Final report on electromagnetic pulse welding

Final report on electromagnetic pulse welding

reproduced, courtesy of Innovaltech

Students: Camille Bandry & Calixte Faucon Promotion: 116 Period: September 2015 - February 2016 Division: Mechanical Project manager ICAM: Amaury Deldicque


Declaration We hereby certify that this material, which we now submit for assessment is entirely our own work, that we have exercised reasonable care to ensure that the work is original, and does not to the best of our knowledge breach any law of copyright, and has not been taken from the work of others save, and to the extent that such work has been cited and acknowledged within the text of our work. date: signed

Camille Bandry

Calixte Faucon

Acknowledgements We would, first and foremost, like to thank M. Amaury Deldicque, our tutor in this thesis, for his support and guidance throughout the project, and for his expertise in numerical simulation. We would also like to thank the teachers and students in the Mechanical department of Icam. We also wish to thank Karina Macocco from Phimeca, for her feedback and advice regarding the bibliographic research, as well as Denis Jouaffre from Innovaltech for his advice and expertise in the experimental aspect of the process.

2 Camille Bandry & Calixte Faucon

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Table of Contents ABSTRACT ......................................................................................................................... 6 NOMENCLATURE .............................................................................................................. 8 TABLES AND FIGURES ..................................................................................................... 10

CHAPTER A

Introduction ............................................................................................ 14

1. Context and Objectives ........................................................................................... 14 1.1. Horizon 2020 .....................................................................................................14 1.2 JOIN-EM ..............................................................................................................15 1.3. Icam ...................................................................................................................17 2. Work Methods ........................................................................................................ 18 3. Document................................................................................................................ 19 3.1. Keywords ...........................................................................................................19 3.2 Units ...................................................................................................................19 3.3 Acronyms............................................................................................................19

CHAPTER B

LITERATURE REVIEW............................................................................... 20

1. Introduction ............................................................................................................ 20 2. Analysis of the microscopic mechanisms occurring in an impact welding ............ 20 2.1. Impact Welding .................................................................................................20 2.1.1. Characterization of the welding by impact .............................................. 20 2.1.2. Theories of weld ....................................................................................... 21 2.1.3. Processes .................................................................................................. 22 2.2. Detailed analysis of the welded interface and the related physical phenomena 28 2.2.1. Interface ................................................................................................... 28


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2.2.2. Jet.............................................................................................................. 31 2.2.3. Intermetallic Interface .............................................................................. 32 2.2.4. Slug ........................................................................................................... 33 2.2.5. Hump ........................................................................................................ 34 2.3. Summary of the analysis of microscopic mechanisms.....................................35 3. Numerical analysis of Impact welding .................................................................... 36 3.1 Introduction........................................................................................................36 3.2. Numerical simulation of a welding process ......................................................36 3.3. Hardening laws and Equation of State ..............................................................39 3.4. Pure Lagrangian Approach ................................................................................40 3.4.1. Parameters of the study ........................................................................... 40 3.4.2. Physical laws and material characteristics ............................................... 41 3.4.3. Modeling strategy..................................................................................... 41 3.4.4. Results ...................................................................................................... 42 3.4.5. Conclusions ............................................................................................... 43 3.5. Eulerian Approach .............................................................................................44 3.5.1. Parameters of the study ........................................................................... 44 3.5.2. Physical laws and material characteristics ............................................... 44 3.5.3. Modeling Strategy .................................................................................... 44 3.5.4. Results ...................................................................................................... 45 3.5.5. conclusions ............................................................................................... 49 3.6. Arbitrary Lagrangian Eulerian Approach (ALE)..................................................49 3.6.1. Parameters of the study ........................................................................... 49 3.6.2. Physical laws and material characteristics ............................................... 49 3.6.3. Method of Modelization........................................................................... 50 3.6.4. Results ...................................................................................................... 51 3.6.5. Conclusions ............................................................................................... 54 3.7. Smooth Particle Hydrodynamics (SPH) ............................................................55 4 Camille Bandry & Calixte Faucon

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3.7.1. Parameters of the study ........................................................................... 55 3.7.2. Physical laws and material characteristics ............................................... 55 3.7.3. Modeling Method ..................................................................................... 56 3.7.4. Results ...................................................................................................... 56 3.7.5. Conclusions ............................................................................................... 57 3.8. Mixed methods .................................................................................................58 3.8.1. Parameters of the study ........................................................................... 58 3.8.2. Physical laws and material characteristics ............................................... 58 3.8.3. Modeling Method ..................................................................................... 59 3.8.4. Results ...................................................................................................... 59 3.8.5. Conclusions ............................................................................................... 61 3.9. Summary of the simulation methods studied...................................................62 4. Conclusion of Chapter B.......................................................................................... 62

CHAPTER C

NUMERICAL MODELLING ....................................................................... 63

1. Introduction ............................................................................................................ 63 2. Finite element method ........................................................................................... 64 3. SPH method ............................................................................................................ 64 3.1. Introduction.......................................................................................................64 3.2. The Kernel approximation .................................................................................66 3.3. The SPH implementation ..................................................................................67 4. Model description ................................................................................................... 68 4.1. Nassiri case study ..............................................................................................68 4.2. SPH model description ......................................................................................69 4.3. Lagrangian model description ...........................................................................72 5. Conclusion of Chapter C.......................................................................................... 75


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CHAPTER D

RESULTS AND DISCUSSION ..................................................................... 76

1. Introduction ............................................................................................................ 76 2. Results ..................................................................................................................... 76 2.1. Effective Plastic strain .......................................................................................76 2.2. Stress .................................................................................................................78 2.3. Pressure .............................................................................................................80 2.4. Velocity ..............................................................................................................82 3. Analysis ................................................................................................................... 84 3.1. Interface ............................................................................................................84 3.2. Pressure .............................................................................................................84 3.3. Effective Plastic Strain .......................................................................................85 3.4. Velocity ..............................................................................................................86 3.5. Stress .................................................................................................................87 4. Conclusion of Chapter D ......................................................................................... 88

CHAPTER E

CONCLUSION AND RECOMMANDATIONS .............................................. 89

APPENDIX 1 ..................................................................................................................... 92 APPENDIX 2 ..................................................................................................................... 94 APPENDIX 3 ..................................................................................................................... 95 APPENDIX 4 ..................................................................................................................... 97 Bibliographic References ................................................................................................ 98

ABSTRACT


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Join'Em aims to enhance the electromagnetic pulse welding technology, and to spread its use in industry. This process will make possible the creation of hybrid components (aluminum-copper), components that are today only made of copper because of its properties. But the increasing demand has risen the price of this material. Widespread classical welding techniques can be limited, unreliable and environmentally damaging, whereas electromagnetic pulse welding requires no additional materials, and can assemble dissimilar materials and produces no waste. The objectives of the following work is, on one hand, to get a clear picture of the phenomena taking place at the interface of the weld, and the numerical modelling strategies adapted to simulate the process through an extensive bibliographic study. This bibliographic study has shown that the most important mechanisms taking place are the jet of material and the morphology of the interface. On the other hand, two numerical simulations were conducted, in one case with a pure Lagrangian approach and the second case, with a pure SPH approach. These results confirm that the most probable plan of action is the use of a mixed method Lagrangian/ SPH which enables the modelization of both the jet and the interface. This model should be extremely refined near the interface to capture the physical phenomena taking place there because of their small length scale.


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NOMENCLATURE Symbol Vw

F m R l C

μ K I

Definition

Dimension (SI)

Detonation velocity Welding velocity Flyer plate velocity Flyer plate velocity observed at stagnation point Re-entrant jet velocity Slug velocity

m.s-1 m.s-1 m.s-1 m.s-1 m.s-1 m.s-1

Angle of incidence Impact angle Bending angle

rad rad rad

Flyer plate thickness Slug thickness Jet thickness

m m m

Process time Gap between the plates Impact acceleration

s m m.s-2

Critical impact pressure Material density

Pa kg.m-3

Total force applied on the tube Mass Average radius of the external tube Overlapping length of both tubes

N kg m m

Discharge energy Capacitance Loading voltage Inductance of the circuit Magnetic pressure Magnetic permeability Constant depending of the geometry of the coil Number of turns of the coil Length of the coil working zone Resistance of the discharge circuit

J F V H Pa m Ω


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!

!"

#

$% $& $' ()* + * *, *, -

. / 0 # 1 2 T

T4556 T6 7 7 8 9

0

N

Induced magnetic force Force induced by the resistance of the plates against deformation Mass of the flyer plate

N

Flow stress Thermally activated Athermal component of the flow stress

Pa Pa Pa

Strain hardening function Plastic strain Plastic strain rate Reference plastic strain rate

s-1 s-1

Shear modulus Shear modulus at reference state

Pa Pa

Yield Strength coefficient Hardening modulus coefficient Strain rate sensitivity coefficient Thermal softening coefficient Hardening coefficient Linear Hugoniot slope coefficient Temperature Temperature of the room Melt temperature

Pa Pa K K K

Grüneisen parameter Grüneisen parameter at reference state Volume Pressure Internal energy per unit reference volume Internal energy Density Initial density Bulk speed of sound

m3 Pa J.m-3 J kg.m-3 kg.m-3 m.s-1

kg


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TABLES AND FIGURES Figure 1: Process principle, electromagnetic welding of tubes [4] ................................ 16 Figure 2: Explanation scheme of a hollow charge [5] .................................................... 20 Figure 3: Micrographic views of different type of interface in Impact welding [6] ...... 21 Figure 4: EXW concept scheme (explosive welding) [13]............................................... 22 Figure 5: Important factors scheme (EXW) [13] ............................................................. 23 Figure 6: MPW concept scheme (Magnetic pulse welding) [6] ..................................... 25 Figure 7: Scheme of the mechanisms of Vaporizing Foil Actuator welding [16] ........... 27 Figure 8: Micrograph of a straight weld interface between copper and aluminum. [5] 28 Figure 9: Micrograph of a wavy interface [7] ................................................................. 28 Figure 10: Wave formation mechanisms [15] ................................................................ 30 Figure 11: Scheme and Micrograph of a vortex interface. [16] ..................................... 30 Figure 12: Scheme of the vortex formation [5] .............................................................. 31 Figure 13: Scheme of flows explicating the jet formation [5] ........................................ 31 Figure 14: Micrograph of the jet made with a very fast motion capture camera [18] .. 32 Figure 15: Micrograph of an inter-metallic compound at an interface Al/Cu [18] ........ 32 Figure 16: Scheme illustrating the formation of the slug [5] ......................................... 33 Figure 17: Scheme of the apparition of the hump, and its purpose in the wave formation [5] .................................................................................................................. 34 Figure 18: Relation between weldability and weld simulation [6]................................. 37 Figure 19: Several categories of accuracy for the simulation of a weld [6] ................... 38 Figure 20: Validation and verification in finite element modeling [22] ......................... 38


