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


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




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




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




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




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)




DESIGN OF MULTI STAGE DEFORMATION PROCESSES




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




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)




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.





COMPUTATIONAL MULTI-STAGE FORMING DESIGNCOMPUTATIONAL MULTI-STAGE FORMING DESIGN


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




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




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




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




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




FRAMEWORK OF CONTINUUM SENSITIVITY ALGORITHMFRAMEWORK OF CONTINUUM SENSITIVITY ALGORITHM




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 ,




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




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




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




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


MULTISTAGE CONTINUUM SENSITIVITY ANALYSISMULTISTAGE CONTINUUM SENSITIVITY ANALYSIS




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



New meshNew mesh

Distorted elementsDistorted elementsin the old meshin the old mesh



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





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




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




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




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




EXTRUSION DIE DESIGN FOR CONTROL OF CHEVRON DEFECTS

Isothermal frictionless,

material withductile damage

area reduction 10.7%

1% initial voidfraction

Power law model




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 ?




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




Preforming StagePreforming Stage Finishing StageFinishing Stage

InitialInitialDesignDesign

IterationIterationNo. 2No. 2

FinalFinalDesignDesign


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)

http://www.mae.cornell.edu/zabaras/Publications/PDFiles/INVITEDTALKS/AFRL-Presentation-April-23-01/movies/dhump_2StageDieDesign.avi




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)


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

http://www.mae.cornell.edu/zabaras/Publications/PDFiles/INVITEDTALKS/AFRL-Presentation-April-23-01/movies/Chenot_2StageDieDesign.avi

http://www.mae.cornell.edu/zabaras/Publications/PDFiles/INVITEDTALKS/AFRL-Presentation-April-23-01/movies/Chenot_2StageDieDesign.avi

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




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




CURRENT CAPABILITIES & FUTURE RESEARCH PLANSCURRENT CAPABILITIES & FUTURE RESEARCH PLANS




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




PREFORM DESIGN FOR POROUS MATERIALPREFORM DESIGN FOR POROUS MATERIAL




EXTRUSION DIE DESIGN FOR CONTROL OF CHEVRON DEFECTS




PREFORM DESIGN – SINGLE STAGE PROCESSPREFORM DESIGN – SINGLE STAGE PROCESS




MULTISTAGE DEFORMATION PROCESSMULTISTAGE DEFORMATION PROCESS




PREFORMING DIE DESIGN FOR CONTROL OF MICROSTRUCTURE

computational design of multistage deformation processes

Documents

design variables

design of preformsdesign

forming design processes

control laboratoryprof

processes innovative

sequence of processes

sensitivity analyses

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