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SUMMARY OF RESEARCH ACTIVITIES AT THE

MATERIALS PROCESS DESIGN AND CONTROLLABORATORY

OF CORNELL UNIVERSITY

Materials Process Design and Control Laboratory

Nicholas ZabarasMaterials 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/

CCOORRNNEELLLLU N I V E R S I T Y

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CCOORRNNEELLLLU N I V E R S I T YMaterials Process Design and Control Laboratory

FEDERAL & INDUSTRIAL SPONSORS

Industrial Sponsors

ALCOA, ATC-Materials Process Design Program

U.S. Air Force Partners

Materials Process Design Branch, AFRL

Computational Mathematics Program, AFOSR

NATIONAL SCIENCE FOUNDATION (NSF)

Design and Integration Engineering Program

NATIONAL SPACE ADMINISTRATION (NASA)

Microgravity Materials Science Program

MaterialsProcess

Design &

ControlLaboratory

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Mathematical and computational background

Computational mathematics and mechanics Inverse problems Computational process and product design Robust design: designing under uncertainty Robust control of continuum systems

Interfacing information technologies with engineering

Applications

Coupled thermal, flow and mechanical problems Deformation processes

Solidification and crystal growth processes Casting and quenching processes Computational materials science

Materials Process Design and Control LaboratoryCCOORRNNEELLLLU N I V E R S I T Y

BACKGROUND AND TECHNICAL AREAS OF EXPERTISE

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Finite element techniques for problems in solid

mechanics, fluid flow, thermal processes andmaterials sciences

Lagrangian large deformation inelastic analysis Stabilized FEM for multiphase flows Modeling of complex materials processes

Residual stresses and damage

Adaptive remeshing and error estimation

Using level set methods, phase field models andfront-tracking techniques to capture moving

interfaces and fronts

Parallel and object-oriented implementations


COMPUTATIONAL TECHNIQUES FOR DIRECT ANALYSIS

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Inverse problems with insufficient initial or boundary conditions

or incomplete material data

Functional optimization techniques for coupled inverseproblems (transport processes/deformation/flow/MHD)

lll-posed problems and regularization techniques

Process or material property estimation using incompleteexperimental continuum data

Model (PDE) estimation for experimental data matching

Non-destructive damaged region shape and propertyidentification

Adjoint and sensitivity techniques implemented using aninnovative OOP approach


INVERSE PROBLEMS

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MELT

SOLID

G ,V

qos

qol

g

Bo



SOLIDIFICATION PROCESS DESIGN

OBJECTIVES

Obtain desired microstructures and/ormacro/micro crystal homogeneity

Controlling the effects of convection on thesolidification microstructures

0.

0001

0.

01

1

100

0.1 10 1000G (k/mm)

Thermal gradient (G) and growthvelocity (V) are the main

parameters that set the form andscale of cast microstructures

V

(mm/s)

DESIGN VARIABLES

Cooling/heating conditions (furnace design)

Electromagnetic stirring and volumetric heating

COMPUTATIONAL METHODS

Continuum sensitivity and adjoint methods

Volume averaging multiphase FEM models

Explicit modeling and design of microstructures

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MaterialProcessDesign

Simulator


AN OBJECT-ORIENTED FRAMEWORK FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION

SensitivityHeat

SensitivityFlow

SensitivityConc

AdjointConc

AdjointHeat

AdjointFlow

DirectFlow

DirectHeat

DirectConc StabNavierStokes

ConvectionDiffusion

MenuUDC

Store4Plotting

LinearSolver

MenuUDC

Store4Plotting

FEM

Direct

Adjoint

Sensitivity

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A gradient based optimization approach to simulated models

competing design objectives and constraints

Development of the continuum sensitivity method (CSM) forcoupled thermal-flow-deformation processes forming process design casting and crystal growth process design

Algorithms for initial design and process sequence in multi-stage process design

Framework for web-based forming design

Multi-length scale design problems

Robust design designing under uncertainty


COMPUTATIONAL PROCESS AND PRODUCT DESIGN

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With minimum cost and environmental impact, DESIGN:Casting processSequence of forming &Thermal stages

such that:


MATERIALS PROCESS DESIGN: AN INTEGRATED APPROACH

FORMING THERMAL PROCESSINGCASTING Response depends on the initial

microstructure and stresses

Non-uniformity on microstructure

persists

Cannot eliminate casting defects

Process response sensitivity to

initial state

Microstructure type and size

Segregation

Non-uniform properties

Surface and internal

cracking

Surface appearance

Residual stresses

Some control on the

size and

microstructure type

Time consuming

Workpiece size limited

Requires knowledge of

initial state

With a given castproduct, design

forming sequencefor shape and state

control

FORMINGCASTING

Design fordesired state

and defect freecast product

Design thermalhistory for

micro-structurecontrol

THERMAL

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A VIRTUAL DEFORMATION PROCESS DESIGN SIMULATOR

MaterialProcessDesign

Simulator

Selection of the sequence ofprocesses (stages) and initialprocess parameter designs

knowledge based expert systems microstructure evolution paths

ideal forming techniques

Selection of the designvariables (e.g. die and

preform parametrization)

Optimizationalgorithms

Continuum multistage processsensitivity analysis consistent

with the direct process model

Assessment of automaticprocess optimization

Reliability of the design touncertainties in the physical

and computational models

Mathematical representation of

the design objective(s) &

constraints Selection of a virtualdirect process model

InteractiveOptimizationEnvironment

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COMPUTATIONAL DESIGN OF FORMING PROCESSES

Press force

Processing temperature

Press speed

Product quality

Geometry restrictions

Cost

CONSTRAINTSOBJECTIVES

Material usage

Plastic work

Uniform deformationMicrostructure

Desired shape

Residual stresses Thermal parameters

Identification of stages

Number of stages

Preform shapeDie shape

Mechanical parameters

VARIABLES

BROAD DESIGN OBJECTIVESGiven raw material, obtain final product with desired microstructureand shape with minimal material utilization and costs

COMPUTATIONAL PROCESS DESIGNDesign 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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Quantify the propagation of uncertainty in material and process

data and its effect on the computed designs

Develop distributed spectral SFEM to quantify, approximate, andcompute the stochatic nature of continuum fields governed byPDEs

Develop mathematical tools that allow us for a trade-off between the achievable design objectives, needed confidence on material and process data and the design reliability

Examine tail probabilities of the output and their importance in

the design reliability


ROBUST DESIGN DESIGNING WITH UNCERTAINTY

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SPECTRAL STOCHASTIC FINITE ELEMENT ANALYSIS AND DESIGN


STOCHASTIC PDEINPUT PARAMETERS

CONSTRAINTSBOUNDARY CONDS.

MODELLED ASRANDOM

PROCESSES

SPECTRAL STOCHASTIC FEM

UNKNOWN FIELDS ARE DISRCETIZED

AS SERIES OF RANDOM VARIABLES

CONSTRAINTS ARE ALSO

STOCHASTIC PROCESSES

OUTPUT FIELDS

OBTAINED AS

PDFS

RANDOM FIELD DISCRETIZATION(1) For Gaussian processes: Karhunen-Loeve expansion

(2) For non-Gaussian processes: Polynomial chaos expansions

where,

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ROBUST MATERIALS PROCESS DESIGN

Initial

deterministicdesign

Select randomvariables &

responses(SFEM)

Select areduced set of

randomvariables

Reliability &Robustness

analysis

ReliableAnd/Or

Robust?

Reliabilitybased designoptimization

Update reducedset of randomvariables

Add probabilisticconstraints

Optimizedprobabilistic

design

No

Yes

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Accelerated processsequence design

Minimal overall cost:force, energy, etc.


