Laser Forming

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Laser Forming

Author:

J.P.J. ADMIRAAL

S2230038

Supervisors:

Prof. Dr. J.Th.M.DEHOSSON

Ir. Dr. V. OCELIK

MSc. H. FIDDER

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, Applied Physics

in the

Materials Science Group University of Groningen

October 31, 2018

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UNIVERSITY OF GRONINGEN

Abstract

Faculty of Science and Engineering University of Groningen

Master of Science, Applied Physics

Response of Ti Microstructure on Laser Forming by J.P.J. ADMIRAAL

In this research the microstructural and bending response to laser forming of commercially pure (CP) titanium grade 2 was studied using experimental and modelling methods. Emphasis was placed on the phase transformation during the laser forming process. The bending angle response is measured in situ for different processing parameters using 3D digital image correlation (DIC). The change in microstructure is observed using electron backscatter diffraction (EBSD). Finite element method (FEM) models are used to analyze the heat transfer and temperature inside the material and simulate the laser forming process.

The thermal expansion of CP titanium grade 2 showed an increase in density during the α to β phase transformation. Evidence of small influence of the phase trans- formation, in dependence of the bending angle on the amount of delivered energy was found. The FEM models proved to be helpful for better understanding the heat transfer inside the metal sheet. A possible relation between the α−βphase transformation and the depth of the laser affected microstructure was found.

DIC proved to be a strong instrument for in situ observation of laser bending. Ex- perimental and simulation results suggest that the laser power has a larger influence on the final bending angle than the laser traverse speed. Sandblasted sheets show significantly higher final bending angle values, where grain size seems to have no influence. The laser bending process results show good repeatability.

The final depth of the laser beam heat affected zone (LHAZ) strongly correlates with the final bending angle. The microstructure of the LHAZ consists of small refined grains at the top layer followed by large elongated grains. Deformation mechanisms slip and twinning were observed in the LHAZ, where the distribution depends on particular processing parameters. Large grains at the top layer of the LHAZ favour pyramidal first order <C+A> slip.

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research project. In addition, I would like to thank Professor J.Th.M. de Hosson for haven given me this opportunity to do my Applied Physics masters project in his research group and for all the great advice during our meetings. I would also like to thank Dr V. Ocelik for the pleasant collaboration during the project. Without his expertise on electron microscopes and laser systems, this project would not have been possible. I could not thank Dr V. Ocelik, without also thanking Herman Fidder.

The laser forming experiments could not be performed on my one, so we worked together as a great team. Herman Fidder was always available for any assistance, experimentally or during the writing of this thesis. Together with Dr V. Ocelik, he helped me to make most out of this research project.

I would also like to thank all the members of the Materials Science Group at the University of Groningen over the last year. I learned a lot from our group meetings and advice I received. I would like to thank Indranil Basu in special for his help with interpretation of my EBSD results. Further I would like to thank Roy Blum and Bas de Jong for their advice and the pleasant conversations we had in our room.

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List of Figures

1.1 Picture of a laser formed car door . . . 1

2.1 Temperature gradient mechanism processing steps . . . 4

2.2 Schematic representation of α−βtransformation . . . 6

2.3 Thermal expansion graph showing α−β phase transformation temperature range . . . 7

2.4 Microstructure CP Ti grade 2 as received . . . 7

2.5 Schematics of the slip systems in titanium . . . 8

2.6 Schematics of the twin systems in titanium . . . 8

3.1 Schematic and picture of the laser setup . . . 9

3.2 Picture of one of the metal sheets used in the experiments . . . 10

3.3 Schematic representation of 3D DIC . . . 11

3.4 Aramis 4M two cameras setup . . . 11

3.5 Laser forming sample with tracking markers . . . 12

3.6 Schematic representation of EBSD . . . 13

3.7 Picture of a prepared EBSD sample . . . 13

3.8 Schematic of the EBSD preparation procedure . . . 14

3.9 Schematic drawing of the EBSD scanning area . . . 14

3.10 FEM and mesh size explained with discretization of function u . . . 15

3.11 Image of the laser heating model’s mesh . . . 16

4.1 DIC right camera image of laser forming . . . 17

4.2 Graph of the laser bending response at 440 W 10 mm/s . . . 18

4.3 Graphs of the laser bending response at 570 W 15 mm/s . . . 18

4.4 Bending response compared for variable laser parameters . . . 19

4.5 Bending angle response for multiple overlapping laser tracks . . . 20

4.6 Bending response compared for different absorption coefficients and grain sizes . . . 21

4.7 Depth of affected microstructure compared for variable laser parameters 22 4.8 IQ maps with highlighted twins and small misorientations of the 570W 20 mm/s track . . . 22

4.9 Zoomed IQ maps with highlighted twins and small misorientations of 720W and 1000W at 20mm/s . . . 23

4.10 KAM map 720W at 20mm/s . . . 24

4.11 Average KAM value graphs plotted against the depth . . . 24

4.12 IPF maps of 510W, 720W and 1000W at 20 mm/s . . . 25

4.13 KAM maps of as received, sandblasted and grain grown sandblasted sheets . . . 26

4.14 Average KAM value graphs of as received, sandblasted and grain grown sandblasted sheets . . . 26

4.15 KAM, IPF and IQ map of the grain grown sheet . . . 27

4.16 3D isosurface plot of the laser heat model . . . 27

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x

4.17 Maximum temperature plotted against the depth position. . . 28 4.18 Laser power plotted against the traverse speed for three maximum

surface temperatures. . . 28 4.19 Laser forming model 3D temperature plot with deformation . . . 29 4.20 Comparison of the measured bending response and the model bend-

ing response . . . 29

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List of Tables

2.1 The chemical composition requirements of CP Ti grade 2 according to, adapted from [1] and the chemical composition of the CP Ti grade 2 used in this research as reported by the manufacturer. . . 5 4.1 Active twinning systems present in substrate as received, after me-

chanical forming and after laser forming, adapted from [7]. . . 23 A.1 Overview of the performed laser tracks on the as received sheets 1, 2

and 3 . . . 35 A.2 Overview of the performed laser tracks on the grain grown sand-

blasted sheet and sandblasted sheet . . . 36 A.3 Overview of the performed overlapping laser tracks on the grain grown

sandblasted sheet and sandblasted sheet . . . 36

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List of Abbreviations

CP Commercially Pure

Ti Titanium

LF Laser Forming

LHAZ Laser beam Heat Affected Zone TGM Temperature Gradient Mechanism HCP Hexagonal Closed-Packed

