Sheet metal forming simulation for automotive applications · Hydro-forming of the close-ended part...
Transcript of Sheet metal forming simulation for automotive applications · Hydro-forming of the close-ended part...
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Sheet metal forming simulation for
automotive applications Prof. Dr.-Ing. K. Roll
Summer School Dortmund, 7. September 2012
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 2
Outline
• Introduction
• History of sheet metal simulation Examples (Springback, Compensation etc.)
Stochastic Simulation
• Necessary Developments in Forming Simulation – Refinement of Materials Models
– Influence of Anisotropy
– Effect of Yield Loci and the Hardening Model
– Failure Models
– Influence of Temperature
– Elastic Tools
– Influence of the Press
– Metamodels
• Simulation of the process chain sheet metal forming – Hemming Simulation
– Rollhemming Simulation
– Metamodels
– Mechanical Joining Simulation
– Welding Simulation
• Simulation of the part properties (Static, Crash, Fatigue..) – Forming to Crash
– Forming to Fatigue
• Outlook
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 3
Sheet Metal Forming Knights Armor (15. Century a. d.)
Source: Prof. Voelkner; TU Dresden
History of sheet metal forming
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 4
Sheet rolling mill (mid of 19. Century a. d.)
Source: Prof. Voelkner; TU Dresden
History of sheet metal forming
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 5
Sheet Metal Forming - History
Production of a front fender
Source: Prof. Voelkner; TU Dresden
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 6
Sheet Metal Forming - today
Production of an engine hood outer
Coil Store Blanking Line Stacking Line
Pressline Destacking Line
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 7
Chronological development of plasticity theory
computational procedures History of sheet metal forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 8
Possible simulation techniques in metal forming
- Smooth Particle Hydrodynamics - Element Free Galerkin Method - Moving Least Square Method Approx. - Reproducing Kernel Particle Method
Upper / Lower Bound Methods
Finite Difference Methods
Finite Element Methods
Boundary Element Methods
Finite Volume Methods
Meshless Methods
- Static Implicit - Static Explicit - Dynamic Explicit
History of sheet metal forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 9
Chronological development of plasticity theory
computational FE-procedures History of sheet metal forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 10
Progress simulation sheet metal forming
B-Column without
Remeshing (1987)
ca. 1400 Elements
(Source: Hora et.al., 1st NUMIFORM)
Deformierte Platine am Ende des Ziehvorganges
Front Fender (2001)
ca. 3500 Elements
Source: M. Gröber, 1st NumiSheet, Zürich)
History of sheet metal forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 11
Progress simulation sheet metal forming
Sidewall with Remeshing
(6 000 000 Elements; 2005)
History of sheet metal forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 12
History of sheet metal forming simulation at Daimler
Year Parts Set-uptime Trial runs
1992 5 3 – 4 weeks 6 - 8
1993 8 2 weeks 5
1995 20 1 week 3
1998 >100 < 2 days 1 - 2
2012 >350 < 1.5 days 1 - 2
Model Size: Die: up to 400.000 Elements
Blank: up to 6.000.000 Elements
Computing Time: from days (1992) to hours on Workstations
or Linux-Clusters
Simulation engineers: 2 in 1992 to 52 in 2011
History of sheet metal forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 13
Simulation chain of the complete forming process
Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 14
Virtual “Die - Making”: Engine Hood Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 15
Finite element model
Punch
Blank
Die
Binder
PunchPunch
BlankBlank
DieDie
BinderBinder
Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 16
Simulation deep drawing process of an Engine Hood
Initial Position Gravity Holding
25 mm to
home
Final
position
Initial PositionInitial Position GravityGravity HoldingHolding
25 mm to
home
25 mm to
home
Final
position
Final
position
Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 17
Simulation of sheet forming processes - examples Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 18
Hydroforming of sheet metal pairs - Failure modes Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 19
Surface defects - door handle
Distribution of Thickness [mm]
( 3 %)
two different forming geometries
Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 20
Surface defects - door handle - Detail
Minor stress [GPa]Minor stress [GPa]
Danger:
compression stress - 0.05 GPa
Better:
only tensile stress + 0.15 GPa
Minor stress [GPa]Minor stress [GPa]Minor stress [GPa]Minor stress [GPa]
Danger:
compression stress - 0.05 GPa
Danger:
compression stress - 0.05 GPa
Better:
only tensile stress + 0.15 GPa
Minor stress [GPa]Minor stress [GPa]
Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 21
Variables influencing springback
Numerical
Time Discretisation
Space Discretisation
type and size of element
Material Model
Convergence Tolerance
Damping, ...