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Figure 21: Flowchart of calculation [25] ......................................................................... 40 Figure 22: Model for a. magnetic analysis b. mechanical analysis [25] ......................... 41 Figure 23: FEM prediction profile of the blank and the driver at different time values: t019 μs(a), t095 μs(b), t0135 μs(c), and t0235 μs(d) [25] .............................................. 42 Figure 24: Profiles of Ti-6Al-4V blank during the deformation [25]............................... 42 Figure 25: Displacement in the X-direction of the driver during the deformation [25] 43 Figure 26: AUTODYN simulation of impact welding, velocity vector [26] ..................... 46 Figure 27: AUTODYN simulation of impact welding : Pressure distribution [26] .......... 46 Figure 28: Simulation of two 6-mm thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 15°-temperature distribution [26] ................................. 47 Figure 29: FEA model with varying mesh densities in three regions [27] ...................... 50 Figure 30: Predicted shear velocity distribution for Vf = 350m/s and α = 7° case [27] .. 51 Figure 31: Predicted shear stress for Vf=350m/s and α=7° case [27] ............................ 52 Figure 32: Comparison of melt layer between FEA model and experimental test [27] 52 Figure 33: Wavy morphology window with respect to collision velocity and impact angle [27] ........................................................................................................................ 53 Figure 34: AUTODYN effective plastic strain distribution. [30] ...................................... 56 Figure 35: AUTODYN shear stress distribution[30] ........................................................ 57 Figure 36: AUTODYN material location [30] ................................................................... 57 Figure 37: Schematic illustration of the case study [31] ................................................ 59 Figure 38: Simulation results of metal jet emission for various plate thicknesses [31]. 60 Figure 39: Schematic illustration of a typical welding window [31] .............................. 60 Figure 40: Simulation results of metal jet emission and hump formation at the collision point [31] ........................................................................................................................ 60


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Figure 41: Simulation results of metal jet emission of Al/Mg lap joints. Initial velocity is fixed 400m/s (a) initial angle is 15° (b) initial angle is 25° [31] ...................................... 61 Figure 42: Flowchart of numerical simulation softwares ............................................... 63 Figure 43: Lagrangian, Eulerian, ALE method comparison [32] ..................................... 64 Figure 44: SPH method illustration of the particles [34] ................................................ 65 Figure 45: SPH method compared to classical methods [34] ........................................ 65 Figure 46: Neighboring particles of a kernel estimate [36] ............................................ 66 Figure 47: Computational cycle for SPH[36] .................................................................. 67 Figure 48: Geometry of the SPH model .......................................................................... 69 Figure 49: Mesh of the SPH model ................................................................................. 69 Figure 50: Material parameters for the SPH model ....................................................... 70 Figure 51: Equation of state parameters for the SPH model ......................................... 70 Figure 52: Boundary condition of the base plate for SPH model ................................... 71 Figure 53: Initial Velocity of the flyer plate for the SPH mode....................................... 71 Figure 54: Geometry of the Lagrangian model .............................................................. 72 Figure 55: Mesh of the Lagrangian model...................................................................... 72 Figure 56: material properties in the Lagrangian model................................................ 73 Figure 57: Application region of the boundary condition in the Lagrangian model ...... 74 Figure 58: Boundary conditions of the Lagrangian model ............................................. 74 Figure 59: Application region of the initial velocity in the Lagrangian model ............... 75 Figure 60: Initial velocity in the Lagrangian model ........................................................ 75 Figure 61: Effective plastic strain for the Lagrangian model at 1μs, 2.5μs, 4μs ............ 76 Figure 62: Effective plastic strain for the SPH model at 1μs, 2.5μs, 4μs ........................ 77 12 Camille Bandry & Calixte Faucon

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Figure 63: Von Mises Stress for the Lagrange model at 1μs, 2.5μs, 4μs........................ 78 Figure 64: Von Mises Stress for the SPH model at 1μs, 2.5μs, 4μs ................................ 79 Figure 65: Pressure for the Lagrange model at 1μs, 2.5μs, 4μs ..................................... 80 Figure 66: Pressure for the SPH model at 1μs, 2.5μs, 4μs ............................................. 81 Figure 67: Velocity for the Lagrangian model at 1μs, 2.5μs, 4μs ................................... 82 Figure 68: Velocity for the SPH model at 1μs, 2.5μs, 4μs .............................................. 83

Table 1: Work package 3 (project proposal) [2] ............................................................. 17 Table 2: Objectives of the work package 3 [2] ............................................................... 17 Table 3: Deliverables of the work package 3 [2] ............................................................ 17 Table 4: Material parameters of the aluminum alloy [25] ............................................. 41 Table 5: Mechanical properties and Johnson-Cook parameters [26] ............................ 44 Table 6: Predicted and measured welding parameters, wavelengths and amplitude of interface profile for a 3 mm titanium flyer impacting a 30 mm mild steel base plate [26] ........................................................................................................................................ 48 Table 7: Material properties for AL6061-T6 and Johnson-Cook model parameters [27] ........................................................................................................................................ 50 Table 8: The physical and equation of state (EOS) parameters of metals [30] .............. 55 Table 9: Physical parameters for the materials [31] ...................................................... 58 Table 10: Analytic conditions for oblique collision [31] ................................................. 59 Table 11: Summary of phenomena modelizable with different simulation techniques 91


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CHAPTER A Introduction Join-Em is a 3 year frame work, that is part of the Horizon 2020 initiative. H2020 is the European research program which invests on different innovating projects such as Join-Em. This initiative aims to strengthen the European economy by financing research with direct industrial applications. With new rules and regulations on environmentally clean technologies being constantly created, outputs from the H2020 projects will enable significant improvements of existing technologies or even the use of alternate processes.

1. Context and Objectives 1.1. Horizon 2020 It cannot be argued that research is an essential investment for the sustainable economic growth of Europe. Horizon2020 is the European initiative to encourage and finance research in the years to come. Under Horizon 2020 has been launch a contractual private-public partnership (PPP) named Factory of the Future (FoF). It regroups a number of projects with the aim to help the European factories to adapt to global competitiveness. FoF aims to develop the necessary key technologies in different sectors to meet customer needs. These needs involve more sustainable, and higher customized quality products. The goal of the Factory of the Future initiative is to combine research efforts coming from both public and private sector to provide innovation for the future. This will lead to the creation of new jobs and a leadership position for some european industries. H2020 was approved by the European parliament and currently finances about 4300 initiatives with these 3 goals: • Scientific excellence: Promote fundamental research and new technologies, development of research infrastructures to attract the best scientists. •

Industrial Primacy: Initiate more private investment in key technologies and emerging sectors, develop the innovative small and medium sized companies to create employment growth.


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•

Social Challenges: Promote innovation to reach the citizens' concerns and the European's objectives in terms of climate, environment, and energy. Develop solutions from multidisciplinary collaboration, particularly with social science. " Horizon 2020 is the biggest EU Research and Innovation program ever with nearly €80 billion of funding available over 7 years (2014 to 2020) – in addition to the private investment that this money will attract. It promises more breakthroughs, discoveries and world-firsts by taking great ideas from the lab to the market." [1]

1.2 JOIN-EM "Global trends are forcing industry to manufacture lighter, safer, more environmentally friendly, more performant and cheaper products: the manufacturing systems engineering sector is aiming at better performing machine components."[3] This drives firms to increase their innovative approach in manufacturing engineering technologies. Today welding technologies are rare, expensive and health damaging. Moreover, it reaches its own limits when joining dissimilar materials. Copper is a material that is very frequently used in today's industry because of its excellent properties, but its price has significantly increased due to the rising demand. Join-Em promotes the possibility to substitute parts currently made only of copper by hybrid copper-aluminum parts [2]. The project will focus on copper-aluminium joining. This approach would help to decrease the copper consumption, but necessitates high quality welds which cannot be obtain using the current joining methods. Join-Em proposes an innovative alternative to the conventional processes. Electromagnetic pulse welding is a high speed technology for joining electricallyconductive metals without mechanical contact and without heat expansion. It is possible for similar and dissimilar materials, including those which are impossible using conventional processes. Pictures of welds are in appendix 1.

"Due to its excellent thermal and electrical properties, copper is the 3rd most frequently used raw material in the world. JOIN’EM directly aims at decreasing the consumption of this high cost material by partially substituting it with aluminum."[3] 15 Camille Bandry & Calixte Faucon

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The most important aim of Join-Em is to provide the prerequisites for the industrial implementation of EMW. The advantages and benefits will be directly exploitable in series production. Join-Em will provide the missing information in the literature, useful for the industries. It will get a profound knowledge as to develop a flexible and cost effective magnetic joining process for metal combination where the conventional processes were found inadequate. "The project will offer a step change in the join performance and reliability" [2]

Figure 1: Process principle, electromagnetic welding of tubes [4] The Join'Em project will be orchestrated by a total of 14 partners including Icam Lille.


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1.3. Icam As a partner in the Join'Em project, Icam acts on different levels. Two divisions of Icam are working on the project separately, the Material department and the Mechanical department. The Mechanical department is involved in Work package 3 :

5

6

7

8

9

10

11

12

13

REfCO

4

ALKE

3

CEGESA

2

CALYOS

1

WHIRLPOOL

Participant number

EWF

Development of simulation strategies

VERTECH

Work package title

M1

Start date or starting event

PHIMECA

3

RECENDT

Work package number

14

ARMINES

8

1

9

16

29

0.4

ICAM

INNOVALTECH

per

BWI

Person-months participant

FRAUNHOFER

Participant short name

4.5

Table 1: Work package 3 (project proposal) [2]

This work package is made up of 5 tasks: T3.1 T3.2 T3.3 T3.4 T3.5

Macroscopic modelling of EMW: determination of acting loads, deformation and impacting conditions. Microscopic modelling of EMW: development of the joint formation and microstructure. Simulations supporting process analysis and optimization, and equipment development in WP2, 4 and 6. Development of a numerical lifetime prediction method for EMW equipment. Development of an industrial multi-scale simulation tool for modelling of EMW.

