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Mikhail Sokolov

THICK SECTION LASER BEAM WELDING OF STRUCTURAL STEELS: METHODS FOR IMPROVING WELDING EFFICIENCY

Acta Universitatis Lappeenrantaensis 655

Thesis for the degree of Doctor of Science (Technology) to be presented with due permission for public examination and criticism in the Auditorium 1382 at Lappeenranta University of Technology, Lappeenranta, Finland, on 28th of August 2015, at noon.

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Supervisors Professor Antti Salminen LUT Mechanical Engineering

Lappeenranta University of Technology Finland

Reviewers Professor Gleb Turichin

Department of Welding and Laser Technologies Peter the Great Saint Petersburg Polytechnic University Russia

Dr. Jonathan Blackburn The Welding Institute Ltd Cambridge

Great Britain

Opponents Professor Gleb Turichin

Department of Welding and Laser Technologies Peter the Great Saint Petersburg Polytechnic University Russia

Dr. Jonathan Blackburn The Welding Institute Ltd Cambridge

Great Britain

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Abstract

Mikhail Sokolov

Thick Section Laser Beam Welding of Structural Steels: Methods for Improving Welding Efficiency

Lappeenranta, 2015 58 p.

Acta Universitatis Lappeenrantaensis 655 Diss. Lappeenranta University of Technology ISBN 978-952-265-838-8

ISBN 978-952-265-839-5 (PDF) ISSN-L 1456-4491

ISSN 1456-4491

Laser beam welding (LBW) is applicable for a wide range of industrial sectors and has a history of fifty years. However, it is considered an unusual method with applications typically limited to welding of thin sheet metal. With a new generation of high power lasers there has been a renewed interest in thick section LBW (also known as keyhole laser welding). There was a growing body of publications during 2001-2011 that indicates an increasing interest in laser welding for many industrial applications, and in last ten years, an increasing number of studies have examined the ways to increase the efficiency of the process.

Expanding the thickness range and efficiency of LBW makes the process a possibility for industrial applications dealing with thick metal welding: shipbuilding, offshore structures, pipelines, power plants and other industries. The advantages provided by LBW, such as high process speed, high productivity, and low heat input, may revolutionize these industries and significantly reduce the process costs. The research to date has focused on either increasing the efficiency via optimizing process parameters, or on the process fundamentals, rather than on process and workpiece modifications.

The argument of this thesis is that the efficiency of the laser beam process can be increased in a straightforward way in the workshop conditions. Throughout this dissertation, the term “efficiency” is used to refer to welding process efficiency, specifically, an increase in efficiency refers an increase in weld’s penetration depth without increasing laser power level or decreasing welding speed. These methods are:

modifications of the workpiece – edge surface roughness and air gap between the joining plates; modification of the ambient conditions – local reduction of the pressure

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in the welding zone; modification of the welding process – preheating of the welding zone. Approaches to improve the efficiency are analyzed and compared both separately and combined. These experimentally proven methods confirm previous findings and contribute additional evidence which expand the opportunities for laser beam welding applications.

The focus of this research was primarily on the effects of edge surface roughness preparation and pre-set air gap between the plates on weld quality and penetration depth. To date, there has been no reliable evidence that such modifications of the workpiece give a positive effect on the welding efficiency. Other methods were tested in combination with the two methods mentioned above. The most promising - combining with reduced pressure method - resulted in at least 100% increase in efficiency.

The results of this thesis support the idea that joining those methods in one modified process will provide the modern engineering with a sufficient tool for many novel applications with potential benefits to a range of industries.

Keywords: laser beam welding, high-power laser, butt-joint, edge morphology, deep penetration welding, structural steel, absorptance

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Acknowledgements

This thesis was carried out at the Laboratory of Laser Processing of Lappeenranta University of Technology, Finland, during the years 2011-2015.

I am especially thankful to Prof. Antti Salminen for providing me the opportunity to pursue this work. It would not be possible to organize all necessary experiments and finish this thesis without your guidance, assistance and support.

I would like to thank Dr. Jonathan Blackburn from The Welding Institute Ltd. and Prof. Gleb Turichin from Peter the Great St. Petersburg Polytechnic University for their valuable comments and examination of this thesis.

I wish to express my gratitude to Academy of Finland, Fimecc Oy and Finnish Funding Agency for Technology and Innovation for funding the research.

I would like to express my thanks to all the people who have had a major contribution to this dissertation, particularly, Prof. Alexander Kaplan from Luleå University of Technology and Prof. Seiji Katayama from Joining and Welding Research Institute, Osaka University of Technology.

I wish to thank all the LUT personnel who helped me in making this research a success, particularly Ilkka Poutiainen, Pertti Kokko and Antti Heikkinen who helped me with the experimental tests and all the lab activities.

My special thanks goes to Peter Jones for improving the language and logic of the journal papers included in this thesis, Anna Unt for the final proofreading of the thesis and to my sister Natalia Sokolova for the graphic design of the figures.

Finally, I express my deep and warmest appreciation to my parents:

, , , .

Lappeenranta, Finland 14th August, 2015 Mikhail Sokolov

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Dedicated to my beloved wife and children Tamara

Serafima and Efim

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List of publications

This dissertation includes seven research publications as follows:

I. Mikhail Sokolov, Antti Salminen, Mikhail Kuznetsov, Igor Tsibulskiy, 2011.

Laser welding and weld hardness analysis of thick section S355 structural steel, Materials & Design, Volume 32, Issue 10, pp. 5127-5131.

II. Mikhail Sokolov, Antti Salminen, Vladislav Somonov, Alexander F.H. Kaplan, 2012. Laser welding of structural steels: Influence of the edge roughness level, Optics & Laser Technology, Volume 44, Issue 7, pp. 2064-2071.

III. Mikhail Sokolov, Antti Salminen, 2012. Experimental investigation of the influence of edge morphology in high power fiber laser welding, Physics Procedia, Volume 39, pp. 33-42.

IV. Mikhail Sokolov, Antti Salminen, 2013. Laser welding of low alloyed steels:

influence of the edge preparation, The Paton Welding Journal, Issue 2, pp. 48- 52.

V. Mikhail Sokolov, Antti Salminen, 2015. The effect of joint edge surface preparation on the efficiency of fiber laser welding of low-alloyed steels, Mechanika, Volume 21 (3)

VI. Mikhail Sokolov, Antti Salminen, 2014. Methods for Improving Laser Beam Welding Efficiency. Physics Procedia, Volume 56, pp. 450-457.