BCC Body-Centered Cubic

TMA ThermoMechanical Analyzer SAS Slovak Academy of Sciences DIC Digital Image Correlation

3D 3 Dimensional

TMA ThermoMechanical Analyzer fps Frames per second

OIM Orientation Image Microscopy EBSD Electron BackScattered Diffraction

CI Confidence Index

FEM Finite Element Method PDEs Partial Differential Equations NMEs Numerical Model Equations PDEs Partial Differential Equations DoFs Degrees of Freedom

P/v(e.g., 440/10) laser power (P) and traverse speed (v) of a formed laser track

IQ Image Quality

KAM Kernel Average Misorientation IPF Inverse Pole Figure

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List of Symbols

F0 Fourier number 1

α_td thermal diffusivity m²s⁻¹

d beam diameter m

v traverse speed m s⁻¹

s thickness m

α_b final bending angle ^◦ α_th thermal expansion coefficient K⁻¹

P power W

A absorption coefficient 1

ρ density kg m⁻³

c_p heat capacity J K⁻¹

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Chapter 1

Introduction

The concentration of titanium in the crust of Earth is 0.6%, when considering structural metals only iron, aluminium and magnesium are more abundant [1]. Accord- ing to Collings et al. [1] titanium and its alloys have two important properties, an excellent corrosion resistance and a high specific strength. Due to the need of light and strong materials, many applications of titanium can be found in the aerospace industry. Titanium not only finds its applications in the aerospace industry, the material characteristics of titanium are also interesting for applications in for instance power plants, human implants and the automotive industry. For all of these applications the titanium needs to be processed and formed to the desired shape.

Forming of metals into jewellery was already performed around 4000BC, but laser forming was not introduced before the end of 20th century [2, 3]. Metal forming is defined as the metalworking process using mechanical plastic deformation to shape metal objects and parts permanently, without changing its mass [4]. For the forming of sheet metal mechanical forming using a tool and die to shape the sheet is used.

Laser forming is an alternative technique for shaping metal sheets, without external forces. Therefore, laser forming is much more flexible than current metal forming techniques. Next to 3D printing, laser forming could for instance be used for proto- types, fabrication of personalized parts and also for applications as small secondary forming for distortion corrections or tuning [5]. An example of an application is the laser formed model of a car door in figure 1.1.

FIGURE 1.1: Picture of a laser formed car door (approximately 1:8 scale of a real door panel). Adapted from [6].

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2 Chapter 1. Introduction

As stated in the paper by Fidder et al. [7], laser forming has a different influence on the change of the microstructure than mechanical forming. The α−β phase transformation in commercially pure (CP) titanium (Ti) grade 2 being an additional microstructural factor, which should be considered regarding laser forming, is also stated in this paper [7]. Previous experimental, analytical and modelling studies on laser forming do not consider phase transformation as a factor, while phase transformation influences the thermal expansion [1, 8, 9]. The microstructure after the laser forming process is characterized by multiple microstructural changes, for example slip, twinning, phase transformation recrystallization, grain fragmentation and grain boundary sliding due to the phase transformation, in the areas with compression and tension [7].

1.1 Research objectives

The contribution of phase transformation to the laser forming process of CP titanium grade 2 is studied within this research. To study this contribution a combination of experimental and modelling methods is used. In situ bending angle measurements of the laser forming with different processing parameters are combined with analysis of the microstructural response and modelling of the temperature field.

In this research the second objective is in situ measuring the bending angle response during laser forming and comparing the bending response for different processing parameters. The laser forming process will be modelled using a finite element model to compare with the experimental results, where the model should help analyzing the heat transfer and temperature inside the metal sheet during the laser forming process.

The general response of the microstructure for different processing parameters is the final objective in this research, where not only the influence of the laser parameters, but also the influence of the grain size and effect of sandblasting on the laser beam absorption coefficient are studied. The temperature field of the finite element model will be compared with the microstructural changes during laser forming.

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Chapter 2

Literature review

2.1 The mechanisms of laser forming

The laser forming (LF) process is used to shape, mostly sheet metal, components without hard tooling or external forces. The high flexibility makes the process interesting for fast prototyping, low-volume manufacturing and forming corrections [5].

The irradiation by a laser beam induces thermal stresses to plastically deform sheet metal. The deformation depends on the processing parameters, the geometry and the material properties of the sheet metal [10].

This chapter details the theoretical background of the laser forming process, with specific emphasis on how the nature of laser induced thermal cycles effects LF mechanisms through control of process parameters such as laser power, speed and spot size.

2.1.1 The process of laser heating

Heating of a component by thermal input from a laser beam is essential for the laser forming process. The process parameters are important for the complexity of the heating process, which can vary from primarily conductive heat transfer to a combination of conductive, radiative and convective heat transfer [11]. Higher laser inten- sities resulting in higher thermal input can lead to solid state phase transformations and melting of the substrate as the temperature rises. Laser forming is generally a process without any melting, as melting negatively alters metallurgical properties in the irradiated area [12–14].

The physical process that leads to heating of the surface when irradiating with a laser beam is called inverse Bremsstrahlung. Inverse Bremsstrahlung can be described as the absorption of photons from the incident light waves that penetrate the metal surface causing excitation of electrons [15]. The energy of the free electrons that move through the lattice structure of the metal is transferred to lattice phonons by collisions, resulting in heating of the metal. The heating rate depends on the metal surface’s absorptivity [16]. The distribution of the heat depends on the intensity distribution of the laser beam. The laser heating is a conduction limited process, where the heat flux depends on the thermal properties of the material. In response to the heating thermal expansion takes place, causing plastic or elastic deformation.

Plastic deformation is caused by compressive stresses in the laser heat affected zone (LHAZ). Compressive stresses are caused by the restriction of thermal expansion

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4 Chapter 2. Literature review

by the substrate’s cold bulk due to the localized nature of laser heating (see section 2.1.2) [11].

During laser heating, phase transformations at higher temperatures alter the microstructure. The change in crystal structure affects the thermal properties of the material, which are important for the laser forming process. Therefore, the temperature dependence of the material properties should be taken into account when con- ducting research on the laser forming process. Thermal properties that are affected are for instance the density, thermal expansion coefficient and thermal conductivity [17]. Phase transformations can be either solid state phase transformations, such as the α−βphase transformation in Titanium, or solid to liquid phase, during melting of a thin surface layer.

2.1.2 Temperature gradient mechanism

Geiger and Vollertsen [10] published about the mechanisms of laser forming in 1993 and their research is still the basis for most of the research on laser forming today.

