German-French Summer School, September 3-7, 2012, Dortmund, Germany Hardening and Damage of...
1
0 0.001 0.002 0.003 0.004 0 0.2 0.4 0.6 0.8 1 Average void radius[m m] Average axial strain atm inim um cross-section M odel Experiment 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 0.8 1 Porosity f Average axial strain atm inim um cross-section M odel Experiment German-French Summer School, September 3-7, 2012, Dortmund, Germany Hardening and Damage of Materials under Finite Deformations: Constitutive Modeling and Numerical Implementation Numerical simulation of DP steel damage using a physically-based GTN model Joseph Fansi a,b,c , Anne-Marie Habraken a , Tudor Balan b , Xavier Lemoine b,c a Departement ArGEnCo, Division MS²F, University of Liège, Belgium b LEM3, Arts et Métiers ParisTech, Metz, France c ArcelorMittal R&D Global Maizières S.A., Maizières-Lès-Metz, France [email protected]; [email protected]; [email protected]; [email protected] Constitutive model • This work is supported financially by ArcelorMittal, via the Agence Nationale de la Recherche et de la technologie (F) • AMH thanks the Interuniversity Attraction Poles Program - Belgian State – Belgian Science Policy P7 INTEMATE and the FRS- FNRS for financial support • The authors thank Eric Maire and Caroline Landron from INSA Lyon (F) and Olivier Bouaziz from ArcelorMittal (F) for fruitful discussion, experimental data, damage models. Acknowledgements M Ben Bettaieb, X Lemoine, O Bouaziz, A-M Habraken, L Duchêne (2010) Mech of Materials 139-156 M Ben Bettaieb, X Lemoine, L Duchêne, A-M Habraken (2012) Int J Num Meth Engng 85, 1049-1072 O Bouaziz, E Maire, M Giton, J Lamarre, Y Salingue, M Dimechiele (2008) Rev Métallurgie 2, 102-107 C Landron, O Bouaziz, E Maire, J Adrien (2010) Scripta Mat 63, 973-6 C Landron (2011) Ductile damage characterization in Dual-Phase steels using X-ray tomography, PhD thesis, INSA- Lyon E Maire, O Bouaziz, M Dimechiele, C Verdu (2008) Acta Mat 56, 4954-64 Conclusions and future work Motivations and objectives Material parameters and identification Results and discussion References Experiments selected for the validation Elasticity Isotropic Hardening Kinematic Hardening Anisot ropy E (MPa) ν K (MPa) n ε 0 C s (MPa) r 0 , r 45, r 90 2×10 5 0.35 1 0.245 0.02 92.04 58.02 1 GTN damage parameters Nucleation law #1 f 0 f c q 1 (t =0) q 2 (t=0 ) q 3 ε n0 A (mm - ³) R 0 i (mm) a α H 2×10 -5 0.0 01 1.5 1 2.25 0.8 5000 0.002 1 0.25 0.55 Nucleation law #2 B (mm -3 ) σ c (MPa) N 0 (mm -3 ) 4500 1100 1300 Elasto-plasticity, Hill’48 anisotropy: Combined isotropic-kinematic hardening: Physically-based void nucleation and growth: plastic incompressibili ty of metal matrix number of voids in reference volume average void radius • Physically-inspired evolution of the numerical void density N : Law #1, [Bouaziz et al., 2008] Law #2, [Landron, 2011] • Physically-inspired evolution of R [Bouaziz et al., 2008] : Phenomenological coalescence modeling (optional): Experiments used for the material parameter identification: • tensile tests along RD, TD, DD • monotonic and reverse shear tests • X-ray tomography measurements on in- situ tensile test identification of damage-related parameters X-ray tomography measurements on in-situ notched tensile test [Landron, 2012] Experimentally measured quantities available (time evolutions): • tensile load • radius of minimum cross-section (r section ) • radius of the notch (r notch ) • number of voids in a reference volume at the centre of the specimen • average radius of the voids in the reference volume Post-treatment of numerical results for confrontation to experiments: • average values over a pre-defined fixed volume • average values over the central cross- section GTN, normality rule: [Landron et al., 2010, Scripta Mat] [Maire et al., 2008, Acta Mat] • Damage (voids) is experimentally observed • In DP steels, damage seem related to the presence of a hard phase ferrite martensite void • X-Ray tomography recently allowed for more physical analyses: • Physically-based scalar models of nucleation and growth • Experimental porosity measurement for damage model validation Objectives of this work : • implement an advanced GTN model in Abaqus/Explicit, based on the previous work of Ben Bettaieb et al. [2010, 2012] • enrich this model with physically-based nucleation / growth models • validate the model with X-Ray tomography data • apply the model to sheet forming problems experimental set-up sampl e proposed 2D mesh Simulation results (example): •Macroscopic quantities fit the experimental ones, within an error range. •Porosity f and its components (N, R) can be compared to experiments, before coalescence starts 0 0.2 0.4 0.6 0.8 1 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Notchradius[m m ] Average axial strain atm inim um cross-section Experiment FE m odel 0 50000 100000 150000 200000 250000 300000 0 0.2 0.4 0.6 0.8 1 Num ber ofvoids/m m³ Average axial strain atm inim um cross-section M odel Experiment . •FE implementation of a complete, up-to- date GTN-type damage model with anisotropy and isotropic-kinematic hardening •Incorporation of recent models of nucleation and growth •Confrontation to X-Ray tomography experimental results •Mesh and post-treatment consistent with experiments •Future work: •Validation in other conditions (triaxiality, strain-path change) •Application to simple sheet forming processes
-
Upload
kendall-gravitt -
Category
Documents
-
view
222 -
download
4
Transcript of German-French Summer School, September 3-7, 2012, Dortmund, Germany Hardening and Damage of...