Robust design leads to a product withmaterial and geometric specifications withdesired confidence intervals:

it accounts for uncertainty/variability in thematerial and process data it provides the sensitivities of the key design

objective related fields with respect to stochasticmaterial and process data or design variables

improves confidence in design when newraw materials/processes are used

Raw Material

Billet

Workpiece

PROCESS DESIGN FOR TAILORED MATERIAL PROPERTIES

MaterialsProcessDesign

Simulator

Tailored materialproperties in the

final product Desired

microstructuralfeatures

Desired spatialdistributions ofstate variables

Controlled texture,recrystallization,

fracture & porosity

Desired shape withminimal material

utilization

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A VIRTUAL ENVIRONMENT FOR AN ACCELERATED MATERIAL AND PROCESS INSERTION

DIGITAL MATERIALSINFORMATION

LIBRARY

Required productwith tailored

material

properties anddesired shape

Response surfaces

Sensitivity of

measurable dataw.r.t. material and

process parameters

etc.

Computed list

of important

material &

process data

and theiracceptable

levels of

variability

Select key material testing

Select best possible sensing for

required measurement accuracy

Select test parameters

Experimental evaluation of

required data

DataMining&

Ma

terial

TestS

election

Virtual

MaterialsProcessDesign

SimulatorRaw material

ReferenceProperties

Library

Development

Simulate material tests

at various conditions

(tension, compression) Simulate deformation

process tests (forging,

extrusion, etc.)

etc.

OFFLINE USE OFVIRTUAL MATERIALS

PROCESS ANALYSIS &DESIGN SIMULATORS

PHYSICAL MATERIALTESTING

UPDATE MATERIAL &PROCESS DATA

Capture StochasticNature of Material & Process

Data?

NoYes Robust designprocess is

completed

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Alloy flow stress

Material point data

Profile output data


DIGITAL ALLOY LIBRARY FOR PCG EXTRUSION DESIGN

Billet input data


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3

4

+

6

_

1

2 5

LIBRARYDirect & Sensitivity fields, Reduced

Basis

+

__

SuperComputing

Process

Modeling

Mathematical

Control

Design

Algorithms

Material

Process

Design of Reference

State

Sensing of

Continuum

fields

Data

Compression

Information

Transmittal Scheme

Data

Uncompression

Initial Design

of Actuators

and Sensors

Computation Analysis

Based Data

Experimental Analysis

Based Data

Change

Parameters

Build Library

Update

Library

Off Line

Experimental

Analysis

Controller

Selection of Choice ofReduced order Sensors andModel Actuators

Data Anal sis

COMPUTATIONAL SENSORICS: ROBUST FEEDBACK CONTROL OF CONTINUUM SYSTEMS

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Reduced-order models for continuum systems

Proper orthogonal decomposition, Karhunen-Loeve basis Reduced modeling based on Voronoi-tesselations

Reduced-order modeling of adjoint and sensitivity fields

Optimality conditions & controllability

Feedback laws for continuum systems sub-optimal and ad hoc feedback laws the design-then-approximate approach to controller design designing locally optimal feedback laws using linear low-

order state models

Robust control and uncertainty

Feedback control of thermal-flow systems


ROBUST CONTROL OF COMPLEX CONTINUUM PROCESSES

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Interfacing information technologies with computational designand control of complex continuum systems and processes

Build digital libraries of process responses, effects of actuation techniques, experimental snap shots, alternative reduced order dynamical models, etc.

Develop distributed techniques for data and dynamical modelmining for continuum systems

Advanced sensing and actuation techniques

Data compression and transmission techniques reduced order models for experimental snapshots


COMPUTATIONAL SENSORICS: INTERFACING IT WITH ENGR

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Data and dynamical model mining for continuum systems

predictive modeling, data classification and regressiontechniques

classification and regression techniques for dynamical models

virtual environments

neural networks for pattern recognition

scaling clustering algorithms for mining association rules

generalized search trees for database systems

information retrieval and distributed databases

digital libraries for continuum systems


DATA AND MODEL MINING FOR CONTINUUM SYSTEMS

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DATA MINING: a statistical methodology for the automatedextraction of predictive information from a large database

DM TYPES: segmentation and classification (binary, multi-class), association rule extraction, sequence detection, andforecasting

DM ALGORITHMS: mainly k-nearest neighbor, neuralnetworks (iterative and non-iterative), rule induction, decisiontrees (i.e. CART), and genetic algorithms

DM MODELS: Built using DM algorithms. Used qualitatively

and quantitatively. Useful models denote interacting andsupporting system components.


DATA AND MODEL MINING

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