As general rule it could be said that for substrates with a thickness in the same order as the laser beam diameter the temperature gradient mechanism (TGM) dominates [8]. From reports on laser forming, TGM is the most reported mechanism [18]. The Fourier number, given in equation 2.1 below, can be used to quantitatively determine which mechanism dominates for a combination of the processing parameters as:

thermal diffusivity (α_td), beam diameter (d), traverse speed (v) and thickness (s) [11]. The Fourier number is given by

F₀ = ^α^td^d

vs² , (2.1)

which can be used for the characterization of the heat conduction nature, where TGM will be dominant for low Fourier numbers (typically smaller than 1 [15]) [19].

FIGURE 2.1: TGM laser bending processing steps: (a) schematic model of laser bending; (b) heating process; (c) cooling process.

Adapted from [20].

In Figure 2.1 the principle of the TGM laser bending process is shown. In this case the laser beam is moving in the positive X direction over the surface of the metal sheet by moving the sheet in the opposite direction. A steep thermal gradient into the substrate is the result of the fast-heated surface by the laser beam, with a relatively slow heat conduction into the sheet. The traverse speed needs to be high enough to maintain the steep thermal gradient. This thermal gradient causes a differential

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so-called counter bending is a result from the bending moment created by the hin- dered thermal expansion and causes some plastic tensile strain at the top. From the moment the thermal stress reaches the temperature-dependent yield strength, any higher stress results into plastic compressive strains [21]. The higher stress is due to additional thermal expansion that is restricted by the surrounding cooler material, with also the material strength reduced, as the temperature rises. Mechanical constraints from the metal sheet can reduce the counter bending [10, 14].

There is thermal elastic contraction of the material at the top layer as the temperature decreases during cooling. Due to the plastic compression the top layer is lo- cally shortened and therefore the metal sheet bends towards the laser (+Z direction) during the cooling process, which is called positive bending. During this cooling process the Young’s modulus and yield stress in the laser heat affected zone return to a significantly higher level and there is some amount of plastic re-straining [21].

The total process of TGM laser bending can be repeated to increase the final bending with every (fully) overlapping pass of the laser beam over the surface of the metal sheet [14].

2.2 CP titanium grade 2

The material of the metal sheets used in this work is commercially pure (CP) tita- nium (Ti) grade 2, which is unalloyed. It only consists of α-phase, with a hexagonal close-packed crystal (HCP) structure, at room temperature. Therefore, the properties are controlled by the grain size and chemistry of the composition. In table 2.1 the chemical composition of CP titanium grade 2 is given, the grade depends mostly on the allowable levels of oxygen and iron and yield strength. The minimum yield strength for this grade of CP Ti is 275 MPa, this in combination of excellent forma- bility and corrosion resistance is the reason that CP Ti grade 2 is widely used for a variety of applications, from aerospace to dentist [1]. In this section the main focus will be on the α−βphase transformation, the microstructure, and the deformation mechanisms of CP Ti grade 2.

TABLE2.1: The chemical composition requirements of CP Ti grade 2 according to, adapted from [1] and the chemical composition of the CP Ti grade 2 used in this research as reported by the manufacturer.

Element Required weight % Reported weight %

Carbon 0.10 max 0.005

Nitrogen 0.03 max 0.009

Oxygen 0.25 max 0.155

Iron 0.30 max 0.040

Hydrogen 0.15 max 0.003

Others, individual 0.10 max 0.070 max

Others, total 0.40 max 0.250 max

Titanium Balance Balance

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2.2.1 Phase transformation

As the material is heated during laser forming, temperatures rise to sub-melting temperatures up to the melting point of approximately 1665^oC at the surface [1].

CP titanium grade 2 has between room temperature and melting point a structural phase transformation from α- to β-phase, influencing the thermal expansion. At room temperature this material is entirely in the α-phase, with a HCP structure.

Between temperatures from about 862^oC to 910^oC a transformation to the β-phase takes place, where the β-phase has a body-centered cubic (BCC) structure. In figure 2.2 the schematic representation of the phase transformation is shown, from BCC (β) to HCP (α) in this representation.

FIGURE 2.2: Schematic representation of the β (BCC) to α (HCP) phase transition, where λ₁ and λ₂ are the two different distortion

modes. Adapted from [22].

For explaining the phase transformation using figure 2.2, Burger’s distortions are considered [23]. The transformation from BCC to HCP can be described with two distortion modes, λ₁and λ₂. λ₁is a shear deformation from the (110) plane of BCC to the hexagonal basal plane. λ₂is a slide displacement along the[1¯10]of the planes.

During the transformation from the BCC to HCP structure and vice versa, the transition goes through a base-centered orthorhombic structure, with both distortion modes happen smoothly and simultaneously [22].

In the book by Boyer et al. [1], a graph on the linear thermal expansion of pure titanium can be found on page 145. In the data from Bell in this graph a phase transformation is shown around 885^oC, where the transformation leads to a small increase in linear thermal expansion. In figure 2.3 the dimension change of a piece of the CP Ti grade 2 used in this work during constant heating with 4^oC/min is shown.

Here a phase transformation is clearly visible, but in contrast to the data from Bell the density increases with about 1.3% during the phase transformation. The thermal expansion rate, however, increases from 7.143 µm/(m^oC) before to 8.114 µm/(m^oC) after the transformation.

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FIGURE2.3: Dimension change during 4^oC/min constant heating, showing the α−β phase transformation temperature range. Mea-

sured by a TMA at the institute of Exp. Physics SAS, Slovakia.

2.2.2 Microstructure and deformation mechanisms

The microstructure of the hot rolled metal sheet, as received, has an equiaxed grain structure throughout the material [24]. An image from the microstructure is shown in 2.4, made with an optical microscope on a polished and chemically etched sample of the CP Ti grade 2. The average grain size is between 70 and 110 µm.

FIGURE2.4: Optical microscope image of the chemically etched microstructure of the CP Ti grade 2 as received.

The main deformation mechanisms for plastic deformation in α titanium is dislo- cation motion, but also deformation twinning plays a major role [25]. α titanium has a large number of dislocation slip and twinning systems. Slip is movement of dislocations along a slip plane, where all atoms in a block move the same distance.

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On the other hand, twinning is the symmetrical intergrowth of crystals, where each concerned plane of atoms moves in the same direction a certain distance, with the amount of movement of each plane proportional to the plane’s distance from the twinning plane [26].

