Accompagner les pratiques des enseignants

Sommaire

General introduction 1

1 Theoretical background 7

1.1 Background on extrusion . . . . . . . . . . . . . . . . . . . . 9

1.2 Background on the metallurgy of AlMgSi alloys . . . . . . . . 11

1.3 Background on homogenization treatment . . . . . . . . . . . 14

1.3.1 Intermetallic phases in the ENAA 6xxx series . . . . . 15

1.3.2 Morphological changes . . . . . . . . . . . . . . . . . . 16

1.3.3 Inuence of the alloy content . . . . . . . . . . . . . . . 18

1.3.4 Improvement of extrudability . . . . . . . . . . . . . . 18

1.4 Surface quality considerations . . . . . . . . . . . . . . . . . . 19

1.4.1 Surface cracking . . . . . . . . . . . . . . . . . . . . . . 20

1.4.2 Pick-up and die-lines . . . . . . . . . . . . . . . . . . . 20

1.5 Micro-mechanisms of ductile fracture . . . . . . . . . . . . . . 21

1.6 Micromechanics-based constitutive model for ductile fracture 23

1.6.1 Local approach to fracture . . . . . . . . . . . . . . . . 23

1.6.1.a Void nucleation . . . . . . . . . . . . . . . . . 24

1.6.1.b Growth of isolated void . . . . . . . . . . . . . 25

1.6.1.c Micromechanical model by Gurson for porous solids . . . . . . . . . . . . . . . . . . . . . . . 26

1.6.1.d Inuence of the void shape . . . . . . . . . . . 28

1.6.1.e Void coalescence conditions . . . . . . . . . . . 28

1.6.2 Uni ed extended model for void growth and coalescence 30

2 The starting point 33

2.1 Introduction on industrial extrusion . . . . . . . . . . . . . . 36

2.2 Material and Industrial testing . . . . . . . . . . . . . . . . . 37

2.2.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2.2 Homogenization tests . . . . . . . . . . . . . . . . . . . 38

2.2.3 Extrusion tests . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Results of the extrusion tests . . . . . . . . . . . . . . . . . . 39

2.3.1 Surface defect A . . . . . . . . . . . . . . . . . . . . . . 41

2.3.2 Surface defect B . . . . . . . . . . . . . . . . . . . . . . 43

2.3.3 Evolution of the extrusion temperature . . . . . . . . . 43

2.4 Microstructure investigation around the surface defects . . . . 45

2.4.1 TEM investigation at the defects locations . . . . . . . 45

2.4.2 DSC investigation at the defects locations . . . . . . . 46

2.4.2.a The DSC methodology . . . . . . . . . . . . . 48

2.4.2.b DSC measurements . . . . . . . . . . . . . . . 49

2.5 First conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 49

3 Microstructure evolution during homogenization 53

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2 Materials and Experimental techniques . . . . . . . . . . . . . 57

3.2.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2.2 Experimental techniques for microstructure analysis . . 58

3.2.2.a Scanning Electron Microscopy (SEM) . . . . . 58

3.2.2.b Quanti cation of the relative
-AlFeMnSi and

-AlFeSi fraction by SEM and EDS . . . . . . 58

3.2.2.c Measurements of the intermetallics shape by Image analysis (IA) . . . . . . . . . . . . . . . . . 60

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.3.1 SEM investigations of the microstructure evolution . . 60

3.3.2 Quanti cation of the microstructure evolution . . . . . 62

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4 Growth and coalescence of penny-shaped voids 71

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2 Void cell calculations with initially penny-shaped voids . . . . 78

4.2.1 Numerical procedures . . . . . . . . . . . . . . . . . . . 78

4.2.2 Results of the unit cell calculations without particle . . 79

4.2.3 Results of the unit cell calculations with particle . . . . 85

4.3 The constitutive model . . . . . . . . . . . . . . . . . . . . . . 89

4.3.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.1.a Before void nucleation . . . . . . . . . . . . . . 90

