Post on 22-Jun-2020
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Experimental and Numerical Characterization ofDamage and Application to Incremental Forming
PhD thesis presentation
Carlos Felipe Guzman
Department ArGEnCoUniversity of Liege, Belgium
February 1st, 2016
Simple geometries
Cooking pots
2
Simple geometries
Manufactured by Deep Drawing
3
More complex geometries
Planes and car prototypes
4
More complex geometries
Implants
Manufactured by ???
5
More complex geometries
Implants
Manufactured by ???
5
Single point incremental formingSPIF
Hirt et al. [2015] Schafer and Dieter Schraft [2005]
A sheet metal is deformed by a small tool.
The tool could be guided by a CNC (milling machine, robot).
6
Single point incremental formingSPIF
Video
7
Single point incremental formingSPIF
Advantages
Dieless, with high sheetformability.
Easy shape generation.
For rapid prototypes, smallbatch productions, etc.
Challenges
Poor geometrical accuracy.
Process slowness.
Characterization of servicelife.
The increased formability.
8
Single point incremental formingSPIF
Advantages
Dieless, with high sheetformability.
Easy shape generation.
For rapid prototypes, smallbatch productions, etc.
Challenges
Poor geometrical accuracy.
Process slowness.
Characterization of servicelife.
The increased formability.
8
The high formability of SPIF
crack
70◦
crack
sine law:
tf = t0 sinα⇒ tf ≈ 0.35
ε� 1.0
9
The high formability of SPIF
crack
Detail:
tf ≈0.25mm
t0 =1.0mm
9
The high formability of SPIFWhy formability is so high?
Forming Limit Curves
Reddy et al. [2015]
10
Methodology
Hypothesis
The crack is preceded by damage.
Damage is governed by microvoid nucleation, growth andcoalescence.
Damage is observed in SPIF [Lievers et al., 2004].
Tasks
1 Implementation of a damage model (Gurson) in the LAGAMINE FEcode.
2 Identification of the material parameters of the damage model.
3 Evaluate the model to understand the process mechanics leading tofracture.
11
Methodology
Hypothesis
The crack is preceded by damage.
Damage is governed by microvoid nucleation, growth andcoalescence.
Damage is observed in SPIF [Lievers et al., 2004].
Tasks
1 Implementation of a damage model (Gurson) in the LAGAMINE FEcode.
2 Identification of the material parameters of the damage model.
3 Evaluate the model to understand the process mechanics leading tofracture.
11
Thesis
Main question
Is the Gurson model with a shear extension able to predict failurein SPIF process?
Objectives
Efficient numerical model.
Limitations of the damage model (if any).
Reproduce the SPIF process mechanics.
12
Thesis
Main question
Is the Gurson model with a shear extension able to predict failurein SPIF process?
Objectives
Efficient numerical model.
Limitations of the damage model (if any).
Reproduce the SPIF process mechanics.
12
Presentation contents
13
Contents
14
Constitutive modeling
Elasticity
ε =1
2Gsσ − ν
E
1
3tr (σ) I
PlasticityHill [1948] yield locus
Fp =
√1
2(σ − X) : H : (σ − X)− σY
(εP)= 0
Isotropic hardening: Swift law
σY
(εP)= K
(εP + ε0
)nKinematic hardening: Armstrong and Fredrick [1966]
X = CX
(Xsatε
P − XεP)
Damage . . .
15
Constitutive modeling
Elasticity
ε =1
2Gsσ − ν
E
1
3tr (σ) I
PlasticityHill [1948] yield locus
Fp =
√1
2(σ − X) : H : (σ − X)− σY
(εP)= 0
Isotropic hardening: Swift law
σY
(εP)= K
(εP + ε0
)nKinematic hardening: Armstrong and Fredrick [1966]
X = CX
(Xsatε
P − XεP)
Damage . . .
15
Constitutive modeling
Elasticity
ε =1
2Gsσ − ν
E
1
3tr (σ) I
PlasticityHill [1948] yield locus
Fp =
√1
2(σ − X) : H : (σ − X)− σY
(εP)= 0
Isotropic hardening: Swift law
σY
(εP)= K
(εP + ε0
)nKinematic hardening: Armstrong and Fredrick [1966]
X = CX
(Xsatε
P − XεP)
Damage . . .