Schematics of the slip systems are shown in figure 2.5, where the most common slip systems are in the three red boxes. These most common slip systems are basal <a>, prismatic 1^storder <a> and pyramidal 1^storder <c+a> systems. Below the names of the slip systems, the plane and direction are given. Slip occurs at high temperatures and low strain rates.

FIGURE2.5: Schematics of the slip systems in titanium, with name, plane and direction. The most common slip systems are inside the

red boxes. Adapted from [27].

In figure 2.6 the schematics of the twinning systems are shown, which can be divided into two tensile and two compression twinning systems. Below the type of the twinning systems are the plane and direction given. Opposite to slip, twinning occurs at low temperatures and high strain rates.

FIGURE2.6: Schematics of the twin systems in titanium, with twin type, plane and direction. Adapted from [27].

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Chapter 3

Experimental Procedure

The experimental procedure presented in this chapter consists of a few methods.

These methods can be roughly divided into the laser bending, the digital image correlation (DIC), the observation of microstructure and the modelling part. A short background, the preparation process and the following steps of the procedure are explained per section on the methods.

3.1 Laser setup

The laser used for the laser forming is a 3 kW Yt:YAG continuous fiber laser from IPG Photonics. The laser has a wavelength of 1.07 µm and the nozzle of the laser beam is tilted at an angle of 9 degree from the -Z to the +X direction to avoid back reflection. A schematic and a picture of the laser setup are shown in figure 3.1. The laser optics with 120 mm focal length are set to a distance of +35 mm out of the focus position, resulting in a laser beam radius of about 2.8 mm, with a Gaussian distribution of power density. To prevent oxidation on the surface of the metal sheet during laser forming there is a second nozzle for Argon gas, which is used as shielding gas. The metal sheet is clamped onto a workbench, which can be moved into the Y-direction. The laser and shielding gas nozzles can be moved together into the X and Z direction. The surface is heated with the laser beam from the edge at the -X direction to the +X direction, where the laser beam is turned on 5 mm before the center of the beam hits the surface and turned off 5 mm after leaving the surface.

FIGURE3.1: Schematic (a) and picture (b) of the laser setup, with the fiber laser nozzle (1) and shielding gas nozzle (2). Adapted from [20].

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10 Chapter 3. Experimental Procedure

The metal sheet is clamped with multiple clamps on one side, shown in figure 3.2.

The metal sheets have dimensions of 200 mm in length, 50 mm in width and 3 mm in thickness and are raised about 1 mm with a spacer at the clamps to avoid contact with the metallic base. The center of the beam is shifted 6 mm in the +Y direction between every single laser track, starting with the first laser track about 50 to 60 mm from the free end of the sheet. This is shown in figure 3.5, with 1 being the first laser track, 2 the second, up to the n^th laser track. Therefore, the surface heated by the laser is always on the same XY plane at the start of every individual laser track.

FIGURE3.2: Picture of one of the metal sheets used in the laser forming experiments.

The metal sheets used in the laser forming experiments are all from the CP Titanium grade 2, described in section 2.2. In the laser forming experiments five variables are studied, namely traverse speed and power of the laser beam, multiple 100%

overlapped laser tracks, the grain size, and the absorption of the surface. The laser forming is studied for the traverse speed of the laser beam of 20, 15, 10 and 5 mm/s, with a range of laser powers depending on the speed. The range of different laser powers was chosen where the lowest power would still result in bending and a small change in microstructure and the highest power would be result in a surface temperature close to the melting point. By repeating the same laser and Y position settings for multiple tracks, 100% overlapping laser tracks are tested. The influence of the grain size is tested for metal sheets as received and a grain grown metal sheet. For the metal sheet with larger grains the grains are grown by heating the sheet in an oven for 5 days just below the α−βphase transformation temperature. Finally, the influence of an increased absorption coefficient is tested by sandblasting the surface of the metal sheet. A table of all laser tracks, with position, laser speeds, laser powers, number of overlapping tracks, if the grains are grown or surface is sandblasted, and final bending angles can be found in appendix A.

3.2 Digital image correlation

For in situ measuring of the bending angle during laser forming of the metal sheet three dimensional (3D) digital image correlation (DIC) is used. For 3D DIC a setup of two cameras, shown in the schematic of figure 3.3, watching the object of interest from different angles are necessary. The cameras need to be focused at the same spot on the object. Before the measurements calibration of the setup is necessary to account for the angle and contrast. The DIC software divides both images of the two cameras in facets, which are groups of pixels. The facets are used to track displacement between a reference and following images, therefore the facets need to be unique. The software looks at the grey levels of pixels in each facet, to measure displacement in sub-pixel resolution, so the contrast and intensity is important for recognition. The size of the facets and overlap with neighbouring facets can be ad- justed. Combining the tracking and comparison of facets in images of both cameras makes it possible to measure displacement in 3D [28].

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FIGURE3.3: Schematic representation of the 3D DIC process steps.

First calibration of the cameras (right), followed by a reference frame, which is used to determine the displacement in all the following

frames. Adapted from [29].

3.2.1 In situ DIC observation of laser forming

The setup used for in situ measuring of the bending angle is the Aramis 4M, which has two 4MP cameras, 2400 x 1728 pixels per camera. The setup is shown in figure 3.4, the angle between the cameras is 24.3^oand working distance is about 470 mm.

For optimal lighting conditions, with a high intensity and contrast, two special blue light lamps are used. This blue light also enables the software to filter interfering ambient light. The frame rate of the cameras is maximum 60 frames per second (fps) for full resolution. For the calibration the corresponding GOM 90 mm calibration panel is used, the calibration deviation was around 0.02 pixels. For the first metal sheet measurements a frame rate of 30 fps was chosen, for all the others the frame rate was maximized for best recognition of the markers used for displacement tracking in the experimental lighting conditions, resulting in a frame rate of 40 fps. The total number of frames per track is between 500 and 1500 depending on the traverse speed of the laser beam and frame rate. The cameras can only watch the end part of the metal sheet, because the scattered light of the laser beam is too bright when inside the view of the cameras.

FIGURE3.4: Picture of the Aramis 4M two cameras in situ setup

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The displacement of the metal sheet needs to be tracked for measuring the bending angle with the 3D DIC during the laser forming. The bending angle α for every frame can be calculated from the difference between the angle at the reference frame and the following frame. The angle is measured for the front side of the metal sheet, marked as B in figure 3.5 and for different positions on the top of the metal sheet, marked as A in figure 3.5. The different positions on the top are used to measure any torsional bending. To calculate these angles the positions of the multiple markers on top (A), front side (B) and base (C) are used. These markers consist of a 0.4 or 0.8 mm diameter black with inner white circle. The markers on the base are used as fixed positions for calculating the bending angle of the metal sheet at the side and top positions.

