multiscale modeling of

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multiscale modeling of ductile polycrystals 
SD Group Leader Michael Ortiz,
Caltech Presenter Alberto Cuitino,
Rutgers Abhishek Bhattacharyya , Guruswami
Ravichandran, Zisu Zhao, Caltech Ronald Cohen,
Xianwei Sha, CIW Emily Carter, Princeton Thomas
Gray, Jennifer Smith, Raul Radovitzky, MIT Kinjal
Dhruva, Stephen Kuchnicki, Rutgers LLNL - Road
Show May 16, 2005
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Dynamic Deformation Length Scale Hierarchy
Polycrystals (Averages)
ms
Multicrystals (DNS)
Oligocrystals (DNS)
Grains (DNS)
time
µs
Subgrain structures
SHPB, SCS
Atomistic
EBSD, SEM, DIC
TEM, OM
ns
nm
µm
mm
length
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Validation

• Simulation-driven design of experiments in close
  collaboration with Experimental Group with
  detailed diagnostics
• Shear Compression Specimen and
• Tensile Test
• Full-field characterization of polycrystal
  response comparison of local features through
  Digital Image Correlation
• Microtexture and microstructure evolution through
  EBSD/OIM
• Effective response Flow stress as a function of
  strain, strain rate and temperature

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Dynamic Deformation Length Scale Hierarchy
Polycrystals (Averages)
ms
Multicrystals (DNS)
Oligocrystals (DNS)
Grains (DNS)
time
µs
Subgrain structures
SHPB, SCS
Atomistic
EBSD, SEM, DIC
Next Talk 1040 AM Ronald Cohen
Thermoelasticity of Fe from first principles
TEM, OM
ns
nm
µm
mm
length
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Dynamic Deformation Length Scale Hierarchy
Polycrystals (Averages)
ms
Multicrystals (DNS)
Oligocrystals (DNS)
Grains (DNS)
time
µs
Subgrain structures
SHPB, SCS
Atomistic
EBSD, SEM, DIC
TEM, OM
ns
nm
µm
mm
length
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Multires Material Validation
SCS
Simulation
Material
VALIDATION
Previous Talk (920 AM) G. Ravichandran
Dynamic shear-dominant deformation experiments
in metals
Experiment
Tests Specimens
Simulation
VALIDATION
Experiment
Dogbone
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Macro-scale validation SCS
Previous Talk (920 AM) G. Ravichandran
Dynamic shear-dominant deformation experiments
in metals
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Macro-scale validation SCS
Dynamic
Evolution History
Deformation
Quasi-static
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What can we get from large-scale polycrystal
simulation?
Taylor averaging
One element per grain
DNS
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Micro-scale validation Dog Bone
Simulations
Simulation Running
Macroscopic Mechanical Response
Surface Roughening Profiles
Local Orientation Changes
Full-Field Deformation
Orientation Mapping from EBSD
Experiment
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Orientation Mapping from EBSD
Al Sample 3
OIM Map of Side A
The grains are matched with those on the other
side and the sample is found to be columnar as
before.
Microstructure of Side A
This picture shows the sample microstructure
under optical microscope . The picture is created
by joining the maps of different areas of the
sample.
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OIM Map of Side A
Grain 1
Grain 8
X0
Grain 2
Grain 9
Grain 10
Grain 3
Grain 5 (note the grain is colored yellow)
Grain 7
Grain 6
Grain 11
Grain 4
Grain 12
Grain 13
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Simulations
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Micro-scale validation Dog Bone
DIC(preliminary testing)

• Samples deformed in uniaxial tension
• Quasi-static rate (10-2/s or lower)
• One image taken every 500 ms
• Quality of correlation varies with deformation
• step between images

Image 1
Image 100
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Micro-scale validation Dog Bone DIC
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Global DIC
Profiles of gray levels
Over-imposed mesh
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Global DIC Dog Bone
Grid is superimposed over sample Grid size (and
deformation) measured in pixels Greater image
resolution allows finer deformations to be
detected
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Global DIC Coarse correlation
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Micro-scale validation example DIC
Digital Camera
Sprayed gray scale pattern onsurface of
undeformed sample
Schematical drawing indicating the initial array
and distorted array containing a matching gray
scale distribution
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Micro-scale validation example Surface
Roughening
Preliminary results
Zygo equipment
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Current Status and In-Progress Activities of
Validation Dynamic response of Polycrystals