Table 2: Objectives of the work package 3 [2]

All of these tasks will lead to a corresponding official deliverable: D3.1: D3.2: D3.3: D3.4: D3.5:

Report on macroscopic modelling of EMW (Due date: M15) [Leader: FRAUNHOFFER]. Report on microscopic modelling of EMW (Due date: M18) [Leader: PHIMECA]. Report on numerical lifetime prediction method for EMW equipment (Due date: M21) [Leader: ARMINES]. Simulations supporting the process analysis, process optimization and equipment development (Due date: M27) [Leader: FRAUNHOFFER]. Report on industrial simulation tool (Due date: M33) [Leader: PHIMECA].

Table 3: Deliverables of the work package 3 [2]


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The Icam Mechanical department is currently working on the Task 3.2. This task aims at developing a microscopic simulation of the joint development. The work will be based on the conditions determined by the macroscopic model of the task 3.1 and the missions of the Work Package 2. Finally, the simulation results will be compared to the experimental results and used to validate the models. We will also use the models to determine the relevant parameters of the weldability window. The planning of the work conducted is in the appendix section.

2. Work Methods During the study, two tools are used to find, organize and analyze each document. First of all, the library online of the Catholic University of Lille. A digital portal which regroups many editor such as Elsevier, Springerlink or Wiley Online and furnishes the rights to use the articles published by these editors. The second tool used is Mendeley, a reference manager. This software allows to regroup the PDF files into a single database, to organize, and to share the articles. These common documents may be highlighted and annotated by any user belonging to the group allowed to access the database. This report is organized in two distinct parts, a bibliographical study and a numerical approach. After a brief introduction of the H2020 framework program the bibliographic research will be introduced. This work is based on two main topics, the different mechanisms of impact welding and phenomena observed, and the different numerical methods available . Then, based on a relevant case study, numerical models and their related results will be presented and discussed.


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3. Document 3.1. Keywords Numerical Simulation, welding, electromagnetic pulse, impact, weldability window, microstructure, wave, interface, joining.

3.2 Units The units used in our project are usually that of the international system. But in some cases the imperial system or a derivative of the international system: mm/ton/s/K can be used, it will be mentioned in the concerned section. For the SPH numerical model, the system used is mm/g/ms to take into account the weight of each particle.

3.3 Acronyms EMF EXW VFAW MPW ALE SPH CWM

Electromagnetic Forming Explosive welding Vaporizing Foil Actuator Welding Magnetic pulse welding Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics Computational Welding Mechanics


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CHAPTER B LITERATURE REVIEW 1. Introduction The process of electromagnetic pulse welding is starting to develop. develop There are currently a few corporations and research facilities with the necessary equipment capable to create these welds. Nevertheless the physics behind this process remains unclear. This has to be remedied medied to enable a large industrial application in the years to come. It is essential to inspect the quality of numerical models and the quality of a weld, therefore an in depth bibliographic study was conducted.

2. Analysis of the microscopic mechanisms occurring in an impact welding To get a clear understanding understand of what is happening at the interface of the weld, weld the microscopic mechanisms were researched. researched

2.1. Impact Welding 2.1.1. Characterization of the welding by impact By the end of the 18th century, the possibility to concentrate the force of an a explosive charge was discovered, discovered, by hollowing this charge just in front of the target. In the beginning of the 20th century, this technology allowed to pierce small armored plates and create massive damage. damage. The phenomenon of impact welding was discovered during World War II. The soldiers used hollow charges to destroy enemy tanks. Sometimes, these charges did not explode and were stuck to the aimed tank, welded. ded. It was the beginning of impact welding (Gallizzi [5]).

Figure 2: Explanation scheme of a hollow charge [5]

Figure 2 shows the mechanisms of a hollow charge. Here, the detonating cord forces the explosion of the main charge. When the beginning of the liner is reached, reached 20 Camille Bandry & Calixte Faucon

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each of the two parts of the metal will collide against the other. This leads to the propulsion of a high speed jet of material which can pierce the armor. We also observe that after the explosion wave, the material is welded. Similarly to the hollow charge load, creating an impact between two plates of material at a high pressure and velocity we observed comparable morphology. Depending on the pressure employed, we obtain different type of interface as shown in figure 3.

Figure 3: Micrographic views of different type of interface in Impact welding [6] 2.1.2. Theories of weld Most of the experimental tests on impact welding proved that the different processes are identical when talking about the phenomenon of welding. The physics of the weld are the same, even if the characteristics may depend on the type of process used for welding. Many articles try to explain the physics behind the weld during an impact welding process. After many debates, there are still two theories defended. The first one says that the weld is made of the melted materials of the two plates. The second one assumes that it is a solid state bonding, without heat interference. Kapil et al.[7] tell us that many experimental work on Impact welding have been driven to understand the physics of the process. Aizawa and Okagawa [8] found evidence of the generation of a high temperature with a sudden solidification at the interface. The rise of the temperature is insufficiently high and the solidification is too fast therefore the work-pieces do not have the time to be heated up largely. The bonding occurs due to an interference between the temperature and the magnetic pressure. This theory has been supported by Gobel et al.[9] who found no diffusion layers at the interface, stating that the melting was responsible for the process. In 2014, Wu and Shang [10] found evidence of intermetallic compounds but no localized


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interface melting was observed. They concluded that a solid state reaction occurs and may lead to an apparition of local melted phases. On the other hand, Brown et al.[11], found, as well as Aizawa and Okagawa, the evidence of high temperatures at the interface but proved the temperature to be lower than the melting threshold of the materials. Even if the pressure and velocities are extremely high, the formation of intermetallic compounds is unlikely because the process is not driven by heat but by magnetic pressure. Brown explains that solid state welding uses high strain rates and plastic deformation. These two factors have been confirmed to be the origin of the weld by Hisashi et al.[12], who have performed physical and numerical experiences and found the temperature to be lower than the melting point. These theories were established for Magnetic Pulse welding and seem to be applicable to other joining processes. The next section is an introduction of the different processes known to obtain an impact welding. 2.1.3. Processes •

a. Explosive welding

Figure 4: EXW concept scheme (explosive welding) [13]

Explosive welding is the first industrial process for Impact welding. This method is based on an explosive foil, applied to the flyer plate. When the explosion is launched, the flyer plate is propelled against the base plate at the same speed as a bullet which is more than several hundreds of m.s-1.


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Figure 5: Important factors scheme (EXW) [13] In Figure 5 we can see an explained diagram of the process where is the detonation velocity, : is the welding velocity, is the flyer plate velocity, is flyer plate velocity observed at stagnation point, the is the re-entrant jet velocity, the is the slug velocity. The angles defined are the angle of incidence, the impact angle and the bending angle. The thicknesses given are the flyer plate thickness, the slug thickness, the jet thickness.

By trigonometric calculations the flyer plate velocity and the welding velocity can be linked. =2 :

=

: (sin

2

)

cos(1/2( − )) sin :

=

tan


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From these equations, we find the correlation between the different velocities and angles. [13] [5] [14] =

sin

:

cos

=

1 2

1 cos ( + ) 2

The duration of the process can be found with the definition of a velocity, it is defined as the time of the process : = = Where

2

:

:²

2

is the initial gap between the plates and

is the acceleration.

The remaining velocities, for the slug and the jet as well as their masses can now be written: =

+

:

=

=

−

:

=

sin

sin

(cos

1 1 + cos ( + )) 2 2

(cos

1 1 − cos ( + )) 2 2

The critical impact pressure is an important characteristic of the welding process and can be expressed in the following equation: K

Where

=

2

:

L

is the critical impact pressure, and

the material density.


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The force given by the detonation can be obtained by the following equation: !& = # = MNO

:²

Where !& is the total force applied on the tube, # the mass, N the average radius of the external tube, l the overlapping length of both tubes. •

b) Magnetic Pulse Welding

Figure 6: MPW concept scheme (Magnetic pulse welding) [6]

Magnetic Pulse Welding is the latest technology in Impact welding. It uses magnetic forces to create the impact. The two materials to be welded are placed into, or around a coil. The different capacitors are charged, and the current is delivered to the coil with an intensity for instance in the order of 1000kA and a frequency of 15 kHz [6]. The current passes through the coil and thus creates the magnetic field around it. This magnetic field leads to the apparition of an induced current in the workpiece, which creates a second magnetic field. Elsen et al. [15] then observed that the Lorentz forces from both sides repel each other. This results in a pressure of around several hundred MPa on the flyer plate which propels it against the base plate. The only difference between electromagnetic welding and explosive welding is the origin of the energy. [14 [7].


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There is no longer a detonation velocity, but a discharge Energy defined by the following expression (Where C is the capacitance and the loading voltage) =

C ² 2

The frequency of the circuit f is written: (= Where

1

2M√ C

is the inductance of the circuit.

The magnetic pressure P6 id defined as follows: =

- RL

L

L

1 02S1L TU V W 9X8 Y− 2M√ 0 2 [: ²

Z

Where μ is the magnetic permeability, K is a constant depending of the geometry of the coil, is the number of turns of the coil, I is the length of the coil working zone, is the resistance of the discharge circuit. The induced magnetic force ! and the force induced by the resistance of the plates against deformation !" can be obtained with the following equation: #

\² = ! − !" \

Where # is the mass of the flyer plate.


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•

c) Vaporizing Foil Actuator Welding

The mechanism of the Vaporizing foil actuator welding are explained in Vivek et al. [16].

Figure 7: Scheme of the mechanisms of Vaporizing Foil Actuator welding [16] This technology is based on the force applied on a material by the pressure of a vaporized aluminum foil. The target plate is fixed and is separated from the flyer by an electrical resistor standoff. The aluminum foil with a size inferior to 100 µm is applied on the flyer sheet. The vaporizing of the aluminum creates a sudden increase of the volume needed by the aluminum and is accompanied by a high pressure pulse. This pulse driven on a low hardness material propels it against the base plate at a velocity up to 700 m.s-1. The impact between the two plates creates the weld. This weld uses a capacitor bank which can deliver a current of 100 kA and the hardness of the plate must be known to determine the thickness of the vaporizing foil. These three processes are all impact assembly techniques. Although they use different sources of energy and methods to propel the flyer plate against the base plate the impact is in all cases the same, they should therefore present identical morphologies.


