Before the development of computational science, heat conduction problems were mainly solved by analytical techniques. Analytical solutions are exact solutions of differential equations; the investigated physical phenomena, for instance the temperature, are solved locally for one single point independently of the rest of the investigated structure resulting in extremely short computational times. These analytical solutions are however only valid for some simple geometries and boundary conditions making their applications for complex industrial geometries directly not possible. Numerical techniques, such as the Finite Element Method, enable overcoming this problem. However, the numerical simulation of the structural heat effect of welding for complex and large assemblies requires high computational effort and time. Therefore, the wide application of welding simulation in industry is not established, yet.
The aim of this study is to combine the advantages of analytical and numerical simulation methods to accelerate the calibration of the thermal model of structure welding simulation. This is done firstly by calibrating automatically the simulation model with a fast analytical temperature field solution and secondly by solving the welding simulation problem numerically with the analytically calibrated input parameters. In order to achieve this goal, the analytical solution of the heat conduction problem for a point source moving in an infinite solid was extended and validated against reference models until a solution for a volumetric heat source moving on a thin small sheet with several arbitrary curved welding paths was found. The potential of this analytical solution by means of computational time was subsequently demonstrated on a semi-industrial geometry with large dimensions and several curved welds.
The combined method was then transferred to an industrial assembly welded with four parallel welds. For this joint geometry, it was possible to apply the extended analytical solution. The calibration of the simulation model was done automatically against experimental data by combining the extended fast analytical solution with a global optimisation algorithm. For this calibration, more than 3000 direct simulations were required which run in less computational time than one corresponding single numerical simulation. The results of the numerical simulation executed with the analytically calibrated input parameters matched the experimental data within a scatter band of ± 10 %. The limit of the combined method is shown for an industrial assembly welded with eight overlap welds. For this joint geometry, a conventional numerical approach was applied, since no analytical solution was actually available. The final simulation results matched the experimental data within a scatter band of ± 10 %.
The results of this work provide a comprehensive method to accelerate the calibration of the thermal model of the structure welding simulation of complex and large welded assemblies, even though within limitation. In the future, the implementation of this method in a welding simulation tool accessible to a typical industrial user still has to be done.

Danksagung V

Abstract IX

Table of content XI

1 Introduction 1

2 State of the Art 3

2.1 Welding simulation 3

2.2 Temperature field simulation 5

      2.2.1 Numerical approach 6

      2.2.2 Analytical approach 6

2.3 Workflow of a structure welding simulation 15

      2.3.1 Assumptions and simplifications 15

      2.3.2 Thermal simulation 18

      2.3.3 Mechanical simulation 19

      2.3.4 Experimental validation 20

2.4 Welding simulation of complex structures 21

      2.4.1 Industrial applications 21

      2.4.2 Techniques to decrease time to solution 23

3 Execution of experiments 25

3.1 Required data for welding simulation 25

      3.1.1 Material properties 25

      3.1.2 Welding process parameters 31

      3.1.3 Welded assemblies 33

      3.1.4 Experimental data 36

3.2 Analytical simulations 38

      3.2.1 Computer and software 38

      3.2.2 Assumptions and simplifications 38

      3.2.3 Plates 39

      3.2.4 Semi-industrial geometry 43

      3.2.5 Wheelhouse and simplified geometries 44

3.3 Numerical simulations 47

      3.3.1 Computer and software 47

      3.3.2 Assumptions and simplifications 48

      3.3.3 Plates 48

      3.3.4 Semi-industrial geometry 49

      3.3.5 Wheelhouse and simplified geometries 50

      3.3.6 Crossbeam 51

4 Results 55

4.1 Experimental results 55

      4.1.1 Temperature field measurement 55

      4.1.2 Distortion measurement 66

4.2 Analytical simulations 68

      4.2.1 Plates 68

      4.2.2 Semi-industrial geometry 76

      4.2.3 Wheelhouse and simplified geometries 77

      4.2.4 Calculation time of analytical solutions 79

4.3 Numerical simulations 80

      4.3.1 Plates 80

      4.3.2 Semi-industrial geometry 84

      4.3.3 Wheelhouse and simplified geometries 85

      4.3.4 Crossbeam 91

      4.3.5 Calculation time of numerical solutions 96

5 Discussion of the results 97

5.1 Validation of analytical temperature field solutions 97

      5.1.1 Validation for plate geometries 97

      5.1.2 Validation for the semi-industrial geometry 109

5.2 Application for simplified geometries 112

      5.2.1 Simplified geometry “parallel weld” 112

      5.2.2 Simplified geometry “overlap weld” 121

5.3 Application for the industrial welded assemblies 125

      5.3.1 Temperature field simulation of the wheelhouse 125

      5.3.2 Temperature field simulation of the crossbeam 129

      5.3.3 Distortion simulation of the crossbeam 132

6 Summary and outlook 139

Nomenclature 143

List of figures 147

List of tables 155

Literature 157

Own Publications 169

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