VII. Mikhail Sokolov, Antti Salminen, Seiji Katayama, Yousuke Kawahito, 2015.

Reduced Pressure Laser Welding of Thick Section Structural Steel. Journal of Materials Processing Technology, 219, pp. 278-286.

In the thesis, these publications are referred to as Publication I, Publication II and so on.

The candidate was the main author of all the publications. The candidate generated all the ideas and conclusions that are presented in the publications. The regular co- author, Professor Antti Salminen, mainly helped to guide the ideas into more comprehensible forms and reviewed the papers prior to the submission to the journals for publication.

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Additional publications

Beside the seven papers appended in the thesis, the candidate has published the following list of publications related to the work. The research work was strongly cooperative with other colleagues and research groups, mainly at Lappeenranta University of Technology.

Main author Review article:

Mikhail Sokolov, Antti Salminen, 2014. Improving Laser Beam Welding Efficiency. Engineering, Volume 6, Issue 9, pp. 559-571

Book section:

Mikhail Sokolov, Harri Eskelinen, 2013. Design Guidelines for Thick Section Butt Joint Laser Beam Welding of Structural Steels. Acta Universitatis Lappeenrantaensis (1456-4491)

Conference proceedings:

Mikhail Sokolov, Antti Salminen, 2013. The effect of edge surface preparation on welding efficiency of laser welding of low-alloyed steels. Proceedings of LAMP2013 - the 6th International Congress on Laser Advanced Materials Processing, 23-26 July, Niigata, Japan.

Mikhail Sokolov, Antti Salminen, 2013. Edge surface preparation in laser welding of low-alloyed steels. The 6th International Conference on Laser Technology in Welding and Material Processing (LTWMP-2013), 27-31 May, Katsiveli, Crimea, Ukraine, 89-91.

Mikhail Sokolov, Antti Salminen, 2012. Influence of edge preparation in laser welding of structural steels. 7-th International Conference "Beam Technologies and Laser Application" (BTLA-2012), 18-21 September, Saint- Petersburg, Russia.

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Symbols and abbreviations

Abbreviation Explanation

ANOVA Analysis of Variance

BM Base Metal

BJ Butt-joint (setup) BOP Bead on Plate

BPP Beam Parameter Product (beam quality factor)

CO2 Carbon Dioxide

DFMA Design For Manufacturing and Assembly DPSSL Diode-Pumped Solid-State Lasers

DT Destructive Test

EN European Norm

ESR Effect of edge Surface Roughness GOST (Russian: ) State Standard HAZ Heat Affected Zone

HLAW Hybrid Laser Arc Welding HPFL High Power Fiber Laser

ISO International Organization for Standardization JIS Japan Industrial Standards

LBW Laser Beam Welding

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Nd Neodymium (60) NDT Non-Destructive Test OVAT One Variable At a Time

WMZ Weld Metal Zone

YAG Yttrium Aluminum Garnet

Yb Ytterbium (70)

Symbol Unit Explanation

dOF µm focal point diameter

d mm depth of penetration

fC mm collimation length

fF mm focal length

fpp mm focal point position EL J/mm laser line energy

PL kW laser power

Ra µm roughness average

t mm material thickness

VW m/min welding speed

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Contents

Abstract ... 3

Acknowledgements ... 5

List of publications ... 7

Additional publications... 8

Symbols and abbreviations ... 9

1 Introduction ...13

1. Background and motivation ...14

1.1 Scientific contribution of the thesis...15

1.2 Outline of the thesis ...16

2 Laser welding theoretical background ...17

2.1 Lasers in Welding ...17

2.2 Keyhole welding ...19

2.3 Laser Welding Process Efficiency ...20

2.4 Absorption as the key to welding efficiency ...25

2.5 Methods to improve efficiency ...26

2.5.1 Surface modifications ...26

2.5.2 Preheating techniques ...26

2.5.3 Ambient conditions modifications ...27

2.6 Summary ...27

2.7 Materials: structural steels ...28

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3 Research goal and methodology ...31

3.1 The research problems ...31

3.2 Selection of the research methods ...33

3.3 Research limitations ...34

4 Overview of the publications ...35

Publication I: Laser welding and weld hardness analysis of thick section S355 structural steel ...39

Publication II: Laser welding of structural steels: influence of the edge roughness level ...42

Publication III: Experimental investigation of the influence of edge morphology in high power fiber laser welding ...44

Publication IV: Laser welding of low alloyed steels: influence of edge preparation ...46

Publication V: The effect of joint edge surface preparation on the efficiency of fiber laser welding of low-alloyed steels ...47

Publication VI: Methods for improving laser beam welding efficiency ... ...48

Publication VII: Reduced pressure laser welding of thick section structural steel ...50

5 Conclusions ...51

5.1 Limitations of this thesis ...54

5.2 Future research topics ...54

Bibliography ...55

Appendix I: Publications ...59

Appendix II: Experimental Set ... 117 67

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1 Introduction

…Laser1 … inter eximia naturae dona numeratum pluri- mis compositionibus inseritur Laser reckoned among the most precious gifts presented to us by Nature, is made use of in numerous preparations.

Pliny the Elder (23-79)

“Naturalis Historia”, XXII, 49 Laser beam welding is a well-studied process with its own history, evolution, and success stories. However, from a technological point of view, there is still room for improvement. The heroes of the story are high power lasers and their victorious march into laser applications, and welding specifically, during the last 15 years.

Industry is often interested in aspects of process which are not purely scientific. The applicability and the possibility of the findings being used in industry were the main motivations.

1 Here “laser” is a name of an extinct species of medicinal plant used in ancient Rome

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1. Background and motivation

This research started in 2011 when the peak reference for laser welding research occurred, according to Scopus analyzer (Elsevier B.V., 2014) as shown in Figure 1.

Finland is in the top 10 countries in the world reporting about laser welding research, as shown in Figure 2. In addition to the active scientific environment, the candidate’s experience of working with thick section structural steel applications as a design engineer has driven this research. Laser welding has wide industrial possibilities and there is considerable industrial motivation behind the research.

