DEVELOPMENT OF A ROBUST COMPUTATIONAL DESIGN SIMULATOR FOR INDUSTRIAL DEFORMATION PROCESSES

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DEVELOPMENT OF A ROBUST COMPUTATIONAL DESIGN
SIMULATOR FOR INDUSTRIAL DEFORMATION PROCESSES

• Nicholas Zabaras (PI) and Shankar
  Ganapathysubramanian
• URL http//www.mae.cornell.edu/zabaras/
• Email zabaras_at_cornell.edu

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VIRTUAL DEFORMATION PROCESS DESIGN SIMULATOR
Mathematical representation of the design
objective(s) constraints

• knowledge based expert systems
• microstructure evolution paths
• ideal forming techniques

Selection of a virtual direct process model
Selection of the design variables (e.g. die and
preform parametrization)
Selection of the sequence of processes (stages)
and initial process parameter designs
Material Process Design Simulator
Optimization algorithms
Assessment of automatic process optimization
Continuum multistage process sensitivity analysis
consistent with the direct process model
Reliability of the design to uncertainties in the
physical and computational models
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DESIGN OF MULTI STAGE DEFORMATION PROCESSES
Initial Product
Node Intermediate preform
1st Stage
Evaluate number of stages n and select a process
sequence p from all feasible paths (j1 m),
such that
Arc Processing Stage
n
Cost Function



?
min
m
i1
ith Stage
Process sequence selection
Finishing Stage(nth)
Final Product
Optimal Path (pth) Feasible Paths (jth)
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BROAD DESIGN OBJECTIVES
Given raw material, obtain product of desired
microstructure and shape with minimal material
utilization and cost
COMPUTATIONAL PROCESS DESIGN
Design the forming and thermal process
sequence Selection of stages (broad
classification) Selection of dies and preforms in
each stage Selection of mechanical and thermal
process parameters in each stage Selection of the
initial material state (microstructure)
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UPDATED LAGRANGIAN FRAMEWORK OF ANALYSIS
CONSTITUTIVE MODEL
CONTACT/FRICTION MODEL
Initial configuration Temperature ?o void
fraction fo
Deformed configuration Temperature
? void fraction f
Reference configuration
Intermediate thermal configuration
Temperature ? void fraction fo
Stress free (relaxed) configuration
Temperature ? void fraction f
GOVERNING PHYSICS

• Mechanical dissipation
• Augmented Lagrangian approach
• Coulomb friction

• Multiplicative decomposition framework
• State variable rate-dependent models
• Hyperelastic constitutive law
• Thermal and damage effects

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DEFINITIONS OF SENSITIVITY FIELDS IN AN UPDATED
LAGRANGIAN FRAMEWORK

xn x (X, tn ?p )
Parameter sensitivity analysis

Qn Q (X, tn ?p )
B
Fr
xn
x

Fn
x x (xn, t ?p)
Design parameters
X
ILn

• Ram speed
• Shape of die surface
• Material parameters
• Initial state

Bo
o
xnxn
xx
o

o
B
xn xn x (Y , tn ?p ? ?p )

o

Qn Qn Q (Y, tn ?p ? ?p )
xn x (X, tn ?s )

__
Qn Q (X, tn ?s )
Fr
Shape sensitivity analysis
X X (Y ?s )
xn
x
B
Fn
X
Bo

FR
x x (xn, t ?s)
BR
ILo
Y
ILn
Main features
XX
o

• Gateaux differential referred to
• the fixed configuration Y
• Rigorous definition of sensitivity
• Key element LRFR FR-1