Material
Young´s Modulus
Yield Strength
Hardening
Pre-Treatment
Plastic Strain
Anisotropy
Geometry
Sheet Thickness
Sheet Dimensions
Radius
Forming Depth
Process Conditions
Forming Process
Tool
Force
Tribology
Forming Velocity
TemperatureVariables
influencing
SpringbackNumerical
Time Discretisation
Space Discretisation
type and size of element
Material Model
Convergence Tolerance
Damping, ...
Numerical
Time Discretisation
Space Discretisation
type and size of element
Material Model
Convergence Tolerance
Damping, ...
Material
Young´s Modulus
Yield Strength
Hardening
Pre-Treatment
Plastic Strain
Anisotropy
Material
Young´s Modulus
Yield Strength
Hardening
Pre-Treatment
Plastic Strain
Anisotropy
Geometry
Sheet Thickness
Sheet Dimensions
Radius
Forming Depth
Geometry
Sheet Thickness
Sheet Dimensions
Radius
Forming Depth
Process Conditions
Forming Process
Tool
Force
Tribology
Forming Velocity
Temperature
Process Conditions
Forming Process
Tool
Force
Tribology
Forming Velocity
TemperatureVariables
influencing
Springback
Variables
influencing
Springback
springback simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 22
Springback - It’s not a new Phenomena
Springback of materials
with constant conditions
TRIP 700 ZE
DP 500 ZE
THM 280 Z
ZE 340 ZE
ZStE180 BK ZE
Source:
voestalpine Desired
Shape
Springback is ALWAYS existing
arises from stored elastic
forming energy
can be reduced
is depending on • material
• process parameters
• evenly distributed
hardening
springback simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 23
After
springback
+ -
After
forming
+ -
elastic
plastic
plastic
Elastic bending stresses
through sheet thickness
Different membrane
stresses in flanges
Original blank
shape
Formed blank
Relaxed blank
After
forming
After
springback
Two Principle Mechanisms of Springback springback simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 24
Complex Testing Part for the Investigation of
Springback Deviations
AA5182
AA6016
DC06
H320 LA
DP600
springback simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 25
Possible Forming Processes Using the Testing Tool
Deep drawing
of the open-ended part
Deep drawing
of the close-ended part
Hydro-forming
of the close-ended part
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 26
Computed Springback Results - Material Influence
DC06 H320 LA
AA5182 AA6016
Displacement
in mm
max. 7,42 mm max. 9,73 mm
max. 15,67 mm max. 19,02 mm
springback simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 27
Computed Springback Results – Effect of Forming Technologies
max. 6,3 mm max. 4,3 mm max. 0,8 mm
Deep Drawing
Open-Ended
Deep Drawing
Close-Ended
Hydro-Forming
> >>
Material: DC06
springback simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 28
Simulation Sidewall Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 29
Sidewall – Steps of Simulation: Deep Drawing Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 30
Sidewall – Steps of Simulation: Springback Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 31
Compensation Program
Die with compensated Geometry
CAD-Geometry
Real-Geometry
Die
Compensation: Changing the
Die - Geometry
Part after Compensation Part after springback
Software based compensation
Source: INPRO
Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 32
Engine Hood Inner - Simulated Springback
Front of part deviates
upwards along bending line
Springback nearly
symmetrical to Y
Deviation
mm
5.0
3.0
1.0
3.0 mm
3.4 mm
Maximum: 4.8 mm
Material: AA 6181 A, Thickness: 1.15 mm
Springback
Deviations from
desired shape
Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 33
Compensation of springback - Hood Inner
Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 34
One recut of tool set
for compensation
of shape deviations
OP40 to
OP60
5 weeks*
5 weeks*
OP20 and
OP30
Savings by simulation-supported Compensation Overall Cycle Time
Each avoided tool recut can
save between 5 and 10 weeks
in overall cycle time
Time period of die process
engineering is constant, due
to parallel run of simulation
and die process engineering
Tool building
SWF
Engineering
Today
10 weeks*
Future
* example: Engine Hood Inner
Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 35
SWF
Today
Tool building
Engineering
One recut of tool set
for compensation
of shape deviations
OP40 to
OP60
70 T€*
80 T€*
OP20 and
OP30
125 T€*
Future
25 T€
Savings by simulation-supported Compensation
Costs
Each avoided tool recut can
saved up to 125 T€
Additional costs of