FIGURE3.5: Picture of a laser forming sample with tracking markers for in situ DIC measurements on the top (A), front side (B) and base (C). 1, 2, 3, . . . , n are formed laser tracks and α is the bending angle.

3.3 Observation of microstructure

For characterization of changes in the microstructure after laser forming a Philips ESEM-XL30 FEG and a Tescan LYRA SEM dual beam microscope were used, both equipped with EDAX TSL orientation image microscopy (OIM) systems. TSL OIM Data Collection 7.3 software is used to collect and index electron backscattered diffraction (ESBD) patterns and TSL OIM Analysis 7.3 and 8.0 were used to analyze the data and create OIM maps. The main technique used for the observation of the microstructural changes is EBSD. In EBSD the pattern of backscattered electrons from the electron beam are collected on a phosphorus screen. A schematic representation of this is shown in figure 3.6, where for EBSD the sample is tilted about 70^ofrom horizontal plane [30].

The reflected pattern of backscattered electrons is called a Kikuchi pattern, where the backscattered electrons of this pattern colliding with the phosphorus screen flu- oresce. The Kikuchi pattern originates from the crystal orientation, where the bright crossing bands visible on the phosphorus screen in figure 3.6 are correlated to the crystallographic planes. A CCD camera converts the pattern to a digital image, which software can convert to an crystallographic orientation. The software uses

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FIGURE3.6: Schematic representation of EBSD. Adapted from [31].

Hough transformation to convert individual bands of the Kikuchi pattern into localized peaks [32]. Combined with the chosen possible crystallographic phases the best crystallographic orientation fit to these peaks is calculated, where the confidence index (CI) gives a measure for the certainty of the fit.

An area on the sample can be scanned with the electron beam to build an image where for every point measured the pixel contains the crystal orientation, phase and confidence index, which can be used to generate different maps based on measured data. The same data cleaning procedure was used for every EBSD scan before the OIM data analysis. First a CI standardization, with minimum grain size of 5 pixels and a grain tolerance of 5^oand then neighbour orientation correlation cleaning, for modifying the crystallographic orientation of points with a CI below 0.1 to that of the majority of neighbouring points, was used. The last step was removing all remaining points with a CI below 0.1, shown as black points on the OIM maps. During this procedure, no more than 5% of all points was modified.

3.3.1 EBSD preparation

For high quality of Kikuchi patterns, it is important to have a flat and damage free surface. To observe the change in microstructure due to the laser forming, a cross section of the laser track at about 1 cm of the starting edge of the laser track is used.

For the cross section the sample is cut with abrasive cutting and with diamond cutting in between laser tracks, visible in figure 3.7a. This is the first step of the whole sample preparation process shown in figure 3.8. Two specimens of each three cross sections of laser tracks are hot mounted together in a conductive resin, as shown in figure 3.7b.

FIGURE3.7: Picture of a prepared EBSD sample, with the cutting process (a) and the mounted cross sections (b).

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The mounted sample is then grinded for about 5 minutes on #220 SiC paper using water as lubricant, followed by grinding on a MD-Largo surface with a 9 µm DiaPro Allegro (diamond) lubricant for about 15 minutes. Finally the sample is polished on a MD-Chem surface using a mix of 90 % 0.04 µm OP-S (colloidal silica) and 10 % hy- drogen peroxide as lubricant and etchant. For the optical microscopy the sample is chemically etched using Kroll’s reagent, containing 100 ml water, 2 ml hydrofluoric acid and 4 ml nitric acid. These preparation procedure steps are based on the Struers application notes by B. Taylor and E. Weidmann [33].

FIGURE3.8: Schematic of the different steps in the EBSD preparation procedure.

3.3.2 EBSD procedure

The area of interest for the change in microstructure due to laser forming was the laser heat affected zone (LHAZ), where also α−βphase transformation is expected.

As a reasonable EBSD step size for being able to detect twins a size of 0.7 µm was chosen, which resulted in a maximum scanned area width of about 700 µm. The width of the LHAZ was between 2.5 and 5 mm, therefore only the center of the LHAZ was chosen for scanning with an EBSD scan. A schematic of the EBSD scanning area is shown in figure 3.9. Before the EBSD scans the microstructure of the LHAZ was observed in the optical microscope to find the depth and the position of the LHAZ’s center. For the height of the EBSD scan about 100 µm was added to the depth of the LHAZ measured with the optical microscope.

FIGURE3.9: Schematic drawing of the EBSD scanning area, with the orange cross section, blue LHAZ and red EBSD scan area.

3.4 Simulation using FEM modelling (COMSOL)

3.4.1 Finite element method (FEM)

Partial differential equations (PDEs) could be described as a kind of mathematical fortune-telling [34]. Usually space- and time-dependent problems in physics are ex- pressed in terms of these PDEs. The difficulty of PDEs is that they cannot be solved analytically for most problems and geometries. Discretization methods can be used

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FIGURE 3.10: FEM and mesh size explained with discretization of function u, in both graphs a and b is the function u (solid blue line) approximated with u_h (dashed red line), which is a linear combina- tion of linear basis functions (ψ_i, represented by the solid black lines).

The coefficients used are denoted by u0 through u7. In graph a the elements are uniformly distributed, in contrary to the distribution in

graph b. Adapted from [35].

To explain how FEM works the graphs in figure 3.10 are used, with the dependent variable in a PDE, function u and its approximation u_h. Function u_happroximates u using linear combinations of basis functions, according to

u_h =

∑

i

u_iψ_i, (3.1)

where u_i are the coefficients of the functions that approximate u with u_hand ψ_i are the linear basis functions [35]. The distribution on the x-axis of 3.10a is uniform, where the distribution on the x-axis of 3.10b is related to the gradient of u. By changing the distribution, the approximation is improved, comparable to adjusting the mesh size of a COMSOL FEM model for areas with, for instance, a large gradient in temperature.

3.4.2 Laser heating model

For the COMSOL model, to simulate the heating of the CP titanium grade 2 metal sheet with a laser beam as heating source, a time-dependent 3D model is used. The dimensions of the samples used in the experimental part (200 x 50 x 3 mm) and a Gaussian laser power density distribution (radius of about 2.8 mm) are used. As material the build in CP Ti grade 2 with corresponding material properties is used.

