contamination [Seferian (1962)]. Addition of steel

powder during welding is a possible way to improve the mechanical properties of the

weld metals.

70

4.1.2 Filler Powders

Filler powder was used for laser welding of oxidized samples to improve the

mechanical properties. The powder was pre-placed in the gap between two sheets.

The use of filler powder is good for poor fit-up sheets. Oxidized samples tend to

increase the oxygen concentration in the weld metals. Deoxidizing elements should be

added to the filler powder to reduce the oxygen content. The deoxidizers combine

with oxygen to form harmless slags that float at the puddle surface. The deoxidizers

include manganese, silicon, titanium and zirconium. The most commonly used

elements are manganese and silicon in Metal-Inert-Gas (MIG) welding wires according

to the American Welding.Society (A WS) classification. Manganese also forms

austenitic structure in the weld metals and is good for welding with high cooling rate

to avoid the martensite structure. Silicon is usually added in proportion to the

amount of manganese in order to assist manganese to combine with oxygen and

nitrogen effectively. Aluminum, titanium and zirconium are very powerful

deoxidizers, about five times as effective as manganese and silicon, but they tend to

make the puddle somewhat sluggish and their effects on welding metallurgy are

complicated.

The chemical compositions of various solid wires are listed in Table 4.2 based

on the A WS classification and technical specifications ofESAB Co. and Hobart

Brother Co., the largest manufacturers of welding products in the world. Based on

71

Table 4.2 Chemical compositions of A WS classification solid wires for mild steels

AWS Chemical Compositions (wt%)

Classification C p s Mn Si Cu Other

AWS ER70S-2 0.07 0.025 0.035 0.90-1.40 0:40-0.70 0.50 Ti, Zr, Al

ESAB Spoolarc 65 0.07 0.011 0.009 0.70 0.40 .. Ti, Zr, Al

AWS ER70S-3 0.0~-0.15 0.025 0.035 0.90-1.40 0.45-0.70 0.50

Hobart BR-3 0.10 0.020 0.020 1.30 0.60 0.118

ESAB Spoolarc 29S 0.09. .O.QJ5 0.013 0.73 0.33

AWS ER70S-4 0.07-0.15 0.025 0.035 1.00-1.50 0.65-0.85 0.50

ESAB Spoolarc 85 0.09 0.015 0.013 0.73 0.33

AWS ER70S-5 0.07-0.19 0.025 0.035 0.90-1.40 0.30-0.60 0.50 Al

ESAB Spoolarc 86 0.07 0.012 0.011 1.19 0.62

AWS ER70S-6 0.07-0.15 0.025 0.035 1.40-1.85 0.80-1.15 0.50

HobartBR-6 0.078 0.015 0.0IO 1.44 0.822 0.115

AWS ER70S-7 0.07-0.15. 0.02~ 0.035 1.50-2.00 0.50-0,80 0.50

ESAB Spoolarc 87HP 0.08 0.QJ5 0.014 1.18 0.53

A WS ER80S-D2 0.07-0.12 0.025 0.025 1.60-2.10 0.50-0.80 0.50 Ni,Mo

Hobart BR-18 0.09 0.0IO -· 2.00 0.55 -- 0.47 Mo

ESAB Spoolarc 83 !).09 0.013 0.012 1.34 0.37 .. 0.38 Mo

72

these data, only manganese and silicon are considered for adding to the filler powder

because these elements are adequate to reduce the oxygen content in the weld metals.

Two kinds of powder are designed for laser welding of oxidized steel samples, as shown

in Table 4.3. The mesh size of the steel powder was in the range of80-100.

Table 4.3 Chemical compositions of filler powders (wt%)

Elements

Powder 1

Powder2

1018 steel

49.16

48.26

4.1.3 Laser Welding Conditions

Pure Iron

49.16

48.26 '.

Manganese Silicon

1.17 0.39

2.32 1.16

A Raytheon 40p W CO2 laser was used for welding experiments. The laser

beam was enclosed in tubes and directed by mirrors to a ZnSe piano convex focusing

lens, as shown in Fig. 1.2. The steel sheets to be welded were clamped by two fixture

plates and several toggles. La~er welding of the steel sheets without or with surface

oxidation was carried out. For the laser welding of oxidized sheets with filler powder,

the fit-up gap was 0.2 mm. Other process parameters are listed below:

• Focal length: 89 mm;

• Position of the focal spot: workpiece surface;

73

• Laser Power: 360 W;

•Welding Speed: 0.2 mm/sec.;

• Shielding gases: argon and heliwn;

• Flow rate of the shielding gases: 20 I/min.;

• Nozzle stand-off height: 18 mm;

• Inner diameter of the nozzle.: 11 mm.

4.2 Miciostructures of the Wefd and Base Metals

The microstructures of the weid and base metals for samples with surface oxide

films are present~d in this section. The results are for w~lding-with no filler powder. j

The purpose of this study is to understfilld the change in microstructure after laser

welding.and find the possible welding discontinuities caused by the surface oxide films

such as porosity and oxide inclusipns.

4.2.1 Microstructure of the Base Metals

The microstructure of AISI 1010 steel is shown in Fig. 4.1. The typical

microstructure of mild steels with less than 0.30% carbon is a combination of pearlite

and ferrite. The carbon content in steels determines the amount of pearlite, and the

74

~

Fig. 4.1 Microstructure of AISI 1010 cold-rolled steel sheets, 500x

75

higher the carbon content, the more pear lite and less ferrite are formed. Actually, the

pearlite structure consists of sliced ferrite and Fe3C. For AISI 1010 steels, the

amount of carbon is less than or equal to 0.10%, mostly ferrite and very less pearlite

are found. Since the steel sheets are cold-rolled at room temperature, the grains are

elongatedin the rolling direction as shown in Fig. 4.1.

4.2.2 Macrostructure of the Weldments

The macrostructure of the weldment with surface oxidation is shown in Fig. 4.2.

It indicates that the weld metal consists of coarse grains and the grain size is much larger

than that of the base metals. This may be due to the low welding speed used in this

experiment and the grains"in the weld zone had enough time to grow. The coarse grains

decreases the ductility and toughness. No oxide inclusions and porosrty are found in

the welq metal. Hig? speed welding max causes welding defects such as oxide

inclusions in the weld metals.

4.2.3 Micr6structure of the Heat-Affected Zone (HAZ)

The weld zone, HAZ and base metal are illustrated in Fig. 4.3. The HAZ can be

divided into three major regions: the grain-coarsening, grain-refining and partial grain­

refining regions. The partial grain-refining region is subjected to a peak temperature

between the effective lower and upper critical temperatures, Ac1 and Ac3 [Diter (1976)].

76

LL

xoor 'SUIJY ap,xo a:l1lJ.111S l!l!M a1dwus aqJ JOJ JlljGUI PJGMJO ampnJjSOJOllW z·i, 'll!d

----: ' .'

'

--- \.

,., HAZ·

Base Metals ' ,'

' Base Metals

Partial grain refining Grain coarsening

Grain refining

Fig. 4.3 Laser weldment of cold-rolled steel sheets

,

The prior pearlite colonies in this region transform into austenite and expand slightly

into the prior ferrite colonies upon heating to above the Ac1 temperature, 'and then

decompose into very fine grains of pearlite and ferrite during cooling. The prior ferrite

colonies remain essentially unaffected. The grain-refining region is subjected to a peak

temperature just above the effective upper critical temperature, Ac3, thus allowing

austenite grains to nucleate. Such austenite grains decompose into small pearlite and

ferrite grains during subsequent cooling, as shown in Fig. 4.4. The grain-coarsening

region is subjected to a peak temperature well above the Ac3 temperature, thus

promoting the coarsening of austenite grains as shown in Fig. 4.5 .

•

78

Fig. 4.4 Grain-refining region in HAZ, 500x

79

Fig. 4.5 Grain-coarsening region in HAZ

80

4.3 Properties of the Weld and Base Metals

Tensile tests were carried out to understand the strength and toughness of the

weld and base metals. Since the weld width was very small (about 0.4 mm), two

grooves were cut on the edges of the weldment to induce rupture in the weld zone

during tensile loading, as shown in Fig. 4.6. This is not a standard size for tensile tests.

So the experimental data obtained by the tensile tests can only be used to compare with

each other in the present work.

v900

"] I 'P~ 1~---'x~W-eld-1 120

Fig. 4.6 Specimen size for tensile test

The oxygen concentration in the weld and base metals was measured by the

Auger Electron Spectrometry (AES). The samples for AES were polished first and then

the testing regions were sputtered for 10 min. to remove the surface contaminants.