15
The damage model
Basic hypothesis
Material deterioration that leads to material failure.
Associated with the evolution of micro voids.
Cross section (2000x)
Anne Mertens, ULg
16
The damage modelVoid evolution
Base material
Nucleation Growth Coalescence
Lassance et al. [2007]
17
The damage modelVoid evolution
Base material
Nucleation Growth Coalescence
Lassance et al. [2007]
17
The Gurson [1977] model
Approach
Micromechanics based yield criterion.
Damage variable: void volume fraction (porosity).
Fp(σ, f , σY ) =σ2eq
σY 2− 1 + 2f cosh
(3
2
σmσY
)− f 2 = 0
18
The Gurson [1977] model
Approach
Micromechanics based yield criterion.
Damage variable: void volume fraction (porosity).
Fp(σ, f , σY ) =σ2eq
σY 2− 1︸ ︷︷ ︸
Von Mises
+2f cosh
(3
2
σmσY
)− f 2 = 0
18
The Gurson [1977] model
Approach
Micromechanics based yield criterion.
Damage variable: void volume fraction (porosity).
Fp(σ, f , σY ) =σ2eq
σY 2− 1 + 2f cosh
(3
2
σmσY
)− f 2︸ ︷︷ ︸
Damage
= 0
18
The Gurson [1977] model
Approach
Micromechanics based yield criterion.
Damage variable: void volume fraction (porosity).
Fp(σ, f , σY ) =σ2eq
σY 2− 1︸ ︷︷ ︸
Von Mises
+ 2 f cosh
(3
2
σmσY
)− f 2︸ ︷︷ ︸
Damage
= 0
Matrix mass conservation:
f = (1− f ) tr εp
1 material parameter:
f0
18
GTN extension
The Gurson-Tvergaard-Needleman (GTN) extension:
Nucleation [Chu and Needleman, 1980].
Void growth (classical volumetric assumption).
Coalescence [Tvergaard and Needleman, 1984].
f = fnucleation + fgrowth
19
GTN extensionTvergaard [1982]
Fp(σ, f ∗, σ) =σ2eq
σ2 − 1︸ ︷︷ ︸Von Mises
+ 2q1f∗ cosh
(−3
2q2σmσ
)− q3 (f ∗)2
︸ ︷︷ ︸Damage
= 0
20
GTN extensionTvergaard [1982]
Fp(σ, f ∗, εPM) =σ2eq
σ2Y
− 1︸ ︷︷ ︸Von Mises
+ 2 q1 f∗ cosh
(−3 q2 σm
2σY
)− q3 (f ∗)2
︸ ︷︷ ︸Damage
= 0
Matrix hardening:
σY = σY (εPM)
2 material parameters:
q1, q2 (q3 = q12)
20
NucleationChu and Needleman [1980]
f = fnucleation + fgrowth
fnucleation = AεPM︸︷︷︸Strain
+B (σeq + cσM)︸ ︷︷ ︸Stress
21
NucleationChu and Needleman [1980]
f = fnucleation + fgrowth
fnucleation = AεPM︸︷︷︸Strain
+B (σeq + cσM)︸ ︷︷ ︸Stress
A(εPM) =1√2π
fNSN
exp
[−1
2
(εPM − εN
SN
)2]
B(σ) = 0
21
NucleationChu and Needleman [1980]
f = fnucleation + fgrowth
fnucleation = AεPM︸︷︷︸Strain
+B (σeq + cσM)︸ ︷︷ ︸Stress
A(εPM) =1√2π
fNSN
exp
[−1
2
(εPM − εN
SN
)2]
B(σ) = 0
3 material parameters:
fN , εN , SN
21
CoalescenceTvergaard and Needleman [1984]
f ∗ =
{f if f < fcrfcr + Kf (f − fcr ) if f > fcr
fcr fFVoid volume fraction (f)
fcr
fu
Effectiveporosity (f ∗)
Kf
Kf =fu − fcrfF − fcr
2 material parameters:
fcr , fF
(fu =
1
q1
)
22
CoalescenceTvergaard and Needleman [1984]
f ∗ =
{f if f < fcrfcr + Kf (f − fcr ) if f > fcr
fcr fFVoid volume fraction (f)
fcr
fu
Effectiveporosity (f ∗)
Kf
Kf =fu − fcrfF − fcr
2 material parameters:
fcr , fF
(fu =
1
q1
)
22
Shear extensions
Coupling of stress and damage history.