Figure 1. Documents by year, search keywords: laser AND welding 0

200 400 600 800 1000 1200

1986 1989 1992 1995 1998 2001 2004 2007 2010 2013

Documetns

Year

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With a wide range of possible materials, welding setups, and consumables, it was important to narrow the list of affecting factors so that their effect on the process itself will be clearly recognizable. Despite the tendency of utilizing laser beam welding for rare and even exotic materials and applications, low-alloyed steels were selected due to their common use by industry, thus maximizing the potential impact of the research. The autogenous laser beam welding process was used for this research with one of its most commonly used joint configuration in thick section – butt-joint (BJ).

1.1 Scientific contribution of the thesis

This thesis experimentally examines the influence of joint design and process- operating conditions on the properties of the welded structures. In addition, methods of welding process efficiency improvement are analyzed and compared. The main purpose of the thesis is to find a straightforward way to increase the efficiency of the laser beam welding process in workshop conditions within the study limits mentioned above. While a variety of definitions of the term “efficiency” have been suggested (described in section 2.3 “Laser Welding Process Efficiency”), this research will use the definition suggested by Lampa (1995) who saw it as the effectiveness of the laser power in producing a deep keyhole during welding. These experimentally proven methods confirm previous findings and contributes additional evidence which expand the opportunities for laser beam welding applications.

The main conclusions of the research are presented in the form of recommendations for minor changes of the design and production processes. A thorough database of experiments is included (Appendix II), which can be useful in further development of the simulation models for keyhole laser beam welding and for the industrial application of these methods.

A detailed presentation of the results, discussion and conclusion can be found in Chapter 4 “Overview of the publications”; and a detailed discussion of the scientific contribution can be found in Chapter 5. “Conclusions”.

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1.2 Outline of the thesis

This doctoral thesis is composed of seven scientific publications concerning laser beam welding. The publications are appended not in chronological order in this thesis but following the logic of topic disclosure.

Chapter 2. “Laser welding theoretical background” introduces the LBW process and defines the process efficiency increase as the motivation of the research. This chapter is not intended as a scientific contribution but as a reference frame to aid the understanding of the contribution of the publications.

Chapter 3. “Research goal and methodology” gives an overview of research topics, methods and limitations of the study.

After the introduction of the subject, summaries of the papers are included in Chapter 4. “Overview of the publications”. These are followed by a general overview of the thesis and some thoughts on possible future research in the subject in Chapter 5.

“Conclusions”.

The final part consists of two Appendixes: Appendix I includes full versions of all seven publications, Appendix II gives detailed information of all the experiments performed during the research.

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2 Laser welding theoretical background

The most in-depth look to the history of welding will bring a researcher to the Bronze Age and forge welding of anno domini. This is far beyond the limits of this thesis. It is important to recognize that joining and welding are important in modern engineering applications. But the greatest breakthrough for joining techniques took place in 20-th century, when riveting started to be replaced by welding. This allowed for an improvement in efficiency, productivity, and significant weight reductions.

Nowadays, laser technology is revolutionizing manufacturing due to its versatility, low heat input and thermal distortion, efficiency, and non-contact character of processing.

2.1 Lasers in Welding

A relatively short history of lasers begins in 1960 with Maiman’s first practical demonstration of a laser. (Maiman, 1960) (Townes, 2007) Since then, laser has been adopted for many industrial processes, including welding. For a long period only three types of lasers were available for welding applications: carbon dioxide lasers – CO2 (from 1970s), Nd: YAG lasers (from 1993) and diode lasers (from 2000s). A new generation of lasers: diode-pumped solid-state lasers (DPSSL) - like disk or fiber lasers, have been the subject of innovative developments in the last decade. (Golnabi, et al., 2006) (Katayama, 2013) High power diode lasers with ever better beam quality are also currently entering the market. (Wu, et al., 2009) (Costa Rodrigues, et al., 2014)

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Figure 3. Nobel Prize in Physics 1964: Aleksandr M. Prokhorov, Nicolay G. Basov, Charles H. Townes. ( The Noble Prize in Physics, 1964)

The first generation of DPSSLs basically replicated the crystal’s geometry and cooling technique of the old flash lamp-pumped laser; consequently rod-type DPSSLs have similar limitations to the previous generation of lasers. The next generations of high- power DPSSLs, that entered market in early 2000, were thin disk and fiber lasers.

These new lasers have multiple advantages in comparison with more traditional industrial welding laser sources: higher efficiency (compared with lamp or diode pumped rod lasers), better beam quality, compact design, and an ability to achieve powers of 30 kW; opening a door for many applications, like thick section laser processing. (Hügel, 2000) (Kratky, et al., 2008)

High power laser welding offers the potential for high-speed processing of different metals. The efficiency of laser beam welding (LBW) of thick sections can be realized in many industrial applications, for example: power plants (Takashi, et al., 2000) (Shimokusu, et al., 2001), shipbuilding (Roland, et al., 2003) (Tsirkas, 2003) and pipelines. (Moore, 2004) (Yapp & Blackman, 2004) (Hecht, 2009)

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2.2 Keyhole welding

Fusion welding processes typically involve the following three steps: melting the metal to form a weld pool on the site of the future joint, permitting the weld pool to grow to the desired size, and maintaining weld pool stability until solidification.

These steps may be achieved using different energy sources: from gas flame and electronic arc to electron or laser beam. Of the energy sources used, the laser beam is notable for having the highest power density currently available to industry that is focusable to a small point (Dawes, 1992).

This high power density (up to 109 W/cm2) leads not only to material melting but also to evaporation of the material at the point of contact, forming a cylindrical cavity in the material which may extend through the entire plate thickness. Over time, the cavity becomes deeper and forms a canal filled with evaporated material along the direction of the incoming laser beam. The stability of the keyhole is governed by the interaction forces of the vapor pressure, the hydrostatic stability of the molten material, and surface tension forces. A schematic view of keyhole welding is shown in Figure 4.

Figure 4. Keyhole scheme

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2.3 Laser Welding Process Efficiency

Throughout this thesis, the term “efficiency” will refer to LBW process efficiency.

Welding process efficiencies can be expressed by different approaches.

The laser energy transfer efficiency is used to describe the ratio of energy that is absorbed by the workpiece over the incident laser energy (Unocic, 2004):

=

(1)

where

- a – laser energy transfer efficiency;

- Ea – total energy absorbed by the workpiece, J;

- PL – laser output power, W;

- t – laser power on time, s;

The laser energy transfer efficiency is always less than unity, since not all of the energy delivered by the laser to the workpiece is absorbed by the workpiece during welding.

