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1
Technical perfection, automotive passion.
Cost-benefit conflict in material modeling
Dr.-Ing. Birgit Reichert
2
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Content
• Introduction
• Modelling philosophies
• Material testing for data input FEM
• Questions
-300
-200
-100
0
100
200
300
-300 -200 -100 0 100 200 300
σ1, N/mm²
σ2,
N/m
m²
str
ess
strain
3
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Faurecia Seating GroupFrames
Safety and comfort
modules
Foam and covers
Mechanisms
Complete seat
4
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Faurecia as global player
710
4
58
12
2008 Faurecia Group Presentation 5
Others
60 PSA
% of sales
18
11
74
Daimler
Renault
VW
1997
* Excluding monoliths
Leading commercial position & successful customer diversification
2
PSA PSA PSA PSA
VAGVAGVAGVAG
RenaultRenaultRenaultRenault----NissanNissanNissanNissan
BMWBMWBMWBMW
GMGMGMGM
ChryslerChryslerChryslerChrysler
FordFordFordFord
28 %28 %28 %28 %
26 %26 %26 %26 %
13 %13 %13 %13 %
13 %13 %13 %13 %
8 %8 %8 %8 %
4 %4 %4 %4 %
2 %2 %2 %2 %3 %3 %3 %3 %
Others Others Others Others 2 %2 %2 %2 %
DaimlerDaimlerDaimlerDaimler1 %1 %1 %1 %
ToyotaToyotaToyotaToyota
2008
6
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
The complex material landscape (steel sheet)
JIS, JFS- focus on tensile strength- TS steps: no system- specimen’s length: 50mm
SAE, ASTM- focus on yield strength- YS steps: no system- specimen’s length: 50mm
EMS.ME- focus on yield strength- YS steps: 40MPa- specimen’s length: 50mm
EN- focus on yield strength- YS steps: 40MPa- specimen’s length: 80mm
7
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Best equivalence of sheet steel by norms • Often old short names in
use
• In Europe EN standards obligatory
• In general only ‘best equivalence’ to other
standards possible (JIS,
SAE, ASTM, JFS,…)
• For the newest steel developments standards
do not exist, only
companies’ information
can be cited
Grade classes Europe Europe China IndiaDeep drawing steel grades EN 10130 SAE J2329 ASTM A 1008M-07a JIS G 3141 JFS A 2001 GB/T 5213 IS 513
cold rolled DC01 - CS SPCC JSC270C DC01 CR1
cold rolled DC03 CR3 DS SPCD JSC270D DC03 CR3
cold rolled DC04 CR4 DDS SPCE JSC270E DC04 CR4
cold rolled DC06 CR5 EDDS SPCG JSC260G DC06 CR5
Deep drawing steel grades EN 10111 SAE J2329 ASTM 1011M-07 JIS G 3131 JFS A 1001 GB 710-91/ GB 711-88 IS 1079
hot rolled DD11 - - SPHC - 08 D
hot rolled DD12 HR2 HR CS Type B SPHD JSH270C - DD
hot rolled DD13 - - SPHE JSH270D 08A1 EDD
hot rolled DD14 HR3 HR DS Type B SPHF JSH270E - -
High strength IF steel grades EN 10268 SAE J2340 ASTM A 1008M-07 JIS G 3135 JFS A 2001 GB/T 20564-3 India
HC180Y CR 180AT - SPFC340 JSC340W CR180IF
HC260Y CR 280AT - SPFC390 JSC390W CR260IF
Microalloyed steel grades EN 10268 SAE J2340 ASTM A 1008M-07a JIS G 3135 JFS A 2001 China IS 14491
HC260LA - CR SS275 - - 260Y
HC300LA CR 300XF CR HSLAS310 Class 2 - - 300Y
HC340LA CR 340XF CR HSLAS340 Class 2 - JSC440R 340Y
HC380LA CR 380XF CR HSLAS380 Class 2 - - 380Y
HC420LA CR 420XF CR HSLAS410 Class 2 - - 420Y
