COMPUTATIONAL DESIGN OF MULTISTAGE DEFORMATION PROCESSES
-
Upload
lafayette-isai -
Category
Documents
-
view
36 -
download
1
description
Transcript of COMPUTATIONAL DESIGN OF MULTISTAGE DEFORMATION PROCESSES
COMPUTATIONAL DESIGN OF COMPUTATIONAL DESIGN OF MULTISTAGE DEFORMATION MULTISTAGE DEFORMATION
PROCESSESPROCESSES
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Prof. Nicholas Zabaras &Prof. Nicholas Zabaras &
Shankar GanapathysubramanianShankar GanapathysubramanianMaterials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering188 Frank H. T. Rhodes Hall
Cornell University Ithaca, NY 14853-3801
Email: [email protected]: http://www.mae.cornell.edu/zabaras/
Computational Mathematics Program
NATIONAL SCIENCE FOUNDATION
Design and Integration Engineering
Program
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
FEDERAL & INDUSTRIAL SPONSORS/COLLABORATORSFEDERAL & INDUSTRIAL SPONSORS/COLLABORATORS
Industrial Sponsors
ALCOA, ATC-Materials Process Design ProgramALCOA, ATC-Materials Process Design Program
U.S. Air Force Partners
Materials Process Design Branch, AFRLMaterials Process Design Branch, AFRL
Computational Mathematics Program, AFOSRComputational Mathematics Program, AFOSR
NATIONAL SCIENCE FOUNDATION (NSF)
Design and Integration Engineering ProgramDesign and Integration Engineering Program
MaterialsMaterialsProcessProcess
Design &Design &ControlControl
LaboratoryLaboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
FROM MATERIALS PROCESS MODELING TO COMPUTATIONAL DESIGN
Materials ModelingMaterials Modeling
incremental improvements incremental improvements in specific areasin specific areas
Development of Designer Development of Designer Knowledge BaseKnowledge Base
time consuming and costly time consuming and costly endeavorendeavor
Difficult InsertionDifficult Insertion of new materials and of new materials and
processes into productionprocesses into production
Numerical SimulationNumerical Simulation
Trial-and-error and with Trial-and-error and with no design informationno design information
Conventional Design ToolsConventional Design Tools
Reliability Based DesignReliability Based Designfor material/tool variability & for material/tool variability & uncertainties in mathematical uncertainties in mathematical
and physical modelsand physical models
Sensitivity InformationSensitivity Information points to most influential points to most influential
parameters so as to optimally parameters so as to optimally design the processdesign the process
Data Mining Data Mining of Designer Knowledgeof Designer Knowledge
for rapid solutions to complex for rapid solutions to complex problems and to further drive problems and to further drive
use of knowledgeuse of knowledge
Accelerated InsertionAccelerated Insertion to new materials and processesto new materials and processes Innovative ProcessesInnovative Processes for traditional materialsfor traditional materials
computational material process design simulatorcomputational material process design simulator
Materials Process DesignMaterials Process Design control of microstructure using control of microstructure using various length and time scale various length and time scale
computational modelscomputational models
Virtual Material Virtual Material Process LaboratoryProcess Laboratory
people
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
A Virtual Laboratory for Materials Process Design
Reliability Based Designfor material/tool variability & uncertainties in mathematical
and physical models
Sensitivity Information points to most influential
parameters so as to optimally design the process
Designer Knowledgefor rapid mining of solutions to complex problems and to
further update the digital library
Materials Process Design control of microstructure using various length and time scale
computational models
Virtual Materials Virtual Materials Process LaboratoryProcess Laboratory
Selection of a virtual direct process model
Selection of the sequence of processes (stages) and initial process parameter designs
Selection of the design variables (e.g. die and
preform parametrization)
Continuum multistage process sensitivity analysis consistent with the direct process model
Optimization algorithms
Interactive Optimization Environment
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
A VIRTUAL MATERIALS 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
Desired Final Shape Selection of Stages
Stage 1Stage 1
Stage 2Stage 2
Stage 3Stage 3
Design of Preforms Design of Dies
??