The second measurable process efficiency is the melting efficiency, which is used to describe the amount of energy that is used to create a molten pool from the energy delivered to and absorbed by the workpiece (Duley, 1998):

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=

(2)

where

- m – melting efficiency;

- VW – welding speed, m/s;

- T – material thickness, m;

- PL – laser power, W;

- t – laser power on time, s;

- 0 – focal point diameter, mm;

- Hm – thermal content of the metal at the melt temperature, J;

With the use of reverse approach (by calculating the energy absorbed by the energy required to melt the weld) the required laser power can be calculated by equation (Lampa, et al., 1995):

= ( ( ) + )

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where

- PL – laser power, W;

- – material density, kg/mm;

- VWM – weld metal volume, mm3/s;

- c – specific heat of fusion, J/kgK;

- Tm – melting temperature, K;

- T0 – room temperature, K;

- L – latent heat of melting, J/kg;

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LBW processing parameters and various other factors have a strong effect on the process efficiencies and, therefore, on weld penetration and geometry (Katayama, 2010) (Salminen, 2010) (Zhang, Chen, Zhou, & Liao, 2013):

- process parameters:

laser power, beam diameter, welding speed, focal point position;

- material physical properties:

reflectivity for used laser beam wavelength, thermal diffusivity,

surface tension,

content of volatile elements, edge surface roughness;

- environment conditions:

air,

atmosphere pressure, shielding gas type, shielding gas flow rate, shielding gas arrangement,

laser inducted metal vapor and plume;

A review of all the possible factors affecting the process efficiency and methods to evaluate the efficiency is beyond the scope of this research. The aim of the thesis is to review and evaluate the most effective solutions thus far reported for improvement of the LBW process efficiency.

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The efficiency of the process can be evaluated as the effectiveness of the laser power in producing a deep keyhole during welding. Such efficiency evaluation has been applied by Lampa et al. (Lampa, et al., 1995) in form of an equation:

=

(4)

where

- VW – welding speed, m/s,

- d – the depth of penetration of the weld, m;

- PL – laser power, W or J/s;

Equation (4) was used in Publications II, Publication III and Publication VI for evaluation of the method’s efficiency.

The power balance during LBW is shown in Figure 5 and can be simplified to equations (Lampa, et al., 1995):

= +

(5)

= + + + +

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where

- PL – incident laser power;

- Pa – absorbed laser power, contributing to the depth of penetration and lateral melting of the material;

- Pd – dissipated laser power: conduction, convention and reflection;

- Pp – laser power prevented from interacting with material by plasma cloud and vapour;

- PR – reflected laser power;

- PC – thermal losses from the weld zone via convection and radiation;

- Pb – laser power used in boiling the material and ionizing vapour;

- PT – conducted losses;

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Figure 5. Power redistribution scheme in keyhole laser beam welding: 1 – Focused laser beam; 2 – Base metal; 3 – Keyhole; 4 – Liquid metal; 5 – Weld; 6 – Dissipating

metal vapour

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2.4 Absorption as the key to welding efficiency

The absorptance is the fraction of the incident laser light which is absorbed by the workpiece. The absorption level is not a steady factor, but a function of laser and metal properties, listed in Table 1.

Table 1: Properties influencing absorption (Bergström, 2005)

Laser Properties Material Properties Process parameters

Power density Composition Welding speed

Wavelength Temperature Focal point position Polarization Surface roughness Focal point size Angle of incidence Surface quality

(oxide layers, dust, etc.) Shielding gas

There are several different mechanisms for describing the beam absorption by a workpiece. In LBW, where laser energy can deeply penetrate the material via the keyhole, the energy absorption process is described by two mechanisms: Fresnel absorption and inverse Bremsstrahlung absorption. The first mechanism refers to the beam absorption at the solid/liquid surface of the material on the keyhole wall and the second one takes place in the partially ionized plume of vapor in the keyhole. These mechanisms are well reported in literature and related articles (Lancaster, 1984) (Dawes, 1992) (Duley, 1998) (Ion, 2005) (Li, 2008) (Steen, et al., 2010). A number of comparative studies and simulation investigations of Fresnel absorption and multiple reflections in the keyhole have been carried out in recent years. (Xiangzhong, 2008) (Kaplan, 2012) (Kaplan, 2012) Publication VI and the review article “Improving Laser Beam Welding Efficiency” mentioned in additional publications provide more detailed information. (Sokolov, et al., 2014)

Based on the literature, absorption improvement methods can be divided into three groups: (Lancaster, 1984) (Dawes, 1992) (Duley, 1998) (Katayama, et al., 2001) (Ion, 2005) (Katayama, et al., 2001) (Blackburn, Allen, Smith, Punshon, & Hilton, 2013)

1. Surface modifications;

2. Preheating techniques;

3. Ambient conditions modifications.

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2.5 Methods to improve efficiency

2.5.1 Surface modifications

The tendency of increased absorption with increased edge surface roughness in the case of using a CO2 laser was noted by Arata and Myamoto (1972). However, this factor has an impact on the absorption level only at the beginning of the welding process; after the stabilization of the keyhole, absorption no longer depends on the optical properties of the surface.

Recent research shows that with use of high power fiber and disk lasers, the edge roughness has a large effect on absorption, due to the multiple reflection undulations.

Bergström et al. (2007) recorded, by reflectance measurements, a trend of increasing absorptance for increasing roughness above Ra 1.5 µm for stainless steels and above 6 µm for mild steels. In Publication II and Publication III, using penetration depth and calorimeter absorbed energy measurements, a correlation between edge surface roughness and absorption in welding of structural steel in a BJ setup was observed.

Modifying surface roughness to improve energy absorption and welding efficiency should not incur additional costs as many manufacturing methods are available and an appropriate method can be chosen in accordance with the required surface roughness.

2.5.2 Preheating techniques

Preheating is used to increase the weld width and depth as well as to prevent a number of defects. Changes in material properties due to high cooling rates (2000-3000 degrees/second) result in high hardness levels and a risk of cold and hot cracking. The critical cooling time between 800° and 500° is very short, so even steel with carbon content lower than 0.2 % tend to form martensitic microstructure in the weld and run a high risk of hot cracking. (Akesson, et al., 1976) (Rosenfeld, et al., 2009)

The objective of preheating is to reduce the cooling rate to fit within the critical range.