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2.2. Detailed analysis of the welded interface and the related physical phenomena 2.2.1. Interface A metallographic analysis show that there are three types of interfaces [13]: •

a. Straight interface The straight welded interface does not present any defaults. There are no waves, no melted areas. Both materials are stuck together without any microscopic interaction. The bonding is made at the atomic scale.

Figure 8: Micrograph of a straight weld interface between copper and aluminum. [5] •

b. Wavy interface The wavy interface presents a regular deformation in the form of a wave. These values are proportional to the thickness and the sound velocity of the materials used for the weld. (Ben Artzy [17])

Figure 9: Micrograph of a wavy interface [7]


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The formation of the waves may be classified into three different theories. This was studied by Kapil et al. [7] A few citations are listed below. • The indentation mechanism. "The indentation of the parent plate that occurs periodically and the formation of a hump ahead of the stagnation point S by the flyer plate and vice versa causes the interface to take the periodic wavy shape. The periodicity of the wavy interface is due to the influence of the period of instability of the re-entrant jet. The indentation occurs due to the high pressures which come into picture when the welding velocity ( : ) is in the vicinity of the parent plate “sound” speed and there is a decrease in this pressure when Vw goes on either side of the sound speed." • The Kelvin-Helmholtz instability " The Kelvin-Helmholtz instability mechanism infers that interface waves are formed when there are discontinuities in the velocities of flow in the interface of the welded members. The interaction of two different fluids with different flow velocities causes interferences and as a result, instabilities occur at the interface of the weld due to the interferences. As a general rule a mass flow, mostly from the material with higher density to the material with lower density is the direct result of the instabilities. The instability with a certain direction and some definite value of velocity causes transfer of material along the weld interface (Fig. 29(a)), and thus to satisfy the law of conservation of energy of the system a flow of material from the side with less concentration gradient occurs immediately. The velocity of both the metals influences the interface waves and gives directionality and shape to the newly created interface".[7] • Rarefaction wave mechanism. "The compressive waves are generated at the collision point. They are reflected as reflection waves by the back surface. the compression waves, compressed from the inner part to meet their corresponding waves at the centre of the bar in a rigid collision. These are then reflected as compression waves towards the interface. It is necessary that the interaction between the compression and refracted waves take place alongside the propagation of the impact point. Due to extreme pressure and heat being put on the collision point, the combination of the interaction of the shock waves together with the movement of both the metals produced the waves at the interface".


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Figure 10: Wave formation mechanisms [15]

•

c. Vortical interface In the case of a wavy morphology, a vortical interface can be formed. The welded joint presents a wavy interface with a vortex into the trough of each wave. The crest at the top the wave is created by the vortex.

Figure 11: Scheme and Micrograph of a vortex interface. [16]

The mechanisms of formation of the vortexes can be compared to the flow of as a viscous fluid around an obstacle [18]. "The confluence of the flyer plate material and the parent plate material behind the re-entrant jet produced conditions similar to the flow of a viscous fluid around an obstacle". The re-entrant jet shears the surface of the parent plate. As a result, the formation of a hump takes place at the point of impact and this hump causes the re-entrant jet to be deflected upwards into the flyer plate jet thus blocking off the re-entrant jet completely. As the re-entrant jet remains trapped, a vortex is formed at the back of the hump, where kinetic energy is dissipated 30 Camille Bandry & Calixte Faucon

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and is the cause of the high temperatures encountered. This might cause phase changes and local melting. [19]

Figure 12: Scheme of the vortex formation [5]

2.2.2. Jet Gallizzi [5] used the analogy with the hollow charge to explain the phenomenon of jetting. In Impact welding, the energy released during the collision creates a substance jet, composed by the materials of the two plates proportionally to their densities. This jet cleans the surface and allows the welding by putting into contact the plates. The origin is identical in shaped charges and in welding process. To explain the jet phenomena, Gallizzi supposed the metals to behave as fluids due to high pressure and velocity. He proposed the following scheme of flow to show the layer which are involved into the jetting. The impact cleans the superficial layer and the oxides, and these particles are forming the jet.

FLOW LINES

Figure 13: Scheme of flows explicating the jet formation [5]


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Figure 14: Micrograph of the jet made with a very fast motion capture camera [18] In Figure 14 the simple arrows indicate the collision points, whereas the double arrows show the jet. 2.2.3. Intermetallic Interface Some scientists agreed to say that melting could be the mechanisms responsible of the weld. Raoelison et al.[20] worked on the inter-metallic phenomena for a copper/aluminum weld and defined the inter-metallic interface and its origin. The inter-metallic interface is characterized by a compound at the interface formed by the metals of the two plates. It is a porous and fragile material.

Figure 15: Micrograph of an inter-metallic compound at an interface Al/Cu [18]


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Analytical calculations based on an energy energy balance have shown that the impact heating enables to melt the Al/Cu interface. The compound is abruptly subjected to a cooling. The high thermal conductivity of the aluminum and copper metal involves an extremely high cooling rate that freezes the randomly randomly spatial distribution of the atoms. This distribution leads to an inter-metallic inter metallic compounds which is porous and fragile because of the diffraction created between the pores.

2.2.4. Slug The "slug" is the material that is deposited upstream of the welding w point of collision. It moves slowly in the direction of the weld for an external observer but moves slowly to the opposite direction when this observer is placed at the stagnation point. The slug is composed by the material of the flyer plate only, although the jet is formed of the materials of the two plates. Gallizzi [5] [

Figure 16:: Scheme illustrating the formation of the slug [5]


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2.2.5. Hump The collision between the two plates creates, downstream of the collision point, a hump by moving some material from the base plate toward the movable plate. This hump appears in many theories as a cause of the formation of waves and vortices. Re-entrant jet

Hump

Figure 17: Scheme of the apparition of the hump, and its purpose in the wave formation [5]


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2.3. Summary of the analysis of microscopic mechanisms The information gathered resumes the research made by many authors up to now. There are still many disagreements between scientists, and more research on the topic is about to be published. As Kapil showed in his paper, the number of publications is exponentially increasing. This short overview represents the beginning of the comprehension for interface creation and its related physical phenomena. As of today, a list of the most important evolutions at the interface of a weld by impact. The formation of a jet, or the apparition of the wave at the interface could be markers of the reliability of the weld, however the research on the topic is not yet completed and some critical information to characterize the strength of a weld could still be missing. Moreover, the mechanisms responsible for the creation of this phenomenon are not known but it is agreed that the pressure, the velocities, and the distortion at an extremely high rate force the solid material to behave as a fluids.


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3. Numerical analysis of Impact welding 3.1 Introduction The bibliographic research on the microscopic mechanisms occurring in an impact welding have given us a good understanding of the different theories related to the welding process, as well as a complete overview of the mechanisms taking place. The second axis of the literary research is oriented towards the models and methods used by researchers to simulate the weld numerically. To do so, different methods and approaches are reported. The study of these articles aims to orient the choice in the modelizing method in terms of quality and reliability, more specifically by being able to reproduce the observed mechanisms.

3.2. Numerical simulation of a welding process Experimental testing of a weld is costly and time consuming, this is why numerical simulations are often used to study a welding process. The computer simulations are used to predict the failures of the weld or analyze the residual stress and distortions. They are also used to develop cracking models or to identify which mechanisms best suit the behaviors observed. However any weld simulations must be performed in parallel to experimental studies. [6] Simulating a welding process proves to be of great interest because the microstructures of the materials are modified and residual stresses and distortions play an essential role in the mechanical assembly of the two components. These distortions and stresses come from temperature gradients and eventually phase transformations occurring during the process. Numerical simulation of welding brings feasibility studies as well as an evaluation of the mechanical strength. [21]


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As explained by Rosenthal and al. [6] a weld simulations can take into account several physics to ensure the weldability of a specific joining process. As evidence, the more the simulation is detailed, the more precise it's results are.

Figure 18: Relation between weldability and weld simulation [6]

For instance the effect of the change in microstructure of the welded materials could be mandatory for a reliable simulation. Due to the different thermal cycles in welding, a thermo-mechanical response and a change in material properties has to be included in the simulations. [22] Therefore, all three analysis namely, thermal, structural and metallurgical, should be conducted concurrently. In simulation, the most important point is to know why it is done, it's purpose. With this information we can determine what kind of model, to be developped according to the accuracy needed, also we can determine when the analysis is done (earlier or later in the development process). A good model has enough accuracy for its purpose. In CWM the main difficulties are that the material model and heat input model need calibration and validation. The numerical simulations can be organized with respect to accuracy in the following figure.


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Figure 19: Several categories of accuracy for the simulation of a weld [6]

Finally it is important to note that, to ensure the quality of the mode, computer simulations of the welds have to follow the validation, qualification and verification procedures in finite element modeling (as shown in Figure 20).

Figure 20: Validation and verification in finite element modeling [22]

"Validation is the process where the accuracy of the model is evaluated by comparison with experimental results whereas calibration is the determination of parameters in order to create a match with some measurements. [...] Verification is the process where it is assured that the finite element model is correct with respect to the conceptual model and Qualification is the same process but between conceptual model and reality." [22] Therefore it is important that many measurements must be used for the Validation and the calibration phases.


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3.3. Hardening laws and Equation of State The numerical models use physical laws to characterize the behavior of the materials: The most commonly used is the Johnson–Cook hardening law that gives the following relation for the yield stress $% . [23] *, ^ − ^bcc V W $% )* , *, , ^+ = ). + /* _ + `1 + 0O1 U Va T1− U *, ^ − ^bcc Where * is the plastic strain, * , is the current strain rate and * , is the reference plastic strain rate. The material constants are . the yield strength coefficient, / the hardening modulus coefficient, 0 the strain rate sensitivity coefficient, # the thermal softening coefficient, and 1 the hardening coefficient. ^ is the temperature of the material, ^bcc is the room temperature and ^ is the melting temperature of the material. The Steinberg-Guinan hardening law is also used in high strain-rate situations. The flow stress in this model is given by: -(8, ^) $% )* , *, , ^+ = e$' ()* + + $& )*, , ^+f -

Where $' is the athermal component of the flow stress, ()* + is the strain hardening function, $& is the thermally activated component of the flow stress, -(8, ^) is the shear modulus dependant on pressure and temperature, - is the shear modulus at reference state. $' ( ≤ $ 'h and $& ≤ $

Where $ 'h is the saturation value of the athermal stress, $ is the Peierls stress, the saturation of the thermally activated stress.