Triaxiality: measure of the stress state.
[Pineau and Pardoen, 2007]
T (I1, J2) =σmσeq
T → 0 =⇒ εf →∞
23
Shear extensions
Coupling of stress and damage history.
Triaxiality: measure of the stress state.
[Pineau and Pardoen, 2007]
T (I1, J2) =σmσeq
T → 0 =⇒ εf →∞
23
Shear extensionsFailure modes
Cavity controlled (T = 1.10) Shear controlled(T = 0.47)
[Barsoum and Faleskog, 2007]
GTN model → No damage is predicted when T = 0.At low triaxiality, void shape evolution becomes important.
24
Shear extensionsFailure modes
Cavity controlled (T = 1.10) Shear controlled(T = 0.47)
[Barsoum and Faleskog, 2007]
GTN model → No damage is predicted when T = 0.At low triaxiality, void shape evolution becomes important.
24
Shear extensions
Nahshon and Hutchinson [2008]
f = fg + fn + fshear
fshear = kωf ω(σ)σdev : εP
σeq
1 material parameter: kω.
Note: ω(σ) is a scalar functions of the stress.
25
Shear extensions
Nahshon and Hutchinson [2008]
f = fg + fn + fshear
fshear = kωf ω(σ)σdev : εP
σeq
1 material parameter: kω.
Note: ω(σ) is a scalar functions of the stress.
25
Contents
26
Numerical implementation
Based on Ben Bettaieb et al. [2011b,a]
Complete GTN model:
Kinematic hardening (classical non-linear).Nucleation and coalescence (GTN model).Shear [Nahshon and Hutchinson, 2008].
Matrix anisotropy (Hill type) [Benzerga and Besson, 2001]:
q =
√1
2(σ − X) : H : (σ − X)
27
Numerical implementation
Based on Ben Bettaieb et al. [2011b,a]
Complete GTN model:
Kinematic hardening (classical non-linear).Nucleation and coalescence (GTN model).Shear [Nahshon and Hutchinson, 2008].Matrix anisotropy (Hill type) [Benzerga and Besson, 2001]:
q =
√1
2(σ − X) : H : (σ − X)
27
Integration scheme
Equations set
Fp(σ,X,H) = 0
dεP = dλ∂Fp
∂σ
dH = h(dεP ,σ,H)
Backward EulerAravas [1987]
εn+1 = εn + ∆tεn+1
∆t = tn+1 − tn
Ben Bettaieb et al. [2011b]
Γ(Y) = 0
Yi ={
∆εp ,∆εq , n1, n2, n3, n4, n5, εPM , f
}N-R iteration
Γi +9∑
j=1
∂Γi
∂YjdYj = 0
28
Integration scheme
Equations set
Fp(σ,X,H) = 0
dεP = dλ∂Fp
∂σ
dH = h(dεP ,σ,H)
Backward EulerAravas [1987]
εn+1 = εn + ∆tεn+1
∆t = tn+1 − tn
Ben Bettaieb et al. [2011b]
Γ(Y) = 0
Yi ={
∆εp ,∆εq , n1, n2, n3, n4, n5, εPM , f
}N-R iteration
Γi +9∑
j=1
∂Γi
∂YjdYj = 0
28
Integration scheme
Equations set
Fp(σ,X,H) = 0
dεP = dλ∂Fp
∂σ
dH = h(dεP ,σ,H)
Backward EulerAravas [1987]
εn+1 = εn + ∆tεn+1
∆t = tn+1 − tn
Ben Bettaieb et al. [2011b]
Γ(Y) = 0
Yi ={
∆εp ,∆εq , n1, n2, n3, n4, n5, εPM , f
}
N-R iteration
Γi +9∑
j=1
∂Γi
∂YjdYj = 0
28
Integration scheme
Equations set
Fp(σ,X,H) = 0
dεP = dλ∂Fp
∂σ
dH = h(dεP ,σ,H)
Backward EulerAravas [1987]
εn+1 = εn + ∆tεn+1
∆t = tn+1 − tn
Ben Bettaieb et al. [2011b]
Γ(Y) = 0