__
xx
xnxn
o
o
o
X X X (Y ?s ? ?s)

o
xn xn x (Y , tn ?s ? ?s)
o

o
Qn Qn Q (Y, tn ?s ? ?s)
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SCHEMATIC OF THE CONTINUUM SENSITIVITY METHOD
(CSM)
Equilibrium equation
Contact friction constraints
Design derivative of equilibrium equation
Sensitivity weak form
Regularized design derivative of contact
frictional constraints
Material constitutive laws
Incremental sensitivity contact sub-problem
Design derivative of the material constitutive
laws
Time space discretized weak form
Incremental thermal sensitivity sub-problem
Incremental Sensitivity constitutive sub-problem
Assumed kinematics
Design derivative of energy equation
Time space discretized modified weak form
Design derivative of assumed kinematics
Conservation of energy
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Design sensitivity of equilibrium equation
o
?
Calculate and such
that
o
o
o
o
o
o
?
?
Fr and x
Constitutive problem
Regularized contact problem
Thermal problem
Kinematic problem
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Sensitivity deformation is a linear
problem Iterations are avoided within
a single time increment Additional
augmentations are avoided by using large
penalties in the sensitivity contact problem
REMARKS
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Rigid Die
Forging rate
Convection/ Radiation
Flash
Conduction
Unfilled die cavity
Damage/microstructure
Unfilled cavity and flash!
Initial design
MATERIAL SYSTEM
1100-Al workpiece Initial temperature 673
K Axisymmetric problem Standard ambient
conditions Design objectives Find preform shape
of minimum volume such that the die is filled
completely and the flash is minimized
Fully filled cavity
Optimal design
0.12
0.10
0.08
Objective (mm2)
0.06
Objetive Function
0.04
0.02
0.00
0
10
20
30
Iteration number
Iteration Numeber
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THE CONTINUUM SENSITIVITY METHOD FOR MULTI-STAGE
DEFORMATION PROCESSES
Generic Forming Stage
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Preforming stage
Preforming Stage
Finishing Stage
Unfilled cavity
MATERIAL SYSTEM
Initial design
1100-Al workpiece Initial temperature 673
K Axisymmetric problem Standard ambient
conditions 2 pre-defined stages - preforming
finishing Design objective Design the preforming
die for a fixed volume of the workpiece such
that the finishing die is filled
Fully filled cavity
Optimal design
Flash
8.0
6.0
Objective Function (x1.0E-05)
Objective (mm2)
4.0
2.0
0.0
0
1
2
3
4
5
6
Iteration number
Iteration Number
14
Preforming stage
Finishing stage
Preforming Stage
Finishing Stage
MATERIAL SYSTEM
1100-Al workpiece Initial temperature 673
K Axisymmetric problem Standard ambient
conditions 2 pre-defined stages - preforming
finishing Design objective Design the preforming
die for a fixed volume of the workpiece such
that the variation in state in the product
is minimum
Scalar state variable (MPa)
Initial design
Height (mm)
Scalar state variable (MPa)
Optimal design
Radius (mm)
Design
In MPa
Initial
Optimal
Average state
Objective
Objective Function
50.2
52.3
Deviation
3.73
1.88
Iteration number
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FUTURE EXTENSIONS TO MULTI-SCALE PROCESS
DESIGN PCG CONTROL DURING EXTRUSION
Peripheral coarse grain (PCG)
Extrusion
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USING COMPUTATIONAL DESIGN TO DEVELOP A DIGITAL
MATERIALS PROCESS LIBRARY
Alloy flow stress
Profile output data
Billet input data
Material point data
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• Testing and further developments for single-stage
  designs - complex 2D geometries
• Regularized contact/ friction sensitivity
  modeling
• Simultaneous thermal mechanical design
• Sensitivity analysis for multi-body deformations
• Multi length scale design
• Control of grain growth, texture and
  recrystallization
• Multi-stage forming design
• Coupling with ideal forming microstructure
  evolution paths based initial designs
• Framework for web-based forming design
• Development of a 3D forming design simulator
• Industrial design applications
• Robust design algorithms

REFERENCES

• Srikanth, A., et.al. Continuum Lagrangian
  sensitivity
• analysis for metal forming processes with
  applications to
• die design, Int. J. Numer. Methods Engr.,
  (2000) 679-720.
• Srikanth, A. and N. Zabaras. Shape optimization
  and
• preform design in metal forming processes,
  Comput.
• Methods Appl. Mech. Engr., (2000) 1859-1901.
• Ganapathysubramanian, S. and N. Zabaras.
  Continuum
• sensitivity method for finite thermo-inelastic
  deformations
• with applications to the design of hot forming
  processes,
• Int. J. Numer. Methods Engr., (submitted)

• Zabaras, N., et.al. Continuum sensitivity
• method for the design of multi-stage metal
• forming processes, Int. J. Mech. Sciences
• (submitted)

ACKNOWLEDGEMENTS
The work presented here was funded by NSF grant
DMI-0113295 with additional support from AFOSR,
AFRL and ALCOA.