The Mie-Grüneisen Equation of state is used to determine the pressure in a shockcompressed solid. It gives a relation between the pressure and the volume at a given temperature. [24] \8 7 = ( )i \9


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Where 7 is the Grüneisen parameter, is the volume, 8 is the pressure and 9 is the internal energy. By integration of the previous equation, this equation of State can also be written in the first order. 8=

0 ²j 7 U1 − jV + 7 2 (1 − 2j)²

Where is the current density, 0 is the bulk speed of sound, 2 is a linear Hugoniot slope coefficient, 7 is the Grüneisen parameter at reference state, E is the internal energy per unit reference volume. The parameter j is the following relation. j = 1− Where

is the initial density

3.4. Pure Lagrangian Approach The pure Lagrangian Approach is a finite element simulation method where a solid is meshed into a certain number of finite elements. For a specific loading the displacement of each of these elements is calculated. The article chosen to illustrate this method is “3D Numerical simulation method of electromagnetic forming for low conductive metals with a driver,” by F. Li, J. Mo, H. Zhou, and Y. Fang. [25] 3.4.1. Parameters of the study The objective of this study is to modelize an EMF process. The physics taken into account are both magnetic and mechanical, the impact of temperature is being neglected. The softwares used are Ansys (magnetism) and Abaqus (mechanical) .

Figure 21: Flowchart of calculation [25]


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3.4.2. Physical laws and material characteristics To model the thermo-visco plastic behavior of the materials the Johnson-Cook constitutive equation defined as follows was used, where the temperature is neglected. k, l

$% = )$ + R* _ + Y1 + 0O1 Z [25] k, m

The material characteristics defined in the study are the following:

Table 4: Material parameters of the aluminum alloy [25]

The study takes in consideration friction with the Coulomb law coefficient fixed at 0.3.

3.4.3. Modeling strategy

Figure 22: Model for a. magnetic analysis b. mechanical analysis [25] The physical domain is divided in several parts: Air, die, coil, blank, holder. The forming model is built in 3D as shown in the figure above and the boundary condition is the magnetic pressure. The dimensions of the flyer plate are defined with a thickness of 0.5mm and the gap between the flyer plate and the coil is set at =1.6mm. The discharge voltage is V=6kV.


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3.4.4. Results The numerical simulation has to solve the Maxwell and Newton equations alternatively. Typical results are presented hereafter:

Figure 23: FEM prediction profile of the blank and the driver at different time values: t019 μs(a), t095 μs(b), t0135 μs(c), and t0235 μs(d) [25]

Figure 24: Profiles of Ti-6Al-4V blank during the deformation [25]


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Figure 25: Displacement in the X-direction of the driver during the deformation [25]

The results of this article are focused on : − the displacements of the flyer plate − the deflection of the blank − the magnetic force of the driver − the velocity − the contact force between the driver and the blank. − These results are coherent with findings in literature but further confirmation with experimental methods would be necessary to confirm their reliability. The error calculated (18%) can be explained by a failure to account for the blank deformation, and the change of inductance between the coil and the blank.

3.4.5. Conclusions This method enables us to calculate important parameters: magnetic field distribution, magnetic force distribution, and interaction between the blank and the driver, all of which are necessary to understand the EMF process. The study also shows that this model is more suitable for small deformation processes (tube compression...) than for large scale deformations where it can only predict the deformation qualitatively. This article is interesting regarding the approach and the methods used to combine both mechanical and magnetic aspects, but it offers no precise results at the interface region which is intuitively where the weld mechanism occurs.


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3.5. Eulerian Approach The pure Eulerian Approach is a simulation method where the mesh is fixed in space and the physical material flows through it. The article chosen to illustrate this method is “Numerical and experimental studies of the mechanism of the wavy interface formations in explosive/impact welding,” by a Akbarimousavi and S. Alhassani. [25] 3.5.1. Parameters of the study The objective of this study is to modelize an EXW process. The physics taken into account are Thermal and Mechanical, the magnetic aspect of the problem is neglected. The software used is AUTODYN 4.1 13. 3.5.2. Physical laws and material characteristics The material law used in this study is the well known Johnson-Cook:

$% = =. + /* _ A=1 + 0 ln *, A=1 − ^ ∗ ) [26] The material properties for the Johnson-Cook equation are:

Table 5: Mechanical properties and Johnson-Cook parameters [26]

For this study the effects of friction are neglected. 3.5.3. Modeling Strategy The model is built in 2D and the dimensions of the flyer plate are 3x40mm and 30x40mm for the base plate. The mesh is refined in the area of the jet, therefore we have a mesh size of 0.02mm near the collision zones. The load and boundary conditions defined are the Impact velocity (250–1000 m/s) and the Impact angle (8–34°).


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3.5.4. Results Both the Jet and the wavy interface can be observed in the simulation which is a form of validation of the model. The wavy interface was observed in certain conditions depending on the material used. For steel the transition to a wavy interface occurred with a plastic strain superior to 0.5 and a shear stress inferior to 0.5GPa. Whereas for titanium the plastic strain had to be superior to 0.9 and the shear stress inferior to 0.5GPa. The apparition of the wavy interface which is supposed to be linked to the creation of a quality weld happens in a certain window. Also the amplitude and wavelength of the waves at the interface were found to be dependent on the flyer plate thickness. One of the most interesting characteristics of this study is that it takes in consideration the thermal aspect. The temperatures observed are lower than the fusion limit, therefore the bonding is considered to be a solid state one. Also at the collision point, the materials are considered to be fluids. Akbarimousavi observed: − the jet − the wavy interface − the temperature − the plastic strain − the shear stress − the speed − the pressure Some of the results obtained in this study are shown in the figures below.


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Figure 26: AUTODYN simulation of impact welding, velocity vector [26]

Figure 27: AUTODYN simulation of impact welding : Pressure distribution [26]


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Figure 28: Simulation of two 6-mm thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 15°-temperature distribution [26]


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Table 6: Predicted and measured welding parameters, wavelengths and amplitude of interface profile for a 3 mm titanium flyer impacting a 30 mm mild steel base plate [26]


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3.5.5. conclusions This study shows very promising results as it is capable of reproducing the two main characteristics of the process known so far, that is the jet and the wavy morphology. Although they cannot yet confirm the presence of a quality weld. The results obtained seem coherent which is a first validation of the model. But the study also shows limits. First of all, the Euler solver is restricted with convergence issues in relation with the resolution of the model. Also the friction is neglected in the model, which implies that the material roughness is neglected. Finally this model is carried out in 2D a simplification not yet confirmed to be allowable.

3.6. Arbitrary Lagrangian Eulerian Approach (ALE) The Arbitrary Lagrangian Eulerian approach is an adaptive method that combines the features of both Lagrangian and Eulerian techniques. The article chosen to illustrate this method is “Arbitrary Lagrangian–Eulerian finite element simulation and experimental investigation of wavy interfacial morphology during high velocity impact welding,” A. Nassiri, G. Chini, A. Vivek, G. Daehn, and B. Kinsey. "The ALE technique [...] maintains a high mesh quality during simulations involving large deformations. [...] ALE consists of two fundamental tasks at each time increment: 1) creating a new mesh and 2) remapping the solution variables from the old mesh to the new mesh. A new mesh is created at a specified frequency for each adaptive mesh domain." [27]

3.6.1. Parameters of the study The objective of this study is to modelize a VFAW process. The physics taken into account are Thermal and Mechanical, the magnetic aspect of the problem is neglected. The software used is ABAQUS 6.13. 3.6.2. Physical laws and material characteristics The material law used in this study is Johnson-Cook:

$% = ). + /* _ +)1 + 0O1* +=1 − ^ ∗ A [27]


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The material properties for the Johnson-Cook equation are:

Table 7: Material properties for AL6061-T6 and Johnson-Cook model parameters [27]

The study takes into account the friction defined by the Coulomb law coefficient fixed at 0.15. 3.6.3. Method of Modelization The model we are studying is built in 2D in plain strain. The dimensions of the flyer plate are 2x12mm and 3x15mm for the base plate. The mesh is divided in three different regions as shown in the figure below with a total of 153 289 elements used. The finest region A is used for the surface of the plates with a quad structured mesh (5 μm×5 μm). Regions B and C are used for the remainder of the geometry, they were auto-meshed with quad elements. The initial feature angle control (IFAC) is a criteria for remeshing: when the angle becomes too big the element is re-meshed, the max angle θC was set to 180°. The impact velocity is set between 250–600 m/s and the impact angle between 3–20°.

Figure 29: FEA model with varying mesh densities in three regions [27]


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3.6.4. Results Some of the results obtained in this study are shown below in figure 30, 31 and 32. The jet phenomenon can't be reproduce, but the wave and interface morphology are successfully simulated. The observed results are: − the collision velocity − the shear stress − the temperature − the wavy interface

Figure 30: Predicted shear velocity distribution for Vf = 350m/s and α = 7° case [27]


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Figure 31: Predicted shear stress for Vf=350m/s and α=7° case [27]

Figure 32: Comparison of melt layer between FEA model and experimental test [27]


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Figure 33: Wavy morphology window with respect to collision velocity and impact angle [27]

Explanations of figure 17: Line b–b represents the maximum collision velocity obtained (3800m/s). Lines c-c and d-d represent the lower and upper limits for the impact angle. Curves e-e and f-f are the lower and upper limits of collision velocities with respect to the impact angle. (Melting temperatures of the material are situated above the f-f line) "The value obtained from the simulation was close to the value found from the analytical formula predicted by Cowan [28] and Carpenter [29] for EXW who linked wave formation to fluid flow around an obstacle:" [27] 2N9&b'_ =o = Where N9&b'_

p&pc_

p&pc_ =q rpsb

+ qt' s A ~ 1400 #/2 rpsb + t' s )

is Reynolds number during the transition and qthe Vickers hardness.