4.3.1 Oxygen Content in the Weld Metals

The relative oxygen atomic concentrations of the base and weld metals obtained

by the Auger Electron Spectrometry are shown in Fig. 4. 7. In the base metal, there is no

81

10

~ d' 8 0 Weld with ·,::;

I surface oxidation '

" 8 6 I I -" ·e Weld with 0 1;j oxidation and

i ...,l;'h filler powder 1_ 4

~ Weld without 0

!!,' surface oxidation t1~ ,, 1~

"lil ' ~ 2 Base metal 1 • ~ . ,1 ~-,;,_, ;r :" -· '

' . ;,,.,.,.'

·\, " -· k ,;, - ~jt

0

Fig: 4.'7 Relative oxygen atomic concentration in base and weld metals

82

'

oxygen and the value of the oxygen concentration shown in Fig, 4.7 is background noise.

The oxygen concentration in the weld metal is slightly higher for sample with surface

oxide film than for samples without oxide film. It appears that the oxide film

decomposes during laser irradiation and a small amount of oxygen is dissolved in the

weld metal. The presence of the small amount of oxygen in the weld metal is probably

due to the low welding speed used in the welding experiments. The iron oxide

decomposes into iron and oxygen, and most of the oxygen is carried away by the

shielding gas. Only a small amount of the oxygen is retained in the weld pool because of

the low solubility of oxygen in liquid iron [Kou (1987)). The low welding speed

provides sufficient time for the .oxide film to decompose completely. This may be the

reason for the absence of oxide inclusions in the weld metals. The addition of steel

powder to the weld zone during welding decreases the oxygen concentration because of

the deoxidizing elements Mn and Si present in the steel powder.

4.3.2 Tensile Strength ufthe Base and Weld Metals

The stress-strain curves obtained by conducting tensile tests are shown in Fig. 4.8.

Based on the stress-strain curves, the ultimate strength can be obtained for the base and

weld metals, as shown in Fig. 4.9. The strengths of the weld metals are higher than the

base metals. This increase in strength is due to the columnar grains in the weld metals and

the grain size in the weld metals is much larger than in the base metals (Fig. 4.2).

83

700

600

500

., 400

~ .,;

f 300 VJ

200

100

0 0

J

• ~ Weld with Oxidation 1 1 and Filler Powder

11,j Weld without Oxidation

, .. ~ /.

1 l~ Weld with Oxidation

j!,,/ :J I ' -.q..__ l ~ Base Metal

l I I

I I

I

I , , I

" / ~·

0.01 0.02 0.03 0.04

Strain

Fig. 4.8 Typical stress-strain curves for base and weld metals

84

0.05

•

700 ' l ◊

600 • ◊

• 0

r • t 0 500 • • .. I :

~ 400 •

~ ~

~ "' .. .; 300 . ,a

l I • Base Metal 5

200 • Welds without surface oxidation • Welds with surface oxidation 0 Welds with oxidation and powder I

L I ◊ Welds with oxidation and powder 2

100

0

Fig. 4.9 Ultimate strength of base and weld metals

85

Large grain size in the weld metals may degrade the toughness.

Figure 4. 9 indicates that the strength is slightly higher for samples with surface

oxide films than without oxide films. The possible reason is that the dissolved oxygen

atoms in the weld metals acts as solutes in the metal matrix deforming the metal lattices.

The deformed lattices enhance the strength of materials. This hardening mechanism is

similar to the solid-solution hardening.

When steel powders are added during welding, the oxygen content in the weld

metals decreases due to chemical reactions among Mn, Si and iron oxide, and the hardening

effect of the oxygen atoms becomes insignificant. Therefore, the strength of the samples

welded by powder 1 (see Table 4.3), that has less Mn and Si than powder 2, is close to the

samples without surface oxidation and slightly lower than the samples with surface

oxidation. When powder 2 is used, the strength is enhanced by the alloying elements Mn

and Si instead of the oxygen atoms, so that very high strength is achieved for the samples

welded by powder 2.

4.3.3 Toughness of the Base arid Wela Metals

The toughness of the tensile test samples is obtained by calculating the area

under stress-strain curves. The values of toughness for the base and weld metals are

shown in Fig. 4.10. The base metals have the highest toughness because of high

ductility. The toughness of the weld metals with powder 1 is improved by the alloying

86

800

700

600

N§ ; 500

.,;-400 "' ! = 300 ~

200

100

0

Base metal

l,j' ,,

\ W', ,.1i-,..1 ~ ·

• . • , •f.:

•,r.l • i)'tl

·l~•h

k~ :1,11,, • .! ,. 11,.f,t,j ~

·· • n•t

Weld wi!hout surface oxidation

Weld with

Weld with surface oxidation

and powder I

~. ' ., ,, .

4'h . ,·J~, . ' . ,. ll. ~ 'v.,, ,l. ·~l'"_,.1. :,,t;_I

""'\i:..,, ':· '~;f'

·i 'Ii' '!, ;'.I, , l~

Fig. 4.10 Toughness of base and weld metals

87

r I

'

elements Mn and Si. It is interesting to compare the toughness of the samples with or

without surface oxidation. It is found that the toughness of the weld metals for samples

with surface oxidation is only a little lower than the weld metals for samples without

oxidation.

In general, the surface oxide films increase the absorption of laser energy and

introduce a small amount of oxygen atoms into the weld metals. The mechanical

properties of the weld metals for samples with surface oxide films are satisfactory.

Their tensile strengths are good and the toughness is acceptable. These results indicate

that surface oxidation is a good technique to improve the absorption without sacrificing

the mechanical properties of the welds.

As mentioned before, the tolerance of the air gap between two steel sheets is

I 0% of the sheet thickness. In the present study, the thickness of the sheets is 0.6 mm

and therefore, the maximum tolerance should be 0.06 mm. The requirement for this

tolerance is usually hard to meet in industries because special clamps must be used or

the sheet edges must be machined. In the present experiments, an air gap of 0.2 mm, 3.3

times more than the maximum tolerance, was used for laser welding by adding steel

powder containing alloying elements (Mn and Si), and the weld metals were found to

have good mechanical properties. The addition of such powders can also decrease the

oxygen concentration in the weld metals to a normal level and enhance the strength and

toughness of weld metals. The use of powder has several advantages such as high

88

absorptivity, flexibility in altering the type and composition of the alloying elements,

and relaxing the strict requirement of fit-up.

89

,. _,.__

CHAPTER 5

MATHEMATICAL MODELING OF WELD DEPTHS

Lasers are used extensively for various types of materials processing including

welding. In almost all cases, the material is melted and partially vaporized. A proper

understanding of these phase change processes is necessary to achieve high quality

materials processing with lasers. When a workpiece is irradiated with a laser beam, a

portion of the laser energy fs absorbed and conducted into the interior of the material.

If the absorbed energy is large enough, the material surface melts and the melting front

propagates into the workpiece. Boiling can also occur at the free surface of the melt.

The laser melting process can be simplified as one-dimensional heat flow

problem with the assumptions that the diameter of the laser beam is large compared to

the region of interest. To simplify the analysis for the heat transfer problem, it is

assumed that the radiation emitted by the free surface of the workpiece is negligible

and that the thermophysical properties of the material are independent of

temperature.

The problem of uniform laser irradiation on a material is described by a model

of heat conduction in a semi-infinite slab. The model ofthis study is based on the

90

Laser Beam

Surface r • .. • + 10

X(lj' Liquid Tz (x, t)

I Solid-liquid . interface T=T m

Solid Ts(x,t) "f X

Fig. 5.1 A semi-infinite slab of laser irradiation

91

following heat transfer problem and the geometry of Fig. 5.1 that shows the molten

and solid regions and the direction of laser irradiation.

5.1 Mathematical Model

The one-dimensional laser irradiation can be described by the following heat

conduction equations, boundary condition and initial conditions

il2 Ti(x,t) 1 fn;(x,t) = O ax2 a, a- 0 !> x !> X(t) (5.1)

i}' T,(x,t) 1 i}T,(x,t) 0 i)i2 a., ilt X(I)!> X <oo (5.2)

J;(x,t) = T,(x,t) = Tm X = X(t) (5.3)

k ili;(x, t) k i)T, (x,t) L dX(t) 1 ax ., ax p ~ X =X(t) (5.4)

-k1 ilT1(x,t) = Al ax x=O (5.5)

Ts(x,t) = To x ➔ oo (5.6)

T,(x,t) = T,, t = 0 (5.7)

X(t)=O t= 0 (5.8)

92

'

The above-mentioned equations are a set of nonlinear partial differential

equations due to the nonlinearity of the Stefan condition (5.4). By solving the heat

transfer problem given by expressions (5.1-5.8), a relationship among the melt depth,

absorbed power density and irradiation time is obtained.