?? ??
?? ??
Shape and parameter
sensitivity analysis
MaterialProcessDesign
Simulator
Thermal parameters
Identification of stagesNumber of stagesPreform shapeDie shape Mechanical parameters
VARIABLES
Ideal forming & microstructure evolution paths based initial designs
Advanced knowledge-based algorithms for process sequence selection
Processing temperature
Press forcePress speed
Product qualityGeometry restrictions
CONSTRAINTSGiven raw
material and desired hardwarecomponent performance,
compute optimal manufacturing process
sequence(s)
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
DESIGN OF MULTI STAGE DEFORMATION PROCESSES
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
ESSENTIAL FEATURES OF A DESIGN SIMULATOR OF INDUSTRIAL PROCESSESESSENTIAL FEATURES OF A DESIGN SIMULATOR OF INDUSTRIAL PROCESSES
Allow consistent application of remeshing, data transfer & adaptivity techniques to sensitivity analysis
Contact/frictional conditions drive most forming design processes and need careful consideration
Extend assumed strain methods to sensitivity analyses (preserve volume)
Mathematically consistent and accurate computation of sensitivity fields
Provide a unified approach to parameter and shape sensitivity / optimization
Efficiency – avoid extensive direct forming simulations (as in surface response methods)
Provide consistent coupling of direct & sensitivity analyses with
knowledge based expert systems
microstructure evolution paths
ideal forming techniques
Oriented towards the design of multi-stage processes
Allow for realistic polycrystalline material constitutive models
Allow for hot forming design and intermediate thermal stages
Interface with commercial solid modelers and optimization tools
Theoretical AspectsTheoretical AspectsApplication AspectsApplication Aspects
MaterialsMaterialsProcessProcessDesignDesign
SimulatorSimulator
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
COMPUTATIONAL DESIGN OF FORMING PROCESSESCOMPUTATIONAL DESIGN OF FORMING PROCESSES
Press forcePress force
Processing temperatureProcessing temperaturePress speedPress speed
Product qualityProduct qualityGeometry restrictionsGeometry restrictions
CostCost
CONSTRAINTSCONSTRAINTSOBJECTIVESOBJECTIVESMaterial usageMaterial usage
Plastic workPlastic work
Uniform deformationUniform deformationMicrostructureMicrostructure
Desired shapeDesired shape
Residual stressesResidual stresses Thermal parametersThermal parameters
Identification of stagesIdentification of stagesNumber of stagesNumber of stagesPreform shapePreform shapeDie shape Die shape Mechanical parametersMechanical parameters
VARIABLESVARIABLES
BROAD DESIGN OBJECTIVESGiven raw material, obtain final product with desired microstructure and shape with minimal material utilization and costs
COMPUTATIONAL PROCESS DESIGN
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)
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
DESIGN OF MULTI-STAGE PROCESSESDESIGN OF MULTI-STAGE PROCESSES
Node: Intermediate
preform
Arc: Processing
Stage
FinalFinalProductProduct
Initial ProductInitial Product
Optimal Path (pth)Feasible Paths (jth)
1st Stage
FinishingStage(nth)
ith Stage
CostCostFunctionFunction == ++ ++CostCost
of Diesof DiesEnergyEnergy
ConsumptionConsumptionMaterialMaterialUsageUsage
i=i=11
nn
minminJ=1J=1
mm
Based on the `designer knowledge’, evaluate practicable Based on the `designer knowledge’, evaluate practicable stage number (stage number (nn) and select a process sequence ) and select a process sequence p p from all from all feasible paths (feasible paths (j=1 … mj=1 … m)), , such that:such that:
such that:such that:• Equipment constraint (press force, ram speed, Equipment constraint (press force, ram speed,
maximum stroke, etc)maximum stroke, etc)• Process temperature constraintProcess temperature constraint• Other process constraintsOther process constraints
• Number of stages - n• Force constraints for each stage• Stroke allocation for each stage• Stage temperature, etc.