Yi ={
∆εp ,∆εq , n1, n2, n3, n4, n5, εPM , f
}N-R iteration
Γi +9∑
j=1
∂Γi
∂YjdYj = 0
28
Numerical validationHydrostatic test Nahshon and Xue [2009]
Gurson parametersq1 1.0 fN 0.04 f0 0.005q2 1.0 εN 0.30 fc 0.15q3 1.0 SN 0.10 ff 0.25
0 0.25
Volumetric strain [−]
0
4.5
Hydrostaticstress ratio [−]
GUR3DextNahshon2009
0 0.25
Volumetric strain [−]
0
0.25
Void volumefraction [−]
GUR3DextNahshon2009
29
Numerical validationHydrostatic test Nahshon and Xue [2009]
Gurson parametersq1 1.0 fN 0.04 f0 0.005q2 1.0 εN 0.30 fc 0.15q3 1.0 SN 0.10 ff 0.25
0 0.25
Volumetric strain [−]
0
4.5
Hydrostaticstress ratio [−]
GUR3DextNahshon2009
0 0.25
Volumetric strain [−]
0
0.25
Void volumefraction [−]
GUR3DextNahshon2009
29
Numerical validationShear test Nahshon and Xue [2009]
Gurson parametersq1 1.0 fN 0.04 f0 0.005q2 1.0 εN 0.30 fc 0.15q3 1.0 SN 0.10 ff 0.25
0 2.0
Equivalent strain [−]
0
2.5
Equivalentstress ratio [−]
kω = 0
kω = 1
kω = 3
GUR3DextNahshon2009
0 2.0
Equivalent strain [−]
0
0.4
Void volumefraction [−]
kω = 1
kω = 3
GUR3DextNahshon2009
30
Numerical validationShear test Nahshon and Xue [2009]
Gurson parametersq1 1.0 fN 0.04 f0 0.005q2 1.0 εN 0.30 fc 0.15q3 1.0 SN 0.10 ff 0.25
0 2.0
Equivalent strain [−]
0
2.5
Equivalentstress ratio [−]
kω = 0
kω = 1
kω = 3
GUR3DextNahshon2009
0 2.0
Equivalent strain [−]
0
0.4
Void volumefraction [−]
kω = 1
kω = 3
GUR3DextNahshon2009
30
Contents
31
Material presentation
DC01 ferritic steel (EN 10330).
1.0 mm thickness.
Microstructure:
Anne Mertens, ULg
Mn C Al Ni,Cu,Cr,P0.21 0.049 0.029 <0.025
32
Experimental setup
Uniaxial Zwickmachine
Bi-axial machine
A B
C
Load capacity: ±100 kN
33
Digital Image CorrelationDIC
Contactless method for displacements and strains.
Pattern tracking.
CMOS cameras, resolution 1280x800
AOI
refstep
34
Experimental test campaignSpecimens
Tensile
Shear
30
120
3
Plane strain
3058
120
R2
35
Plasticity tests
Tensile and shear test
0 0.5
Strain [−]
0
500
Stress [MPa]
45
RD,TD
Tensile
Shear
Bauschinger test
36
Plasticity tests
Tensile and shear test
0 0.5
Strain [−]
0
500
Stress [MPa]
45
RD,TD
Tensile
Shear
Bauschinger test
-0.5 0 0.4
Strain [-]
-300
0
300
Stress [MPa]
10%20%
30%
Precharge degree
36
Plasticity tests
Tensile and shear test
0 0.5
Strain [−]
0
500
Stress [MPa]
45
RD,TD
Tensile
Shear
Bauschinger test
-0.5 0 0.4
Strain [-]
-300
0
300
Stress [MPa]
30%
Stagnation
36
Identification of material parameters
Hill [1948] parameters → Classicalsimulated annealing.
Hardening (K , n, ε0, Cx , Xsat) →Inverse optimization (OPTIM).
error norm =
√√√√ N∑i=1
(yFEi − y exp
i
)2
Initialparameters
FEMsimulations
Numerical-experimentalcomparison
New set
Acceptable?