25 T€ per tool set during die
process engineering due to
additional human and
computational resources
* example: Engine Hood Inner
Examples of forming simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 36
2. Compensation
Deviation from CAD-Model
mm 1.0 0.5 0.0
Without Compensation
Modifications locally applied on mesh of tools
Several iterations reduce shape deviations from
CAD-Model (desired shape)
KDS
1. Compensation
Material: TRIP 700
Thickness: 1.4 mm
Semi-Automatic Iterative Compensation Examples of forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 37
Stochastic Simulation
Source: Autoform
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 38
Stochastic Simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 39
Stochastic Simulation – Variation of Parameters
Basic simulation:
AutoForm Final Validation – Setup
Blank: original
Lube: 0.15
BHkraft: 145t (half)
New Simulation:
AutoForm Final Validation – Setup
Blank: smaller
Lube: 0.11; BHkraft: 145t (half)
Failure Failure
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 40
Predictable Variables Using Sheet Metal Forming
Simulation State of the art in sheet forming simulation
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 41
Simulation vs. Reality
Factor Reality Simulation
Production stroke rate Not constant Not in the model
Machine Elastic Not in the model
Tool Elastic Rigid
Characteristics of the direction of draw Not constant Not in the model
Coefficient of Friction Not constant Constant
Temperature Not constant (Not) in the model
Topology of blankholder surface Not constant Not in the model
Material Complex Simple models
Material characteristics Not constant (Not) constant
Necessary Developments in Simulation Engineering
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 42
Components of material modeling for sheet metal
forming
zzyzxz
zyyyxy
zxyxxx
zzyzxz
zyyyxy
zxyxxx
Plastic
hardening
Yield locus
Flow rule
Definition of in-plane transition for elastic
to plastic material response
Definition of material work
hardening based on plastic flow
Defines the correlation of
stress and strain state
x
y
Refinement of Materials Models
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 43
Yield Curves - Method of Extrapolation
DP600
0
0,2
0,4
0,6
0,8
1
1,2
0 0,2 0,4 0,6 0,8 1 j
GPa
DP600_Voce
DP600_Swift
DP600_Gosh
DP600_Hocket_Sherby
DP600_Ludwik
DP600_Tensile test
DP600_Layered compression test
Refinement of Materials Models
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 44
Effect of flow-curve approximation on the
simulation result
Section length [mm]
thic
kn
ess
red
ucti
on
[%
]
Section length [mm]
thic
kn
ess
red
ucti
on
[%
]
Refinement of Materials Models
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 45
Yield loci models for sheet in-plane anisotropy
Barlat2000
Hill48
Barlat89
xx
yy
Hill48(Barlat89_M2)
Barlat89_M8
MATFEM_A8
A chosen yield locus
defines the correlation
of yield stress
depending on the
actual stress state and
rolling direction in the
sheet plane. Recent developments
concentrated on more
and more complex
functions to describe a
constant anisotropy.
Influence of Anisotropy
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 46
Todays choice for material model and failure
prediction
Source: Dr. Kessler; TKS
Numisheet 2008
Influence of Anisotropy
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 47
Yield locus models for sheet metal forming
Source: Dr. Kessler; TKS
Numisheet 2008
Influence of Anisotropy
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 48
Yield locus calibration – parameters to be determined
Influence of Anisotropy
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 49
Yield Surface DP600
Hill 1948 Barlat-Lian 1989 Barlat-Lian 1996
Biaxial Stress Factor
Hill 1979
Hill 1990
= Combination Hill 48 + Hill 79
Simulation
Experiment
Hill 1948 Barlat-Lian 1989 Barlat-Lian 1996
Biaxial Stress Factor
Hill 1979
Hill 1990
= Combination Hill 48 + Hill 79
Simulation
Experiment
Influence of Anisotropy
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 50
Influence of Yield-Loci Model to Failure Description
Source: Heinl, BMW; Dr. Kessler, TKSE; SFU 2010
Influence of Anisotropy
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 51
The assumption of isotropic material hardening
x
y
Monotonic expansion of the
yield locus
Isotropic material hardening:
All directions gain the same
hardening
The hardening rule specifies the expansion
of the yield locus in case of plastic
deformation.
