Material characterization for stamping simulation of automotive body components A fundamental study on the identification of the macromechanical post- necking behaviour of metallic materials A thesis in partial fulfilment of the requirements for the degree of Master of Science in Automotive Engineering Supervisors: Prof Graziano Ubertalli Mr Daniele De Caro Mr Matteo Ferrea Author: Saeid Ghaffari Politecnico di Torino Turin, Italy March 2021 Collegio di Ingegneria Meccanica, Aerospaziale, dell'Autoveicolo e della Produzione Table of Contents Chapter One: Material matters ............................................................................................ 20 Macromechanical material characterization for stamping simulation ................... 21 1.1.1 Yield criteria ................................................................................................... 21 1.1.2 Flow stress curve and strain hardening laws .................................................. 22 1.1.3 Forming limits ................................................................................................ 23 How to characterize materials ............................................................................... 23 Metal forming simulation ...................................................................................... 25 1.3.1 The Fidelity of a Simulation Model ............................................................... 26 Material matters ..................................................................................................... 27 1.4.1 Materials ......................................................................................................... 27 1.4.2 Material testing and challenges ...................................................................... 35 Challenges in material model selection for forming simulation ............................ 36 Goals and Approaches ........................................................................................... 37 1.6.1 Scopes............................................................................................................. 37 1.6.2 Methodology .................................................................................................. 38 Chapter Two: Post-necking flow curve identification through tensile testing .................... 39 Introduction: four classes of methods to identify post-necking hardening behaviour.............................................................................................................................. 40 First level of approximation .................................................................................. 41 Second level of approximation with respect to the problem of diffuse necking ... 41 Third level of approximation with respect to the problem of diffuse necking ...... 42 Virtual fields method ............................................................................................. 44 Extending tensile test data using Siebel and Schwaigerer’s model ....................... 45 2.6.1 Methodology .................................................................................................. 45 2.6.2 Measurement setup ......................................................................................... 46 1 2.6.3 Stress-strain curve evaluation......................................................................... 47 Optimization algorithms for material modelling ................................................... 49 Chapter Three: Hardening laws investigation on Novelis AA5000, Constelium AA5000, Constelium AA6000 ................................................................................................................ 50 Introduction ........................................................................................................... 51 An introduction into common strain hardening laws ............................................ 52 3.2.1 Hollomon hardening law ................................................................................ 53 3.2.2 Swift hardening law ....................................................................................... 54 3.2.3 Voce hardening law (classical Voce saturation law) ..................................... 56 3.2.4 Swift-Voce hardening law .............................................................................. 58 3.2.5 Hollomon-Voce hardening law ...................................................................... 59 3.2.6 Hockett-Sherby hardening law ....................................................................... 62 3.2.7 Swift/Hockett-Sherby hardening law ............................................................. 64 3.2.8 k-exponent function ........................................................................................ 66 Hardening laws investigation on Novelis and Constelium data sheets ................. 66 3.3.1 Novelis AA5000 tensile test results ............................................................... 66 3.3.2 Constelium AA5000 tensile test results ......................................................... 80 3.3.3 Constelium AA6000 tensile test results ......................................................... 93 Chapter Four: Hydraulic bulge test ................................................................................... 107 Introduction ......................................................................................................... 108 Hydraulic bulge test and tensile test .................................................................... 109 Bulge test equipment ........................................................................................... 111 Data collection and analysis of hydraulic bulge test ........................................... 112 4.4.1 Indirect method ............................................................................................ 113 4.4.2 Direct methods ............................................................................................. 124 ISO 16808 recommended procedure for hydraulic bulge test ............................. 127 2 4.5.1 Determination of the curvature and strains at the pole................................. 128 4.5.2 Calculation of biaxial stress-strain curves .................................................... 129 From yield point to fracture by combining tensile test data with bulge test data 130 4.6.1 Introduction .................................................................................................. 130 4.6.2 Tensile test data extrapolation using scaled bulge test data ......................... 131 4.6.3 Plotting flow curve using anisotropy of the material ................................... 133 Post-necking identification using ISO 16808 procedure ..................................... 135 4.7.1 Aluminium 6000 Novelis ............................................................................. 135 4.7.2 DP600 1.2mm Arcelor ................................................................................. 143 Chapter Five: Post-necking tensile stress–strain behaviour identification of AHSSs using Digital Image Correlation technique ...................................................................................... 150 Introduction ......................................................................................................... 151 Bridgman method: Yes, but not for a Flat Specimen .......................................... 151 Behind the scene: Theory .................................................................................... 154 5.3.1 Hill’s 1948 Yield Criterion: A short review ................................................. 155 Necking: criteria and mechanism ........................................................................ 161 5.4.1 Criteria and prediction .................................................................................. 161 Tensile test results of CP 1400HD subsize specimen using DIC technique and GOM Correlate SW ........................................................................................................... 162 5.5.1 Position of the neck ...................................................................................... 163 5.5.2 Equivalent stress and equivalent plastic strain evaluation ........................... 167 5.5.3 Necking mechanism in CP 1400HD subsize specimen using DIC technique 177 Tensile test results of QP 1180-subsize specimen using DIC technique and GOM correlate SW....................................................................................................................... 182 A review on the proposed method ....................................................................... 189 Chapter Six: Validation of the equivalent flow stress curve using FEA ........................... 190 3 Introduction ......................................................................................................... 191 Finite element modelling and analysis ................................................................ 191 6.2.1 Pre-processing .............................................................................................. 191 6.2.2 Post-processing: analysis of the numerical results ....................................... 196 6.2.3 Further investigation on FE results .............................................................. 205 A review on the FEA of the tensile test ............................................................... 213 Chapter Seven: Conclusion and possible future