Identifiedparameters
yes
no
37
Identification of material parameters
Hill [1948] parameters → Classicalsimulated annealing.
Hardening (K , n, ε0, Cx , Xsat) →Inverse optimization (OPTIM).
error norm =
√√√√ N∑i=1
(yFEi − y exp
i
)2
Initialparameters
FEMsimulations
Numerical-experimentalcomparison
New set
Acceptable?
Identifiedparameters
yes
no
37
Identification of material parameters
Tensile test
0 0.2
Strain [−]
100
400
Stress [MPa]
Expnum
Bauschinger test
-0.4 0 0.4
Strain [−]
-300
0
300
Stress [MPa]
Expnum 10%
30%
38
Identification of material parameters
Tensile test
0 0.2
Strain [−]
100
400
Stress [MPa]
Expnum
Bauschinger test
-0.4 0 0.4
Strain [−]
-300
0
300
Stress [MPa]
Expnum 10%
30%
38
Contents
39
GTN characterizationMethodology
Difference with plasticity
Microscopic scale,heterogeneous deformation.
Force vs. displacement insteadof stress vs. strain.
Coupling between variables.
40
GTN characterizationMethodology
Difference with plasticity
Microscopic scale,heterogeneous deformation.
Force vs. displacement insteadof stress vs. strain.
Coupling between variables.
40
GTN parameters characterization
Automatic optimization (OPTIM) issues
CPU time, iterations, etc.
Sensitivity of nucleation, coalescence parameters.
Introduction of weights in the error norm.
Approach:
d1 d2Displacement
Force Plasticity Nucleation Coalescence
Lagamine Optim
41
GTN parameters characterization
Automatic optimization (OPTIM) issues
CPU time, iterations, etc.
Sensitivity of nucleation, coalescence parameters.
Introduction of weights in the error norm.
Approach:
d1 d2Displacement
Force Plasticity Nucleation Coalescence
Lagamine Optim
41
Macroscopic test campaign
R = 5
T ≈0.6-0.7
ω ≈0.25-0.4
R = 10
T ≈0.5-0.7
ω ≈0.2-0.4
hole
T ≈0.35-0.6
ω ≈0.0
shear
T ≈0.0
ω ≈1.0
42
Force predictions
Nucleation Coalescence ShearSet name f0 fN εN SN fc fF kω
set1 0.0055 0.135 0.25set2 0.0008 0.0025 0.175 0.42 0.0045 0.145 0.25set3 0.0025 0.170 0.075
0 2.5 5.0
Displacement [mm]
0
3000
6000
Force [N]
R=5R=10
hole
0 1.25 2.5
Displacement [mm]
0
500
1000
Force [N]
shear
43
Force predictions
Nucleation Coalescence ShearSet name f0 fN εN SN fc fF kω
set1 0.0055 0.135 0.25set2 0.0008 0.0025 0.175 0.42 0.0045 0.145 0.25set3 0.0025 0.170 0.075
0 2.5 5.0
Displacement [mm]
0
3000
6000
Force [N]
R=5R=10
hole
0 1.25 2.5
Displacement [mm]
0
500
1000
Force [N]
shear
43
Force predictions
Nucleation Coalescence ShearSet name f0 fN εN SN fc fF kω
set1 0.0055 0.135 0.25set2 0.0008 0.0025 0.175 0.42 0.0045 0.145 0.25set3 0.0025 0.170 0.075
0 2.5 5.0
Displacement [mm]
0
3000
6000
Force [N]
R=5R=10
hole
0 1.25 2.5
Displacement [mm]
0
500
1000
Force [N]
shear
43
Strain prediction
0 2.75 5.5
Displacement [mm]
0
0.30
0.6
Strain [−]
R=10
hole
Strain localization is not captured
44
Strain prediction
0 1.25 2.5
Displacement [mm]
0
0.20
0.4
Shear strain [−]
shear
44
DIC vs. FE predictionsAxial strain
notch R = 5
DIC Numerical
0.45
−0.05
notch R = 10
0.40
0.00
45
DIC vs. FE predictionsAxial strain
hole
DIC Numerical
0.60
0.00
shear
0.10
−0.25 46
Discussion
Results
Loss on load carrying capacity is captured.