5 .2 Method of Solution

Sharma et al. (1967) obtained an approximate analytic solution for a one-

dimensional phase-change heat conduction problem with time-dependent surface

temperature. This procedure is extended in this section to the heat flux boundary

condition involving laser irradiation to solve the one-dimensional phase-change

problem given by expressions (5.1-5.8). In this procedure, a temperature distribution

that satisfies the boundary and interface conditions (5.3-5.6) is assumed. It also

satisfies the governing heat conduction equations at a few specific points such as x= 0

and x= X(t). This type of approximation resulted in a temperature profile in the

vicinity of the boundary within 20% of the correct value for the problem solved by

Sharma et al. (1967). In the liquid metal region, a temperature profile that satisfies the

boundary conditions (5.3) and (5.5) is assumed, that is

AI ri(x,t}=rm--fx-X(t)]+ 'l/(t)[1-X2(1)]

k1 0 5. x5. X(t) (5.9)

By using expression (5.9), Eq. (5.1) is satisfied at x= 0 to obtain the following expression

93

for lJl{t}:

lJl(t) = Al dX (t)

2a1k

1(1 + X(t) dX(t)) dt

a1 dt (5.10)

So the temperature profile in the liquid region is

M M dXW T,(x,t)= Tm --[x-X(t)]+ -------·--'-'--[x' -X2(t)J,O:,; x:,; X(t) (5.11)

k, 2 [J X(t) dX(t)J dt a.,k, + a.

1 dt

In the solid metal region, a temperature profile that satisfies the boundary conditions

(5.3) and (5.6) is assumed, that is

r,(x,t)= Tm- (Tm- To){ I- exp[-b(t)(x- X(t))J} X(t):5 x< oo (5.12)

By using expression (5.12), Eq. (5.2) is satisfied atx=X(t) to obtain the following

expression for b(t):

b(t) = _.!_ dX(t) a, dt

So the temperature distribution in the solid metal region is given by

(5.13)

1 dX(t) T,(x,t)= Tm -(Tm -T0){1-exp[---d (x-X{t))J}

a,, t X(t)=,;x<oo (5.14)

Substituting Eqs. (5.11) and (5.14) into Eq. (5.4), the following differential equation is

obtained for X(t):

dX(t) _ 4AIX(t) 2AI }

-:it - p[cp{Tm -T.)+L]{1+ 1+ a.,p[cp(Tm -Tn)+L]

(5.15)

94

Solving Eq. (5.15) with the boundary condition (5.8), the penetration depthX(t) can

be expressed as a function of the power density I and irradiation time t as follows

[ ½]½ [ ½]½ X(t)= _b"+(!J.+a',)2 + _ba_(!J.+a',)2 _ a,m, (5.16)

2 4 27 2 4 27 16AI

where a0

3a;m; (192( Alf t + 31) 256( Alf a,m;

(5.16a)

ba = _-5!:.J._[ a;m: (288A212

t + 47)+ t(l8A2I

2t+ 3a1m;)] (5_16b)

BAI 256( AI j a,m; m,

m, = p[cp(Tm -T0 )+L] (5.16c)

Eq. (5.16) represents a relationship among the melt depth X(t), absorbed laser power

density AI and laser irradiation time t. It should be noted that Eq. (5.16) is obtained

by approximating the temperature profiles as given by expressions (5.9) and (5.12).

To study the effect of such approximation, another temperature profile is examined in

the liquid region. This temperature profile, which satisfies the governing Eq. (5.1) and

the boundary conditions (5.3-5.5) is given by

AI AI dX(t) x 3

T, =Tm --[x-X(t)J+--------'-'-[---i' j,O::;,x::;,X(t) (5.17) k, 2ka [ 2+ X(t) dX(t) J dt X(t)

1 1 2a1 dt

Following the same procedure as above, the rate of melting and the melt depth are

found to be

95

2AI dX(t) = r;: AJX(t) }

dt [k,(Tm-To)la,+pL]{l+, I+ ai[k,(Tm-To)la,+pL] (5.18)

and

[ ½]½ [ ½]½ X(t) = - b, + (b; + Ui) , + - b, - (b; + a;) , - a,rn, (5.19)

2 4 27 2 4 27 16AI

where a,= 3a~ni, (48(Aljt+Jl) I 6( Al j a,ni,

(5.19a)

b, =- a, [ a~rn; (72A11

2t + 47)+ 3t(3A

21

2t+2a,ni,)]

Al 32( Al j a,ni, rn, (5.19b)

rn, = p[cp{Tm -T0)+L] (5.19c)

5 .3 Results and Discussion

Results are obtained by using Eqs. (5.15), (5.16), (5.18), and (5.19) for various

materials with thermophysical properties and absorptivities as listed in Tables 5.1

and 3.2. All of the results of this section are based on Eqs. (5.15) and (5.16) and CO2

laser unless stated otherwise.

5. 3 .1 Laser Melting Process

Experimental studies for laser drilling of fused quartz [Duley and Young

(1973)] and sapphire [Ready (1978)], and spot welding of stainless steel [Semak et al.

96

Table 5.1 Thermophysical properties of metals [Lynch (1974) and Touloukian et al. (1976, 1977))

Aluminum Copper Iron Titanium Tungsten Stainless Fused Steel Quartz

p(kgm"') 2700 8960 7870 4510 19250 7900 2650

L (I05Jkg"1) 3.97 2.05 2.66 4.37 1.92 3.0 1.46

Tm (K) 933 1358 1810 1953 3653 1700 1743

T, (K) 2723 2833 3273 3533 6203 3273 2270

k,(Wm"'K·') 226 397 80 22 180 17 1.67

CXs(IO~m's') 96.8 115 22.7 9.6 68 4 0.73

ki(wm·1K·1) 92 170 41.5 28 71 30.4 2.873

a1 (IO~m's') 38 43 7.6 8.23 24.6 4.9 1.5•

• Data at 1500 K

97

(1994)] showed that the melt depth increased rapidly at the beginning of laser

irradiation and then slowly after a certain time.

Similar trend is also exhibited by Eqs. (5.16) and (5.19). These two equations

represent the dynamics of laser melting process. The results obtained from

Eq. (5.16) are compared to the experimental data for laser drilling of fused quartz

[Duley and Young (1973)] as shown in Fig. 5.2. The curves are plotted with an

assumption that the absorptivity of fused quartz is 60%. This figure shows a

reasonably good agreement between the theory and experiment. For large irradiation

times, the theoretical results seem to over-estimate the melt depth. This may be due

to the fact that the effects of vapor and plasma, which affect the propagation of the

incident laser beam and absorb a portion of the laser energy, are ignored in this model.

Therefore, the models represented by Eqs. (5.16) and (5.19) are accurate when the

vapor and plasma are not very strong, which is usually the case at the beginning of

the irradiation process.

The variations in the melt depth and the rate of melting with time for various

metals are shown in Figs. 5.3 and 5.4. At the beginning, the melting velocity is high

and then it decreases to a low value. This trend is the same as those observed in

experimental studies [Duley and Young (1973), Ready (1978), Serna!< et al. (1994)].

The average melting velocity, vis obtained by integrating Eq. (5.15), that is

98

15

@ 10

1 ~

5

0 0

Power density I=6xl07

W/m2

A=~O}'o-•

. --· • • • • --• • --

-- - - - - • Eq. (5.16) , --Eq. (5. 19)

• Experiment [Duley and Young (1973)]

1 2 3 4 5 6

Time, second

Fig. 5.2 Variation of melt depth with laser irradiation time for fused quartz.

99

35

30

25

~ 20 .c· -t "il 15 ::8

10

5

0 0

.,,, Power density I=I0

9W/m2 .,,, .,,,

.,,,

1

.,. .,,, .,.

.,. .,,, .,. ,,, ., ,,, . .,. ,,, . .,. /:,.,,..,,,. .. -······

,,, .,. . /..,..

✓-✓ •

......... ---· /,, ...... ·

/ .... •···~· ---------/ . · :.>····· -- Aluminum, A=6.4 %

/. ;.:.•··· - - - Copper, A=5. I %

- · - · - Titanium, A=I3.7 % Iron, A=I3 %

Stainless steel, A= I 4 %

2 3 4 5 6 7 Time, second

Fig. 5 .3 Variation of melt depth with laser irradiation time for metals.