• Validation against SCS experiments
• Comparisons of micro-features texture evolution
  under dynamic conditions reproduced in two
  different cases
• DNS ASC Platforms are the enablers
• Validation against Dog Bone Tensile test
  experiments
• Comparisons of micro-features texture evolution
  under static conditions
• Grain profile from EBSD
• Strain localization from DIC
• Surface roughening profiles
• Local orientation changes
• DNS ASC Platforms are the enablers

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Coupling (multiscale) Plasticity and Diffusion
during void growth and coalescence in solids
Alberto Cuitino1, Kinjal Dhruva1, Michael
Ortiz2 1 Department of Mechanical Aerospace
Engineering,Rutgers University,NJ 2 Graduate
Aeronautical Laboratories,California Institute of
Technology
ASC Road Show,LLNL May 16,2005
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Coupling (multiscale) Plasticity and Diffusion
during void growth and coalescence in solids

• Dynamic fracture is characterized by high strain
  rates that are associated with impulsive loading.
  As a result of such impulsive loading there is a
  build up of tensile stresses in materials leading
  to a fracture mechanism commonly referred as
  spall damage.

Void Growth in Crystals
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Velocity Driven Interfaces

• Complex geometries and complex topological
  changes can be represented by using implicit
  functions to represent interfaces that are
  growing under an arbitrary velocity field.
• Subsequent interface motion under the velocity
  field v is governed by the equation

• Velocity field for subsequent motion of may
  depend on any of the following factors
• Position
• Time
• Geometry of interface (e.g. its normal or its
  mean curvature)

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Velocity Driven Interfaces
Velocity Field
fplasticity
fvacancies

• Dynamic Elasto-Plasticity
• Mechanics Equations
• Hardening Laws
• Flow Rule

Vacancy Diffusion -Surface Bulk
diffusion -Diffusivity of material -Curvature and
gradients
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Velocity Driven Interfaces
Elasto-plastic Equations
Diffusion Equation
Elasto-Plastic Equations in Conservative Form
Subject to Boundary Conditions

Radial Return Method
Mie-Gruneisen e.o.s
Yield Criteria
Radial Return
Equations governing plastic deformation
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Approach

(Diffusion Eqn.)
(Dynamic Elasto-plastic eqns.)
Why Periodic Boundary Condition ?
Implicit Boundary Conditions ensure that the
solution domain can be used as a Representative
Cell
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Key Features of Scheme

• GHOST METHOD
• Ghost nodes are created corresponding to each
  grid node that have a neighboring point lying on
  interface.
• Values of flow variables at ghost nodes are
  computed using a local reconstruction scheme.
• Standard numerical schemes are used over the
  entire domain once the ghost nodes are defined

LEVEL SET REPRENTATION The advance of
level-set is governed by solution of
equation
This method represents a complex geometry using
an implicit level- set function f(X,t)
defined at every grid point having the following
properties f(X,t)lt0 Inside the
interface f(X,t)gt0 Outside the interface
f(X,t)0 Interface

• IMAGE ANALYSIS
• Complex topological changes associated with void
  growth are very hard to quantify.
• The image analysis capabilities of MATLAB allows
  us to analyze the properties associated with void
  growth like
• -Area
• -Effective Radius
• -Growth Rate

(Sethian, Aslam)
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Evolution of Single Void Under Different Mechanism
Void Growth by Diffusion
Void Growth by Plasticity
Combined Void Growth
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Void Growth and Coalescence in Multiple Voids
Effective Plastic Deformation
Stress Along x-axis (Sx)
U-velocity
Void Interface
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Animation for 2D Void Growth of Multiple Voids
U-velocity
Stress(Sx)
Effective Plastic Deformation (Ep)
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Stages in Evolution of Multiple Void
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Simulations for 2D 3D Multiple Void Growth
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Animation with Contour Profile at Void Interface
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Conclusion and Planned Work

• Conclusions
• A framework for an efficient numerical scheme
  incorporating the physical phenomena behind void
  growth and coalescence was developed.
• Numerical scheme was found to be stable during
  the complex topological changes that were
  encountered during void growth and subsequent
  coalescence.
• The rate of void growth can be estimated using
  the techniques of image analysis.
• In Progress
• Introduce multiscale model.
• Large number of voids utilizing ASC Platform.
• Exploring shock-capturing schemes such as
  upwinding methods