For computation of the laser heating model the COMSOL physics "Heat transfer in solids" is used, which includes computation of the heat conduction, convective heat flux and general inward heat flux.

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The used mesh for the laser heating model is shown in figure 3.11, where the mesh is more refined around the laser track. The model has 76005 degrees of freedom (+21662 internal). The model is solved for a time range depending on the speed, with a step size of 0.01 seconds. The solving time of the model is between 6 and 10 minutes on a typical PC.

FIGURE3.11: Image of the laser heating model’s mesh. The dimensions are equal to the experimental sheet dimensions and the mesh is

refined around the laser track.

3.4.3 Laser forming model

The laser heating model is relatively easy for a time-dependent 3D model, where the laser forming model is much harder regarding the involved physics phenom- ena. The basis is the laser heating model, but a combination of COMSOL physics are added. To compute the mechanical forming the COMSOL physics "Solid mechanics" is added, which includes an isotropic linear elastic material with perfectly plastic behaviour when the stress is higher than the yield stress. The yield stress is temperature dependent, and the sample is fixed on one end, similar to the real experiment. To couple both COMSOL physics thermal expansion and temperature coupling is added to the model. As the combination of physics is much more difficult to compute, the time to solve with a coarser mesh size is between 16 and 24 hours on a typical PC. The degrees of freedom (DoFs) is at 7878 much lower due to the coarser mesh size, but the number of internal DoFs is much higher at 70878.

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Chapter 4

Results

The results chapter has three parts. The first part contains the measured bending response of the laser forming, using the ARAMIS 3D camera setup in conjunction with the DIC software. The results dealing with the microstructural response to the laser forming are in part two. The final part consists of the simulation results from the COMSOL model and a comparison with the experimental results.

4.1 In situ DIC observation of laser forming

The 3D camera setup and ARAMIS DIC software enabled to measure the displacement of the markers on the sample during the laser forming and calculate the bending angle on multiple positions on the free end of the metal sheet. A single measurement of one laser track consisted of around one second before the laser was switched on to about 10-15 seconds after the laser left the formed sample, continually measuring the change in bending angle in comparison to the reference frame. In figure 4.1 is the view of one of the DIC cameras shown, with an overlay of all the tracked markers as green dots, divided in the base, side and top groups. In this figure the calculated angles for this frame in comparison to the reference frame are also shown. On the left part of the figure a few previous formed tracks are visible.

FIGURE4.1: Image of the right camera in the ARAMIS DIC software showing one frame with an overlay containing the calculated angles

and recognized markers.

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18 Chapter 4. Results

The calculated bending angles as a function of the DIC cameras frame number are plotted in a graph shown in figure 4.2 for a track with laser power 440 W and traverse speed of 10 mm/s. The laser parameters of the tracks in this chapter are abbreviated to power/speed, e.g., 440/10. The bending angle change during the laser forming contains noise, but the bending response is clearly visible for the duration of the measurement.

FIGURE4.2: Graph of laser bending angle change during laser forming of track 440/10, recorded at 40 fps. On the y-axis is the bending

angle, on the x-axis the frame number.

FIGURE 4.3: Graph of the laser bending angle change during laser forming of track 570/15 plotted against the time (a) and the graph of

its derivative (b).

In figure 4.3a the calculated angle in degree as function of time for the measurement of laser track 570/15 is shown. The derivative of this graph, shown in figure 4.3b, is used to analyze the bending response more in depth. The bending response starts with a small amount of bending in the -Z direction, as predicted in the theory, followed immediately by bending with a constant speed in the +Z direction. At the moment the radius of the laser beam touches the edge of the metal sheet at the end of the laser track, the bending accelerates. This so-called edge effect is visible in all

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The bending response is uniform over the whole width, there is no torsional motion visible.

4.1.1 Line energy dependence of bending angle

For the estimation of the final bending angle for laser forming, Vollertsen [36] used the elastic-bending theory. The equation for the bending angle model, with laser forming using the temperature gradient mechanism, is given by

α_b= ^3α^th^PA

ρc_pvs², (4.1)

where α_th is the thermal expansion coefficient, P the laser power, A the absorption coefficient, ρ the density, c_p the heat capacity of the treated material, v the laser traverse speed, and s the sheet thickness [36]. If only the laser parameters P and v would be varied, the size of the final bending should be linearly proportional to P and v according to the equation

α_b∝ P

v, (4.2)

where ^P_v will be called line energy (J/mm). In the experiments the bending response of multiple tracks, with for every individual track different laser parameters, is measured.

FIGURE4.4: The final change in bending angle during LF compared for different values of the laser parameters power and traverse speed, with the final bending angle plotted against the line energy (P/v).

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To compare these measurements of the bending angle for different laser power and traverse speed, the bending angle versus the line energy is used, shown in figure 4.4. In this figure the laser bending with higher traverse speeds results in a higher final bending angle for the same line energy, differing from what is expected from the model by Vollertsen of equation 4.1. For every individual traverse speed, the bending angle is almost linearly dependent on the laser power. For the 10, 15 and 20 mm/s traverse speeds, the lower and higher laser powers, show a relatively lower bending response. The higher laser power tracks are close to or with visible melting.

4.1.2 Multiple overlapping tracks

Not only single laser tracks are studied, also the bending response for overlapping tracks is measured. For overlapping tracks the same laser procedure from the -X starting position to the +X direction is repeated multiple times at the same Y position. Between every overlapping laser track, the laser nozzle is moved from the end of the laser track to the starting position, with the laser beam interrupted. In figure 4.5 the results for different laser powers at a traverse speed of 10 mm/s are shown. Here the individual change in the bending angle per overlapping track (scan) is given. The second overlapping track, where the surface area is changed during the first laser track, shows a higher bending response in comparison to the first, for all used laser powers. After the maximum bending angle in the second track the bending response slowly decreases in following tracks and achieves an almost stable bending angle value in sixth track. The bending response shows good repeatability as it follows from almost identical values measured on two different samples using the same laser power of 410 W.

FIGURE4.5: Individual bending angle response for multiple overlapping laser tracks (scans), given for three different traverse speeds.

4.1.3 Influence of grain size and sandblasting

To study the effects of the grain size, the grains of one of the titanium sheets were grown to about three to four times in their size by heating for five days just below the phase transformation temperature. The influence of the absorption coefficient is also studied, by gently sandblasting the metal sheet’s surface for a rougher surface to increase the absorption. The three samples, one titanium sheet as received, one with only a sandblasted surface and one with grown grains and sandblasted surface, were all laser formed with a traverse speed of 15 mm/s and for different laser

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sandblasted metal sheets with normal grain size, especially for lower laser powers.