The optimum preheating temperature depends on many factors: base metal composition, welding speed, workpiece thickness, external temperature, pressure and

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2.5.3 Ambient conditions modifications

Katayama et al. (2001) highlighted the potential for reduced pressure high power laser welding. In later experiments, with stainless steel, Katayama et al. (2011) with a laser power up to 26 kW achieved an acceptable quality single pass weld of 75 mm penetration depth at 1 m/min speed and 1 kPa ambient pressure. To achieve the stated low pressure level, a vacuum chamber was sealed up, and the pressure was lowered by rotary pumps. This method has certain limitations set by the size of the workpiece and use of the method in industry, as the welding process time would have to be increased significantly. Blackburn et al. (2013) using a 5kW Yb-fiber laser at reduced pressure achieved 11 mm penetration at a welding speed of 1 m/min using a sliding vacuum seal – a significant increase in penetration depth (up to 200%) as well as quality improvement compared with welding under atmospheric pressure (Katayama, et al., 2011). Although this technology requires additional equipment and increase in the preparation time, further research in this field would be of great help to improve the LBW efficiency. This method is experimentally investigated in Publication VII.

2.6 Summary

Taken together, described methods suggest that LBW efficiency can be increased without increasing laser power level or decreasing welding speed, but through increase in the absorption.

While in the recent years there has been an increasing amount of literature about preheating techniques and reduced pressure laser welding, the effect of the edge surface roughness was surprisingly neglected. Moreover, the current standards and recommendations for LBW in BJ configuration are based on the notion that the best joint preparation is polished edge surfaces without any gap between the plates, i.e. as close to bead on plate as possible (Lappalainen, et al., 2012). International (ISO 15609- 4, 2004) and European standards (EN 1011-6, 2005) do not state that a variation of joint and edge surface preparation parameters have any positive effect on LBW efficiency.

These tendencies certainly limit LBW applications due to requirements for additional machining and zero gap tolerance.

Based on the above mentioned reasons, the focus of this research was primarily on the effects of edge surface roughness preparation and pre-set air gap between the plates on the weld quality and penetration depth. To date, there has been no reliable evidence that such modifications of the workpiece result in a positive effect on the welding efficiency. Preheating techniques and reduced pressure laser welding were investigated in combination with the two factors mentioned above.

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2.7 Materials: structural steels

High and growing global demand for steel products can be illustrated by the demand set by the growth of the economy of China. Steel production estimations, presented by Chen et al. (2014), are shown in Figure 6.

Figure 6. Total steel production in China from 2010 to 2050: solid line – estimated, dotted lines – low and high production scenarios (Chen, et al., 2014).

The demand for structural steels, used in common applications, from town buildings to offshore structures, grew after the “oil-shocks“ in the 70‘s and further world interest in mining the seabed. (Lodge, et al., 2014)

The typical microstructure of structural steels is pearlite-ferrite. However, it is important to mention that steel alloy of 0.20% carbon form a pearlite-ferrite microstructure, only when it is cooled slowly from high temperature during processing. In the case of fast cooling, the normal pearlite-ferrite microstructure will not form, instead other microstructures - bainite or martensite may result as shown in CCT phase diagram in Figure 7. (Krauss, 2005)

With the use of fusion welding methods, including LBW, high temperatures in the vicinity of the fusion line bring metal in the heat affected zone close to the melting temperature. LBW has the lowest line energy compared with laser arc hybrid welding and arc welding processes, and the highest cooling rates (2000-3000 degrees/second), as can be seen from simulation results shown in Figure 8. The acicular martensite

500 600 700 800 900

2005 2015 2025 2035

Total steel production in China, Mt

Year

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Table 2.

Figure 7. Continuous cooling transformation diagram of EN S355: A - austenite; C - cementite F - ferrite; M - martensite. (Berns, et al., 2008)

Figure 8. Simulated laser beam welding: S355 steel, laser power (PL)= 15 kW, welding speed (vW) = 1.5 m/min; focal point position (fpp) = -7.5 mm; heat-affected zone (HAZ) and weld metal zone (WMZ) (left), temperature as function of time at

the border of HAZ and base metal (BM). Simulation by commercial software LaserCad (Institute of Laser and Welding Technologies)

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Table 2. Alloying composition and mechanical properties of test materials used in welding experiments

S355 Steel EN 10025 Chemical composition, wt%

C max Si max Mn max P max S max

0.16 0.19 0.44 0.01 0.01

Mechanical Properties

Min Yield Strength, MPa Min Tensile Strength, Mpa Hardness, HV

205 400 235

St 3 Steel GOST 380-94 Chemical composition, wt%

C max Si max Mn max P max S max

0.16 0.19 0.44 0.01 0.01

Mechanical Properties

Min Yield Strength, MPa Min Tensile Strength, Mpa Hardness, HV

205 400 235

SM400A Steel JIS G3106 Chemical composition, wt%

C max Si max Mn max P max S max

0.23 - 2.5 x C 0.035 0.035

Mechanical Properties

Min Yield Strength, MPa Min Tensile Strength, MPa Hardness, HV

205 400 235

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3 Research goal and methodology

In this chapter, the research goal is introduced and the applied research methodology is explained. This chapter also discusses the reasoning behind the selection of the applied research approaches and the data collection process.

3.1 The research problems

The main purpose of the research was to determine a method of increasing the efficiency of the LBW in workshop conditions within the study limits mentioned in the next section. The main output of the research is a list of changes of the design and production processes that will result in an increase in the LBW process efficiency.

The main conclusions are that there are two essential parameters to deal with this particular welding method, materials and setup: absorption during metal - laser beam interaction and the thermal cycle of the welding process. The former gives an increase in penetration depth, and the optimal choice for the latter one reduces the hardness in the weld zone and the probability of defect formation. The classification of possible methods of efficiency improvements can be classified into three groups:

1. Edge surface modifications;

2. Preheating techniques;

3. Ambient conditions modification.

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Research topics discussed in publications are shown in Table 3.

Table 3. Thematic profile of the publications: research problems

Research topic Publication

I II III IV V VI VII

Optimal process

parameters

× × ×

Effect of edge surface

roughness preparation

× × × × × ×

Effect of increased air gap

between the steel plates

× × ×

Problem of high hardness in the HAZ and possible

solutions

× × ×

Reduced pressure LBW

method

× ×

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3.2 Selection of the research methods

All research topics required an experimental investigation. In each research publication two output parameters were analyzed: one numerical – penetration depth;

one categorical – quality of the weld. Most common design of experiments scheme was two factors design, however, on some cases “One variable at a time” (OVAT) and

“Analysis of variance” (ANOVA) methods were utilized. Table 4 gives an overview of the varied, and therefore investigated, factors.