100

8

3.5

3

1. 2.5

' -~ j 2

' bO

·ii J

1.5 - -1

·o.5

0

' ' -' ' ' ' -

0.1

' ' ' - '

-

-- Aluminum, A=6.4 %

- - - Copper, A=5.l %

- · - · - Titanium, A=l3.7 %

Iron, A=13 %

Stainless Steel, A= 14 %

Power d;nsity 1=109 W/m2

' ' ' -- -- ----- ·-··---.. ~-~-~-~~-;:_~;_;:;_;::;_::-~ ::-".:::.:: -- -

1

Melt depth, mm

Fig. 5.4 Dynamics of melt depth oflaser irradiation.

101

X

ii=-1 JdXdX X

O dt

(5.20)

where Xis the melt depth. Substituting Eq. (5.15) into Eq. (5.20) and integrating the

resulting expression, the average melting velocity is found to be

v = - 1 1 +-------x -In 1 + 1 +-------x _ a. { 4AI [ ✓ 4AI X a.,p[ cp{Tm -To)+ L] a.,{ cp(Tm -T0 } + L]

-(1-ln2)} (5.21)

Eq. (5.21) is an expression for the average melting velocity which is a function of the

laser power density, melt depth and thermophysical properties of the workpiece.

5.3.2 Effect of Laser Power Densi,h' on the Melt Depth

The melt depth is related to the laser power density as given by Eq. (5.16) and

plotted in Fig. 5.5. The melt depth increases rapidly with increasing power density

when the power density is low, and increases slowly at higher power densities. This

means the melt depth depends on the laser power density nonlinearly. In the case of

laser welding, the melt depth increases in the similar manner when the laser power

increases [Ready (1978), Semak et al. (1994), Mazumder (1983)]. It should be noted

that the laser beam moves relative to the workpiece in the case of laser welding, but

the present model is based on stationary laser beam and workpiece. In spite of this

difference, the results of this model can be applied to the case of laser welding by

appropriately choosing the irradiation time. For example, the laser irradiation time, t,

of this model can be replaced by the laser-substrate interaction time, frFDr/v0 for the

102

r

Ei Ei

1 ~

10

1

0.1

., . ;· ~ .. -:-: Laser irradiation time t=2 s , .,,, ' - · ::..· ,::_ ... •. -·

.,, .,,,,.. .. -· .. .,,,, ... , , .,,,,,. -··· .-· ., .,,,. ._,,,,,,. ..... ,, ., _ ... -· , ,.

, ,-~ , . , .,,, ;i;..

, .,·✓. ... -, . . ,,,, ~-~ . "" .. ,. .

~ / " . ,, / . . ,, / , . ,, / , . Aluminum, A=6.4 %

Copper, A=5.I %

Titanium, A=l3.7 %

Iron, A=13 %

Stainless steel, A= I 4 %

/

107 10" 109

Power density, W/m2

Fig. 5.5 Variation of melt depth with laser power density.

103

10'0

case of laser welding, where Do is .the laser beam diameter and v0 is the welding speed.

The results of Fig. 5.5 show that the relationship between the melt depth and power

density is not a simple form of either parabolic or exponential.

Based on the thermophysical properties [Lynch (1974) and Touloukian (1976,

1977)] of different materials as listed in Table 5 .1, it is found that

Al)( >>1 a1p[ cp(Tm -T0 ) + L]

(5.22)

when the power density I;:= 1010 W/m2. Eq. (5.15) can then be simplified as

dX (t) - { C1.1Al }Y, dt - P[ cp(Tm - To)+ L]X ( t) for Jzl 010 W/m2 (5.23)

The solution ofEq. (5.23) that satisfies the boundary condition (5.8) is

X(t)=l.31( a1Alr )Y, p[ cp(Tm - To)+ L]

(5.24)

The average melting velocity for the workpiece of thickness X0, can be obtained by

integrating Eq. (5.23) as follows

v= 2{ a1A1 }½ p[c;(Tm -T0)+L]X

(5.25)

Eqs. (5.23), (5.24) and (5.25) are valid for high laser power densities (I;::1010 W/m2).

Eq. (5.25) shows that the average melting velocity is proportional to the square root of

the power density, and that it decreases as the melt depth increases. This trend has

been observed in experimental studies conducted by Bergmann and Hartmann (1994).

104

II"

Eq. (5.24) provides a relationship among the melt depthX, power density I and

irradiation time t for high power densities ( kl 010 W/m2). The theoretical results are

compared to the welding experimental data for 304 stainless steel [Bransch (1992)] and

copper alloy (NAR!oy-Z, Cu 3 wt.% Ag-0.5 wt.% Zr) [Singh et al. (1996)] as shown

in Figs. 5.6 and 5.7, where the laser irradiation time for the welding experiment is

determined from tu= Dofvo- The absorptivity of stainless steel at just below the melting

temperature ( solid state) is 14% (see Table 3.2). The absorptivity for the liquid state

at the melting temperature should be higher because there is a jump in the absorptivity

when the solid phase changes to t!Je liquid phase. Also, Table 3.2 shows the

theoretical values of absorptivities-which may be different from the actual values. For

this reason, Figs. 5.6 and 5.7 are plotted for two different absorptivities, and the model

predictions are found to agree well with experimental results.

The validity of the model of this study is also examined by comparing Eq.

(5.24) to Metzbower's empirical relation for HY 130 and ASTM A710 steels as given

below [Metzbower (1994)]

X = 0.10618? ( a )1.2os• kT -

m VoDo

This relation can be rewritten as

x = 0.0834Jao.2os•t1-20,6

pc"T Do.•m ' m O

(5.26)

(5.27)

105

1.6

1.4 Power Density !=5.lx10

10 W/m

2

1.2

Ei 1 Ei

t " 0.8 ""' -ii ;:;;

0.6

0.4 --Eq. (5.24)

• Experiment [Bransch (1992))

0.2

0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Time, second

Fig. 5.6 Variation of melt depth with laser irradiation time for 304 stainless steel.

106

~ -s" fr A .=: " ::E

3

2.5

2

1.5

1 l

--Eq. (5.24), copper, A=S. I %

- - - - • Eq. '(5.24), copper, A=l .0 %

• Experirr_ient [Singh (1996)], laser beam diameter 0.5 mm

/ ---,; !---·-----·-

... .,..- ...

--------.

0.5 v-0

0 0.02 0.04 0.06 0.08 Time, second

Fig. 5.7 Variation of melt depth with laser irradiation time for copper and NAR!oy-Z.

107

The functional dependence of the meh depth on the laser intensity and thermophysical

properties are similar in Eqs. (5.24) and (5.27), and only the exponents are different.

It is interesting to note in Fig. 5 .5 that the melt depth for copper is less than

most metals at low power densities and larger than many metals at high power

densities. Copper is generally difficult to melt because of its high thermal conductivity

and low absorptivity compared to most metals. At low power densities, the melting

velocity is low compared to the speed of heat conduction in the substrate. Therefore,

the conduction loss of the iripttt laser energy will be more in copper than in most

metals. This will lead to lower melt depth for copper at low power densities as shown

in Fig. 5 .5. On the other 'ii.and, at liigh power densities, the melting velocity is high

compared to 'the rate of heat loss· due to conduction in the workpiece. Therefore, the

conduction loss in the solid portion of the workpiece is less than in the case oflow

power densities. Most of the laser enei:gy deposited at the melt surface will be

conducted to the liquid-solid interface due to high thermal conductivity of copper, and

will be utilized to melt 'the suo~trate. This will give rise to higher melt depth for

copper at higher power densities as shown in Fig. 5.5. Similar thermal phenomenon is

responsible for higher melt depth in aluminum as shown in Fig. 5.5. Additionally,

aluminum and copper have lower melting temperatures and latent heat of fusion than

many metals, which means less sensible and latent heats are required to melt these two

metals. This can also contribute to higher melt depths for copper and aluminum.

108

The heating phenomena in copper and stainless steel substrates are investigated

by using Rosenthal's moving point heat source model [Rosenthal (1941)]. The

maximum depth, Z= Zmax atx=y=O for the isotherm T=Tm is given by the following

expression [Rosenthal (1941)]:

211:(T,. -To)kZmax (-voZmax) = exp Q 2a (5.28)

The depth for copper is found to be Jess at low heat input and more at high heat input

than for stainless steel as shown jp. Fig; 5.8, where the thermophysical properties of

liquid copper and stainless steel are used. Similar trend can be found if the

thermophysical properties of solid copper and stainless steel are used.

It should be noted that the model is based on the occurrence of melting due to laser

irradiation. However, the workpiece may not melt if the power density is very small. This

means that the power density, irradiation time, or a combination of these two parameters

must be large enough to induce melting for the model of this study to be applicable. The

times to reach the melting and boiling temperatures at the substrate surface are discussed

next.