Microalloyed steel grades EN 10149 SAE J2340 ASTM 1011M-07 JIS G 3134 JFS A 1001 GB/T 20887-1 IS 5986
S315MC HR 300XF HR HSLAS310 Class 2 - JSH440R HR315F -
S355MC HR 340XF HR HSLAS340 Class 2 - JSH490R HR355F Fe 490
S420MC HR 420XF HR HSLAS410 Class 2 - JSH540R HR420F -
S460MC - HR HSLAS450 Class 2 - JSH590R HR460F -
S500MC HR 490XF HR HSLAS480 Class 2 - - HR500F -
S550MC HR 550XF HR HSLAS-F550 - - HR550F -
S600MC - HR UHSS 620 - - HR600F -
S650MC - - - - HR650F -
S700MC - HR UHSS 690 - - HR700F -
Dual phase steel grades draft EN 10338 SAE J2745 ASTM A 1008M-07a JIS G 3135 JFS A 2001 GB/T 20564-2 India
HCT450X CR DP440T/250Y - SPFC440 JSC440W CR260/450DP -
HCT500X CR DP490T/290Y - SPFC490 - CR300/500DP -
HCT600X CR DP590T/340Y - SPFC590 JSC590Y CR340/590DP -
HCT780X CR DP780T/420Y - SPFC780Y JSC780Y CR420/780DP -
HCT980X CR DP980T/550Y - SPFC980Y JSC980Y CR550/980DP -
Dual phase steel grades draft EN 10338 SAE J2745 - JIS G 3134 JFS A 1001 China -
hot rolled HDT580X HR DP590T/300Y - SPFH590Y JSH590Y - -
Complex phase steel grades draft EN 10338 SAE J2745 ASTM A 1008M-007a JIS G 3135 JFS A 2001 China India
HCT600C - - - - - -
HCT780C - - - - - -
HCT980C - - - - - -
Complex phase steel grades draft EN 10338 SAE J2745 ASTM 1011M-07 JIS G 3134 JFS A 1001 China India
HDT750C - - - - - -
HDT780C - - - JSH780R - -
HDT950C - - - - - -
Martensite phase steel grades draft EN 10338 SAE J2745 ASTM 1011M-07 JIS G 3134 JFS A 1001 China India
hot rolled HDT1200M - - - - - -
America Japan
cold rolled
cold rolled
cold rolled
cold rolled
hot rolled
hot rolled
8
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Modeling philosophiesExperimental data• using the unprocessed experimental data
(materials database)
• extrapolation by mathematical trend
Empirical derived models• e.g. flow stress functions• parameter without physical meaning• determination of parameters by fitting to
experimental data of material
Continuum mechanics models• physical interpretable parameters• fitting of model parameters to experimental data
of material
Microstructurally based models• involving microstructure-related internal variables.• determination of model parameter by certain set of
experiments
Ab initio modeling• applying quantum mechanics• parameter-free determination
Models represent
macroscopic
behaviour
Models represent
metal-physical
mechanisms
str
ess
strain
str
ess
strain
DATEN
ZEIT ; KRAFT ; WEG ;BREITENAENDERUNG ;
0.0; 1.062636e+002; 0.0; 0.0
0.0; 1.015853e+002; 0.0; 0.0
0.0; 1.015853e+002; 0.0; 0.0
0.0; 1.973226e+002; 0.0; 0.0
0.0; 1.916418e+002; 0.0; 0.0
0.0; 1.857940e+002; 0.0; 0.0
1.953125e-002; 1.849586e+002; 4.952637e-005; 3.607978e-004
5.953125e-002; 1.839561e+002; 1.481264e-004;-6.943555e-005
9.595312e-001; 1.904723e+002;-7.475736e-004;-4.480221e-005
1.059531e+000; 1.914748e+002;-8.966403e-004; 3.460645e-004
1.679531e+000; 1.948164e+002;-1.920274e-003; 2.654394e-004
9
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
0.01
0.10
1.00
10.00
100.00
1 10 100 1000 10000 100000 1000000 10000000
cycle to failure Ni
str
ain
am
plit
ud
e,
%
h