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3.6.5. Conclusions This method enables us to calculate important parameters: the collision velocity, the shear stress, the temperature, the wavelengths, the dynamic impact angle, and the fusion zones, all of which are relevant to understand the EMF process. This study also confirms its accuracy with ratios of 10.4 and 11.6 for the wavelengths and amplitudes from experiments and numerical simulation. The method of modelization used for this method is very interesting because not only are the results obtained coherent and conclusive but the model defined is rather simple to reproduce, even in other numerical techniques. One of the major flaws though is that in this study, Nassiri considers the wavy morphology to be the characteristic of a good weld. This theory is in the majority of cases not considered to be true. If this theory turns out to be incorrect, the conslusions obtained in the article would have to be revised.


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3.7. Smooth Particle Hydrodynamics (SPH) "SPH is a grid-less Lagrangian hydrodynamics using particles, unlike conventional Lagrangian techniques, SPH avoids mesh tangling and is therefore much more robust in its treatment of problems with large material distortions."[30] The article used to illustrate this method is “Numerical study of the mechanism of explosive/impact welding using Smoothed Particle Hydrodynamics method,” by X. Wang.

3.7.1. Parameters of the study The objective of this study is to modelize an EXW process. The physic taken into account is only mechanic, masgnetism and thermal aspect of the problem are neglected. The software used is AUTODYN.

3.7.2. Physical laws and material characteristics The local Mie-Grüneisen equation of state is used in this study to determine the pressure in a solid compressed by a shock. 7 = ( s )i [30]

Table 8: The physical and equation of state (EOS) parameters of metals [30]

A simple elastic / perfectly plastic strength model is adopted, and the friction is neglected is this study.


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3.7.3. Modeling Method The model is built in 2D and the dimensions of the flyer and base plate are 1x10mm. The particles have a size Δr is 20μm with approximately 50 000 particles. The load and boundary conditions defined are the Impact velocity (500–1000m/s) and the Impact angle (5–25°) and the study is set in a free boundary, no failure mode. 3.7.4. Results The variables and parameters observed in this study are: − the shear stress − the plastic strain − the pressure − the material position − the jet velocity − the impact velocity and angle "The main physical parameters, such as shear stress and plastic strain which determine the success or failure of the welding were identified. Simulations show that the shear stresses in the flyer and base The phenomenon such as jetting and the interfacial waves observed in explosive welding were all successfully reproduced in simulations, and the predicted impact velocities and the interfacial waves are in agreement with previous experimental results."[30]

Figure 34: AUTODYN effective plastic strain distribution. [30]


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Figure 35: AUTODYN shear stress distribution[30]

Figure 36: AUTODYN material location [30] 3.7.5. Conclusions This study has made it possible to model the main features of the explosive/impact welding process. The SPH method produced good results with both the wave structure and the jetting phenomenon reproduced. Therefore, even though SPH is a new technique of simulation, it is suitable to model the EMW process. The article concludes that a quality weld takes place only when the effective plastic strain and the shear stress exceed a minimum value. "The greater shear stress and effective plastic strain of the contact area were, the greater interface wave could be obtained, and the values of plastic strain and shear stress were higher in the interfaces when waves were present."[30] The study also shows that a solid state welding is more probable than fusion.


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3.8. Mixed methods Here the Lagrangian and SPH methods are coupled, the boundary between SPH and Lagrange solver regions are connected using a join function. The articled chosen to illustrate this method is “Simulation and experimental analysis of metal jet emission and weld interface morphology in impact welding,” by S. Kakizaki. [31] 3.8.1. Parameters of the study The objective of this study is to modelize an MPW process. The physic taken into account is only mechanical, the magnetic and thermal aspect of the problem are neglected. The software used is AUTODYN. 3.8.2. Physical laws and material characteristics The Mie-Gruneisen equation of state is used in this study to determine the pressure in a solid compressed by a shock. 7 = ( s )i [31] The Steinberg-Guinan equation is used as the material strength model: $% )* , *, , ^+ = e$' ()* + + $& )*, , ^+f

x( ,y) xm

[31]

Table 9: Physical parameters for the materials [31]

In this study friction is neglected.


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3.8.3. Modeling Method

Figure 37: Schematic illustration of the case study [31]

The length of the plate was assumed to be infinite (perpendicular to the plane), because the symmetry system was 2D planar. The SPH region was set to be 100–300 μm in thickness. The different parameters of the study are stated in the following table:

Table 10: Analytic conditions for oblique collision [31] 3.8.4. Results The variables and parameters observed in the study are: − the plate thickness and width − the initial velocity − the initial angle − the collision velocity − the collision angle. All of the Physical, mechanical and chemical parameters of the material were taken from the AUTODYN database. Here are some of the observed results:


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Figure 38: Simulation results of metal jet emission for various plate thicknesses [31]

Figure 39: Schematic illustration of a typical welding window [31]

Figure 40: Simulation results of metal jet emission and hump formation at the collision point [31]


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Figure 41: Simulation results of metal jet emission of Al/Mg lap joints. Initial velocity is fixed 400m/s (a) initial angle is 15° (b) initial angle is 25° [31]

The composition of the metal jet was found to be governed by the relative density difference between the two metals to be welded, and the hump is formed with an initial angle superior to 20°. As for the interface, with a collision velocity of 150 m/s, a straight interface is observed, with a collision velocity of 400 m/s a wavy interface observed, and with a collision velocity of 400 m/s with a high or low collision angle (5° or 25°), a wavy interface is observed. 3.8.5. Conclusions The SPH method was successfully used to investigate the relationship between interface morphology and welding parameters (collision angle and velocity). The metal jet emission and weld interface morphology (3 patterns) were reproduced and the hump formation was observed ahead of the collision point. This method seems promising as it enables us to reproduce the main identified features of impact welding


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3.9. Summary of the simulation methods studied After studying these different methods of modelization, we have realized that there is no consensus between researchers on the weldability. Each article defines its own parameters and criteria and comes to different conclusions. This shows that the physics behind impact welding is not yet fully understood. These different parameters and conclusions are summarized in appendix 3. First of all, it is important to note that most articles do not mention the parameters chosen to state that a quality weld is created. In other cases, for example in the ALE approach, the characteristic of a good weld is considered to be a wavy interface. According to the study of microscopic mechanisms, that is not unanimously considered true. It is essential for the model to be validated that a characteristic of a weld be identified. Also the simulations are often "confirmed by experimental studies" but no details are given as to these experimentations. This is however a crucial point to be exploited. An experimental approach has to be conducted in parallel to the numerical approach to obtain conclusive results.

4. Conclusion of Chapter B As of today it is impossible to come to a unanimous conclusion, but the rising interest on this subject, and the increasing amount of articles being published show that it is important to stay up to date with recent developments. According to the information extracted from the articles the most probable course of action seems to be a mixed method with Lagrange and SPH. SPH being applied to the interface area whereas the outside of the plates could be meshed with a classic finite element method. The most important microscopic phenomena that need to be modelized are the jet and the wavy morphology at the interface, as they are widely known and admitted as essential to the creation of a quality weld.


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CHAPTER C NUMERICAL MODELLING 1. Introduction In this chapter the basic concepts behind the finite element method and the SPH method will be rapidly outlined, both of these methods are used in the following chapter. The softwares used for all of these methods function with the same structure, defined in the following figure. The pre-processor is what enables us to create the model with its corresponding geometry, mesh, material properties and load and boundary conditions. With this information the input file for the solver is created. The solver analyses the data and exports its results. The results are accessible through the post processor modulus where the graphical interface enables the interpretation.

Figure 42: Flowchart of numerical simulation softwares Different editors develop softwares capable of numerical simulation. The main ones being MSC Software, ANSYS and LSTC. A non exhaustive list of the different existing softwares can be found in appendix 4.


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2. Finite element method The finite element method was developed in the 1950's and is widely known, documentation on the subject is abundant. The three main types of methods are Eulerian, Lagrangian and ALE (Arbitrary Lagrangian Eulerian), these three methods have their pros and cons defined in the following figure: [32], [33]

Figure 43: Lagrangian, Eulerian, ALE method comparison [32]

3. SPH method 3.1. Introduction This method not being widespread in the field of mechanics, a short description is made here. Wang & Al [30] state "Smoothed Particle Hydrodynamics (SPH) is a relatively new mesh-less method, which is a computational technique for the numerical simulation of the equations of fluid dynamics without the use of an underlying numerical mesh. That is to say, a set of moving interpolation points which follow the fluid motion is de-fined instead of relying on the use of a computational mesh. Furthermore, SPH method is a Lagrangian formulation based computational method where the coordinates move with the object, which was originally developed for astrophysics and shock simulations. At present, it has been applied to various fields, such as hypervelocity deformation, detonation, and fluid dynamics. The name Smoothed Particle Hydrodynamics includes the term ‘particle’, however the particles are not simply interacting mass points."


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Figure 44: SPH method illustration of the particles [34]

SPH method solves: • conservation of mass • conservation of momentum • conservation of energy if necessary

There are 3 typical values for particles • M: mass • d: distance between particles • h: smoothing length

With this method, there are 2 discretization parameters: h and d.