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
COMPUTATIONAL MULTI-STAGE FORMING DESIGNCOMPUTATIONAL MULTI-STAGE FORMING DESIGN
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
Desired Final ShapeDesired Final Shape Selection of StagesSelection of Stages
Stage 1Stage 1
Stage 2Stage 2
Stage 3Stage 3
Design of PreformsDesign of Preforms Design of DiesDesign of Dies
??
?? ??
?? ??
Design of SequencesDesign of Sequences Knowledge-based methodsKnowledge-based methods
Design of PreformsDesign of Preforms
Design of DiesDesign of Dies
Shape and parameter Shape and parameter sensitivity analysissensitivity analysis
Die and process parameter Die and process parameter sensitivity analysissensitivity analysis
Design Design ObjectiveObjective
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
MACROSCOPIC CONSTITUTIVE FRAMEWORKMACROSCOPIC CONSTITUTIVE FRAMEWORK
BBo BB
FF e
FF p
FF
FF
Initial configurationInitial configuration Temperature: o
void fraction: fo
Deformed configurationDeformed configuration Temperature: void fraction: f
Intermediate thermalIntermediate thermalconfigurationconfiguration Temperature:
void fraction: fo
Stress free (relaxed) Stress free (relaxed) configurationconfiguration Temperature: void fraction: f
Thermal expansion:Thermal expansion:
Inelastic response:Inelastic response:• Flow rule:
Is the viscoplastic potential• Internal variable evolution• Damage evolution
FFp .FF
p –1.DDp
= sym(Lp) = = dT
FF = I.FF
–1.
Hyper-elastic constitutive lawHyper-elastic constitutive law
Mechanical dissipationMechanical dissipation
(1) Multiplicative decomposition framework(1) Multiplicative decomposition framework
(3) Radial return-based implicit integration algorithms(3) Radial return-based implicit integration algorithms(2) State variable rate-dependent models(2) State variable rate-dependent models
(4) Damage and thermal effects(4) Damage and thermal effects
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
THE DIRECT CONTACT PROBLEMTHE DIRECT CONTACT PROBLEM
r
n
Inadmissible region
Referenceconfiguration
Currentconfiguration
Admissible regionImpenetrabilityImpenetrability ConstraintsConstraints
Coulomb Friction LawCoulomb Friction Law
Coulomb friction law assumed at the die-work piece interface
Augmented Lagrangian approach to enforce impenetrability and frictional stick conditions
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
DEFINITION OF PARAMETER SENSITIVITY
oFn + Fn
X
xn
Fn
Bo
x+xoo
Fr + Fr
xB
xn + xn = x (Y , tn ; p + p)o ~
Qn + Qn = Q (Y, tn ; p + p)o ~
x = x (xn, t ; p)^
B’n
xn = x (X, tn ; p )~
Qn = Q (X, tn ; p )~
I+Ln
Two stage state variable sensitivity contourTwo stage state variable sensitivity contourw.r.t. parameter changew.r.t. parameter change
Design ParametersDesign Parameters
• Ram speedRam speed
• Shape of die surfacesShape of die surfaces
• Material parametersMaterial parameters
• Initial stateInitial state
Fr
x + x = x (x+xn , t ; p + p)^o o
oxn+xn
B n
B’
State sensitivity0.00600.00540.00480.00420.00360.00300.00240.00180.00110.0005
-0.0001-0.0007-0.0013-0.0019-0.0025
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
DEFINITION OF SHAPE SENSITIVITY
X = X (Y; s )
oFR + FR
Y
X
X+Xo
xn+xn
o
xn
oFn + Fn
FR
Fn
BR
Bo
I+Lo
x+xoo
Fr + Fr
x B
xn + xn = x (Y , tn ; s + s)o ~
Qn + Qn = Q (Y, tn ; s + s)o ~
x = x (xn, t ; s)^
B n
xn = x (X, tn ; s )~
Qn = Q (X, tn ; s )~
I+Ln
Stress Sensitivity15 100.0014 89.2913 78.5712 67.8611 57.1410 46.439 35.718 25.007 14.296 3.575 -7.144 -17.863 -28.572 -39.291 -50.00
Stress sensitivity contourStress sensitivity contourw.r.t preform shape changew.r.t preform shape change
Main FeaturesMain Features