109

100

§ 10 ·~ e N

i .,, ~ 1 ::8

0.1

102

-copper

- Stainless Steel

103

Rosenthal model (point source)

x=JF0, T=T, T =300, v=0.2 mm/s m 0

104

Heat input, W

105 106

Fig. 5.8. Variation of melt depth with heat input for copper and stainless steel based on Rosenthal's model, where thermophysical properties of liquid phase are used.

110

5.3.3 Melting and Vaporizing'Times

Due to laser irradiation on the surface of a solid material, the surface

temperature increases. The time for the surface to reach the melting temperature, tm,

can be obtained by the following expression [Incropera and DeWitt (1990)):

t = _n:k~;~(I',~m_-_T~, )_2 m 4a,(AI)2 (5.29)

After the surface melts the temperature distribution in the liquid region, T1, and the location of

the solid-liquid interface can be respectively expressed by Eqs. (5.18) and (5.19). The

condition for the surface to reach the boiling temperature is TFT, atx=O. Applying this

condition to Eqs. (5.18) and (5.19), the time at which the surface of the workpiece begins to

boil can be written as

t' • k,(T,-Tm)P[cp(T,,,-To)+L]+ a.,p [cp(Tm-T,;)+L]([1+ k,(T,-Tm) ]½ -J} 2(AI/ 3(AI/ a.,p[cp(Tm -T0)+L]

(5.30)

It should be noted that according to the model of this study, t,' represents the time for

temperature rise from the melting to the boiling point at the substrate surface.

Therefore, the total time, t., for the substrate surface to reach the boiling temperature

from the beginning of laser irradiation is given by

fv =f: +fm (5.31)

The times to start melting and boiling are shown in Table 5 .2 for several materials.

111

As shown in Table 5.2, the time to initiate boiling is very short at high laser

power densities. This means that vapor and plasma dominates the process after a

short time oflaser irradiation. Vapor and plasma will affect the laser-material

interactions. Since the effects of vapor and plasma are not considered in this study,

the present model will over-estimate the results at high power densities.

Table 5.2 Times to melt and vaporize at different power densities

Power Density (Wm"') 10' 109 10"

Time (second) Im a I, Im t, t., I,

Aluminum 4.4 16.0 4.4x10·2 l.6xl 0· 1 4.4xl04 l.6xlo·'

Copper 46.1 102.2 4.6xl0'1 1.02 4.6x10·' I.Ox 10·2

Iron 3.0 21.9 3.0x10·2 2.2x10·1 3.0xl04 2.2x10·'

Titanium 0.6 2.0 5.8x10·' 2.ox10·2 5.8x10·' 2.ox10·'

Stainless Steel 304 0.56 2.86 5.6xlo·' 2.9x!o·' 5.6x10·' 2.9xl0'4

Fused Quarti l.75xl0·' 3.69x!O·' l.8xl0·' 3.7x10·' l.8xl0'7 3.7xl0"7

• Eq. (5.29) is used to determine tm.

bThermal properties at 1500K are used as that in liquid phase (melting point 1743K)

and the absorptivity of 60% is assumed.

112

CHAPTER 6

MATHEMATICAL MODELING OF WELD POOL

6.1 Mathematical Model

When a workpiece is"iiraqiated with a laser beam, the absorbed laser energy is

conducted to the bottom of the workpiece. For thin substrates with high thermal ,I

diffusivity; the temperature can be considered uniform along the thickness. The

absorbed laser energy is also conducted in the x and y directions. The workpieces are

melted by the absorbed energy to form a molten pool, usually called weld pool. A

laser beam o:r'Gaussian intensity distribution is scanned along the x axis at a constant

speed v. When the melting process reaches a quasi-steady state, the shape of the

weld pop! does not change with ti111~- A mathematical model is presented to • ~" I

determine the weld pool shape in the quasi-steady state. The welding process with a

moving Gaussian laser beam is illustrated in Fig. 6.1.

Basically, the conduction welding process can be described by the heat

conduction equation. Since the temperature is considered to be uniform along the

113

Focusing lens --➔

Shielding gas

I I I ~ Guassian laser beam I I

!> I I Steel sheet C> I I / J

X ~

/ Weld pool

I

Moving(> Steel sheet

!>

y

Fig. 6.1 A laser beam irradiates on surface of steel sheets to form a weld pool

114

thickness, the welding process becomes a two-dimensional heat conduction problem

with a moving Gaussian heat source. Carslaw and Jaeger (1959) described the heat

conduction equations in a moving coordinate. If the Gaussian beam is considered as

the heat source in the problem, the governing equation for the process can be

expressed as

air a2r var 2AP -2rx'+y)1,t -+-=-----e ax2 a/ a ax 1tkd,f,

for which the boundary conditions are

T=To

ar =O ay

when x➔~00 and y➔i00

aty=O

(6.1)

(6.2)

(6.3)

The solution ofEq. (6.1) provides the temperature distribution in the steel sheets to

be welded with a Gaussian laser beam. Based on this solution, the shape of the weld •

pool can be obtained by tracing the isotherm corresponding to the melting point of the

sheet.

6.2 Method of Solution

Defining the following dimensionless variables

X x=-

1 r, 0

115

(6.4)

Ji= y ro

T-To T. -1 -T --_ 'T."'o

m

p _ vr0 ,--a

'

(6.5)

(6.6)

(6.7)

the governing Eq. (6.1) and boundary conditions (6.2) and (6.3) are transformed into

the following dimensionless expressions:

aiy; + aiy; = P ay; ax; aJ{ ' ax

(6.8)

2AP -2(,',+'1! -~--e rckd(Tm - To)

T1=0 when x 1➔±00 and y 1➔±00

ay; =O a½

Letting T, = y; eP· x, 12

aty1=0

Expressions Eqs. (6.8-6.10) are simplified as

"iYT, "iYT, _(P,)2

T 2AP -2(,',+,1)-P,x,12 -+-- - ,- e ax; aJ{ 2 rckd(Tm -T0 )

T :F 0

ar, = o a½

whenx1➔±00 andy1➔±00

aty1=0

Eq. (6.12) is solved by using the following Fourier transform pair,

116

(6.9)

(6.10)

(6.11)

(6.12)

(6.13)

(6.14)

integral transform:

T2(>.1 ,A2) = J:J: T,(x1, )1 )e''''' eo.,y, dx,dJ.'i (6.15)

inversion formula:

T,(x,, )1) = ( ~ J J:J: T,('),.,1 ,'),.,,)e-o.,,, e-o.,y, d>.1d>.2 (6.16)

Applying the integral transform ( 6.15) to Eq, ( 6.12) and satisfying the boundary

conditions (6.13) and (6.14), the temperature distribution in the term of the Fourier

transform variables (,l1 and ,l2) is found to be

T,('),.,1,'),.,,J = J('),.,, ,'),.,1_)

~+~+(~J (6.17)

where J('),.,i,'),.,2) = J- J- f(x1,)1)e''"'''ef).'y'dx,dJ.'i (6.18)

2AP -2(i;+l,)-P,x,l2 e and f ( x, ')1) = -rrkd-:-:-:(:;;;Tm ___ "'To) I (6.19)

Applying the inversion formula (6.16) to Eq. (6.17), the temperature distribution is

found to be

___ l_J- J- J('),.,1,'),.,iJ 2

-,,,x,e-''"'"'d)..1d).,

2 (6.20)

T,(x1,J1)- 4n2 - -~+~+(P,/2)

To clarify the evaluation of the integrals in Eq. (6.20), Eq. (6.18) is rewritten as

J('),.,,,'),.,2) = J" f:J(~;r1)e''",<e''" 1"~drJ (6.21)

117

~

which transforms Eq .. ( 6.40) into the following form:

T;(x1,yi) = _ _!_ J" J" J" J" f(~,'11) -o.,r,,-;Je-o..,ry,-~)df.cfrJdJ,.,

1dJ,.,

2 (6.22)

4n2 - - - .,..'Ki +t!i+(P,/2)2

Let '),,,1 = pcoscp, '),,,2 = psincp

x1 - ~ = rcos0, y-T] = rsin0

and ' ( -;) -,"l.,(y,-~) J'I J'I -,,.,, x, e Ul\,JUl\,2 "J" e 2

H=f _ _ ~+J!,+(P,/2)

(6.23)

(6.24)

(6.25)

Substituting expressions (6.23) and (6.24) into Eq. (6.25), the function His simplified

as

2 -fpr cru(cp-8)

J"J • e H= --- dpdcp o O p2+(P,/2)2p

(6.26)

Since the Bessel function of the first kind of order zero (J0) is given by [ Abramowitz

and Stegun (1964)]

1 52• Jo(-z) = 2n: o e-tz=!~-•!dcp

and J 0(-z) = J 0(z)

the function H can by written as

" pJo(Pr) dp H=2n:fo p2+(P,/2j

(6.27)

