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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: [email protected]. DEFORMATION PROCESS DESIGN FOR TAILORED MATERIAL PROPERTIES. - PowerPoint PPT Presentation
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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: [email protected]
Optimization based design of deformation processes Mathematically consistent & accurate continuum sensitivity finite element analysis Unified approach towards shape and parameter sensitivity analysis Oriented towards the design of multi-stage processes
Optimumdeformation process
Billet Product
DEFORMATION PROCESS DESIGN FOR TAILORED DEFORMATION PROCESS DESIGN FOR TAILORED MATERIAL PROPERTIESMATERIAL PROPERTIES
Minimal overall cost:force, energy, etc.
MaterialsMaterialsProcessProcessDesignDesign
SimulatorSimulator
Tailored material properties in the
final product Desired microstructural
features
Desired spatialdistributions of state variables
Controlled texture,recrystallization,
fracture & porosity
Desired shape withminimal material
utilization
Accelerated processsequence design
APPROACH
Interactive Optimization Environment
Given process constraints ¶meters
Desired productproperties
VIRTUAL DEFORMATION PROCESS DESIGN SIMULATORVIRTUAL DEFORMATION PROCESS DESIGN SIMULATOR
MaterialMaterialProcessProcessDesignDesign
SimulatorSimulator
Selection of the sequence of processes (stages) and initial process parameter designs
• knowledge based expert systems• microstructure evolution paths• ideal forming techniques
Selection of the design variables (e.g. die and
preform parametrization)
Optimization algorithms
Continuum multistage process sensitivity analysis consistent with the direct process model
Assessment of automatic process optimization
Reliability of the design to uncertainties in the physical and computational models
Mathematical representation of the design objective(s) &
constraints Selection of a virtual direct process model
Interactive Interactive Optimization Optimization EnvironmentEnvironment
Node: Intermediate
preform
Arc: Processing
Stage
FinalProduct
Initial Product
Optimal Path (pth)Feasible Paths (jth)
1st Stage
FinishingStage(nth)
ith Stage
DESIGN OF MULTI STAGE DEFORMATION PROCESSES
CostFunction = + +Cost
of DiesEnergy
ConsumptionMaterialUsage
i=1 n
minm
Evaluate number of stages n and select a process sequence p from all feasible paths (j=1 … m), such that:
Ideal forming & microstructure evolution paths based initial designs
Advanced knowledge-based algorithms for process sequence selection
Process sequenceselection
Given raw material, obtain product of desired microstructure and shape with minimal material utilization and cost
Design the forming and thermal process sequenceSelection of stages (broad classification)Selection of dies and preforms in each stageSelection of mechanical and thermal process parameters in each stageSelection of the initial material state (microstructure)
Press force
Processing temperaturePress speed
Product qualityGeometry restrictions
Cost
CONSTRAINTSOBJECTIVES
Material usage
Plastic work
Uniform deformation
MicrostructureDesired shapeResidual stresses Thermal parameters
Identification of stagesNumber of stagesPreform shapeDie shape Mechanical parameters
VARIABLES
COMPUTATIONAL DESIGN OF METAL FORMING PROCESSES
BROAD DESIGN OBJECTIVES
COMPUTATIONAL PROCESS DESIGN
GOVERNING PHYSICS
UPDATED LAGRANGIAN FRAMEWORK OF ANALYSIS
BBo BB
FF e
FF p
FF
FF
Initial configuration Temperature: o
void fraction: fo
Deformed configuration Temperature: void fraction: f
Intermediate thermalconfiguration Temperature:
void fraction: fo
Stress free (relaxed) configuration Temperature: void fraction: f
Referenceconfiguration
r
n
Inadmissible region
Currentconfiguration
Admissible region
CONSTITUTIVE MODEL CONTACT/FRICTION MODEL
Multiplicative decomposition framework State variable rate-dependent models Hyperelastic constitutive law Thermal and damage effects
Mechanical dissipation Augmented Lagrangian approach Coulomb friction
DEFINITIONS OF SENSITIVITY FIELDS IN AN UPDATED LAGRANGIAN FRAMEWORK
x = x (xn, t ; p)^
xn = x (X, tn ; p )
Qn = Q (X, tn ; p )
oFn + Fn
X
xn
Fn
Bo
x+xoo
Fr + Fr
xB
xn + xn = x (Y , tn ; p + p )
Qn + Qn = Q (Y, tn ; p + p )o ~
B’n
I+Ln
Fr
oxn+xn
B n
B’
X = X (Y; s )
oFR + FR
Y
X
X+Xo
xn+xno
xn
oFn + Fn
FR
Fn
BR
Bo
I+Lo
x+xoo
Fr + Fr
x B
xn + xn = x (Y , tn ; s + s)
Qn + Qn = Q (Y, tn ; s + s)
x = x (xn, t ; s)
B n
xn = x (X, tn ; s )Qn = Q (X, tn ; s )
I+Ln
X + X= X (Y; s + s)
Fr
Parameter sensitivity analysis
Design parameters Ram speed Shape of die surface Material parameters Initial state
Shape sensitivity analysis
Main features Gateaux differential referred to the fixed configuration Y Rigorous definition of sensitivity Key element: LR=FR FR
-1 oo
~o
~
~
__
o
~~
__
~o
o
~
^
Equilibrium equation
Design derivative of equilibrium
equation
Material constitutive
laws