elastic portion
plastic portion
total strain S-N line
Manson-Coffin S-N line
Manson-Coffin elastic portion
Manson-Coffin plastic portion
HX340LAD
0
100
200
300
400
500
600
700
800
900
1000
0 0.1 0.2 0.3 0.4
true plastic strain, -
tru
e s
tre
ss, N
/mm
²
H
0.004s-1 at 296K
1s-1 at 296K
20s-1 at 296K
200s-1 at 296K
experiment
experiment
experiment
experiment
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
minor strain, -
majo
r str
ain
, -
HX420LAD, 1.0mm
0
100
200
300
400
500
600
700
800
900
0,00 0,20 0,40 0,60 0,80 1,00
true plastic strain, -
tru
e s
tress,
N/m
m²
h
Experiment
Input for FEM
Estrin-Mecking
Formingflow curve (quasi-static)forming limit diagramyield locus
Crashflow curves
(dynamic)
Fatigue strain S-N curves
friction, spring back,
fracture
bake hardening, fracture
fracture
Youngs-Modulus
Poisson ratio
anisotropy coefficient
friction coefficient
specific weight
specific heat capacity
…
-300
-200
-100
0
100
200
300
-300 -200 -100 0 100 200 300
σ1, N/mm²
σ2,
N/m
m²
10
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
180
230
280
330
380
430
480
530
580
630
680
0.00 0.20 0.40 0.60 0.80 1.00
true plastic strain, -
true
str
ess,
N/m
m²
h
tensile testHollomon (2 Parameter)
Swift (3 Parameter)Gosh (4 Parameter)Voce (3 Parameter)
Hockett-Sherby (4 Parameter)Estrin-Mecking (3 Parameter)
Empirical derived models for flow curvestensile test quasi-static ( )
( )
( ) ( )
( ) ( )
( ) ( )
( )
( ) ( )
−⋅−+=−
⋅−⋅−−=−
−⋅−+=
−+=
+=
⋅=
⋅+=
*
exp:
exp)(:
exp:
:
:
:
:
222
122
0
r
SiSf
HS
HSf
r
SiSf
n
iSf
n
iSf
n
Hf
n
Lf
kMeckingEstrin
n
mCCCkSherbyHockett
kVoce
DCkGosh
CkSwift
CkHollomon
CkLudwik
S
S
H
L
ϕ
ϕσσσϕ
ϕϕ
ϕ
ϕσσσϕ
ϕϕϕ
ϕϕϕ
ϕϕ
ϕσϕ
microstructural interpretation of Voce for fine grain or
precipitation hardened single phase microstructure
(1909)
(1948)
microstructurally interpreted by Kocks-Mecking for coarse
grain and single phase microstructure (1981)
(1945)
(1952)
(1977)
(1975)
(1984)
180
230
280
330
380
430
480
530
580
630
680
0.00 0.20 0.40 0.60 0.80 1.00
true plastic strain, -
tru
e s
tre
ss,
N/m
m²
h
Kocks-Mecking (Voce) and Estrin-Mecking are presented currently as modules of the One Internal Variable Model (OIVM)
11
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Application of fitting functions to HX180YD
2
__
1
)( ModelliExperimenti
n
i
yy −Σ=
Minimising sum of flow curve and hardening rate:
Constraints: - experimental tensile curve is
of priority- stress at true plastic strain 0
is not lower than Rp0.2 (205MPa)
Differential quotient of tensile flow curve dσ/dε versus σ
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tress, M
Pa
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tress, M
Pa
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
ha
rde
nin
g r
ate
, M
Pa
HX180YD tensile
HX180YD bulge
Hollomon
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
ha
rde
nin
g r
ate
, M
Pa
HX180YD tensile
HX180YD bulge
Sw ift
12
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Application of fitting functions to HX180YD
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tress, M
Pa
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