Figure 45: SPH method compared to classical methods [34]

SPH Disadvantages • CPU expensive • Boundary conditions are limited (complex) • Instability in tension

SPH Advantages: • No connectivity between particles • Lagrangian frame • Discontinuities: crack propagation, failure • High gradients: shock waves • High deformations • Easy to handle: Particles = Points


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3.2. The Kernel approximation The Lagrange and Euler methods are based on grids, they assume a connectivity between the nodes, whereas SPH uses a kernel approximation. With this approximation, there is no assumption on which nodes are neighbors. It is based on randomly distributed interpolation points to calculate spatial derivatives. This is illustrated in the following figure.[35]

Figure 46: Neighboring particles of a kernel estimate [36] "A continuum represented by a set of interacting particles is considered [...] Each particle I interacts with all the other particles J that are within a given distance (usually assumed to be 2h) from it. The distance h is called the smoothing length. The interaction is weighted by the function W(x-x',h) which is called the smoothing (or kernel) function. Using this principal, the value of a continuous function, or it's derivative, can be estimated at any particle "I" based on known values at the surrounding particles "J" using the following kernel estimates"[36] The standard Kernel approximation expression is written: < (=XA >≈ }• (=X ~ A•=X − X ~ , ℎA\X ~ [36]

"Where ( is a function of the three-dimensional position vector X, \X' is a volume where W is a kernel function, the angular bracket < (=XA > denotes a kernel approximation, X ~ and X ~ are location of the point of mass I and particles J within the smooth length ℎ from particle I respectively. The variable ℎ is the smooth length corresponding to the mesh size in FEM or FDM analysis." [30]


Kernel function W must satisfy the follow conditions: [30]

‚ •=X − X ~ , ℎA\X ~ = 1 •

OS#ƒ„ •=X − X ~ , ℎA = (X − X ~ ) •(X − X ~ , ℎ) = 0

when ⎸X − X ~ ⎹ > ‡ℎ, ‡ is a constant that related to smooth function of X point. Derivatives are integrated using kernel function as: 〈∇ ∙ ((X)〉 = ‚ [∇ ∙ ((X ~ )W(x − x ~ , h)dx ~ •

〈∇ ∙ ((X)〉 = − ‚ ((X ~ ) ∙ ∇W(x − x ~ , h)dx ~ •

3.3. The SPH implementation "The calculation cycle is similar to that for a Lagrange zone, except for the steps where a kernel approximation is used. Kernel approximations are used to compute forces from spatial derivatives of stress and spatial derivatives of velocity are required to compute strain rates. In addition SPH requires a sort of the particles at least once every cycle in order to locate current neighboring particles. When variable smoothing is used (h can vary locally in space and time) the smoothing length is updated twice per cycle."[36]

Figure 47: Computational cycle for SPH[36] 67 Camille Bandry & Calixte Faucon

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4. Model description 4.1. Nassiri case study The base model chosen for the simulations carried out is the Nassiri case [27]. The methods of modelization used in this articles are described in the ALE approach. This model was chosen amongst of all of the articles studied, it is simple yet precise in the wanted areas. The regionned mesh with precise elements only at the interface simplifies the calculations and therefore reduces the running time. The material studied is aluminum with the impact angle α=7° and the flyer plate velocity Vf=350m.s-1

Figure 29: FEA model with varying mesh densities in three regions [27] In the following section, the numerical models solving the mechanic equations are presented with an SPH approach, and a classiscal implicit Lagrangian approach.


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4.2. SPH model description The SPH model is developed using the Nastran sol700 solver, with Patran and LS prepost to develop the model and analyze the results. The unit system used is mm/g/msec. •

Geometry of the model

Figure 48: Geometry of the SPH model The model is built in 3D with a base plate of 15mm by 3mm by 1mm and a flyer plate of 12mm by 2mm by 1mm. These two plates are placed with a 7° angle between them, and as they are touching at the initial contact point, there is no gap in this model. The dimensions used here are identical to the ones used by Nassiri but in a 3 directional environment, which will enable comparison between the results. •

Meshing

Figure 49: Mesh of the SPH model The mesh is achieved with 0D elements, with each of these particles free from the others. Two studies were carried out, the first with 132454 elements and a second much finer with 451691 elements.


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•

Material properties

Figure 51: Equation of state parameters for the SPH model

Figure 50: Material parameters for the SPH model

The material used for both the base plate and the flyer plate is aluminum (alu_2024_T351) with a density of 0.00287 g.mm-3, a shear modulus of 27600 MPa, a yield stress of 265 MPa and a hardening modulus of 2000 MPa. The equation of state used is Mie Grüneisen with a constant C equal to 5328, a constant S1 equal to 1.3380001, a Grüneisen gamma of 2 and a first order volume of 0.48mm3.


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•

Load and boundary conditions

Figure 52: Boundary condition of the base plate for SPH model

Figure 53: Initial Velocity of the flyer plate for the SPH mode

The bottom of the base plate is fixed with a boundary condition, all of the degrees of freedom are set to 0, and an initial velocity of 350mm.ms-1 is given to the flyer plate.


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4.3. Lagrangian model description The Lagrangian model is developed using the MSC Marc solver, and Mentat is used to develop the model and analyze the results. The unit system used is mm/T/sec.

•

Geometry of the model:

Figure 54: Geometry of the Lagrangian model The model is built in 2D with a base plate of 15mm by 3mm and a flyer plate of 12mm by 2mm. These two plates are placed with a 7° angle between them, and as they are touching at the initial contact point, there is no gap in this model. The dimensions used here are identical to the ones used by Nassiri, this will enable comparison between our results and his. •

meshing

A B Figure 55: Mesh of the Lagrangian model

C


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The mesh is made of linear quad elements of 2D plain strain type, and it is refined near the interface. Different regions are defined. The finest mesh is located near the impact zone (A in Figure 55), an intermediate mesh is defined in the middle of the plates (B in Figure 55), and a larger mesh is defined on the outer-most part of the plates as we predict few changes in these regions (C in Figure 55). The re-meshing option is applied to the model, therefore once the elements are deformed beyond a certain point, they are remodeled into a new structure. The initial number of elements is 1828, but this changes as the mesh is restructured. The maximum number of elements obtained is 18940 towards the end of the simulation, and the final number of elements is 9478. •

Material properties

Figure 56: material properties in the Lagrangian model The material used for both the base plate and the flyer plate has a mass density of 2.7e-9 t.mm-3, a Young Modulus of 70000 MPa, and a Poisson's ration of 0.279. The plastic properties are defined according to the Von Mises yield criterion with a coefficient A equal to 289 MPa, a coefficient B equal to 108 MPa, an exponent N of 0.42, a coefficient C equal to 0.011 and an exponent M of 1.34. The initial strain rate is set at 1 s-1, the room temperature is set at 23 K and the melt temperature of the material is 653 K.


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•

Load and Boundary conditions The bottom of the base plate is fixed with a boundary condition, all of the degrees of freedom are set to 0.

Figure 57: Application region of the boundary condition in the Lagrangian model

Figure 58: Boundary conditions of the Lagrangian model An initial velocity of 350000 mm.s-1 is given to the flyer plate.


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Figure 59: Application region of the initial velocity in the Lagrangian model

Figure 60: Initial velocity in the Lagrangian model

5. Conclusion of Chapter C This chapter outlines the procedures used to create the Lagrangian and SPH models modelizing the impact welding process. The studies were conducted according to the Nassiri case, where the main geometry is reused, this will enable the comparison between the models. The results of these studies are shown and discussed in the following chapter.


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CHAPTER D RESULTS AND DISCUSSION 1. Introduction The first simulations were made with two different types of solver. The first one is a Lagrangian implicit solver namely the Marc Mentat Software, and the second one is a Smoothed Particles Hydrodynamics (SPH) using Natran Sol 700 Software. Both tools are from the MSC software corporation. Here the different results observed are presented and followed by a discussion on the benefits and defaults default of the two types of modelizations. modelization

2. Results 2.1.. Effective Plastic strain

Figure 61: Effective ctive plastic strain for the Lagrangian Lagrangian model at 1μs, 2.5μs, 4μs


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Figure 62: Effective plastic strain for the SPH model at 1μs, 2.5μs, 4μs


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2.2. Stress

Figure 63: Von Mises Stress for the Lagrange model at 1μs, 2.5μs, 4μs


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Figure 64: Von Mises Stress for the SPH model at 1μs, 2.5μs, 4μs


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2.3. Pressure

Figure 65:: Pressure for the Lagrange model at 1μs, 2.5μs, 4μs


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Figure 66: Pressure for the SPH model at 1μs, 2.5μs, 4μs


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2.4. Velocity

Figure 67:: Velocity for the Lagrangian model at 1μs, 2.5μs, 4μs


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Figure 68:: Velocity for the SPH model at 1μs, 2.5μs, 4μs


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3. Analysis 3.1. Interface The two numerical approaches namely SPH and Lagrangian were used to observe the evolution of several physical quantities during the welding process. The measurements made have shown an evolution of the dynamic angle from 7° up to 10.6° (in 3.5µs) with the Lagrangian model and 9° for the SPH model. Compared to the initial impact angle, this augmentation is expected, and is correlated to Nassiri's results. A 0.3 mm small penetration of the flyer plate into the base plate is noted. An elongation of approximately 0.6mm along the X axis is also observed. These kinds of deformation are reproduced by the tests, but are not necessarily a characteristic of an efficient weld. With the SPH model, no evidence of the presence of the phenomena described in the literature (jet or hump) could be observed. The interface stays straight, and there is no apparition of a wavy morphology. The absence of phenomena is due to the imprecision of the model and he number of particles being insuficient. The particles' size is indeed bigger than the length scale of the phenomena. This prevents the modelizing of the microscopic mechanisms. The Lagrangian model does not replicate the phenomena either. The elements are also too big to allow the creation of the wave. Moreover, the jet cannot be seen because the deformation of the elements is too high and when we should observe it, the re-meshing erases it. This numerical approach is not suitable to capture the very high distorsion of the material that occurs near the collision point.

3.2. Pressure Both models present the same pressure plot, the highest pressure is at the collision point as expected. The pressure repartition is stronger in the base plate. The maxima are around 4.9 GPa in the Lagrangian method and locally around 6 GPa in the SPH method. The average pressure is around 3 to 4 GPa in both models. According to literature, these values are in the expected range. A difference of 1.1 GPa between the two maxima is observed. One should keep in mind that the discretization is not the same between the two models and also an DPH method is inherently less accurate than a classical finite element model.


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The highest pressure is at 2.5 µs for both simulations. The pressure does not show much disturbance with the SPH model and stays in the range of 5.5 to 6 GPa. The pressure with the Lagrangian model is subject to a large rise and then a reduction is observed. It is not constant at the collision point, the pressure peaks must be linked to the shock waves.

3.3. Effective Plastic Strain The predicted fields for two approaches look similar. The maximum strain is localized at the interface. The deformation is in the range of 40% or even more, which is in accordance to the literature. By doing some experimental tests like hardness measurements, the welding area could be identified to the plastic strain field predicted by numerical simulation. The deformation in the Lagrangian model reaches a peak at more than 80% at the end of the weld, at the collision point, which is too much. This could be due to a small default in the geometry when a re-meshing occurs. A small decrease of plastic strain between the weld at 1µs and the same point at 4µs is observed. On the contrary, the SPH model does not present such a decrease and the effective plastic strain is constant along the interface and it presents a constant period. The critical deformation of 61% seems to follow the shape of the wavy interface. However no such interface is found because of the coarseness of the discretization. It does not appears in Lagrangian model. In both models an increase of the effective deformation is observed at the bottom-left corner. This may be due to boundary effects occurring during the simulation. In the Lagrangian model, the average is between 18% and 45% which is low for the minimum value but it is in the range of the literature. The maximum deformation is approximately 88% in some very particular points upstream of the collision point. By contrast with SPH, no periodicity in the values of effective plastic strain is noticed. A decrease of the values after the collision point is observed, which is not supposed to be present. The effective plastic strain remains the same when the weld is over and a constant value should be observed. The model reaches its limit because the re-meshing will disturb the results. The Lagrangian approach is more frequently used for solid simulations and the fluid-acting part of the material creates some inconsistencies with reality. Yet this point needs to be confirmed.