Table 4. Research methods of the publications

Varied factors Publication

I II III IV V VI VII

Material: steel grade S355 S355/ St 3

S355/

St 3 St 3 S355 S355 SM400A Laser model YLR IPG

30000

IPG YLR 15000

IPG YLS 10000

IPG YLR 15000

IPG YLR 10000

IPG YLR 10000

Tru Disk 16002 Number of

experiments 40 80 72 25 16 48 46

Welding parameters

× × ×

ESR, machining type

× × × × × ×

Air gap in the joint

× × ×

Preheating

temperature

×

Experimental sets are presented in detail in Appendix II. Specimen designation for the experiments was done as follows:

Where X is the number of the set of experiments and NN is the order number of the experiment. For example, the specimens welded during the third experiment of the first set were assigned by index 103.

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3.3 Research limitations

With a range of possible materials, welding setups and consumables, it was important to narrow the list of affecting factors so that their effect on the process itself would be recognizable. Despite the tendency of utilizing laser beam welding for rare and even exotic materials and applications, low-alloyed steels (described in Table 2) were chosen as the most common application. Relatively complicated welding techniques, like laser-hybrid welding, were not considered in this study. The autogenous laser beam welding process was chosen for investigation with common joint configuration – closed square butt-joint. More representative forms of the research limitations are shown in Figure 9.

Figure 9. Research limitations

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4 Overview of the publications

In this chapter an overview of the publications included in the thesis and the most important results are introduced. Additionally to this chapter, the results of the research are presented in the second part of the thesis, consisting of the seven publications, in original publication form and in full length. Experimental sets are presented in detail in Appendix II.

The relationship between the experimental series and the publications, and the relationships between the publications, are shown in Figure 11. Experimental series are numbered in the chronological order, with the varied parameters shown as explained in Figure 10.

The publications included in this thesis have been published separately in scientific venues, which have all employed a peer-review process before acceptance for publication. In this chapter, each of these publications, their objectives, results, and relation to the whole, are discussed.

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dOF focal point diameter, µm EL laser line energy, J/mm

ESR effect of edge surface roughness fC collimation length, mm

fF focal length, mm fpp focal point position, mm HAZ heat affected zone PL laser power, kW t material thickness, mm VW welding speed, m/min

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Figure 11. Experimental sets and relationships between the thesis publications

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List of publications:

- Publication I: Laser welding and weld hardness analysis of thick section S355 structural steel

- Publication II: Laser welding of structural steels: Influence of the edge roughness level

- Publication III: Experimental investigation of the influence of edge morphology in high power fiber laser welding

- Publication IV: Laser welding of low alloyed steels: influence of edge preparation

- Publication V: The effect of joint edge surface preparation on the efficiency of fiber laser welding of low-alloyed steels

- Publication VI: Methods for improving laser beam welding efficiency

- Publication VII: Reduced pressure laser welding of thick section structural steel

In the following, the publications are summarized based on the objectives, results and impact as regards the whole thesis study.

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Publication I: Laser welding and weld hardness analysis of thick section S355 structural steel

Research objectives

The study investigated thick section laser beam welding of 355 structural steel performed with a HPFL in a closed square edged BJ. The purpose of the experimental study was to identify the optimal processing parameters for the autogenous LBW and identify the existing problems. The optimal welding parameters were described in a form of quality windows. The optimization factor was the maximum welding speed for each power level that resulted in an acceptable full penetration weld without imperfections. However, the absence of visual imperfections does not mean that the weld has acceptable mechanical properties, therefore the hardness tests were carried out to evaluate the level of changes in the material structure in HAZ and WMZ.

Results

The laser power was tested at five levels and the welding speed was set to reach the highest value for each thickness (20 and 25 mm). Results of 40 OVAT experiments were examined and weld quality windows were built. Quality analysis was performed with both NDT and DT. However, only DT (visual analysis of several macrosections) was chosen due to ease of implementation. An example of quality assurance for LBW is shown in Figure 12.

Figure 12. Example of quality assurance procedures – x-ray results and macrosections of samples 137 and 138. Sample 138 demonstrate critical

imperfections – pores on both DT and NDT testing.

To summarize the results with respect to all the welding parameters varied in the research, a re-designed version of the weld quality windows was formulated and is shown in Figure 13.

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Figure 13. Weld quality windows, for steel S355, of two thicknesses (t), focusing length (fF) = 300 mm, focal point diameter (dOF) = 420 µm.

-16 -14 -12 -10 -8 -6 -4 -2 0

400 600 800 1000 1200

Focal point position, mm

Line Energy, J/mm

t = 25 mm

Acceptable Weld Critical Imperfections Cut Through

Incomplete penetration

-16 -14 -12 -10 -8 -6 -4 -2 0

400 450 500 550 600 650

Focal point position, mm

Line Energy, J/mm

t = 20 mm

Acceptable weld Critical Imperfections Cut Through

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Relation to the whole

The main goal of the first publication was to investigate the performance and potential of deep penetration LBW. The influence of the welding parameters on the weld quality and penetration depth was evaluated and the problem of high hardness was identified. A possible solution – reduction of the welding speed to minimum acceptable levels is an extreme, as it reduces the efficiency of the process. Another way to reduce the cooling rates is the use of the preheating – it is discussed in Publication VII. In all further publications dealing with S355 steel the welding parameters were chosen from the weld quality windows determined in Publication I.

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Publication II: Laser welding of structural steels: influence of the edge roughness level

Research objectives

An important conclusion of the previous publication is that LBW process principles, effects of the process parameters and general physics of the process are well studied and the vector of the research is pointing to the direction of possible ways to increase the efficiency of the process. Therefore Publication II serves as an opening theme to the thesis. The first method for increasing LBW efficiency is formulated in the research objective of the study as optimization of the edge surface roughness levels to maximize the penetration depth of the weld.

Results

Several sets of experiments showed that there was a significant positive correlation between the joint edge surface roughness and laser beam absorption in structural steels in butt-joint laser beam welding. These findings were supported by calorimeter measurements and validated in three sets of experiments. The welding parameters were chosen based on the results described in Publication I, therefore most of the welds were of acceptable quality, as shown in Figure 14. All welds with surface edge roughness 8 µm Ra were with critical imperfections: incompletely filled groove and porosity, and this roughness was not recommended for future experiments.