ha
rde
nin
g r
ate
, M
Pa
HX180YD Zug
HX180YD Bulge
Ludw ik
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tress, M
Pa
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
ha
rde
nin
g r
ate
, M
Pa
HX180YD Zug
HX180YD Bulge
Voce
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tress, M
Pa
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
ha
rde
nin
g r
ate
, M
Pa
HX180YD Zug
HX180YD Bulge
Gosh
13
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Application of fitting functions to HX180YD
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tre
ss
, M
Pa
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
ha
rde
nin
g r
ate
, M
Pa
HX180YD tensile
HX180YD bulge
Hockett-Sherby
0
100
200
300
400
500
600
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
true plastic strain, -
tru
e s
tre
ss
, M
Pa
0
500
1000
1500
2000
2500
3000
3500
200 300 400 500 600
true stress, MPa
hard
en
ing
rate
, M
Pa
HX180YD tensile
HX180YD bulge
Estrin-Mecking
Comments: - best simultaneous fit to flow curve
and hardening rate for models with 4 parameters (Hockett-Sherby or Gosh)
- best model working with 3 parameters is Estrin-Mecking; superior to Swift or Ludwik and similar to Gosh due to minimising criteria
- application of model using two parameters is difficult (Hollomon)
- if it comes to parameterise models for application of stochastic analysis then one may care for as less model parameters as possible
14
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Cost assessment for basic testing
• Chemical composition• Metallography• Tensile tests on sheet specimens
- longitudinal, transversal, diagonal
- statistically reliable (e.g. according to SEP 1240)
• Flow curve up to high strains
⇒⇒⇒⇒ 1000 - 1250€ for one material
15
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Yield criteria familiesYield criteria
Hill's family σ0 σ30 σ45 σ75 σ90 σb τ r0 r30 r45 r75 r90 rb A1 A2Hill48 X X X X
Hill79 X X X X
Hill90 X X X X X X
Hill93 X X X X X X X X
Chu95 X X X X X X
Lin, Ding96 X X X X X X X X
Hu2005 X X X X X X X X
Hosford's family σ0 σ30 σ45 σ75 σ90 σb τ r0 r30 r45 r75 r90 rb A1 A2
Hosford79 X X X X
Barlat89 X X X X X
Barlat91 X X X X X
Karafillis, Boyce93 X X X X X X X X
Barlat96 X X X X X X X X X
BBC2000 X X X X X X X X X
Bron-Besson2003 X X X X X X X X X
Barlat2003 X X X X X X X X X X
BBC2003 X X X X X X X X X X
Aretz-Barlat2004 X X X X X X X X X X
A1: anomalous behavior of first kind
A2: anomalous behavior of second kind
16
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Other yield criteria approaches
• Budiansky (polar coordinates)• Ferron (polar coordinates)• Vegter (Bézier interpolation)• …
σ 1 /σ f
σ 2 /σ f
reference point
hinge point
equi bi-axial
plane strain
uni-axial
pure shear
σ
σλ
σ
σλ λ
σ
σλ
σ
σ
1
2
1
2
1
2
1
2 1
⋅
⋅ ⋅ ⋅
⋅
+
= (1- ) + 2 (1- ) + 2
i
r
i
h
2
i
r
Second order interpolation between the reference points i and i+1 (here i= 1, 2, 3, 4).
Hinge points are the intersectionpoints from the known slopes inthese reference points.
Orientation dependency described via cosine interpolation.