Effect of Yield Loci and the Hardening Model
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 52
Industrial aspects of material modeling for steel
grades - Simplification procedure in daily practice
So
urc
e:
Dr.
Kessle
r, T
hyssen
Kru
pp
Ste
el
N
um
ish
eet
2008
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
IYL
No
rmaliz
ed
str
ess
2
2
SYL
Material hardening
Normalized stress 11
Assuming isotropic hardening
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Barlat m=8 SYL
Normalized stress 11
No
rmaliz
ed
str
ess
2
2
► Industrial simulation is mostly based on isotropic hardening!
Effect of Yield Loci and the Hardening Model
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 53
Drawback of the actual modeling method
Modern high strength steel grades may show a stress state dependent
hardening – this is hardly to fit with conventional model assumptions
• Reasons can be found in phase
transformations or micro-structure
The up to now used approach with
constant yield locus and one single
hardening curve can definitely not cover
these effects!
Do we have alternative modeling options
for industrial simulation tasks? 0.0
0.5
1.0
1.5
2.0
0.0 0.1 0.2 0.3 0.4
Equivalent strain / -
Eq
uiv
ale
nt
str
ess /
GP
a
U-Tension
Stack compression
Hydraulic Bulge
Shear
Effect of Yield Loci and the Hardening Model
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 54
Alternative ways for hardening with the
Gen_Yld* model
xx
yy
Effect of Yield Loci and the Hardening Model
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 55
Yield curve comparison for different load paths
3.0 Isotropic hardening
Barlat 2000
0.0
0.5
1.0
1.5
2.0
2.5
0 0.25 0.5 0.75 1
Equivalent strain / -
Eq
uiv
ale
nt
str
ess /
GP
a
uniaxial tension compression biaxial tension shear
3.0
Equivalent strain / -
Anisotropic hardening
Hill ´48
0.0
0.5
1.0
1.5
2.0
2.5
0 0.25 0.5 0.75 1
Eq
uiv
ale
nt
str
ess
/ G
Pa
Effect of Yield Loci and the Hardening Model
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 56
0
100
200
300
0 10 20 30 40 50 60 70
drawing depth / mm
pu
nch
fo
rce / k
N
experimental Hill48 anisotropic
Yld89 isotropic Yld2000 isotropic
Results in comparison – punch force prediction
• anisotropic hardening approach leads to a better punch force prediction
Effect of Yield Loci and the Hardening Model
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 57
Results in comparison - distribution of major strain
0.0
0.1
0.2
0.3
0 50 100 150
section length / mm
ma
jor
str
ain
/ -
Experimental
Hill48 anisotropic
Yld89 isotropic
Yld2000 isotropic
better prediction
with anisotropic
model
Effect of Yield Loci and the Hardening Model
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 58
Material failure due to cracking Experiment – Simulation comparison
Failure Models
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 59
Prediction of Failure – Cross Die (TRIP 700)
Experiment Simulation
Failure predicted by FLC
Thinning [%] Failure predicted by „numerical thinning“
Failure Models
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 60
A new Model for Failure Prediction and Damage
Dynamic Models with Damage
Models: von Mises, Gurson, Gurson-JC
Anisotropic Yield Locus
Models: Barlat89, Barlat2000, Hill48, Mat_TRIP
Plastic Strain
Thickness
Damage
Transfer of Variables
Crash Simulation
Forming Simulation
•Energy absorption
•Prediction of structural folding patterns
•Correct description of yield locus
•Anisotropy
Failure Models
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 61
Concept:
Coupling of a damage model to an unaltered material model for forming simulations
Damage
model
Forming material model
Crash material model with
damage
p ,
tp ,,
Damage
Mapping
Forming simulation Crash simulation
A new Model for Failure Prediction and Damage
Failure Models
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 62
Gurson
BarlatGurson
p ,
thicknessp ,,
Damage f
Mapping
Forming simulation Crash simulation
extended
Johnson-
Cook
(GISSMO)
Barlat Mat_024
p ,
thicknessp ,,
Damage D
p ,
extended
Johnson-
Cook
(GISSMO)
Mapping
Mapping
Forming simulation Crash simulation
1.) Using the Gurson
model
2.) Using an extended
Johnson-Cook model
(GISSMO)
Gurson
BarlatGurson
p ,
thicknessp ,,
Damage f
Mapping
Forming simulation Crash simulation
Gurson
BarlatGurson
p ,
thicknessp ,,
Damage f
MappingMapping
Forming simulation Crash simulation
extended
Johnson-
Cook
(GISSMO)
Barlat Mat_024
p ,
thicknessp ,,
Damage D
p ,
extended
Johnson-
Cook
(GISSMO)
Mapping
Mapping
Forming simulation Crash simulation
extended
Johnson-
Cook
(GISSMO)
Barlat Mat_024
p ,
thicknessp ,,
Damage D
p ,
extended
Johnson-
Cook
(GISSMO)
MappingMapping
MappingMapping
Forming simulation Crash simulation
1.) Using the Gurson
model
2.) Using an extended
Johnson-Cook model
(GISSMO)
A new Model for Failure Prediction and Damage Failure Models
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 63
A new Model for Failure Prediction and Damage
Failure strain vs. Triaxiality (plane stress)
Modification for GISSMO:
Failure strain can be defined arbitrarily
Tabulated input of failure Strain vs. Triaxiality
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
2,2
-0,2 0 0,2 0,4 0,6 0,8
η
εf
Failure strain
curve can be
determined using
coupon tests of
several distinct
triaxialities
Failure Models