0
0.001
0.002
0.003
0.004
0 0.2 0.4 0.6 0.8 1
Aver
age
voi
d ra
dius
[mm
]
Average axial strain at minimum cross-section
Model
Experiment
0
0.02
0.04
0.06
0.08
0.1
0 0.2 0.4 0.6 0.8 1
Poro
sity
f
Average axial strain at minimum cross-section
Model
Experiment
German-French Summer School, September 3-7, 2012, Dortmund, Germany Hardening and Damage of Materials under Finite Deformations: Constitutive Modeling and Numerical Implementation
Numerical simulation of DP steel damageusing a physically-based GTN model
Joseph Fansia,b,c, Anne-Marie Habrakena, Tudor Balanb, Xavier Lemoineb,c
a Departement ArGEnCo, Division MS²F, University of Liège, Belgiumb LEM3, Arts et Métiers ParisTech, Metz, France
c ArcelorMittal R&D Global Maizières S.A., Maizières-Lès-Metz, France
[email protected]; [email protected]; [email protected]; [email protected]
Constitutive model
• This work is supported financially by ArcelorMittal, via the Agence Nationale de la Recherche et de la technologie (F)• AMH thanks the Interuniversity Attraction Poles Program - Belgian
State – Belgian Science Policy P7 INTEMATE and the FRS-FNRS for financial support• The authors thank Eric Maire and Caroline Landron from INSA Lyon
(F) and Olivier Bouaziz from ArcelorMittal (F) for fruitful discussion, experimental data, damage models.
Acknowledgements
M Ben Bettaieb, X Lemoine, O Bouaziz, A-M Habraken, L Duchêne (2010) Mech of Materials 139-156
M Ben Bettaieb, X Lemoine, L Duchêne, A-M Habraken (2012) Int J Num Meth Engng 85, 1049-1072
O Bouaziz, E Maire, M Giton, J Lamarre, Y Salingue, M Dimechiele (2008) Rev Métallurgie 2, 102-107
C Landron, O Bouaziz, E Maire, J Adrien (2010) Scripta Mat 63, 973-6C Landron (2011) Ductile damage characterization in Dual-Phase steels
using X-ray tomography, PhD thesis, INSA-LyonE Maire, O Bouaziz, M Dimechiele, C Verdu (2008) Acta Mat 56, 4954-64
Conclusions and future work
Motivations and objectives Material parameters and identification Results and discussion
References
Experiments selected for the validation
Elasticity Isotropic Hardening Kinematic Hardening AnisotropyE (MPa) ν K (MPa) n ε0 C s (MPa) r0, r45, r90
2×105 0.35 1 0.245 0.02 92.04 58.02 1
GTN damage parameters Nucleation law #1f0 fc q1(t=0) q2(t=0) q3 εn0 A (mm-³) R0
i (mm) a αH
2×10-5 0.001 1.5 1 2.25 0.8 5000 0.0021 0.25 0.55
Nucleation law #2
B (mm-3) σc (MPa) N0 (mm-3)
4500 1100 1300
Elasto-plasticity, Hill’48 anisotropy:
Combined isotropic-kinematic hardening:
Physically-based void nucleation and growth:
plastic incompressibility of metal matrix
number of voids in reference volume
average void radius
• Physically-inspired evolution of the numerical void density N :
Law #1, [Bouaziz et al., 2008]
Law #2, [Landron, 2011]
• Physically-inspired evolution of R [Bouaziz et al., 2008]:
Phenomenological coalescence modeling (optional):
Experiments used for the material parameter identification:• tensile tests along RD, TD, DD• monotonic and reverse shear tests• X-ray tomography measurements on in-situ tensile test
identification ofdamage-related
parameters
X-ray tomography measurements on in-situ notched tensile test[Landron, 2012]
Experimentally measured quantities available (time evolutions):• tensile load• radius of minimum cross-section (rsection)• radius of the notch (rnotch)• number of voids in a reference volume at the centre of the specimen• average radius of the voids in the reference volume
Post-treatment of numerical results for confrontation to experiments:• average values over a pre-defined fixed volume• average values over the central cross-section
GTN, normality rule:
[Landron et al., 2010, Scripta Mat]
[Maire et al., 2008, Acta Mat]• Damage (voids) is experimentally observed
• In DP steels, damage seem related to the presence of a hard phase
ferritemartensitevoid
• X-Ray tomography recently allowed for more physical analyses:• Physically-based scalar models of nucleation and growth• Experimental porosity measurement for damage model validation
Objectives of this work :• implement an advanced GTN model in Abaqus/Explicit, based on the
previous work of Ben Bettaieb et al. [2010, 2012]• enrich this model with physically-based nucleation / growth models• validate the model with X-Ray tomography data• apply the model to sheet forming problems
experimental set-up sample proposed 2D mesh
Simulation results (example):
•Macroscopic quantities fit the experimental ones, within an error range.• Porosity f and its
components (N, R) can be compared to experiments, before coalescence starts
0
0.2
0.4
0.6
0.8
1
1.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Not
ch ra
dius
[mm
]
Average axial strain at minimum cross-section
Experiment
FE model
0
50000
100000
150000
200000
250000
300000
0 0.2 0.4 0.6 0.8 1N
umbe
r of v
oids
/mm
³Average axial strain at minimum cross-section
ModelExperiment
.
• FE implementation of a complete, up-to-date GTN-type damage model with anisotropy and isotropic-kinematic hardening• Incorporation of recent models of nucleation and growth• Confrontation to X-Ray tomography experimental results•Mesh and post-treatment consistent with experiments
• Future work: • Validation in other conditions (triaxiality, strain-path change)• Application to simple sheet forming processes