12 14 16 18 20

0 1.6 3.2 4.8 6.4 8 9.6

Penetration depth, mm

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Figure 15. Hypothesis check, St 3, line energy (EL) = 420-450 J/mm

The conclusion about positive effect of the edge surface roughness of about 6.3 µm on the penetration depth is checked by one sample t-test. The “null hypothesis” is that penetration depth for edge surface roughness of 3.2 - 4.8 will be the same or higher as for the optimum 6.3 µm. From Figure 15 it can be seen that the data is quite symmetric and so t-test can be used even though the sample is small. Since p value is definitely lower than = 0.05, there is a low probability (< 1%) of achieving deeper penetration with non-optimum edge surface roughness.

Relation to the whole

Possible explanation for the positive effect of the edge surface roughness of 4.8 - 6.3 µm on the penetration depth was suggested: the joint surface itself does not play a significant role as it melts and partly evaporates during the first milliseconds of the keyhole formation, but the air gap in the joint between the plates plays the critical role.

The next three publications focused on further investigation of the identified correlation.

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Publication III: Experimental investigation of the influence of edge morphology in high power fiber laser welding

Research objectives

The main question addressed in Publication III was to evaluate the joint effect of both surface roughness and the air gap between the plates. It was suggested that minor changes in both design and production processes may give a positive effect on the efficiency and quality of the welds.

Results

It can be seen from re-arranged results shown in Figure 16 that conclusions stated in Publication II were validated. Furthermore, increasing the gap between the plates up to 0.1 mm gives an additional 5-10% increase in penetration paired with optimum edge surface roughness of about 6.3 µm Ra.

10.0 11.0 12.0 13.0 14.0 15.0 16.0

0.0 1.6 3.2 4.8 6.4 8.0 9.6

Penetration depth, mm

Surface edge roughness, Ra m

No additional gap 0.05 mm additional gap 0.10 mm additional gap Low quality zone Acceptable quality zones

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Relation to the whole

The results show a clear correlation the joint effect of both gap and edge surface roughness on the penetration depth. Those conclusions were later validated by analysis of the same effect with a different low-alloyed steel and other welding and optic parameters, described in Publication IV. These results bring to the conclusion that recommended butt-joint setup for laser beam welding includes both certain edge surface roughness, preferably achieved by proper choice of the cutting method, and a minor gap.

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Publication IV: Laser welding of low alloyed steels:

influence of edge preparation

Research objectives

The design of the experiments was based on the results described in Publication III to validate them with St 3 steel instead of S355 steel and with a different welding setup.

Results

As the focal point diameter was larger (dOF = 420 µm, compared with dOF = 300 µm) than that used in Publication III, an air gap of 0.2 mm, compared with 0.1 mm used in Publication III was used. An air gap of 0.3 mm was also used, but the resulting welds were of unacceptable quality as shown in Figure 17.

Figure 17. Depth of penetration of St 3 steel at different pre-set air gap: laser power (PL) = 15 kW, welding speed (vW) = 2 m/min, focal point position (fpp) = -7.5 mm,

focal length (fF) = 420 mm, focal point diameter (dOF) = 400 µm 0

2 4 6 8 10 12 14 16 18 20

Penetration depth, mm

no air gap 0.2 mm air gap 0.3 mm air gap

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Publication V: The effect of joint edge surface preparation on the efficiency of fiber laser welding of low-alloyed steels

Research objectives

Utilization of the previous findings in industry intend the use of long length welds, and the necessary machining of the whole edge surface of both steel plates may neglect the benefit that the use of optimal edge surface provides. Comparison of different butt-joint setups, including asymmetrical edge surface preparation, was performed in Publication V.

Results

According to the results, an abrasive water jet cut joint edge with low-speed shot- blasting of the edge surface gave deeper penetration with the same line energy compared with a machined joint edge. Too high quality of a joint edge was found to decrease the penetration depth and the quality. Additionally, it is important to state that a set-up with constant roughness level among the edge length gave a more stable process with deeper penetration and higher stability than a welding process with varied edge surface roughness. However, modifying surface roughness should not incur additional costs as many manufacturing methods are available and an appropriate method can be selected on the stage of product design in accordance with the desired surface roughness.

Relation to the whole

The findings, collected in Publication II, Publication III, Publication IV and Publication V, support the development of clear recommendations for edge surface roughness preparation in thick section LBW with high power lasers. Combined together, the conclusions of Publication II to Publication V give a clear view on the output of the pre- determined edge surface roughness and additional air gap between the plates in BJ setup on the quality and penetration depth: a “safe zone” for these parameters was identified and validated with the use of different materials, process and laser parameters.

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Publication VI: Methods for improving laser beam welding efficiency

Research objectives

The methods described in section “2.4 Absorption as the key to welding efficiency”

were experimentally investigated and analyzed in Publication VI. The effects of penetration depth and weld quality are analyzed and compared.

Results

Analyzing the effect of two factors - variation of the edge surface roughness in LBW in reduced pressure conditions, or, with preheating up to 120 °C - did not reveal any cumulative effect. Each factor produces peculiar effects without any correlation with the other. Preheating reduces the hardness level. With a reduction of the ambient pressure in the welding zone there was a significant increase in penetration depth. In the case of thick section LBW a 50% increase in penetration at the same level of line energy was observed. Using roughed edge surface instead of a polished one gave 7- 8% increase in penetration. The results are shown in Table 5.

Table 5. Experimental investigation of methods for improving laser beam welding

No Method Effect

Penetration Quality

1 Modification of the workpiece – edge surface

roughness 10-15% increase No effect, if

within optimal roughness level

2 Modification of the ambient conditions - reduced pressure

50-100% increase Strong increase in hardness level

Modification of the No effect at Thorough

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Relation to the whole

In addition to modifying the workpiece through surface preparation, two more ways to increase the absorption in workshop conditions were experimentally investigated:

lowering the pressure in the welding zone and by modifying the process with preheating. Reduction of the ambient pressure in the welding zone to 0.1 kPa provides significant – up to 100% - increase in penetration. Preheating up to 120 °C does not provide a perceptible increase in the penetration. However, preheating provides a reduction in the maximum hardness level. Several of the above described methods may be used together to promote an additional increase in efficiency. The relationships and causalities of these factors require further investigation.

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Publication VII: Reduced pressure laser welding of thick section structural steel

Research objectives

Initial research of the LBW in reduced pressure environment was reported in Publication VI. The effect of focal point position, additional air gap and edge surface roughness were investigated. Laser beam welding of 40 mm SM400A steel was performed with a high-power disk laser at speed of 1 m/min and with 16 kW laser power.