Strain localization is not captured.
Limitations of the GTN model.
Source of errors
Parameters q1 and q2 were not calibrated.
Hardening stagnation.
Mesh sensitivity.
47
Contents
48
Literature review summary
Simulate SPIF is not easy
Small contact zone with a very long path.
High strains.
Incremental deformation, simulation time.
Sensitivity of force prediction to FE choice, constitutive law.
Boundary conditions, grip modeling.
49
Literature review summaryShape inaccuracies
Springback, bending.
Elastic strains.
50
Literature review summaryFormability
Forming Limit Curve (FLC):classic approach.
Through the thickness shear,Bending-under-tension, cycliceffects, etc.
51
Literature review summaryDamage
Definition
Mechanism of degradation leading to fracture (Damage 6= formability)
Malhotra et al. [2012].
Shear itself cannot explainhigher fomability:
Early localization: Noodletheory.
52
Literature review summaryDamage
Definition
Mechanism of degradation leading to fracture (Damage 6= formability)
Malhotra et al. [2012].
Shear itself cannot explainhigher fomability:
Early localization: Noodletheory.
52
Finite element type
• ••••
•• ••• ⊗
⊗⊗
⊗
Shell
• •
•••
•• •
••⊗
⊗...
Solid-shell
• •
•••
•
• •
••
⊗
Brick
RESS solid-shell element [Alves de Sousa, 2006].
Numerical technique: Enhanced assumed strain (EAS)
ε = εcom + εEAS
53
Finite element type
• ••••
•• ••• ⊗
⊗⊗
⊗
Shell
• •
•••
•• •
••⊗
⊗...
Solid-shell
• •
•••
•
• •
••
⊗
Brick
RESS solid-shell element [Alves de Sousa, 2006].
Numerical technique: Enhanced assumed strain (EAS)
ε = εcom + εEAS
53
Line testDescription
Most basic SPIF test.
Experimental data by Hans Vanhove (KULeuven).
54
Numerical-Experimental validation
Shape: top and bottom surface
-91 0 91
X [mm]
-6
0
1
Z [mm]
Exp
GTN+shear
cross section
x
y
55
Numerical-Experimental validation
Shape: top and bottom surface
-91 0 91
X [mm]
-6
0
1
Z [mm]
Exp
GTN+shear
Force
0 0.2 0.8 1.0 1.8
Ref. Time [s]
0
1000
2000
Force [N]
Exp
GTN+shear
55
Two-slope pyramidDescription
For shape accuracy assessment.
Experimental DIC shape by Amar Behera (KULeuven).
60◦
30◦
y
z
1 35 52 6 52 35 1
60
90
182
182
x
y
56
Numerical predictionsExperimentally there is no crack!
Shape: bottom surface
0 45 90
X [mm]
-90
-45
0
Z [mm]
expnum
cross section
x
y
57
Numerical predictionsExperimentally there is no crack!
Shape: bottom surface
0 45 90
X [mm]
-90
-45
0
Z [mm]
expnum
Forces: no experiments available
0 225 450
Ref. Time [s]
0
3000
6000
Force [N]
no coalescence
with coalescence
With coalescence, the model predictsfracture. . . prematurely
57
Cone testDescription
Benchmark for failure angles.
DC01, 1.0 mm ⇒ α =67◦
α
x
z
182mm
30mm
DC01 steel, 1.0 mm⇒ failure angle: 67◦
φ182mm
x
y
58
Numerical predictions
Force prediction (no experiments)
0 300 601
Ref. Time [s]
0
1250
2500
Force [N]
45
47
48
50
Fz s(48◦)
The crack is predicted at α =48◦
59
Numerical predictions
Force prediction (no experiments)
0 300 601
Ref. Time [s]
0
1250
2500
Force [N]
45
47
48
50
Fz s(48◦)
Aerens et al. [2009] formula:
Fz s = 0.0716Rmt1.57dt
0.41∆h0.09
. . . (α− dα) cos (α− dα)
α =47◦ 1219.70Nα =48◦ 1222.49Nα =67◦ 1158.01N
The crack is predicted at α =48◦
59
Analysis of fracture prediction
1 Predicted force overestimation.
2 Bad modeling of the deformation.
3 Limitations of the GTN model.
Porosity for the 47◦ cone
no fracture
Porosity for the 48◦ cone
εf ≈0.8
60
Analysis of fracture prediction
1 Predicted force overestimation.
2 Bad modeling of the deformation.
3 Limitations of the GTN model.
Porosity for the 47◦ cone
no fracture
Porosity for the 48◦ cone
εf ≈0.8
60
Contents
61
Conclusions
Contributions
Fully implicit implementation of the GTN+shear model.