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 64
A new Model for Failure Prediction and Damage
Simulation of Cross - die formability test using GISSMO coupled to Barlat :
• Failure spot predicted correctly at the
same position
• Less damage predicted in areas that are
not close to failure
Real failed part
Simulation of Cross - die formability test using GISSMO coupled to Barlat :
Linear accumulation GISSMO n=2 Linear accumulation Linear accumulation GISSMO n=2 GISSMO n=2
• Failure spot predicted correctly at the
same position
• Less damage predicted in areas that are
not close to failure
Real failed part
• Failure spot predicted correctly at the
same position
• Less damage predicted in areas that are
not close to failure
Real failed part Real failed part
Failure Models
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 65
Press Hardening - Process Modeling Subdivision into Partial Stages
more computational efficiency
use of different time scales
use of different tool models
use of different solvers
Handling Gravity & Waiting
Forming Quenching
temperature temperature
geometry
(stress, strain)
temperature
geometry
(stress, strain)
Influence of Temperature
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 66
Press Hardening of a roof frame Prediction of Die Temperature
Time after tool closing
1 s 4 s 8s
Influence of Temperature
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Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 67
Press Hardening of a roof frame Prediction of Punch Temperature
Time after tool closing
1 s 4 s 8s
Influence of Temperature
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 68
Press Hardening of a Roof Frame Temperature Change during Forming
Influence of Temperature
-
35
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 69
Thermo-mechanical coupling of sheet forming
processes
Die
Punch
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
X-IP
TRIP
H320LA
90 ... 80 ..ηΔTcρdVεσηw pV
eqeq
Forming of XIP-Steel in a cross-die
extrem strain hardening of X-IP-Steel
Influence of Temperature
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 70
Thermo-mechanical coupling of sheet forming
processes
Temperature after Forming - TRIP 700
Influence of Temperature
-
36
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 71
Damaging of TRIP-steel within deep drawing Influence of Temperature
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 72
Cracks after the forming process
Influence of Temperature
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37
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 73
Forming of Magnesium sheets using a heated tool
Magnesium sheet at 200°C Final part: roof inner
Tool with heating system Heated blankholder
Influence of Temperature
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 74
Sheet metal forming Application of different heat treatment methods Influence of Temperature
Without heat treatment With heat treatment
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38
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 75
Sheet metal forming Application of different heat treatment methods
0
Ext. Subroutine
Forming simulation
External Subroutine to
introduce heat treatment
Calibration
Influence of Temperature
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 76
We need for high-strength steel a thermo-mechanical coupled
simulation in order to respect the temperature distribution in the
sheet during the forming process
We have to respect the Influence of the Temperature in the Material
model
Temperature calculation give information about the thermal load of
the tool
Temperature dependence of the friction must be considered
Heating up of sheet and tool by frictional heat can be considered
Thermo-mechanical coupling of sheet forming
processes Conclusion
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39
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 77
Elastic tools in the simulation of sheet metal forming
Rigid model
Elastic model
• local deformations caused by sheet thickening
• Consideration of local load application
More accurate simulation of the draw in
Variations:
1. Models with elastic volume elements
2. Condensation of the tool stiffness on effective areas
Substructuring
3. Modal Analysis
Elastic Tools
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 78
Elastic tool: Example
binder
die
die
punch
elastic plate spacer
pressure pad
binder
die
die
punch
elastic plate spacer
pressure pad
Elastic Tools
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40
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 79
Comparison between rigid and elastic
simulation models
ca. 6,6 mm ca. 6,6 mm
-0,1
Distance along the section [mm]
Section +0.30
+0.20
+0.10
0
-0.10
[mm]
Elastic Tools
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 80
Comparison between rigid and elastic
simulation models Elastic Tools
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41
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 81
Blankholder Surface
Dimensions
2700 x 1660 x 550
Blankholder
pressure: 2,0 N/mm²
Real Die: Blankholder ca. 7 Mio. Elements Elastic Tools
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 82
Structural optimization of tools
Original structure Optimized structure (weight reduced)
Elastic Tools
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42