• Mathematically rigorous Mathematically rigorous definition of sensitivity fields definition of sensitivity fields
• Gateaux differentials (directional Gateaux differentials (directional derivatives) referred to fixed derivatives) referred to fixed YY in the configuration in the configuration BB RR
• Key element: Key element: LLRR==FFRR FFRR--11
(velocity design gradient)(velocity design gradient)
o
X + X= X (Y; s + s)o ~
~ Fr
x + x = x (x+xn , t ; s + s)
^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 and 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
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
FRAMEWORK OF CONTINUUM SENSITIVITY ALGORITHMFRAMEWORK OF CONTINUUM SENSITIVITY ALGORITHM
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
KINEMATIC SENSITIVITY ANALYSISKINEMATIC SENSITIVITY ANALYSIS
Design sensitivity of equilibrium equation
Calculate such that x = x (xr, t, β, ∆β )oo
Continuum Lagrangian configurationContinuum Lagrangian configuration
Direct differentiationDirect differentiation
Finite element discretizationFinite element discretization
Continuum equilibrium equation (Updated Continuum equilibrium equation (Updated Lagrangian)Lagrangian)
Parameter sensitivity LR = 0o
Shape sensitivity LR = FR FR
-1
Discrete linear sensitivity Discrete linear sensitivity equilibrium equation equation
K x = fK x = f
Driving ForceDriving Force
xo
BBnn
BBnn
BBnn
o
Calculate Linear relationship between T and F , Calculate Linear relationship between T and F ,
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
SENSITIVITY CONSTITUTIVE FRAMEWORKSENSITIVITY CONSTITUTIVE FRAMEWORK
What do we need from the sensitivity constitutive sub-problem to solve the sensitivity kinematic problem ?
o oo
oo oo oo
o
o o
Relation between T and Ee , Ee and Fe and finally Fe and F
Evolution of Fp , s and F
where V = T, s, Fe
Evolution of the state sensitivity as a linear function of F , co o
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
Regularization introducedRegularization introduced
1.1. Contact sensitivity Contact sensitivity assumptionassumption
2.2. Friction sensitivity Friction sensitivity assumptionassumption
SENSITIVITY ANALYSIS OF CONTACT/FRICTIONSENSITIVITY ANALYSIS OF CONTACT/FRICTION
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
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
ParameterParameterSensitivitySensitivityAnalysisAnalysis
ShapeShapeSensitivitySensitivityAnalysisAnalysis
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
SENSITIVITY ANALYSIS OF CONTACT/FRICTIONSENSITIVITY ANALYSIS OF CONTACT/FRICTION
Sensitivity of Contact TractionsSensitivity of Contact Tractions
Sensitivity of gap and inelastic slipSensitivity of gap and inelastic slip
Normal traction:Normal traction:
Stick:Stick:
Slip:Slip:
RemarksRemarks
1.1. Sensitivity Sensitivity deformation is a deformation is a linear problemlinear problem
2.2. Iterations are Iterations are preferably avoided preferably avoided within a single time within a single time incrementincrement
3.3. Additional Additional augmentations are augmentations are avoided by using avoided by using large penalties in the large penalties in the sensitivity contact sensitivity contact problemproblem
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PERFORMANCE OF ASSUMED STRAIN ANALYSISPERFORMANCE OF ASSUMED STRAIN ANALYSIS
Without stabilization (mesh A)
F-bar method B-bar methodF-bar method B-bar method
With stabilization (mesh A)
With stabilization (mesh B)Modified sensitivity weak form (stabilized F-bar method)
Sensitivity of the assumed deformation gradient
Fh
Bn
Fndev
Fvol
Fhvol
Fh
Fh=Fh Fhvol dev
Fh
oJh
J
13
1 - εε Fh
o+Fh
o ave=
1 - ε3 ∑
a = 1
NINT
Jhaξ a tr Fh
o