The sheet that was only sandblasted shows a similar value of the final bending angle.

The absorption coefficient seems to be an important factor for the bending response, while the grain size has no evident influence.

FIGURE4.6: Bending response compared for the CP Ti grade 2 sheet as received, sheet with sandblasted surface and sheet with both sandblasted surface and grown grains. Bending response measured at dif-

ferent laser powers, with a 15 mm/s traverse speed.

4.2 Microstructural changes in laser forming process

To study the change in microstructure due to the laser forming, the microstructure of the laser track’s cross sections was analyzed as described in section 3.3. To local- ize the position of the EBSD scan area, the microstructure was first observed with an optical microscope. The measured maximum depth of the laser heat affected microstructure, shown in figure 4.7, looks very similar to the bending response results of figure 4.4. Therefore, the depth of the affected microstructure and the bending response seems related to each other. In this section the changes in microstructure are studied closer using the experimentally collected EBSD maps for laser tracks performed at different conditions.

4.2.1 Different laser processing parameters

The laser heat affected microstructure, whose depth figure 4.7 shows to be related to the final bending angle, consists of multiple changes in microstructure in. As seen in the paper by Fidder et al. [7], the laser forming has multiple effects on the microstructure, for example with respect to twinning. To study and compare the microstructure of the different cross sections of the laser tracks, first the image quality (IQ) maps, with highlighting of small misorientations and the expected twins, as discussed in section 2.2.2, were compared. IQ maps consist of a grayscale map, with

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FIGURE4.7: The depth of affected microstructure compared for different values of the laser parameters power and traverse speed, with the maximum depth plotted against the line energy on the left. An example of the measured depth on an optical microscope image on the right, with the 615/15 laser track on the grain grown sandblasted

metal sheet.

the contrast arising from multiple sources, including grain boundaries, topography, phase and local strain [37].

FIGURE4.8: IQ maps with highlighted twins and small misorientations of the cross section of the 570/20 track. The figure contains of the complete scanned area with numbered sections (left), a zoomed area around the surface (top right) and a legend for the highlighted small misorientations and twins used in all IQ maps (bottom right).

The first IQ map, left in figure 4.8, shows the center of the affected microstructure for the cross section of the 570/20 track. The microstructure can be divided into four sections, where the first section consists of the small grains at the surface. The second section is below the first and is characterized by the high amount of twins and grain boundaries with small misorientation angle. Both these sections are better visible in the zoomed IQ map shown at the right of figure 4.8. Here can be seen that the small grains at the surface also contains small misorientations and some twins.

The types of twins are shown in the legend of figure 4.8, where the 34.8^oand 84.7^o

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section two are slightly grown in comparison to the not affected substrate, but the grains of the third section are grown even further, mostly in the Z direction. In this section going all the way to the bottom of the affected zone, the number of twins is low and the amount of small misorientations is decreasing in comparison to the top sections. The last section microstructure seems unaffected and has a regular grain size, almost no small angle boundaries and a small amount of 84.7^oand 64.3^otwins.

FIGURE4.9: Zoomed IQ maps with highlighted twins and small misorientations of the cross sections of the 1000/20 (a) and 720/20 (b)

tracks.

In the comparison of the two top sections, the grains at the surface are larger for higher laser powers, as visible in figure 4.9. In figure 4.9a, the 1000/20 track even shows very small grain on top of the small grains at the surface, which could be a sign of melting. Further, twins of mostly the 84.7^otype are visible in the second section. From the different expected twins in the CP Ti grade 2, the 64.3^ocompression twin type was not present in the laser affected area in the study by Fidder et al. [7], as shown in table 4.1, but was present in the substrate and after mechanical forming.

TABLE4.1: Active twinning systems present in substrate as received, after mechanical forming and after laser forming, adapted from [7].

Twinning system

Rotation Angle @ Axis Twin type Substrate Mechanical forming

Laser forming 11-21 <11-26>

34.80^o@ <1-100> Tensile × X X

10-11 <10-1-2>

57.00^o@ <11-20> Compression × × X

11-22 <11-2-3>

64.30^o@ <1-100> Compression X X ×

10-12 <10-1-1>

84.70^o@ <11-20> Tensile X X X

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The next EBSD map that is used to analyze the microstructure is the kernel average misorientation (KAM) map. The KAM map consists of the average misorientation of the, in this case, first nearest neighbouring kernels, which is related to local strain level [38]. The KAM values are calculated for kernels having a maximum misorientation of 5^o.

FIGURE 4.10: On the left a first neighbour KAM map of the cross section of the 720/20 track. On the left the average map values over the width of the KAM map plotted against the distance into the depth.

In figure 4.10 on the left, the KAM map for the 720/20 track is shown. For easier analysis and comparison, the average map value over the whole width of the EBSD scan is taken and plotted against the depth, shown on the right in figure 4.10, to see a relation between the depth and the degree of local misorientation. As can be seen in this figure the degree of local misorientation is related to the depth of the affected microstructure. Close to the surface is the KAM value the highest and towards the bottom of the affected microstructure it decreases.

FIGURE4.11: The average map values over the width of the KAM map plotted against the distance into the depth, for the 510/20 (a)

and 1000/20 (b) tracks.

For lower and higher laser powers, the KAM values show a similar pattern, as shown in figure 4.11. Only the average values close to the surface are higher for lower powers (figure 4.11a), where for higher powers (figure 4.11b) the average values decrease slower towards the bottom of affected microstructure. Outside the

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FIGURE4.12:[100]IPF maps of the 510/20 (left), 720/20 (center) and 1000/20 (right) tracks.

To compare and analyze the crystal orientation in the microstructure also the inverse pole figure (IPF) maps were used. In [100] IPF maps, the crystal direction parallel to the sample normal designates the color according to the color keys shown in the legend in figure 4.12 [38]. In figure 4.12 the IPF maps for the three laser powers, 510 W, 720 W and 1000 W are compared. The orientation in the affected microstructure seems similar to the substrate, but the large grains obviously influence the average orientation significantly. The misorientations in the large grains and the larger twins are also clearly visible in these [100] IPF maps.