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 83
Next Step: Forming simulation with elastic Tools and elastic Press (ca. 134.000 Volumelements)
Influence of the Machine
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 84
Simulation of a Forming Machine with different Loads
(0,5 and 0,92 x nominal Force) Influence of the Machine
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43
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 85
From process simulation to press line simulation
Process simulation
Rigid die model
Elastic die model
Elastic machine model (static)
Dynamic machine model
Press line simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 86
Forming simulation with elastic Tools and elastic Press
Conclusions:
Forming Simulation with elastic Tools increase the accuracy of the
simulation.
•Local deformations caused by sheet thickening
•Friction Forces are more accurate
•Consideration of local load application
•More accurate simulation of the draw in
•Better calculation of the stresses and deformations of the Tool
Problems:
How we can handle the elastic properties of Tool and Machine in an economic way?
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44
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 87
Simulation chain of the complete forming process
Model
Setup
CAD Discretization Tool generation
Forming
Gravity Holding Stamping
Progressive
Processes
Trimming Flanging Hemming Springback
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 88
Workflow Sheet Metal Part Production Simulation of the process chain sheet metal forming
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45
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 89
Problems:
• Each operating step (drawing, cutting, hemming etc.) need
a “own “ FE - Mesh
• Data must be mapped between the FE - Meshes statically and
kinematically compatibly
• Simulating the assembly process parts the different FE – Meshes
of the parts must be brought by best fit into the correct position.
How we can handle the springback of the assembled part?
• In which operation step we have to compensate the springback
of the assembled part?
• How can we simulate the influence of the adhesive bonding in the
hemming operation?
Simulation of the forming process chain
Solved Progress ?
Simulation of the process chain sheet metal forming
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 90
Trimming operation (OP30) Trimming Simulation
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46
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 91
Scrap Flow Simulation Trimming Simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 92
Simulation Hemming
hemming of
curved edges
Hemming Simulation
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47
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 93
Front Fender – (Roll in) Experiment vs. Simulation
Hemming Simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 94
Frontfender – Flange radius Experiment vs. Simulation
Hemming Simulation
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48
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 95
Rollhemming
General procedure
Inner part
> 90°
~45°
Roller
After flanging
Pre-hemming
Final-hemming
Step 1
Step 2
• Incremental forming with a roller
•Application robotically manipulated
hemming roller
•Example:
Tangential compression
Tangential tension stress
Hemming roller
Flange
Hemming bed
Stress in Y [MPa]
Flange
Roller Hemming
Rollhemming Simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 96
Rollhemming Simulation Rollhemming Simulation
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49
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 97
•Identification of relevant factors by Design of Experiments
DEAEAC
AEFBEBDCDEF
ABCACE
BAFCFABA
ACDABD
FBC
ADFE
ADEACF
DFADBFCEDC
300025002000150010005000
Te
rm
Standardisierter Effekt
13
A Krümmung XY
B Krümmung Z
C Blechdicke
D Abkantradius
E Falzkanal
F Vordehnung
Faktor Name
Pareto-Diagramm der standardisierten Effekte
(Antwort ist REL, Alpha = ,05)
Radiuseinsatzlinie (REL)
konvexkonkav
2,34
2,28
2,22
2,16
2,10
HochpunktTiefpunkt 1,150,95
1,51,0
2,34
2,28
2,22
2,16
2,10
30 100
Krümmung XY
Mit
telw
ert
Krümmung Z Blechdicke
Abkantradius Falzkanal Vordehnung
Haupteffektediagramm für RELDatenmittelwerte
prestrain rolling direction flange length
Development of a metamodel Metamodel
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 98
Generation of response Surfaces
• for example, by a sum of weighted
Gauss bells, with the parameter you are
looking for using the method of least
squares
• Minimization through local search
Source: FCE Frankfurt Consulting Engineers GmbH
Metamodel
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50
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 99
Meta model as a basis of a forecast tool for the
planning process of Rollhemming
•Result forecast based on FEM calculations of rollhemming
Metamodel
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 100
Joining: Simulation of Clinch - Process Mechanical Joining Simulation
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51
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 101
Joining: Simulation of Riveting Mechanical Joining Simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 102