aξ a Fh
-1ξ a N Jh
-1Fh tr Fh
o
Fh
-1Fh
-+
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
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
MULTISTAGE CONTINUUM SENSITIVITY ANALYSISMULTISTAGE CONTINUUM SENSITIVITY ANALYSIS
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
MULTISTAGE SENSITIVITY ANALYSISMULTISTAGE SENSITIVITY ANALYSIS
DDMDDM DDMDDM
FDMFDMFDMFDM
StateState StressStress
Validation of multistage sensitivitiesValidation of multistage sensitivities
X = X (Y, to ; )Q = Q (Y, to ; )
x = x (X, t ; X , Y )~
X + X= X (Y, to ; Y + Y)o
Q + Q= Q (Y, to ; Y + Y)o
x + x = x (X + X, t ; X , Y + Y)o o~
Y + Y
oFY + FY
Y
X
X+Xo
x+xo
x
oFX + FX
FY
Y
X
Y
FX
Bi
Bo
B’ B’o
B
I+Lo
Multi-stage sensitivity featuresMulti-stage sensitivity features• Sequential transfer of sensitivitiesSequential transfer of sensitivities• Shape sensitivitiesShape sensitivities• Parameter sensitivitiesParameter sensitivities
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
New meshNew mesh
Distorted elementsDistorted elementsin the old meshin the old mesh
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
INTRODUCTION TO REMESHING & DATA TRANSFERINTRODUCTION TO REMESHING & DATA TRANSFER
• Better-conditioned mesh qualityBetter-conditioned mesh quality• Accurately describe evolving boundary Accurately describe evolving boundary • Reasonable size of elements Reasonable size of elements
Generation of New MeshGeneration of New Mesh
• Consistency with constitutive equationsConsistency with constitutive equations• Satisfy equilibriumSatisfy equilibrium• Compatibility of history variablesCompatibility of history variables• Compatibility with boundary conditionsCompatibility with boundary conditions• Minimization of numerical diffusionMinimization of numerical diffusion
Data Transfer RequirementsData Transfer Requirements
• Mesh distortion criterionMesh distortion criterion• Error criterionError criterion• Conditioning of stiffness matrix Conditioning of stiffness matrix
Criteria for RemeshingCriteria for Remeshing• Criterion for inner anglesCriterion for inner angles• Aspect ratio Aspect ratio • Diagonal ratioDiagonal ratio• Interference with dieInterference with die
Mesh Quality CriteriaMesh Quality Criteria
• Shape function based method for nodal Shape function based method for nodal datadata
• Distance averaging using Gauss point Distance averaging using Gauss point datadata
Data Transfer Methods DevelopedData Transfer Methods Developed
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
Thermal Thermal Sub-problemSub-problem
Constitutive Sub-problemSub-problem
Contact& Friction
Sub-problemSub-problem
Remeshing &Data TransferSub-problemSub-problem
Updated Lagrangian Weak Form for Direct AnalysisUpdated Lagrangian Weak Form for Direct Analysis
Thermal Thermal Sub-problemSub-problem
Constitutive Sub-problemSub-problem
Contact& Friction
Sub-problemSub-problem
Remeshing &Data TransferSub-problemSub-problem
Updated Lagrangian Weak Form for Sensitivity AnalysisUpdated Lagrangian Weak Form for Sensitivity Analysis
Kinematic Kinematic Sub-problemSub-problem
Kinematic Kinematic Sub-problemSub-problem
DIRECT AND SENSITIVITY PROBLEMS FOR HOT FORMINGDIRECT AND SENSITIVITY PROBLEMS FOR HOT FORMING
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
DESIGN SENSITIVITY ANALYSIS WITH REMESHINGDESIGN SENSITIVITY ANALYSIS WITH REMESHING
Without remeshingWithout remeshing With remeshingWith remeshing
DDMDDM
FDMFDM
Initial solutionInitial solution
Optimization with remeshingOptimization with remeshing
Optimization without remeshingOptimization without remeshing
Desired shapeDesired shape