(6.28)

(6.29)

Also, the modified Bessel function of the second kind of order zero (K0) is given by

[Abramowitz and Stegun (1964)]

118

K0

( er)= r• PJo(Pr) Jo p' +d dp (6.30)

Substituting Eqs. (6.29) and (6.30) into Eq. (6.22), the following expression is

obtained

l I_ I_ Ti(x1 ,y) = -- K 0(P,rl2)f(~,11)~dr] 21t - -

(6.31)

where r=.J(x,-~j+(y-riJ (6.32)

Substituting expression (6.24) into Eq. (6.31) and simplifying the resulting expression,

T2(x1,yi} is found to be

T-(x ") = lAP e-l(x/+y/)-P,x,ll r· re-2''K (Pr/2)1 (mr)dr (6.33) 2 '' .,, rckd(Tm -To) Jo o ' o

where Io(mr) is the modified Bessel function of the first kind of order zero, which is

given by [Abramowitz and Stegun (1964)]

1 f'' 10

( z) = - e' ,os/p-O) dq> 2rc o

(6.34)

By using Eq. (6.11), the dimensionless temperature distribution T1(x1,yi} is obtained

as follows:

"'( ) 2AP -2rxf+>1Jf. -2,'K (P 12)1 ( )d , 1 x,, J? = . e re O ,r O mr r rckd(Tm -1'0) o

(6.35)

where m=4✓(x1 +P,l8j+/ (6.36)

Eq. (6.35) is an exact solution to Eq. (6.1) subject to the boundary conditions

(6.2) and (6.3). This is the temperature distribution in the workpiece due to a moving

119

Gaussian laser beam. Although Eq. (6.35) is concise, it has an integral that needs to be

evaluated numerically. An asymptotic expression for the integral can be obtained by

expanding 10(mr). The integrand is zero for large values ofr in Eq. (6.35). Also,

T1(x1,yI}=0 for large values ofx1 andy1 according to the boundary condition (6.9).

Therefore m must be small for non-zero values of T1(x1,yI). For small values of mr,

10(mr) can be approximated as [Weast and Selby (1975)]

I 0(mr) "'1 + rtll 4

(6.37)

Substituting expression (6.37) into Eq. (6.35), the dimensionless temperature profile

is found to be

where

T.(x y,) = lAP e-ir,!,+l,J[K'(P)+ ,,I K'(P)] I I, 1 nkd(Tm - To) I e 4 1 e

K;(P,)=-1-w (P;)eP.'1., 2F, -½-• 32

K;(P,)=-1-w_ (P;)J-''"' 4F, Y,,o 32

(6.38)

(6.39)

(6.40)

Here, Wis the Whittaker function given by the following relations [Abramowitz and

Stegun (1964), Bateman (1954)]

W_y;_.(x) = -x½ E,(-x)/>

W_r,, 0(x) = -(1 + x)x½ E,(-x)?> - x½e-1,

120

(6.41)

(6.42)

where E; is exponential integral [Weast and Selby (1975)]. Therefore, Eqs. (6.39) and

(6.40) can be written as

K;(P,) = ~ ep/ I 32 £.(- P; J s.jii; ' 32

(6.43)

K•(P) = _ .Jr,, eP/10,[(l + P;JeP/1.,E(- P;J+ e-P/16,] 2 ' ]6--J2 32 I 32

(6.44)

Finally, the dimensionless approximate temperature distribution is given by

{ [( J2 ] } _ 2AP -irx/+l,J • P, • T,(x1 ,yi}-----e Ki(P,)+ x1 +- + I, K2(P,)

nkd(Tm -T0) 8 (6.45)

6.3 Results and Discussion

Eq. (6.45) represents an approximate temperature distribution in the

workpiece in a quasi-steady state due to a moving Gaussian laser beam under the

quasi-steady state condition. The expression is relatively simple and easy to use for

calculating the temperature profile. The solution can be utilized to analyze the effects

of process parameters on the process stability, laser heating efficiency, and the weld

width and length. Such analysis is useful to understand the energy transfer process

and the interaction between the laser beam and workpiece. The mathematical model is

also useful to develop an adaptive process monitoring system. For example, when a

change in the welding speed caused by an unexpected motion of the translation stage

121

is detected by sensors, a signal is fed back to the control system and the process

parameters can be adjusted automatically based on the model results.

Based on the temperature distribution, the weld pool shape can be obtained by

determining the melting temperature isotherm. This provides a relationship among the

weld pool shape, process parameters and the properties 9f the workpiece. In this

section, the mathematical expression for the temperature profile and the weld pool

shape and width are discussed.

6.3.1 CoefficientsK,' andK,'

To calculate the temperature distribution given by Eq. (6.45), the values of the

coefficients K; and K; must be obtained first. Both coefficients are functions of the

Peclet number as given by Eqs. (6.43) and (6.44). These two coefficients are not

related to any other parameters. They can be plotted or listed in a table as a function

of the Peclet number so that they are readily available for determining the temperature

distribution in various situations. The numerical values of the coefficients K; and K;

are listed in Table 6.1, and the relations are also plotted in Fig. 6.2. Both Table 6.1

and Fig. 6.2 are convenient for other researchers to obtain the values of K; and K;.

In laser welding, the Peclet number is usually small because of the small

diameter of the laser beam, r0• Since the model is based on the Gaussian laser beam, it

is valid for any heat input with Gaussian energy distribution. For example, the

122

Table 6.1 Variation of coefficients K; and K; with Peclet number P,

Peclet Number P, K' I K' 2

0.560 0.1050 0.800 0.2700 0.0984 0.980 0.2670 0.0922 1.260 0.2570 0.0856 1.600 0.2460 0.0767 1.790 0.2380 0.0720 2.200 0.2230 0.0680 2.530 0.2100 0.0557 2.830 0.1990 0.0502 3.010' 0.1875 0.0452 3.580 0.1750 0.0390 4.000 0.1630 0.0340 4.380 0.1530 0.0300 5.060 0.1380 0.0244 6.450 0.1100 0.0156 7.380 0.0980 0.0125 8.000 0.0910 0.0108 8.940 0.0800 0.0087 9.800 0.0720 0.0061 12.65 0.0470 15.00 0.0380 16.97 0.0295, 17.89 0.0000 20.40 0.0000 25.00 0.0000

123

,-

0.35

0.3

0.25

• N

~

• . 0.2 ~ -

Ji -~ 0.15

1--------- ~:: I

!S " 0 u

0.1 I- -.. . . L

0.05 ·-..... ____ ·--..... --- .

0 0 5 10 15 20

Pe

Fig. ,6.2 Variations of coefficients K • and K • with Peel et number Pe I 2

124

current intensity distribution ofTIG (Tungsten-Inert-Gas) arc is usually considered

Gaussian [Kou (1987)] and therefore, this mathematical model can be applied to the

TIO arc welding. However, the cross-section of the TIO arc is much larger than the

laser beam and therefore, the Peclet number is very large for TIO welding.

6.3.2 The Weld Pool Shape

Using Eq. (6.45) and the values of the coefficientsK; and K; given in the last

' section, the temperature distribution in the workpiece can be obtained. Based on the

temperature profile, the weld pool ~haj>e'can be determined;h3/, locating the isotherm

corresponding to the melting point of the work:piece. This JI!ean; that .the

dimensionless temperature T1 is equal to 1 along the boundary of the _weld pool. So

Eq. (6.45) becomes

2AP e-2rif+Y!J{K;(P,,)+[(x1 + ~)2 + j,]K;{P,,)} = 1

1tkd(Tm -To) (6.46)

to represent the weld pool shape.

The weld pool shape obtained from Eq. (6.46) is compared to experimental

results. Figure 6.3 is a photograph of a laser weld pool after solidification as reported

by Voelkel (1992) from his conduction mode welding experiments. The basic welding

conditions for the pool are as follows:

• Material: AISI 5130;

125

9Zl

'XQj, 'UO!illO!J!P!JOS l:llJll JOOd pJaM l:lSllJ V £'9 'zi!d

• Laser type: cw CO2;

• Power: 1.25 kW;

• Laser beam diameter: 0.61 mm;

• Welding speed: 5.0 mm/s;

• Shielding gas: helium;

• Nozzle diameter: 25 mm.

Using these welding parameters, T1(X1,YJ is calculated from Eq. (6.45), and the

weld pool shape is determined from Eq. (6.46). by assuming that the absorptivity is

35% for the cold-rolled steel she~ts frqm Qhapter 3. The melt depth dis taken as 0.2 '

mm in the calculation. To account for the later\t heat of melting Lm, an effective

specific heat of the workpiece, Cp,, is used where the effective specific heat

Cp,= Cp+ L,,/Tm. Other thermophysical properties of steels are taken from Table 5.1

for the calculation.