17
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Experimental data for describing yield loci
1
6
5 4 32
Uniaxial tension 0°
Uniaxial tension 90°
Strain plane 0°
Strain plane 90°
Equibiaxial tension
Pure shear tension
σ1
σ2
Point 1: σ0Point 2: σ1 = 2σ2 (ε2 = 0)
Point 3: σ1 = σ2 = σbPoint 4: σ1 = σ2/2 (ε2 = 0)
Point 5: σ90Point 6: σ1 = -σ2 = τ
yiel
d st
ress
angle to rolling direction0 15 30 45 60 75 90
Lank
ford
val
ue
angle to rolling direction0 15 30 45 60 75 90
Tensile tests with different angle to rolling direction
Tensile tests: r0, r90, r45, (r15, r30, r60, r75)
σ0, σ90, σ45, (σ15, σ30, σ60, σ75)
Hydraulic bulge test: σb
Biaxial tensile tests: σb, further biaxial stress combinations (σ1 = x⋅σ2)
Shear test: τ
18
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Determination of FLC
• Uniaxial tensile test (3)• Hydraulic bulge test (5)• Punch stretching test• Keeler test (4)• Hecker test• Marciniak test• Nakajima test (2)• Hasek test (1)
-0.4 -0.2 0.2 0.4
0.6
0.4
0.2
ε2
ε1
0.0
12
34
5
-0.4 -0.2 0.2 0.4
0.6
0.4
0.2
ε2
ε1
0.0
12
34
5
19
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Forming seat tracks
• Bending (bending limit curve, …)• Spring back (Chaboche, Backhaus, Yoshida, …)• Failure (Gurson, EWK, CrachFEM, …)
grain boundaries
failure in deep drawing
failure in bending
20
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Cost assessment for advanced testing
• Chemical composition• Metallography• Tensile tests on sheet specimens
- longitudinal, transversal, diagonal- statistically reliable (e.g. according to SEP 1240)
• Flow curve up to high strains• Plane strain and shear• Forming limits • Hole expansion and bending
⇒⇒⇒⇒ 5000 - 7000€ for one material
21
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Dynamic tensile testing for crash
Typical ranges of strain rate covered by conventional load frames, servo-hydraulic machines and bar
testing systems
Schematic of tensile Split Hopkinson Bar System
Schematic of Servo-hydraulic System
Specific requirements needed for load measurement,
direct measurement of strain and specimen geometry
22
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Johnson-Cook
( ) )1983(1ln10
210
−
−−
++=
m
roommelt
roomn
TT
TTCC
ε
εεσσ
&
&
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25 0.3
true plastic strain, -
true
str
ess, N
/mm
²
H
0.004s-1 at 296K
1s-1 at 296K
20s-1 at 296K
250s-1 at 296K
experiment
experiment
experiment
experiment
350
400
450
500
550
600
650
700
750
800
850
0 0.05 0.1 0.15 0.2
true plastic strain, -
tru
e s
tre
ss, N
/mm
²
H
0.008s-1 at 296K
0.91s-1 at 296K
13.14s-1 at 296K
81.7s-1 at 296K
experiment
experiment
experiment
experiment
DC06 HCT600X
23
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Tanimura
( ) ( ) ( ) )1992(log0
kmnEDCBA ε
ε
εεεσ &
&
&+
−+⋅+=
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25 0.3
true plastic strain, -
true
str
ess, N
/mm
²
H
0.004s-1 at 296K
1s-1 at 296K
20s-1 at 296K
250s-1 at 296K
experiment
experiment
experiment
experiment
350
400
450
500
550
600
650
700
750
800
850
0 0.05 0.1 0.15 0.2
true plastic strain, -
true
str
ess, N
/mm
²
H
0.008s-1 at 296K
0.91s-1 at 296K
13.14s-1 at 296K
81.7s-1 at 296K
experiment
experiment
experiment
experiment
350
400
450
500
550
600
650
700
750
800
850
0 0.05 0.1 0.15 0.2
true plastic strain, -
tru
e s
tre
ss,
N/m
m²
H
0.008s-1 at 296K
0.91s-1 at 296K
13.14s-1 at 296K
81.7s-1 at 296K
experiment
experiment
experiment
experiment
suggested fit by steel supplier
DC06
HCT600X
24
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
One Internal Variable Models (OIVM)
0
100
200
300
400
500
600
0 0.1 0.2 0.3 0.4
true plastic strain, -
true
str
ess, N
/mm
²
H
0.004s-1at 296K1s-1at 296K