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CLOSED-DIE PREFORM DESIGN PROBLEMCLOSED-DIE PREFORM DESIGN PROBLEM
Preform design processPreform design process
Force reductionForce reduction
Objective:Objective: Preform design to Preform design to minimize required forceminimize required force
Optimal preform shapeOptimal preform shape
Initial preform
Optimized preform
For
ce
Stroke
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PREFORM DESIGN FOR POROUS MATERIALPREFORM DESIGN FOR POROUS MATERIAL
Objective: Minimize the flash and the
deviation between the die and the workpiece for a Preforming shape and volume designMaterial:- 2024-T351Al, 300K,
5% initial void fraction, varying elastic properties
(using Budiansky method), co-efficient of friction
between die & workpiece = 0.1
Product using guess Product using guess preformpreform
Product using optimal Product using optimal preformpreform
Distribution of shear Distribution of shear modulus in productmodulus in product
Iteration index
No
nd
imen
sio
nal
ized
ob
ject
ive
fun
ctio
n
0 2 4 6 8 10 120.003
0.004
0.005
0.006
0.007
0.008
4
5
67
8
8 2.58E+047 2.55E+046 2.51E+045 2.48E+044 2.45E+043 2.42E+042 2.38E+041 2.35E+04
Shear modulus (MPa)
2
2
4
6
7
7
8 2.59E+047 2.55E+046 2.52E+045 2.49E+044 2.45E+043 2.42E+042 2.39E+041 2.36E+04
Shear Modulus (MPa)
r - axis
z-
axis
0 0.5 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 Initialprefrom
Optimalpreform
Variation of preform Variation of preform shape with shape with
optimization iterationsoptimization iterations
Iteration number
Non
-dim
ensi
onal
obj
ectiv
e
Objective:Objective: Design the extrusion die Design the extrusion die for a fixed reduction of the for a fixed reduction of the workpiece s.t. chevron workpiece s.t. chevron defects are avoided.defects are avoided.
Initial design has chevron Initial design has chevron defects, characterized here defects, characterized here by the void fraction being by the void fraction being > 1%.> 1%.
Optimal extrusion process design
Initial extrusion process design
3
45
r - axis
z-
axis
0 1 2
-0.5
0
0.5
1
1.5
6 1.00E-025 9.00E-034 8.00E-033 7.00E-032 6.00E-031 5.00E-03
Initial void fraction = 0.01
Void fraction
Region of interest1
2
3
45
6
r - axis
z-
axis
0 1 2
-0.5
0
0.5
1
1.5
6 1.00E-025 9.00E-034 8.00E-033 7.00E-032 6.00E-031 5.00E-03
Void fraction
Initial void fraction = 0.01
Region of interest
0 1 2 3 4 5 6 7 8 9
0.88
0.89
0.9
0.91
0.92
0.93
0.94
Iteration indexN
on
dim
ensi
on
aliz
ed O
bje
ctiv
e fu
nct
ion
r - axis0.48 0.49 0.5 0.51
0.05
0.1
0.15
0.2
0.25
Final
Initial
z -
axis
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
EXTRUSION DIE DESIGN FOR CONTROL OF CHEVRON DEFECTS
Isothermal frictionless,
material withductile damage
area reduction 10.7%
1% initial voidfraction
Power law model
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
OPTIMAL PREFORM DESIGN EXAMPLE
Stress Sensitivity100.00
85.0070.0055.0040.0025.0010.00-5.00
-20.00-35.00-50.00
????
DESIGN OBJECTIVESDESIGN OBJECTIVES • Desired shapeDesired shape• Minimize material utilization Minimize material utilization • Minimize plastic work/forceMinimize plastic work/force• Desired microstructure, orDesired microstructure, or• Some of their combinationsSome of their combinations
CONSTRAINTSCONSTRAINTS • Press forcePress force• Equipments Equipments • Press temperaturePress temperature• CostCost• Material useMaterial use
Final productFinal product
DesignDesignproblemproblem
Equivalent stress sensitivity contour (14 remeshing operations)Equivalent stress sensitivity contour (14 remeshing operations)
Continuum Continuum shapeshape
sensitivity sensitivity analysisanalysis
OptimizationOptimization
Optimum preform shape ?Optimum preform shape ?