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3.4. Velocity The velocity is at his highest at the collision point. A residual velocity is observed behind the weld. All of the remaining areas remain unchanged. This plot is in coherence with the theoretical studies. Moreover, for a similar velocity impact, the velocity remains in the range of the literature in the Lagrangian approach with a value over 1200 m/s. The experiences state that the welding velocity has to be at least more than three times the initial velocity. Nassiri gave a weldability window which establishes the formation of a weld for a welding velocity higher than 1000 m/s. To compare with the theory, the equation used is the following: :

=

tan

Using this equation, the velocity reaches 2850 m.s-1, which is much higher than the results given by the experiences and the simulations. This equation uses the incidence angle α and by replacing it with the dynamic angle β, we find a value closer to our simulations. We are able to criticize this equation, which is disturbed because of the non-linear behavior at high strain rates according to Nassiri. The SPH approache is in the range of 600 m.s-1. These values are far from the theory. A pattern in velocity distribution in the values from 300 m.s-1 to 700 m.s-1 is also observed. This pattern may be caused by the resultant of the re-entrant jet, which is linked to the period of the waves. This SPH model is less precise than the Lagrangian model. However the studies have shown that a higher density of particles may allow more accurate values of velocity, and may allow the modelization of the jetting phenomenon. Also the lack of accuracy in the SPH model may be due to different material and plasticity laws. The possibility that a mistake has been made while initiating calculations cannot be excluded and further studies nee to be conducted.


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3.5. Stress For both models, the maximum stress is localized at the interface, on a length of 6mm from the collision point. It moves along the interface following the collision point and with a constant value. The maximum stress for the SPH model is 1500 MPa at 2.5µs and the maximum for the Lagrangian model is 460 MPa at 4µs. The values are all along the interface in the same range, and the localization of the maximum is due to different calculation methods. However, we may notice that he SPH model presents a stress three times higher than the Lagrangian model. The SPH model is less accurate, because it calculates the results with a simplified hardening law. Both SPH models presents the same range of results. This is a simplified modelization, the next step is to use the Johnson-Cook equation to get a higher precision in the results. However it is already clear that the 450 000 particles is more coherent and can present better results. It is more suitable for the calculations, but it is not yet sufficient for the study we are conducting. Furthermore, we also noticed a strong rise of the stress at the bottom left corner of the base plate. The stress reaches 400 MPa with the Lagrangian method and 1000 MPa with the SPH method.


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4. Conclusion of Chapter D The results found concerning the global shape of both plates, the small increase of dynamic angle, the flattening of the base plates are conform to the literature. This leads us to trust the models made. However, the calculations are sometimes fooled by the remeshing or are limited by the coarseness of the discretization and cannot give the real value. The characteristic values of pressure and strain are in the range of the experimental tests and the theory, although some incoherence with the values of Stress and velocity for the SPH model were noticed. But this may be due to the use of a simplified Hardening law. The studies have shown that the SPH model is more accurate than the Lagrangian for every fluid behavior calculations. However it's preciseness must be increased by using the appropriate Johnson-Cook law. The tests made showed that the 450 000 particles model is more suitable than the 150 000 particle study. It is not yet sufficient, and must be increased in the number of particles. But the computer power used has reached its maximum capacity. The number of particles needed to obtain a precise result with the full SPH model cannot be reached. The only area which presents an important need of high quality modelization is the interface area. Thus a mixed model, a Lagrangian approach where there is no deformation must be used, and an SPH approach where there are high deformations.


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CHAPTER E CONCLUSION AND RECOMMANDATIONS This paper is the conclusion of a 5 month work on the H2020 research project JoinEm. It gives a good picture of the recent search made in the magnetic pulse welding domain. The scientific study that has been carried out in this paper only scratches the surface of electromagnetic impulse welding, a topic that is vast and still undergoing change. Many disagreements between the scientists remain and the number of publication is exponentially increasing. The bibliographic research is a work in progress, and it has to evolve with time to stay up to date with the recent findings to come. This work has been made under the Initiative Horizon2020 which aims to enhance the new technologies in Europe and give to the industries leadership on different sectors by employing these technologies. The European Union finances around a hundred research projects with more than 80 billion Euros. Join-Em is one of these initiatives, driving its research on electromagnetic pulse welding. The Magnetic Pulse Welding could be used to replace components made only from copper material, by components which are formed by an assembly of copper and aluminum. Aluminum has a good thermal and electrical conductivity and is cheaper and lighter than copper. The objectives of Join-Em is to study this technology and make it applicable in an industrial environment. Thus Join-Em should be able to understand the process of this welding and to simulate it by numerical methods. It requires to work upon both macroscopical and microscopical approaches to find out for each particular welding the right process parameters. The literature draws a list of several phenomena, and the most important are regrouped here. The main phenomenon observable is the so called jet of particles which can be observed with a high speed camera. Composed of the oxides and the superficial layers of the two plates, it is the only phenomenon observable during the welding. The presence of the jet does not state the quality of the weld, however its absence guarantees the non reliability of the welding process. The jet could be used as a criterion to verify the numerical models. 89 Camille Bandry & Calixte Faucon

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The second main characteristic is the morphology of the interface. Three types of morphology namely flat, wavy or vortical could be observed. The weld can be of good quality with any of these morphology and this does not permit to characterize the strength of a weld. However, the simulation of the interface is possible with some numerical methods, thus the morphology of the interface could be a good criteria to verify the model. The comparison between the numerical studies and the experimentations must give the same results of wavelength and morphology. The last phenomenon which is important according to the literature is the hump. It is a small amount of material of the base plate that pops up in front of the impact point. It is included in several theories about the formation of the waves. It may be the origin of the formation of the vortexes. Numerically it is identifiable, and may be used as a criteria of the validity for the models. However the research is not yet completed and some information are still missing to characterize the strength of a weld. Also, the mechanisms responsible for the creation of these phenomena are not known, but it is agreed that the pressure, the velocities, and the distortion at an extremely high rate force the solid material to behave as a fluid. In the second part of this report, the different methods of simulation all have their pros and cons, reliability, complexity, and also the different phenomena they are capable to modelize. There are five different methods of numerical studies namely : - The Lagrangian method is made for solids, it is rigid and not suited to perform simulation with very high rate of deformation. Physical quantities such as pressure, plastic strain, velocity, can be simulated but phenomena such jet or hump cannot be accessed. - The Eulerian method is suited for materials undergoing very large deformation, the mesh is fixed and studies the flow of materials passing through. It is suited to model EPW as it can modelize all the main phenomena. - The ALE method consist in mixing the two previous methods. It is also a very good candidate for modelling EPW. - The SPH model is a meshless method. It is very accurate and can modelize precisely all physical phenomena (jet, hump, interface). However it is power consuming. Combining different numerical methods and thus mixing their advantages is certainly the best course of action.


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Hereafter is presented a table which sums up the expected results for each numerical approach.

Observable phenomena

Lagrangian

Euler

ALE

SPH

Mixed Euler Lagrange

Mixed SPH Lagrange

jet

0

1

0

1

1

1

interface

0

1

1

1

?

1

hump

0

1

0

1

1

1

Table 11: Summary of phenomena modelizable with different simulation techniques

The first modelizations made using two different methods of simulation are in overall agreement by the literature. The predicted fields between the two methods show similar trends but show some discrepancies regarding the peak values. The origin of the observed differences could be linked either to the material strength models or to the mesh densities which are not the same in both cases. The next step in the simulation work is to refine the SPH simulations, to include Johnson-Cook hardening law and even the thermal aspect. However, according to the available computer power, the solution could be to mix both methods, Lagrangian where the deformation is kept low, and the SPH for the interface where the material deformation is high. Besides Eulerian or ALE models need to be developed.


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APPENDIX 1



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APPENDIX 2


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APPENDIX 3 Method

Conclusions Parameters such as magnetic field distribution, magnetic force distribution, and interaction between the blank and the driver can be calculated by this method.

Pure Lagrangian [25]

The experiment demonstrates that the calculation of the mechanical model is more suitable to the small deformation processes. For large-scale deformation processes, it can only predict the deformation qualitatively. The impact conditions at the collision zone in explosive welding were successfully reproduced using a pneumatic gas gun.

The straight, wavy interfaces and jetting phenomena were modeled and reproduced.

The numerical analysis predicted a hump in the interface at impact, the jet and wave formation (with their magnitude and velocity).

Pure Eulerian [26]

Theories claiming that the bonding occurred when the collision velocity was higher than a threshold value are not supported by this study. Temperatures near the interface during the impact were predicted to be lower than the melting temperatures of both materials

The amplitude and wavelength of the interface profile were shown to be dependent on flyer plate thickness.

The bonding mechanism theory seems to be a solid state welding process.


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Wavy morphology is assumed to be the characteristic of a good weld. ALE [27]

Wavy morphology occurs if the process parameters (impact velocity, impact angle) are within a specific range. Shear instability mechanisms are the cause of the wavy morphology. The main features of the explosive/impact welding process were modeled.

SPH [30]

Shear stress and plastic strain which determine the success or failure of the welding were identified.

This paper confirmed that bonding is likely to be a solid state welding process. The metal jet emission and weld interface morphology were reproduced successfully.

Three patterns of interface morphology were obtained: straight, wavy, and vortical.

The composition of the metal jet was governed by the relative Mixed Methods [31] density difference between the two metals to be welded.

The metal jet was collected during magnetic pulse welding of Al/Cu and Cu/Al. The experimental results were in good agreement with the simulation results.

Hump formation was observed ahead of the collision point.


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APPENDIX 4


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Bibliographic References [1]

https://ec.europa.eu/programmes/horizon2020/en/what-horizon-2020

[2] P. S. Forms, “Horizon 2020 Call : H2020-FoF-2014 Topic : FoF-04-2014 Type of action : IA Proposal number : SEP-210152839 Proposal acronym : HuManPlace,” 2014. [3]

http://www.join-em.eu/index.html

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