The three-dimensional view of the temperature distribution T1(x1,y1 is shown

in Fig.'6.4: The temperature profile is symmetric with respect to they axis and the

peak temperature is a little behind the origin on the negative x axis because of the low

welding speed. In Fig. 6.5, the theoretical weld pool shape obtained from Eq. (6.46) is

compared to the experimental weld pool shape obtained in Fig. 6.3. The theoretical

values agree well with the experimental data. However, the shape is almost circular

127

3

2.5

2 :-, -~ 1.5 -1!, h"

1

0.5

0

-2 -1

2

Fig. 6.4 Three-dimensional view of the temperature distribution (Ti(x1,y1)) in laser conduction welding of AISI 5130 steels (A=35%, v=5 mm/s, P=J.25 kW, d=0.2 mm, r0=0.31 mm)

128

;:;

1.5

0.5

0

-0.5

-I

--Eq. (6.46)

• Experiment [Voelkel (1992)]

•

A=35%, P=l.25 kW v=5 mm/s, d=0.20 mm k=ll.5 W/mK, T =1800 K, r =0.31 mm

m 0 -1.5 L_,.___,_L.L..i..JL.L~__J__~__._...__i___,_L.L...L_J-L..~--'-~--'-~

-1.5 -1 -0.5 0 0.5 1.5

•,

Fig. 6.5 Weld pool shape under the irradiation of a Gaussian laser beam

129

due to the low welding speed. For high welding speeds, the peak temperature will be

behind the origin on the negative x axis. The distance between the position of the

peak temperature and the origin of the coordinate system can be found by setting

dT/dx=O using Eq. (6.45). Also, the weld pools is elongated in the laser scanning

direction;.and the weld-widths is determined by setting dy/dx=O using Eq. (6.46).

6.3.3 Weld Width

The expression for weld pools is given by Eq. (6.46) and it is in good

agreement with experimental results. ·The weld width can be predicated by measuring

the maximum widtl, of the weld pool shape in they direction. Figure 6.6 is a

micrography of a typical laser \veld surface. The weld widths a'r~ measured at the

surface and the depths are obtained from the weld cross-section. The weld width and

laser welding conditions are listed in Table 6.2. Theoretical weld width can be

calculated from Eq. (6.46) or Eq. (6.35) for the conditions listed in Table 6.2. Since

the welding speeds in the experiments are small which result in small Peclet number,

the coefficientsK; and• K; are not available from Table 6.1 because the values of

exponential integral, E;, can not be found in Mathematical Handbook. Eq. (6.35) is

used and the weld widths are calculated numerically by using the MathCAD software.

The calculated weld widths are compared to experimental data in Table 6.2 as well as

in Fig. 6. 7. It is found that the theoretical results exhibit the same trends as the

130

1£1

Table 6.2 Weld widths and laser welding conditions

Specimen Al A2 C2

Laser type cw CO2 cw CO2 cw CO2

Laser Power P, (W) 360 360 360

Scanning Speed v, (mm/s) 0.7 2.5 2.5

Absorptivity A,(%) 35 35 50

Melt depth d, (mm) 0.36 0.32 0.45

Laser Beam radius r, (mm) 0.2 0.2 0.2

Surface condition As-received As-received Oxide films

Experimental weld width (mm) 0.6 0.48 0.52

•'

experimental data. The weld widths increase with decreasing welding speeds.

It should be noted that this mathematical model is valid for conduction

welding. The convection in the weld p9ol is not considered in this model. It is driven

by the surface tension caused by the temperature gradient in the weld pool and it can

also affect the pool geometry.

6.3.4 Comparison between the Exact and Approximate Solution

To investigate the accuracy of the approximate temperature distribution

(Tapprox) given by Eq. (6.45), it is compared with the exact temperature distribution

(T exact) given by Eq. (6.35). For this purpose, the error, L1T, is defined as

132

I/ r

11

I l

~

f I

1

0.8

0.6

0.4

0.2

0 0

Laser power: 360 W Laser beam size: 0.2 mm Shielding gas: argon AJSJ 1010 steel

--Analytical results, Eq. (6.34) • Experiments

0.5 1.5

Welding speed, nun/s

2 2.5

Fig. 6.7 Variation of weld width with welding speed.

133

3

T exact - T approx

t..T = [ 2AP ]

rtkd(Tm - T0)

(6.47)

Substituting Eqs. (6.35) and (6.45) into Eq. (6.47), then

t..T = e-irxJ+y/J J: re-1'1K0(P,,r/2)/0(mr)dr-[ K;(P,,)+ ~K;(P,,)] (6.48)

L1Tis plotted as a function ofx1 for various values of the Peclet number in Fig. 6.8

where y 1 is taken equal to x1 for simplicity. The error is found to be insignificant at

large distances from the laser beam center. Figure 6.8 shows that the approximate

solution is applicable over the entire substrate surface for large Peclet numbers within

very small error. Such large Peclet number are encountered in arc welding. For small

Peclet numbers, that are encountered in laser welding, the exact solution should be

used in the region covered by the laser spot. Since the weld pool is larger than the

laser spot size, the approximate solution can be used to analyze the weld pool shape

with small error.

134

h -s:i

0.4 ~-~--~--~--~-~~-~--~--~---.

0.35

0.3

0.25

0.2

0.15

0.1

0.05

r I \

I \ I \ I \ I r • I ,' \

\ \

' ' I I • , -, ' ' I: .. '

I • \

Pe=0.56 Pe=0.80 Pe=l.60 Pe=3.0l

• • • Pe=7.38

... I• ..... ..... . . ... I• ... ...

ol:!-: .. -. - -- -- --- ....

-0.05 L.._.J..._....JL....._..L_....JL..... _ _J_ _ __J __ ..J...._......L __ .J

0 I 2 3 4 5 6 7 8 9

XJ (=y1)

Fig. 6.~ Error in the approximate temperature compared to the exact temperature

at various location. y 1 is taken equal to x I for this comparison.

135

CHAPTER 7

CONCLUSIONS

Laser welding of sheet metals is an important application of high power laser,

and has many advantages over conventional welding techniques. There are a few

problems in applying this technology in industry. This study addresses various

aspects of these problems, and leads to the following conclusions based on laser

welding experimental studies and theoretical analysis.

(1) The temperature-dependent absorptivities of CO2, COIL and Nd: Y AG

lasers for various metals are obtained theoretically. It is found that the absorptivities

of COIL and Nd:YAG laser are 2.84 and3·.16 times higher than the CO2 laser. The

absorptivity increases with increasing temperature of the metal. However, the values

for CO2 laser-is always less than 15% even·at•the melting point of the metal. The

surface condition of metals has a strong effect on the laser energy absorption. The

absorptivity of cold-rolled sheet metal is higher than the theoretical absorptivity of

the corresponding polished metals. Surface roughness and oxide films can enhance the

136

'I r !

absorption significantly. The reflectivity of as-received steel sheets decreases from

65-80% to 30-40% with surface oxide films for CO2 laser.

(2) Mechanical testing·of laser-welded components show that the tensile

strength of weld metals is usually higher than the base metals. The oxygen

concentration in the weld metals is higher for samples with surface oxide films than

for specimens without surface oxidation. Therefore the toughness of the weld metal is

degraded, but it is still comparable to the toughness of the weld metals for samples

without surface oxidation. Possible reasons for enhanced tensile strength of the weld

metals are the presence of coarse grains and solid solution of oxygen atoms in the weld

metals. This new welding.techniq"ue improves the utilization of!aser energy with

minimal-reduction in the weld toughness. When steel powders consisting of Mn and

Si ·are. added to bridge the gap between two sheets, the oxygen content in the weld

metals decreases and the toughness of the weldment increases. Another contribution

of this experiment is a technique for the tensile test of small weldments by introducing

notches at the edges ofweldments.

(3) A relationship among the melt depth, laser intensity and irradiation time is

obtained by developing a mathematical model for the dynamics of the melting process.

The model shows that the melt depth increases rapidly with time at the beginning of

laser irradiation and then increases slowly. The melt depth also increases rapidly with

intensity and then increases slowly for higher intensities. According to this model,

137

the average rate of melting increases as the intensity increases, and it decreases as the

melt depth increases. The times to reach the melting and boiling temperatures at the

substrate surface are found to be very short (about a few microseconds) for high laser

intensities.