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PREFORM DESIGN – SINGLE STAGE PROCESSPREFORM DESIGN – SINGLE STAGE PROCESS
UnfilledUnfilledcavitycavity
FlashFlash
MoreMoreflashflash
Much moreMuch morematerial with amaterial with aconventional conventional
designdesign
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 10 20 30Iteration Numeber
Obj
etiv
e Fu
nctio
n
Objective:Objective: Minimize the flash and Minimize the flash and the deviation betweenthe deviation between the die and the workpiecethe die and the workpiece
for a for a Preforming shape designPreforming shape design
The sameThe samematerial in amaterial in a
conventional conventional designdesign
The sameThe samematerial withmaterial withan optimum an optimum
designdesign
NoNoflashflash
Fully filledFully filledcavitycavity
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Preforming StagePreforming Stage Finishing StageFinishing Stage
InitialInitialDesignDesign
IterationIterationNo. 2No. 2
FinalFinalDesignDesign
UnfilledUnfilledcavitycavity
LessLessunfilledunfilledregionregion
FullyFullyfilledfilledcavitycavity
Objective:Objective: Minimize the gap between Minimize the gap between the finishing die and the the finishing die and the workpieceworkpiecein a in a • two stage forging;two stage forging;• with given finishing die;with given finishing die;• unknown die but prescribed unknown die but prescribed stroke in the preforming stroke in the preforming stage.stage.
IN A MULTISTAGE DESIGN PROBLEMIN A MULTISTAGE DESIGN PROBLEM
0.0
2.0
4.0
6.0
8.0
0 1 2 3 4 5 6
Iteration Number
Ob
jec
tiv
e F
un
cti
on
(x
1.0
E-0
5)
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
Finishing StageFinishing Stage
InitialInitialDesignDesign
IterationIterationNo. 3No. 3
FinalFinalDesignDesign
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1 2 3 4 5 6 7 8
Iteration Number
Obj
ectiv
e Fu
nctio
n (x
1.0E
-04)
UnfilledUnfilledcavitycavity
LessLessunfilledunfilledregionregion
FullyFullyfilledfilledcavitycavity
Objective:Objective: Minimize the gap between Minimize the gap between the finishing die and the the finishing die and the workpieceworkpiecein a in a • two stage forging;two stage forging;• with given finishing die;with given finishing die;• unknown die but prescribed unknown die but prescribed stroke in the preforming stroke in the preforming stage.stage.
MULTISTAGE DEFORMATION PROCESSMULTISTAGE DEFORMATION PROCESS
Preforming StagePreforming Stage
Design the preforming die for a fixed volume
of the workpiece such that the variation in state in the
product is minimum
Preforming Stage Finishing Stage
State variable ( MPa )55.21053.48751.76450.04048.31746.594
State variable ( MPa )54.43151.72949.02846.32643.62540.923
1100-Al workpieceInitial temperature 673 KAxisymmetric problem Standard ambient conditions 2 pre-defined stages - preforming & finishing
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
Radius (mm)
Hei
gh
t (m
m)
Optimal design
Initial design
Average state
Initial Optimal
Deviation
50.2 52.3
3.73 1.88
DesignIn MPa
Finishing stage
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
Iteration number
Ob
ject
ive
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PREFORMING DIE DESIGN FOR CONTROL OF MICROSTRUCTURE
Preforming stage
Objective:Objective:
FUTURE RESEARCHFUTURE RESEARCH
Testing and further developments for single-stage Testing and further developments for single-stage designs with complex 2D geometriesdesigns with complex 2D geometries
Design of processes for microstructure and Design of processes for microstructure and damage controldamage control Multi-length scale design modelsMulti-length scale design models
Sensitivity analysis for texture-sensitive Sensitivity analysis for texture-sensitive designdesign Modeling and design of grain growth Modeling and design of grain growth
Simultaneous thermal & mechanical design Simultaneous thermal & mechanical design