Joining: Simulation Tack-setting Mechanical Joining Simulation
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52
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 103
Joining: Simulation of Spot Welding
0.75 mm
1 Per. 3 Per.
6 Per. 10 Per.
Processing conditions: flat upper electrode, 2.8 kN, AC1
Processing time: 1, 3, 6,10 periods
Welding Simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 104
Forming to Welding Distortion
Welding Lines
Welding Simulation
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53
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 105
Forming to Welding Distortion Welding Simulation
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 106
Simulation of the part properties (Static, Crash,
Fatigue..)
Results of the forming
simulation are input for
• Crash - analysis
• Static analysis
• Fatigue analysis
• Static analysis
of the tool
Results of the forming
simulation are input for
• Crash - analysis
• Static analysis
• Fatigue analysis
• Static analysis
• Welding distortion
Simulation of the part properties
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54
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 107
Simulation of the part properties (Static, Crash,
Fatigue..)
Problems:
• Each simulation method (static, crash, etc. ) needs a " own " FE - Program
(exception Forming - Crash with explicit codes)
• Each simulation method (static, crash, etc. ) needs a „own“ FE - Mesh
• Each simulation method has " own " material and failure models
• Data must be mapped between the programs statically and kinematically
compatibly.
• Today it is only possible to interpolate Scalars such as thickness, plastic
strain, etc.
• Which influence does the " damage " have by the mapping process on the
characteristics of the component?
• With the extrapolation of Tensors still many questions are open (e.g.: as
equilibrium can be achieved with mapping?)
Solved Progress ?
Simulation of the part properties
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 108
Coupling Crash - Forming Simulation
Crash - / Staticsimulation Formingsimulation
(Prototyp Dies)
Job No. 1
Today
Styling
Formingsimulation
(Hard Dies)
Formingsimulation
Crash - / Staticsimulation
Tomorrow
With Forming
History
Crash - / Staticsimulation Formingsimulation
(Prototyp Dies) Crash - / Staticsimulation Formingsimulation
(Prototyp Dies)
Job No.. 1
Today Today
Styling
Formingsimulation
(Hard Dies)
Formingsimulation
Crash - / Staticsimulation
Tomorrow
With Forming
History
Formingsimulation
(Hard Dies)
Formingsimulation
Crash - / Staticsimulation
Forming simulation
(Hard Dies)
Formingsimulation
Crash - / Staticsimulation
Tomorrow
With Forming
History
Forming to Crash
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55
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 109
Crash - Forming Simulation - Example
50285 Nodes
Crash Model:
10855 Elements
10759 Nodes
Forming Simulation Modell:
Thickness-Distribution after Mapping
49007 Elements (AUTOFORM)
50285
Crash Model:
10855 Elements
10759 Nodes
Forming to Crash
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 110
Crash-Forming Simulation
§
Forming properties from 64 parts are mapped to the Crash - Simulation
Forming to Crash
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56
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 111
Crash-Forming Simulation
•Euro-NCAP-Test (deformable Wall): 64 km/h with 40% Overlapping
Standard
With Influence of Thickness &
plastic strain
-
Forming to Crash
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 112
Crash to Forming: Failure and Damage
Three Point Bending Test B-column
Forming to Crash
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57
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 113
Crash to Forming: Failure and Damage
Three point Bending Test B-column
Experiment Simulation
with forming
simulation
Simulation
without forming
Simulation
Failure at 196 mm
Buckling at 82.1 mm
Barlat + Failure Source: FhG - IWM, Freiburg
Forming to Crash
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 114
Fatigue - Part of the Suspension System Forming to Fatigue
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58
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 115
Fatigue - Stress Calculation
+15%
+16%
+16%
+9%
+16%
+16%
“Classical Simulation with
Constant Sheet Thickness
Simulation with Sheet Thickness
after the Forming Process
Forming to Fatigue
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 116
Fatigue - Failure
+52%
+47%
+15%
+55%
+108%
+108%
1.