Extensive experimental data and material identification.
Good shape prediction in SPIF (FE element type).
Issues
The chosen damage model is capable to predict failure in theSPIF process but not accurately.
GTN model uncouples the hardening and damage.
Force prediction in SPIF.
62
Conclusions
Contributions
Fully implicit implementation of the GTN+shear model.
Extensive experimental data and material identification.
Good shape prediction in SPIF (FE element type).
Issues
The chosen damage model is capable to predict failure in theSPIF process but not accurately.
GTN model uncouples the hardening and damage.
Force prediction in SPIF.
62
Perspectives
Modification of the hardening in the GTN model [Leblond et al.,1995].
Implement different type of damage model [Lemaitre, 1985; Xue,2007].
Effect of hardening stagnation on damage.
SPIF
Remeshing + Damage in LAGAMINE.
Different EAS modes solid-shell.
63
Perspectives
Modification of the hardening in the GTN model [Leblond et al.,1995].
Implement different type of damage model [Lemaitre, 1985; Xue,2007].
Effect of hardening stagnation on damage.
SPIF
Remeshing + Damage in LAGAMINE.
Different EAS modes solid-shell.
63
Experimental and Numerical Characterization ofDamage and Application to Incremental Forming
PhD thesis presentation
Carlos Felipe Guzman
Department ArGEnCoUniversity of Liege, Belgium
February 1st, 2016
Material presentationTexture measurements
Incomplete pole figures:
(110) (200) (211)
Philip Eyckens, KULeuven
65
Shear extensions
Xue [2008]
f ∗ → D
D = Kf
(q1 f + Dshear
)Dshear = kg f
1/3gθ(σ)εeq εeq
Nahshon and Hutchinson [2008]
f = fg + fn + fshear
fshear = kωf ω(σ)σdev : εP
σeq
1 material parameter: kg or kω.
Note: gθ(σ) and ω(σ) are scalar functions of the stress.
66
Shear extensions
Xue [2008]
f ∗ → D
D = Kf
(q1 f + Dshear
)Dshear = kg f
1/3gθ(σ)εeq εeq
Nahshon and Hutchinson [2008]
f = fg + fn + fshear
fshear = kωf ω(σ)σdev : εP
σeq
1 material parameter: kg or kω.
Note: gθ(σ) and ω(σ) are scalar functions of the stress.
66
Shear extensions
Xue [2008]
f ∗ → D
D = Kf
(q1 f + Dshear
)Dshear = kg f
1/3gθ(σ)εeq εeq
Nahshon and Hutchinson [2008]
f = fg + fn + fshear
fshear = kωf ω(σ)σdev : εP
σeq
1 material parameter: kg or kω.
Note: gθ(σ) and ω(σ) are scalar functions of the stress.