4.2.2 Influence of surface modification and substrate grain size.

The KAM maps of the laser tracks formed on the sandblasted sheet (4.13b) and the grain grown sandblasted sheet (4.13c) differ from the KAM maps observed on the as received sheets tracks (4.13a). In figure 4.13 three KAM maps are compared, all for 615/15 tracks, on the as received, sandblasted and sandblasted large grain size substrate. Figure 4.13b, from the sandblasted sheet, shows a sharper interface between the substrate and affected microstructure in comparison to the as received sheet in figure 4.13a. The KAM map in figure 4.13c, from the grain grown sandblasted sheet, has next to a sharp interface between the substrate and affected microstructure also the section just below the surface with low KAM values.

Figure 4.14 shows a comparison of the corresponding KAM value profiles, averaged over the whole map width. The graph of the as received sheet in figure 4.14a is similar to what we saw in the other as received sheets with 20 mm/s traverse speed tracks. Figure 4.14b, from the sandblasted sheet, shows indeed a sharp interface between the substrate and affected microstructure and the average map value is relatively equal in the affected microstructure. The KAM map in figure 4.14c, from the

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FIGURE4.13: KAM maps of the 615/15 laser track cross section of the as received (a), sandblasted (b) and grain grown sandblasted (c) sheets, showing the difference in KAM value distribution in the

LHAZ.

grain grown sandblasted sheet, has next to a sharp interface between the substrate and affected microstructure also the section just below the with very low average KAM values.

FIGURE4.14: The corresponding average over the width KAM value profiles for the 615/15 laser track cross section of the as received sheet (a), sandblasted sheet (b) and grain grown sandblasted sheet (c), showing a strong interface between the LHAZ and surrounding

substrate for the sandblasted sheets.

Figure 4.15 shows a closer look of the section just below the surface from the grain grown sandblasted sheet. In this figure not only the KAM map, also the IPF and IQ map are shown of the 570/15 track, which shows the same low KAM values just below the surface. On the IQ MAP, dark lines with small misorientations around them, are visible. Using ah11¯23iplane tracer at the surface can show that the black lines are very likely to be pyramidal first order <C+A> slip planes, emerged during the high temperature deformation.

4.3 Finite Element Modelling using COMSOL

In this section the models of the laser heating and laser forming will be discussed and compared to the experimental results.

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FIGURE4.15: KAM (left), [100] IPF (center) and IQ map (right) of one large grain just below the surface of the grain grown treated sheet 570/15 track, with ah11¯23iplane tracer in the IQ map for comparison

to the assumed pyramidal 1^storder <C+A> slip planes.

4.3.1 Laser heating FEM model and comparison with experiment

The laser heating model consists of a 3D time dependent model using the COMSOL physics "heat transfer in solids" and CP Ti grade 2 as material. An 3D isosurface plot is used to shows the temperature and heat transfer inside the material, which is experimentally impossible to obtain. An example of the isosurface plot for the 440/10 track is shown in figure 4.16. The maximum temperature value is almost constant as laser beam moves over the plate, until the laser beam approaches the edge, there the maximum temperature rises causing the earlier discussed edge effect.

For example, for the 440/10 track the maximum temperature rises from 1390 K to 1510 K.

FIGURE4.16: An 3D isosurface plot of the laser heat model, showing isosurfaces of different temperatures between the maximum and minimum temperature and arrows representing the total heat flux.

In the 3D isosurface plot the heat transfer during the laser forming process is vi- sualized. To study the temperature gradient in the material better, the maximum temperatures during the laser forming process in the center of the track from bottom to top of the sheet are plotted. These plots are shown in figure 4.17 for 410/10 and

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720/20. The maximum temperatures increased exponentially from bottom to top surface. By highlighting the temperature range of the α−βphase transformation in figure 4.17, a depth until which phase transformation occurred could be estimated.

The estimated depths of about 300 µm for 410/10 and about 550 µm for 720/20 are very similar to the experimentally measured depth of the affected microstructure.

Therefore, the change in microstructure observed by EBSD could be related to the α−βphase transformation.

FIGURE 4.17: Maximum temperature in the track’s center plotted against the height position of the thickness. The α−βphase transformation temperature range is highlighted and the depth determined.

FIGURE4.18: The laser power plotted against the laser traverse speed for three maximum surface temperatures.

To study the relation between laser power, laser traverse speed and temperature gradient for the laser bending, different combinations of laser power and traverse speed were compared for three maximum surface temperatures. The results are shown in figure 4.18 for the maximum surface temperatures of 1325 K, 1546 K and 1734 K.

The same laser speeds as in the experiments, 5, 10, 15 and 20 mm/s, and the laser speeds 25 and for the highest temperature 30 are used. The laser powers result from the combination of the chosen maximum temperature and laser speed. From the

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equation 4.1 from the model of Vollertsen is not correct for the P/v dependence of the final bending angle.

4.3.2 Laser forming FEM model and comparison with experiment

The laser forming model was more difficult regarding the involved physics phenom- ena. In the model was included the COMSOL physics "Solid mechanics", for the elastic and plastic behaviour using the temperature dependent yield stress, together with the temperature coupling and thermal expansion. One frame of the 3D temperature plot with deformation (scale factor 20) for 440/10 is shown in figure 4.19.

The bending starts with a small amount of bending in the -Z direction, followed by bending in the +Z direction. At the moment the laser beam leaves the sheet’s surface the bending begins to stop, very similar to the experimental results.

FIGURE4.19: One frame of the laser forming model 3D temperature plot with deformation (scale factor 20) for 440W 10 mm/s

FIGURE4.20: Comparison of the experimentally measured bending response (left) and bending response of the laser forming FEM model

(right), with the bending angle against the time in seconds.

For better comparison of the bending, the bending angle over time is plotted for the model. In figure 4.20 a comparison of the bending angle model plot is shown on the left. On the right in figure 4.20 the experimental determined bending angle plot is shown. The bending behaviour is very similar, only the small amount of bending in

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-Z direction is larger in the model and the final bending angle is significantly smaller.

The coarser mesh of the laser forming model causes fluctuations in temperature during the laser heating, resulting in the visible fluctuations in the bending angle over time plot.

Laser Forming

Laser Forming

Abstract

Contents

List of Figures

List of Tables

List of Abbreviations

List of Symbols

Chapter 1

Introduction

1.1 Research objectives

Chapter 2

Literature review

2.1 The mechanisms of laser forming

2.2 CP titanium grade 2

Chapter 3

Experimental Procedure

3.1 Laser setup

3.2 Digital image correlation

3.3 Observation of microstructure

3.4 Simulation using FEM modelling (COMSOL)

∑

Chapter 4

Results

4.1 In situ DIC observation of laser forming

4.2 Microstructural changes in laser forming process

4.3 Finite Element Modelling using COMSOL