Results

Reduced pressure laser beam welding shows great promise in thick section applications. With a power level of 16 kW, a 32 mm penetration depth weld of acceptable quality was achieved. It is interesting to note that in some cases penetration depth was above 37 mm. However, an incompletely filled groove beyond the limits of acceptable quality was formed. Such welds would be of acceptable quality after additional post-processing to fill the groove, for example, with a single pass arc- welding.

Relation to the whole

A map of preferable welding parameters was formed based on the experimental study. With a focal point position of -20 mm a 36 mm deep weld of acceptable quality in butt-joint setup with a pre-set air gap of 0.3 mm and polished edge surface (Ra 0.4 µm) in 0.1 kPa pressure conditions was performed. An acceptable quality weld of 32 mm in depth was produced at the same conditions but with the use of 0.1 mm gap and a rough edge surface (Ra 3.2 µm). A further increase in penetration depth (> 37 mm) led to an incompletely filled groove; however, without any other critical imperfections.

Due to extreme cooling rates during the welding process, hardness levels of > 400 HV5 were noticed in the fusion zone of the welds. As such high hardness is above acceptance limits for critical applications, hardness reduction techniques, like

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5 Conclusions

A first personal reflection in the beginning of the research was that LBW is a well- studied process, and trends for further research included the use of high laser power

30 kW) and welding of specific materials, like rarely used titanium alloys. However, first impressions are often deceptive.

Optimal process parameters

Generalized rules for LBW of structural steels with HPFLs use power 10 kW: 1 kW power level for 1 mm penetration depth at 2 m/min welding speed. Focal point position for thick section welding is recommend to be in the middle of the steel plate, in formula view: -0.5 × thickness. Effect of the shielding gas, chemical and feed parameters were not investigated, but Ar at 20 l/min was acceptable in all cases when welding at normal pressure.

High hardness of the welds

It was found that structural steels tended to suffer from an increase in hardness in the heat affected and fusion zones up to 450-600 HV, compared with a base material hardness level of 160-200 HV.

An increase in the welding speed showed an increase of the average weld hardness and a decrease of the average HAZ width. An increase of the laser power showed a decrease in the average weld hardness and an increase of the average heat HAZ width. With the line energy increasing there was a tendency of the hardness of the weld to reduce.

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In industrial applications, the hardness level should conform to the requirements laid down at the design stage and the provisions of the relevant application standard.

Weld zone hardness levels achieved during experiments are the beyond acceptable limits for oil and gas industry offshore structures (250 HV) (ISO 15156-2, 2009) and shipbuilding applications (400 HV) (Lloyd’s Register of Shipping, 1996). Strict limits for the hardness of parent materials and of welds and their HAZ for the oil and gas industry play important roles in determining the sulfide stress cracking susceptibility.

Hardness test results can be interpreted that way to evaluate the resistance of the weld to hydrogen embrittlement, as constant contact with oil and pressed gas implies high concentration of hydrogen sulfide. However, standard ISO 15156-2 does not take into account the specifics of the LBW process compared with traditional welding methods.

Due to high temperature any moisture in weld zone evaporates and due to high welding speed and cooling rate the hardness in the weld metal zone increases.

Considerably more work will need to be done to determine the amendment of the limits of hardness levels for the case of LBW with the hardness levels achieved.

Additional modifications to the process are required to reduce the difference in hardness between the base material and the weld zone. Preheating may be performed with the use of electric heaters, flame torches or even additional laser beams, and induction heating is also available. All these methods are proven to reduce hardness in the weld zone and HAZ. However, the combination of these techniques with reduced pressure conditions has not been tested, thus far.

Edge surface roughness preparation and pre-set air gap between the plates

The absorptance of the structural steel in butt-joint laser beam welding has a significant dependence on the edge surface roughness at laser power of 10 kW. The influence of the roughness level has a tendency to increase with an increase in laser power and results in 10-15% increase in efficiency at 15-20 kW power level, compared with the polished edge surface without air gap. The maximum penetration depths were achieved at roughness level of around Ra 6.3 µm.

An increased air gap of 0.1-0.2 mm gave a deeper penetration level and better weld quality. The size of the air gap depends on the laser spot size. Full penetration welding at edge surface roughness levels higher than Ra 8.0 µm produced a weld of unacceptable quality.

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Reduced pressure LBW method

Reduced pressure laser beam welding provides a significant increase in penetration depth and weld quality. With ambient pressure decreases, the evaporation is promoted and less laser energy is used for material evaporation, therefore the efficiency of the welding process is increased. The combination of an optimized edge surface roughness and a pre-set air gap with this method provides an additional increase in penetration depth.

Laser beam welding of 40 mm low-alloyed structural steel welded with a speed of 1 m/min and 16 kW laser power at the focal point position of -20 mm (inside of the material) produced a 36 mm deep weld of acceptable quality in butt-joint setup with a pre-set air gap of 0.3 mm and polished edge surface (Ra 0.4 µm) in 0.1 kPa ambient pressure conditions.

Due to extreme cooling rates during the welding process, high hardness levels were noticed in the fusion zone of the welds. As such high hardness is above acceptance limits, hardness reduction techniques are required.

Current method was able to achieve penetration depths of at least 100% deeper than the welds made at atmospheric pressure, and, therefore, the efficiency of the process was doubled. This is clearly not the limit.

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5.1 Limitations of this thesis

It is, however, important to recognize the limitations of the findings of this study;

namely, the process parameters (welding speed, power level, focal point position), optical parameters (focusing lens focal length, focal point diameter) and the materials (low-alloyed structural steels) used in the experimental sets.

5.2 Future research topics

To apply the methods described in the thesis, substantial design engineering is required to utilize locally reduced pressure for ready to use sliding seam chamber, or other method capable to provide the local pressure reduction in the welding zone with the possibility for LBW. At the time of finalizing of the thesis, prototypes of local pressure reduction devices for laser welding were at the stage of general testing.

Utilization of both, reduced pressure and preheating for reduction of the high hardness of the welds, can be a complex but rewarding engineering challenge.

Use of the X-ray, high speed imaging analysis or other keyhole monitoring methods are needed to ascertain the phenomena underlying described results.

The experimental results of this thesis can be useful in further development of the simulation models for keyhole laser beam welding.

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