DYNAMICAL EVOLUTION OF TEXTURE IN POLYCRYSTALLINE METALS UNDER HIGHSTRAIN RATE CONDITIONS

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DYNAMICAL EVOLUTION OF TEXTURE IN POLYCRYSTALLINE
METALS UNDERHIGH-STRAIN RATE CONDITIONS

• Zisu Zhao
• Raul Radovitzky
• Department of Aeronautics and Astronautics
• Massachusetts Institute of Technology
• Cambridge, MA

Stephen Kuchnicki Alberto M. Cuitiño Department
of Mechanical and Aerospace Engineering Rutgers
University Piscataway, NJ
International Symposium on Plasticity and its
Current Applications Quebec City, Canada July
7-11, 2003
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Main Motivation

• Physically-based models that properly capture the
  physics (e.g. multiscale modeling)
• Algorithms and modeling techniques that properly
  exercise the models (e.g. DNS or Taylor)
• Implementation and computational capabilities
  that provide proper spatial and temporal
  resolution (e.g. massive parallel environments)

• To develop high-fidelity models and simulation
  capabilities for describing multiphysics
  scenarios subjected to high strain rates, for
  example fluid-solid systems under explosive
  conditions

Pressure
Detonation
Only the solid region is shown
Plastic Deformation
ASCI Center for the Dynamic Response of Materials
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Models Multiscale Paradigm
time
hours minutes seconds microsec nanosec picos
ec femtosec
Multiphysics Multicomponent Systems
Grains

• Resolve (as opposed to model) mesoscale behavior
  exploiting the power of high-performance
  computing
• Enable full-scale simulation of engineering
  systems incorporating micromechanical effects.

Single Crystal
Stainier, Cuitino and Ortiz (JMPS) 2002 Cuitino
et al (JCAMD) 2002
Energetics
distance
Å nm micron
mm cm meters
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Objectives

• Quantitative assessment of microstructural
  effects in macroscopic material response through
  Direct Numerical Simulations (DNS) computation of
  full-field solutions of polycrystals
• Inhomogeneous plastic deformation fields
• Grain-boundary effects
• Stress concentration
• Localization of slip and dislocation pile-up
• Constraint-induced multislip
• Size dependence (inverse) Hall-Petch effect
• Texture evolution
• Assess the degree of approximation of main field
  approaches, such as Taylor, by consistently
  comparing Taylor to DNS

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Inhomogeneities
Taylor Anvil Test
Direct Numerical Simulation (DNS)
Taylor Average
Radovitzky and Cuitino, 2003
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InhomogeneitiesTaylor anvil test 100 grains
1M elements
Plastic Activity
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Inhomogeneities (grain to grain)Taylor anvil
test 100 grains 1M elements
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Inhomogeneities (within grains)
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Textures

• Selection of a well-characterized case
  experimental test (rolling)
• Selection of a well-characterized grain shape and
  topology (Space filling polyhedron)
• Selection of a well-know material model (Pierce,
  Asaro, Needleman)

Advantages1. Retains basic properties of grain
shape and topology (usually violated by
grain-growth models due to meshing
difficulties)2. Boundaries are flat, sharp
interfaces3. Easy to mesh4. Highly scalable
(with the aid of scalable meshing)5. Useful tool
for polycrystal simulations DisadvantagesRestric
tive grain geometry and topology
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Single Crystal accumulated slip
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Single Crystal 111 Pole Evolution
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Single Crystal Misorientation
Accumulated misorientation between crystals
initial orientation and current orientation
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Polycrystals

• Sample size 1e-3 x 1e-3 x 1e-3 (m3)
• Strain speed -50 (m/s)
• 3 grains along each side
• 91 grains were used
• parallel computing on 91 processor
• crystalline orientations were assigned randomly
  to each grain
• 10368 tetrahedral elements
• 42 reduction was reached.

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Polycrystals 111 Pole Evolution
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Polycrystals Texture (42 reduction)
Levels 1, 2, 3, 4
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Orientation Distribution Function
Texture components in rolled FCC metals.
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Polycrystals Texture (49 reduction)
Levels 1, 2, 3, 4, 5
TAYLOR
Same mesh to keep the same spatial resolution
(91 orientations per sampling point)
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Taylor and DNS
RD
RD
DNS
TAYLOR
TD
TD
TAYLOR (Blue) DNS (Red)
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Taylor - DNS
Levels 1, 2, 3
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Taylor and DNS

1
C
S
B
G
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Taylor and DNS
F
F
j 2
j 2
j 1
j 1
Sharper Texture
DNS
TAYLOR
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Taylor and DNS
Macroscopic Response
TAYLOR
DNS
Stiffer Response

• Number of orientations
• Spatial Resolution

Two issues
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Taylor Orientations
91 orientations per sampling point
or 384 orientations per sampling point
Negligible differences are observed
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Taylor Resolution
O subdivision 10,368 tetrahedral elements 1
subdivision 82,944 tetrahedral elements
More high-frequency dumping for coarser meshes
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DNS Orientations
384 grains 50 reduction
Increase number of orientations by reducing
spatial resolution within each grain. Extreme
case one element per grain,
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Taylor and DNS
Spatially resolved DNS
Lowest Resolution DNS
Taylor
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Role of Spatial Resolution on DNS
192 cells/grains
12,288 cells/grains
1,536 cells/grains
Required to properly capture the physics at
mesoscale
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Feasibility with current platform
103 elements

• 1Gel at our disposal (1Mel/proc x 1000
  processors), 1000 elements
• per direction
• 25K elements/2 grains to resolve inhomogeneous
  plastic fields
• (many more for subgrain structures, PSBs,
  etc.)
• 80K grains (40 per side)
• 2 mm specimen size for 50 mm grain size

103 e
109
103 e
2 grains (25K at subdivision 2) 1 full grain
(12K at subdivision 2) 8 1/8 of grain (12K at
subdivision 2)
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Summary and future work

• Two complementary full-field studies are
  considered to investigate the texture evolution
  Direct Numerical Simulation (DNS) of each crystal
  and a mean field approach, Taylor-averaging
  (TA).  
• DNS allows for explicit account of
  microstructural features including grains shape,
  size, orientation and distribution in macroscopic
  response
• Size Dependency
• Other metals (BCC)
• Grain Boundary effects
• Multiscale models

With the increasing of grains number, grains
sizes are reduced
Stainier, Cuitino and Ortiz (JMPS) 2002
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ABAQUS 1 element - 1 grain, 512 grains, 50
reduction