20s-1at 296K250s-1at 296K500s-1at 296K
experimentexperimentexperiment
experimentexperiment
Estrin-Mecking
extended by heat effects
350
450
550
650
750
850
950
0 0.05 0.1 0.15 0.2
true plastic strain, -tr
ue s
tress, N
/mm
²
H
0,008s-1 at 296K
0,91s-1 at 296K
13,14s-1 at 296K
81,7s-1 at 296K
experiment
experiment
experiment
experiment
Hybrid model extended by
dislocation self organisation,
two-phase description and
heat effects
25
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
200
250
300
350
400
450
500
550
600
650
700
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
true plastic strain, -
tru
e s
tress,
MP
a
HX260YD tensile
HX260YD bulge
HX260YD model
Identifying family parameters for OIVM
200
250
300
350
400
450
500
550
600
650
700
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
true plastic strain, -
tru
e s
tress,
MP
a
HX220YD tensile
HX220YD bulge
HX220YD model
200
250
300
350
400
450
500
550
600
650
700
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
true plastic strain, -
tru
e s
tress,
MP
a
HX180YD tensile
HX180YD bulge
HX180YD model
Model constants:
Taylor factor M: 3
Numerical constant α: 0.5
Shear modulus G: 80769 MPa
Burgers vector b: 2.5 x10-10m
Normalising strain rate ε0: 1000s-1
Material parameters to adjust:
Grain size d
Recovery factor k20
Exponent n
Exponent m
Family parameters determined:
a and b for d
c and d for k20
e and f for n
g and h for m
and use of yield strength for each alloy·
HX180YD, HX220YD and HX260YD by Estrin-Mecking:
HX180YD HX220YD HX260YD
26
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Application of family parameters
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
true plastic strain, -
true
str
ess, N
/mm
²
H
0,004s-1 at 296K
1s-1 at 296K
20s-1 at 296K
200s-1 at 296K
experiment
experiment
experiment
experiment
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
true plastic strain, -
true
str
ess, N
/mm
²
H
0,004s-1 at 296K
1s-1 at 296K
20s-1 at 296K
250s-1 at 296K
experiment
experiment
experiment
experiment
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
true plastic strain, -
true
str
ess, N
/mm
²
H
0,004s-1 at 296K
1s-1 at 296K
20s-1 at 296K
200s-1 at 296K
experiment
experiment
experiment
experiment
HX180YD HX220YD HX260YD
Family parameters determined:
a and b for d
c and for k20
e and f for n
g and h for m
and use of yield strengths for each alloy
Heat conduction parameters:
Heat transfer parameter β: 0.018s-1
Specific heat capacity cspec: 477 Nmkg-1K-1
Material density ddens: 7800 kgm-3
Heat dissipation factor χ: 1
27
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Other models for strain rate dependence
• Extended Hollomon• Cowper-Symonds• 10 Parameter model• Bergström• Zerilli-Armstrong• Mechanical Threshold (MTS)• …
28
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Cost assessment complete process chain
• Formability testing: 5000 – 7000€• Strain rate dependence of material
⇒⇒⇒⇒ 10.000 – 15.000€ for one material
(plus joinability testing and evt. fatigue testing)
29
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
General questions
• How to come from the material testing to the models of choice?
• How to ensure reliable FEM input data worldwide?
• How to deal with the customer diversification?
30
Technical perfection, automotive passion.Cost-benefit conflict in material modeling
Potential criteria for model choice
• Accuracy of model prediction proved by simulating standard material tests by FEM
• Number of model parameters
• Financial efforts for the material tests to determine the model parameters
• Number of materials the model chosen is applicable to
• Modular character of model
• Level of commercialisation
• …
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