Multi-stage forming designMulti-stage forming design Optimization framework with multiple Optimization framework with multiple constraints and competing objectives constraints and competing objectives Coupling with ideal forming & microstructure Coupling with ideal forming & microstructure evolution paths based initial designsevolution paths based initial designs Reduced order models for design & controlReduced order models for design & control
Robust materials process designRobust materials process design
Development of a 3D forming design simulatorDevelopment of a 3D forming design simulator Use most features of the 2D simulatorUse most features of the 2D simulator Remeshing & contact algorithms Remeshing & contact algorithms Industrial design applicationsIndustrial design applications
CURRENT CAPABILITYCURRENT CAPABILITY
2D forming process design2D forming process design Thermo-mechanical analyses for Thermo-mechanical analyses for materials with ductile damagematerials with ductile damage Design objectivesDesign objectives
Shape optimizationShape optimizationForce minimizationForce minimizationMaterial utilization ratesMaterial utilization rates
Forming process design considering Forming process design considering thermal effects in the diethermal effects in the die
Remeshing & data transferRemeshing & data transfer Effective remeshing based on geometric Effective remeshing based on geometric criteriacriteria Accurate data transfer techniquesAccurate data transfer techniques Assumed strain sensitivity methodsAssumed strain sensitivity methods
Other important featuresOther important features Very accurate and efficient computation of Very accurate and efficient computation of sensitivity fields (gradient calculation)sensitivity fields (gradient calculation) Innovative OOP for multistage designInnovative OOP for multistage designAccurate kinematics & contact modelingAccurate kinematics & contact modeling State variable-based constitutive modelingState variable-based constitutive modeling
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
CURRENT CAPABILITIES & FUTURE RESEARCH PLANSCURRENT CAPABILITIES & FUTURE RESEARCH PLANS
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
REFERENCESREFERENCESCONTACT VIA http://www.mae.cornell.edu/zabaras/http://www.mae.cornell.edu/zabaras/
S. Ganapathysubramanian and N. Zabaras, "Computational design of deformation processes for materials with ductile damage", Computer Methods in Applied Mechanics and Engineering, in press
S. Ganapathysubramanian and N. Zabaras, "Computational design of deformation processes for materials with ductile damage", Computer Methods in Applied Mechanics and Engineering, in press
N. Zabaras, S. Ganapathysubramanian and Q. Li, "A continuum sensitivity method for the design of multi-stage metal forming processes",
International Journal of Mechanical Sciences, submitted for publication
N. Zabaras, S. Ganapathysubramanian and Q. Li, "A continuum sensitivity method for the design of multi-stage metal forming processes", International Journal of Mechanical Sciences, submitted for publication
S. Ganapathysubramanian and N. Zabaras, "A continuum sensitivity method for finite thermo-inelastic deformations with applications to the design of hot forming processes", International Journal for Numerical Methods in Engineering, Vol. 55, pp. 1391--1437, 2002
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PREFORM DESIGN FOR POROUS MATERIALPREFORM DESIGN FOR POROUS MATERIAL
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
EXTRUSION DIE DESIGN FOR CONTROL OF CHEVRON DEFECTS
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PREFORM DESIGN – SINGLE STAGE PROCESSPREFORM DESIGN – SINGLE STAGE PROCESS
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
MULTISTAGE DEFORMATION PROCESSMULTISTAGE DEFORMATION PROCESS
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
MULTISTAGE DEFORMATION PROCESSMULTISTAGE DEFORMATION PROCESS
Materials Process Design and Control LaboratoryMaterials Process Design and Control Laboratory
CCOORRNNEELLLL U N I V E R S I T Y
CCOORRNNEELLLL U N I V E R S I T Y
PREFORMING DIE DESIGN FOR CONTROL OF MICROSTRUCTURE