4.3.1.b Void nucleation condition . . . . . . . . . . . . 91

4.3.1.c Void growth model . . . . . . . . . . . . . . . . 92

4.3.1.d Void coalescence condition . . . . . . . . . . . 93

4.3.2 Assessment of the model . . . . . . . . . . . . . . . . . 94

4.3.2.a Assessment of the void coalescence condition . 94

4.3.2.b Assessment of the void growth model . . . . . 94

4.4 Parametric study and discussion . . . . . . . . . . . . . . . . 95

4.4.1 No nucleation stage - low to large stress triaxiality . . . 96

4.4.2 No nucleation stage - very low stress triaxiality . . . . 99

4.4.3 Delayed void nucleation . . . . . . . . . . . . . . . . . . 103

4.4.4 Simple model for the ductility of metals with penny shape voids . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5 Micromechanics of low and high temperature fracture in 6xxx Al alloys 113

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

5.2 Materials, Experimental methods and Mechanical data reduction scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.2.2 Characterization of the damage nucleation and evolution 119

5.2.3 Tensile tests . . . . . . . . . . . . . . . . . . . . . . . . 121

5.2.4 Inverse procedure to determine uniaxial ow properties 122

5.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 125

5.3.1 Mechanical tensile tests . . . . . . . . . . . . . . . . . . 125

5.3.1.a Nominal stress-strain relationships . . . . . . . 125

5.3.1.b Yield stress evolution . . . . . . . . . . . . . . 129

5.3.1.c Uniform elongation - Hardening behavior . . . 129

5.3.1.d Inverse identi cation of the materials ow curves 133

5.3.1.e True average fracture strain f . . . . . . . . . 133

5.3.2 Fracture mechanisms . . . . . . . . . . . . . . . . . . . 140

5.3.2.a In situ tensile tests at room temperature . . . 140

5.3.2.b Interrupted tensile tests at high temperature . 143

5.3.2.c Fracture surface . . . . . . . . . . . . . . . . . 144

5.4 Micromechanical modeling . . . . . . . . . . . . . . . . . . . . 146

5.4.1 Physical model . . . . . . . . . . . . . . . . . . . . . . 146

5.4.2 Micromechanics-based full constitutive model . . . . . 149

5.4.2.a Introduction . . . . . . . . . . . . . . . . . . . 149

5.4.2.b Before void nucleation . . . . . . . . . . . . . . 151

5.4.2.c Void nucleation condition . . . . . . . . . . . . 151

5.4.2.d Void growth model . . . . . . . . . . . . . . . . 152

5.4.2.e Onset of void coalescence . . . . . . . . . . . . 156

5.4.2.f Void coalescence . . . . . . . . . . . . . . . . . 158

5.4.3 Numerical method and problem formulation . . . . . . 158

5.4.4 Results of the modeling . . . . . . . . . . . . . . . . . . 160

5.4.4.a Parameters indenti cation . . . . . . . . . . . 160

5.4.4.b Deformation at room temperature . . . . . . . 162

5.4.4.c Deformation at high temperature . . . . . . . 163

5.5 Discussion and conclusions . . . . . . . . . . . . . . . . . . . 166

6 Parametric study and optimization of extrusion conditions171

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.2 Inuence of the homogenization temperature and holding time 174

6.3 Inuence of the Mg and Si content . . . . . . . . . . . . . . . 176

6.4 Inuence of the Mn content . . . . . . . . . . . . . . . . . . . 177

6.5 Inuence of Fe content . . . . . . . . . . . . . . . . . . . . . . 178

6.6 Inuence of the thermal treatment on Mg2Si dissolution . . . 179

6.6.1 Mg2Si phase dissolution/growth . . . . . . . . . . . . . 180

6.6.1.a The dissolution/growth model . . . . . . . . . 180

6.6.1.b Results . . . . . . . . . . . . . . . . . . . . . . 183

7 Conclusions 189

A E
ect of the anisotropy distribution parameter 0 207

B Important geometrical relationships 213

C Expressions for the parameters of the void growth model 217

D Klocker formulation for void aspect parameter k 223

E Flow curves identi cation 227