Design derivative of the material
constitutive laws
Design derivative ofassumed kinematics
Assumed kinematics
Incremental Sensitivityconstitutive sub-problem
Time & space discretizedmodified weak form
Time & space discretized weak form
Sensitivity weak form
Contact & frictionconstraints
Regularized designderivative of contact &frictional constraints
Incremental sensitivity contact
sub-problem
Conservation of energy
Design derivative of energy equation
Incrementalthermal sensitivity
sub-problem
SCHEMATIC OF THE CONTINUUM SENSITIVITY METHOD (CSM)
Continuum problem Differentiate Discretize
Design sensitivity of equilibrium equation
Calculate and such that x = x (xr, t, β, ∆β )oo
o
FFrr and and xxoo
Kinematic problem
oλ and x o
Regularized contact problem
Pr and F,o
o
Constitutive problem
THE CONTINUUM SENSITIVITY METHOD SUB-PROBLEMS
Thermal problem
o
o
o
Consider the non-differentiability of contact and frictionconditions
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
THE CONTINUUM SENSITIVITY CONTACT SUB-PROBLEM
y = y + y
υ
r
υ + υo
r + rox + x o
X
y = y ( ξ )
DieDie
o
oy + [y]
x = x ( X, t, β p )~
x = x ( X, t, β p+ Δ β p )~
B0
B΄
Bx
ParameterParameterSensitivitySensitivityAnalysisAnalysis
υ
r
υ
r
y,ξ ξy
o
+
x = x ( X, t, β s )B0
B’0
BR
X + X
X
o
x = x ( X + X , t, β s+ Δ β s )~
oX = X (Y ; β s+ Δ β s )~
Y
X = X (Y ; β s )
~
~
x + xB΄
o
By = y ( ξ )Die
y = y ( ξ )
x
ShapeShapeSensitivitySensitivityAnalysisAnalysis
REGULARIZATION
Contact and friction
sensitivity assumptions
REMARKS
Stress Sensitivity100.00
85.0070.0055.0040.0025.0010.00-5.00
-20.00-35.00-50.00
Convection/ Radiation
Conduction
Rigid DieForging rate
Unfilled die cavity
Flash
Damage/microstructure
A ONE-STAGE HOT FORMING PREFORM DESIGN PROBLEM
MATERIAL SYSTEM
1100-Al workpieceInitial temperature 673 KAxisymmetric problem Standard ambient conditions
Design objectivesFind preform shape of minimum volume such that the die is filled completely and the flash is minimized
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 10 20 30Iteration Numeber
Ob
jeti
ve F
un
ctio
n
Unfilled cavityand flash!
Optimal design
Fully filledcavity
Initial design
Iteration number
Ob
ject
ive
(mm
2)
THE CONTINUUM SENSITIVITY METHOD FOR MULTI-STAGE DEFORMATION PROCESSES
Sequential transfer of sensitivities from one stage to the next
Design Objective
Knowledge-based methods
Shapesensitivity analysis
Die and process parameter sensitivity analysis
Selection of stages
Design of preforms
Design of dies
Generic Forming Stage
1100-Al workpieceInitial temperature 673 KAxisymmetric problem Standard ambient conditions 2 pre-defined stages - preforming + finishing
Design objectiveDesign the preforming die for a fixed volume of theworkpiece such that the finishing die is filled
PREFORMING DIE DESIGN PROBLEM FOR SHAPE CONTROL
MATERIAL SYSTEM
Preforming stage
Finishing stage
Rigid Die
FlashFlash
Preforming Stage Finishing StageUnfilledcavity
Fullyfilledcavity
0.0
2.0
4.0
6.0
8.0
0 1 2 3 4 5 6Iteration NumberO
bje
ctiv
e F
un
ctio
n
(
x1.0
E-0
5)
Iteration number
Optimal design
Initial design
Ob
ject
ive
(mm
2)
Preforming Stage Finishing Stage
State variable ( MPa )55.21053.48751.76450.04048.31746.594
State variable ( MPa )54.43151.72949.02846.32643.62540.923
I t e r a t i o n i n d e x
O b j e c t i
v e f u n c t i
o n
0 1 2 3 4 5 6 7 8
0 . 0 5
0 . 1
0 . 1 5
0 . 2
0 . 2 5
Ob
ject
ive
Fu
nct
ion
1100-Al workpieceInitial temperature 673 KAxisymmetric problem Standard ambient conditions 2 pre-defined stages - preforming + finishing
Design objectiveDesign the preforming die for a fixed volume of the workpiece such that the variation in state in the product is minimum
PREFORMING DIE DESIGN FOR CONTROL OF MICROSTRUCTURE
MATERIAL SYSTEM
Preforming stage
Radius, r (mm)
He
igh
t,h
( mm
)
0 0.5 11.2
1.25
1.3
1.35
1 .4
1.45
1.5
1.55
1
2
3
4
5
6
7
Average state
Initial Optimal
Deviation
50.2 52.3
3.73 1.88Iteration number
Ob
ject
ive
Scalar statevariable (MPa)
Scalar statevariable (MPa)
Radius (mm)
Hei
gh
t (m
m)
Optimal design
Initial design
DesignIn MPa
Finishing stage
Extrusion
Peripheral coarse grain (PCG)
FUTURE EXTENSIONS TO MULTI-SCALE PROCESS DESIGN:PCG CONTROL DURING EXTRUSION
Need to couple grain growth/ orientation and recrystallization simulation models with CSM based computational design for explicit control of micro-structural features in deformation processes
Alloy flow stress
Material point data
Profile output data
Billet input data
USING COMPUTATIONAL DESIGN TO DEVELOP A DIGITAL MATERIALS PROCESS LIBRARY
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)
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
ACKNOWLEDGEMENTS
The work presented here was funded by NSF grant DMI-0113295 with additional support from AFOSR, AFRL and ALCOA.
FORTHCOMING RESEARCH EFFORTS
Zabaras, N., et.al. “Continuum sensitivity method for the design of multi-stage metal forming processes”, Int. J. Mech. Sciences (submitted)
REFERENCES