( 4) The temperature distribution in sheet metals is obtained by solving the

two-dimensional heat conduction problems for moving Gaussian laser beam

irradiation. The width of the weld pool can be determined from the temperature

profile by calculating the widtlr of the isotherm corresponding to the melting point of

the workpiece. The width and shape of the weld pool obtained from this model are in

good agreement with experimental results. The weld pool shape looks like a circle

when the welding speed is low, and it is elongated in the laser beam scanning direction

for high welding speeds. The influence of various process parameters on the weld

width is analyzed in this study by using the mathematical model.

138

CHAPTER 8

FUTURE WORK

Absorption of laser energy is an important process in laser welding of sheet

metals. The absorptivity of polished metals is an optical property of materials, but it

is affected strongly by the surface condition. Since most metals are machined in

industrial applications, it is necessary to investigate the absorptivity of the metals

with various machined surfaces. Experiments have shown that surface oxidation could

improve the absorption, but the mechanism of the interaction between lasers and

oxide film is not clear. The interaction may induce a continuous change in

absorptivity during welding. It is necessary to investigate the dynamics of the

. interaction-laser-oxide film and its effect on laser energy absorption.

Experiments in this study indicate that the absorptivity is improved

significantly by surface oxidation of steel sheets. Another possible method for the

improvement of the absorptivity is an application of mixed shielding gases such as

Ar+O2, CO2 or Ar+CO2, He+O2 to increase the laser energy absorption. It is necessary

139

to investigate the effects of the mixed shielding gases on laser energy absorption and the

mechanical properties of the weld metals.

Mechanical test of the weld metals is a problem because the laser weld width is

very small and it is usually less than I mm. In this study, grooves were cut on both

edges of the weldment to induce rupture in the weld zone during tensile loading. Since

the specimen does not conform to the standard size for tensile test, further study is

necessary to understand the relationship between the strengths of the grooved samples

and the ASlM (American Standard for Testing and Method) and A WS (American

Welding Society) standard specimens. If any relation exists, the grooved samples

provide a means of measuring the mechanical properties of small specimens. Such a

method can be applied to the welds of laser-tailored blanks produced in excess of 15

million blanks in the automotive industries in 1997.

In the mathematical model for weld depth, phase change, which makes the heat

conduction problem difficult to solve, is considered in this study. The effects of the

vapor and plasma plumes are not considered in this model. The plume can absorb laser

energy requiring more energy to carry out welding. The interaction between the laser

beam and plasma plume is not clear. Also, the energy needed to create the vapor should

be considered in order to predict the melt depth accurately in laser conduction welding.

In the mathematical model for weld pool length and width, an expression for

two-dimensional temperature distribution in the workpiece is obtained. The

140

convection of molten metals in the weld pool is not considered. It is caused by the

temperature gradient which leads to surface-tension-driven themocapillary flow in the

weld pool. The effects of convection on the weld pool shape, and the mechanical

strength and metallurgical properties of the weldment need to be analyzed.

,

141

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Xie, J. and Kar A. (1997), Mathematical Modeling of Melting during Laser Materials Processing, Journal of Applied Physics, Vol. 81, No. 7, pp. 3015-3022.

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,--------------------------------------------- -----

VITA

,Jian Xie was born on June 9, 1962 in Sichuan Province, China. He studied at the

Xi'an Ji110tong University in 1979 and receiyed B.S. in Mechanical Engineering in 1983.

After graduation, he was employed as an associate R&D engineer in the Research

Institute of Electric Welding Machines, Chengdu, China. He went back to the Xi'an

Jiaotong.University for graduate studi,;:s in 1985. After receiving his M.S. degree in

Materials Science and Engineering in 198~, he joined the Research Institute of Electric

Welding Machines as a R&D engin~r. In January 1995, he began his graduate studies in

the Materials Science and Engineering Program of the Department of Mechanical,

Materials and Aerospace Engineering at the University of Central Florida (UCF) for his

Ph.D. He worked with Dr. Kar in the Laser-Aided Manufacturing and Materials

Processing (Lf,MMP) Labqratory at the Center for Research and Education in Optics

and Lasers \C!IBOL). \

He received numero,us awards during his professional career and graduate studies. (. ··'

In China, he was recognized as an Excellent Researcher at the Research Institute of

Electric Welding Machines in .1990, and awarded the Youthful Prize of Science and

Technology in Sichuan Province in 1991. During his doctoral studies at UCF, he received

the Doctoral Enhancement Award in 1996, Supplemental Fellowship Award in 1997 and

also Dr. Austin L. Grogan Memorial Scholarship in 1997.

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He will join the Edison Welding Institute, Columbus, Ohio, as a Research Engineer

after completing his doctoral program.

His work has been discussed in several technical journals and presented in

numerous technical conference as listed below:

• Journal Publications:

I. J. Xie and A. Kar, Melting and Vaporization for Large-area Film Removal with a

Chemical Oxygen-Iodine Laser, Journal of Applied Physics, Vol. 82, No. 10,

November, 1997, pp. 4744-4751.

2. J. Xie and A. Kar, Mathematical Modeling of Melting during Laser Materials

Processing, Journal of Applied Physics, Vol. 81, No. 7, 1997, pp. 3015-3022.

3. J. Xie and A. Kar, J. Rothenflue and W. Latham, Temperature-dependent

Absorptivity and Cutting Capability of CO2, Nd: YAG and Chemical Oxygen­

Iodine Lasers, Journal of Laser Applications, Vol. 9, No. 2, 1997, pp. 77-85.

• Conference Publications/Reports:

1. J. Xie and A. Kar, Laser Welding of Cold-Rolled Steel Sheets, 1997 International

Conference on Applications ofLaser-ahd Electro-Optics (ICALEO' 97),

November 17-20, San Diego, California, Laser Institute of America.

2. J. Xie and A. Kar, Thermal Analysis for the Application of High Power lasers in

Large-area Materials Processing, Final Report to Air Force Office of Scientific

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Research, Bolling Air Force Base, DC and AF Philips Laboratory, AF Contract#

F49620-93-C-0063, 31 Pages, February, 1997.

3. J. Xie, A. Kar, J. Rothenflue and W. Latham, Comparative Studies of Metal Cutting

with High Power Lasers, XI International Symposium on Gas Flow and Chemical

Lasers and High Power Laser Conference (GCL/HPLO 96), Edinburgh, UK,

August 25-30, 1996, pp. 764-767.

4. J. Xie and A. Kar, Analysis for the Laser Welding of Copper, Proceeding of 1995

International Conference on Applications of Laser and Electro-Optics

(ICALEO'95), San Diego, California, Laser Institute of America, I 995, pp. 969-978.

• Journal and conference publications before joining UCF:

I. J. Xie and Y. W. Shi, Fracture Toughness for the Specimens with Shallow Cracks,

Engineering Fracture Mechanics, Vol. 32, No. 3, 1989, pp. 329-337.

2. J. Xie and Y.W. Shi, Effect of Yield Stress and Specimen Size on the Position of Fracture

Toughness Peak (FTP) in Ji-a/W Curves, Engineering Fracture Mechanics, Vol.33,

No.6, 1989, pp. 907-912.

3. J. Xie and Y.W. Shi, Influence of Stress State on the Size and Feature of Dimples on

Fracture Surfaces, Proceedings of the 7th International Conference on Fracture

(ICF7), Houston, 1989, Vol. 5, pp. 3465-3472.

4. J. Xie and Y.W. Shi, Fracture Toughness of Pipeline Steels and Their Weldment with

Shallow Cracks, in IIW Asian Pacific Regional Welding Congress, Australia, 1988.

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5. J. Xie and Y.W. Shi, Some New Methods in Determining the Onset of Crack Growth

and the Application in the Specimens with Shallow Cracks, in IIW Asian Pacific

Regional Welding Congress, Vol. I, pp. 499-504, Australia, 1988.

6. J. Xie and S. Nie, The-State-of-the-Art in Resistant Spot Welding (Part I), Journal of

Electric Welding Machines, No. I, 1994, pp. 1-8.

7. J. Xie and S. Nie, The-State-of-the-Art in Resistant Spot Welding (Part 2), Journal of

Electric Welding Machines, No. 2, 1994, pp. 22-30.

8. J. Xie and Y. Shuai, and Q. Wang, Computerized Controller with the Function of

Automatic Quality Monitoring in MIAB Welding, Journal of Electric Welding

Machines, No. 6, 1991, pp. 17-21.

9. X. Yin, J. Xie, X. Gu, Resistance Brazing Technology and Equipment for High-power­

motor Commentators, Journal of Electric Welding Machines, No. 5, 1991, pp. 19-22.

10. J. Xie and H.Y. Yang, Study on the Friction Welding Technology of Aluminum and

Copper Tubes, Journal of Electric Welding Machines, No. 4, 1987, pp. 22-24.

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