1.
2.2.
Simulation with Sheet Thickness
after the Forming Process
“Classical” Simulation with
Constant Sheet Thickness
Ranking List of Failure
Forming to Fatigue
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59
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 117
• Warm forming and hot forming
• Press hardening (22MnB5), hot stamping
• New lightweight materials (Al, Mg, Ti?)
• Hybrid composites (sheet metal / textiles, sheet metal / polymer,
sandwich sheets, sheet metal / fiber-reinforced polymers, …)
• Tailored (engineered) blanks, bonded blanks, patchwork blanks
special sheets for lightweight design
• Aluminum fusion alloys and cladded blanks
• Functionally graded materials
• Tailored heat treated blanks (Al, 22MnB5)
• Cold forming of HSS, AHSS, UHSS
• Mechanical joining processes
• Servo presses
• Special technologies (EMF, superplastic forming,..)
Trends in Metalforming I Outlook
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 118
This has the following consequences for the simulation
• Thermal-mechanical coupling will have to be the standard
• Heating methods (induction, conduction) will have to be simulated
• Tooling properties (thermal, elastic) will have to be considered
• Structural optimization of tools and dies will be required
• In the long term the system machine-tooling-process will have
to be simulated
• The real time has to be used and shown
• Development of new, sophisticated material models
• Joining technologies for new materials will have to be
simulated as well
• Adhesives in mechanical joining processes will have
to be simulated
Trends in Metalforming II Outlook
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60
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 119
Vision: the future simulation environment
Source: Dr. Haufe, DynaMore
Rückfederung Kompensation
Walzen Mapping Crash - Umformen
; ; ; ; ; ; T
Mapping
Beurteilung des Gefüges
Anisotropie in Dickenrichtung
Oberflächenqualität etc.
Möglichst universales, durchgängiges Materialmodell oder größtmö gliche Kompatibilität!
Glühen Fügen
Beurteilung der Herstellbarkeit
Anisotropie in der Ebene
Umformbarkeit etc.
Energieaufnahme
Entwicklung Bauteilgeometrie
Div. Anforderungen aus Crash/Festigkeit/ Steifigkeit
Beurteilung des Gefüges
Beurteilung der Wärmeeinflusszone
Rückfederung Kompensation
Springback Compensation
Rolling Annealing Mapping Crash-simulation - Forming
Beurteilung des Gefüges
Anisotropie in Dickenrichtung
Oberflächenqualität etc.
• texture
• grain size
• strength
• transformation
• ductility
One description of the material for all simulations if possible
Joining
Beurteilung der Herstellbarkeit
Anisotropie in der Ebene
Umformbarkeit etc.
• yield locus
• hardening
• phase transformation
• damage
• accuracy
Energieaufnahme
Entwicklung Bauteilgeometrie
Div. Anforderungen aus Crash/Festigkeit/ Steifigkeit
•Energyconsumption
•Intrusion
•Stiffness
•Fatigue
Beurteilung des Gefüges
Beurteilung der Wärmeeinflusszone
•depend on joining Technique
•thermal wakening
•mechanical
hardening
•Welding distortion
Mapping
Outlook
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 120
Vision of Digital Factory
Facility
Line
Cell
Operation
Specific
Process
Building
Worker Focus :
• technical processes
• facility components
• quality
• costs
• capacities
Focus :
• technical processes
• facility components
• quality
• costs
• capacities
Not a single production facility
will
without having been completely
supported by digital planning
methods
Not a single production facility
will
without having been completely
supported by digital planning
methods
be planned
be built/
go into operation
be working
be planned
be built/
go into operation
be working
Facility
Line
Cell
Operation
Specific
Process
Building
Worker
Facility
Line
Cell
Operation
Specific
Process
Building
Worker Focus :
• technical processes
• facility components
• quality
• costs
• capacities
Focus :
• technical processes
• facility components
• quality
• costs
• capacities
Not a single production facility
will
without having been completely
supported by digital planning
methods
Not a single production facility
will
without having been completely
supported by digital planning
methods
be planned
be built/
go into operation
be working
be planned
be built/
go into operation
be working
Outlook
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61
Sheet metal forming simulation for automotive applications Prof. Dr.-Ing. K. Roll Sommerschool Dortmund 2012; Slide 121
Thank you for your attention!