66
Integration schemeConsistent tangent matrix, algorithm approach
σ = σ(ε)
dσ = D : dε ; D :=∂σ
∂ε
εn εn+1
σn
σn+1
Dalgo
Dcont
67
Integration schemeConsistent tangent matrix, algorithm approach
σ = σ(ε)
dσ = D : dε ; D :=∂σ
∂ε
εn εn+1
σn
σn+1
Dalgo
Dcont
σn+1 = C :(εn+1 − εPn+1
)
dσ = C : dε− C : d∆εP
Linearization
Relate dε with d∆εP
67
Integration schemeConsistent tangent matrix, algorithm approach
σ = σ(ε)
dσ = D : dε ; D :=∂σ
∂ε
εn εn+1
σn
σn+1
Dalgo
Dcont
K : ∂∆εP = L : ∂σ Kim and Gao [2005]approach
D = C− C(K + LC)−1LC
∂Fp
∂σ,∂Fp
∂∆εP,∂Fp
∂Hβ,∂2Fp
∂σ2,
∂2Fp
∂σ∂∆εP, . . . Extension to
Kinematic hardening
67
Numerical validationHydrostatic test, Aravas [1987]
0 0.4
Volumetric strain [−]
0
2.5
Hydrostaticstress ratio [−]
GUR3DextAravas1987
0 0.4
Volumetric strain [−]
0
0.4
Void volumefraction [−]
GUR3DextAravas1987
Elasto-plastic parameters Gurson parameters
E 210 GPa K 1200 MPa q1 1.5 fN 0.04 f0 0
ν 0.3 ε0 3.17 × 10−3 q2 1.0 εN 0.30 fc -n 0.1 q3 2.25 SN 0.10 ff -
68
Tensile testAravas [1987]
0 1.0
Equivalent strain [−]
0
1.8
Equivalentstress ratio [−]
GUR3DextAravas1987
0 1.0
Equivalent strain [−]
0
0.1
Void volumefraction [−]
GUR3DextAravas1987
Elasto-plastic parameters Gurson parameters
E 210 GPa K 1200 MPa q1 1.5 fN 0.04 f0 0
ν 0.3 ε0 3.17 × 10−3 q2 1.0 εN 0.30 fc -n 0.1 q3 2.25 SN 0.10 ff -
69
Numerical validationShear test Xue [2008]
Gurson parametersq1 1.5 fN 0.04 f0 0.00q2 1.0 εN 0.20 fc 0.05q3 2.25 SN 0.10 ff 0.25
0 4.0
Matrix plastic strain [−]
0
500
Equivalentstress [MPa]
kg = 0
kg = 0.25
kg = 3GUR3DextXue2008
0 4.0
Matrix plastic strain [−]
0
1.2
Damage [−]
kg = 3
kg = 0.25
kg = 0
GUR3DextXue2008
70
Numerical validationShear test Xue [2008]
Gurson parametersq1 1.5 fN 0.04 f0 0.00q2 1.0 εN 0.20 fc 0.05q3 2.25 SN 0.10 ff 0.25
0 4.0
Matrix plastic strain [−]
0
500
Equivalentstress [MPa]
kg = 0
kg = 0.25
kg = 3GUR3DextXue2008
0 4.0
Matrix plastic strain [−]
0
1.2
Damage [−]
kg = 3
kg = 0.25
kg = 0
GUR3DextXue2008
70
State variables analysis
0 0.2 0.8 1.0 1.8
Ref. Time [s]
0
f0
0.002
0.004
Porosity [−]
elem=118
elem=404
elem=690
indent 1
indent 2
71
State variables analysis
0 0.2 0.8 1.0 1.8
Ref. Time [s]
0
f0
0.002
0.004
Porosity [−]
elem=118
elem=404
elem=690
indent 1
indent 2
71
SPIF line testState variables analysis
0 0.2 0.8 1.0 1.8
Ref. Time [s]
-1.0
0
1.5
Triaxiality [−]
elem=118
elem=404
elem=690
0 0.2 0.8 1.0 1.8
Ref. Time [s]
0
6 · 10−4
1.2 · 10−3
Hyd. strain [−]
elem=118
elem=404
elem=690
72
SPIF line testState variables analysis
0 0.2 0.8 1.0 1.8
Ref. Time [s]
-1.0
0
1.5
Triaxiality [−]
elem=118
elem=404
elem=690
0 0.2 0.8 1.0 1.8
Ref. Time [s]
0
6 · 10−4
1.2 · 10−3
Hyd. strain [−]
elem=118
elem=404
elem=690
72
SPIF Two-slope pyramidMesh and boundary conditions
x
y
•O •P
(ux)O = − (ux)P(uy )O = − (uy )P(uz)O = (uz)P
73
SPIF Two-slope pyramidNumerical predictions
Porosity f
Eq. macro. strain εq
74
SPIF Two-slope pyramidNumerical predictions
Porosity f Eq. macro. strain εq
74
Cone testMesh and boundary conditions
x
y
•O•O
•P
75
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