A Method for Combining Experimentation and Molecular Dynamics Simulation to Improve Cohesive Zone Mo

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A Method for Combining Experimentation and
Molecular Dynamics Simulation to Improve Cohesive
Zone Models for Metallic Microstructures
Jacob Hochhalter1,2 Miguel Aguilo1 Prof.
Anthony Ingraffea1 Dr. Edward Glaessgen2 Prof.
Wilkins Aquino1
1School of Civil and Envr. Engineering Cornell
University Ithaca, NY
2Durability, Damage Tolerance Reliability
Branch NASA Langley Research Center Hampton, VA
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Outline

• Multiscale Fracture Simulation
• Molecular Dynamics (MD) Simulation
• Extracting Cohesive Zone Model (CZM) Parameters
• The Scale Issue
• Experimental Measurements
• Full-Field, High-Resolution Strain Mapping
• Inverse Problem
• Reconstructing CZM Parameters
• The Uniqueness Issue
• Combine 2, 3, and 4 to Help Reconcile the
  Issues

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Multiscale Fracture Simulation
RD
ND
250 ?m
RD
Structural Detail
Microstructural Scale
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Multiscale Fracture Simulation The Scale Issue
Must assert the crack growth mechanisms and
calibrate critical values of metrics that
simulate those mechanisms
Observed Crack Path
Plasticity 1
1Maniatty et al., IJNME 60 (2004)
Fracture 2
Cohesive Zone Model (CZM)
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2Park et al., JMPS 57 (2009)
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Combine Two Approaches to Determine CZM
Parameters
VIC

• The Scale Issue
• Computing atomic motion becomes intractable
• 1 ?m cube of aluminum gt 15 billion atoms
• lt 1 ?s (with Accelerated Dynamics)
• Highly idealized material (purity, structure)

• The Scale Issue
• Observing atomic motion is currently not
  possible
• 1 nm displacement resolution
• 1 s observation snapshots
• Fabrication of a pure crystal is
  difficult/impossible

?

• What comparisons can be made - qualitatively,
  quantitatively?
• What damage processes can we begin to reconcile?
• What inherent differences between modeling and
  testing must be overcome?

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MD Simulation Extracting MD-Based Cohesive Zone
Model (CZM) Parameters
System size MD domain 40 nm (360,000
atoms) FEM region 1 ?m (15,000 d.o.f.)
Nanometer-Scale CZVE 1250 atoms
Response from Concurrent Multiscale
Typical Values at Microscale ?p 500 MPa ?0
1 ?m
Tractions Displacements
Crack Tip Constitutive Response
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1Yamakov et al., JMPS 54 (2006) 1899
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Experimental Procedure
Single Crystal Aluminum
Vacuum Arc Melter / Crystal Puller
Development of Bi-crystals
100 ?m
Load Stage
10-50 nm gold spheres
?m
VIC Displacement Field
SEM
Displacement resolution lt 1 nm
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Inverse Problem Reconstructing CZM Parameters
from Experiment
The spatial distribution of material properties
can be reconstructed from the measured system
response to an applied load using the finite
element method and optimization algorithms.
Reconstruct Material Properties e.g. Youngs
Modulus, Poisson Ratio, CZM Parameters, etc.
Known Geometry, Boundary Conditions, etc.
Measured System Response e.g. displacements
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Inverse Problem Flowchart
Measure displacement field, ue
Define potential-based CZM
Initialize
MD-based CZM
No
Take current values as solution
Yes
Reconcile the distinct CZMs
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Gradient-Based Optimization Computing the
Gradient
- The cost is 2m1 times the cost of solving one
forward problem - Additional perturbation
parameter that has no physical meaning Easy
Finite Difference
Too Costly for Typical Microstructures
- The cost is m1 times the cost of solving one
forward problem No perturbation parameter
Direct Method
- The math is tedious The cost is 2 times the
cost of solving one forward problem No
perturbation parameter
Adjoint Technique
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Inverse Problem Mathematical Statement
Consider the following optimization problem
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Inverse Problem Reconstructing Material Model
Parameters
Geometry Boundary Conditions
Shear Modulus
Target Solution
Adjoint Technique Approximation
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Combine to Help Reconcile the Scale and
Uniqueness Issues

Ductile
Brittle

• MD-Based CZMs Supply a Physical Basis to the
  Uniqueness Issue
• Inverse Methods Supply an Approach to Reconcile
  MD with Experiment

Park et al., JMPS 57 (2009) 891
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Yamakov et al., JMPS 54 (2006) 1899
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Summary

• Methods for extracting cohesive zone models (CZM)
  from molecular dynamics (MD) simulations have
  been developed and provide qualitatively accurate
  models.
• A VIC experimental method that uses an SEM to
  measure displacements at sub-nanometer resolution
  provides surface data during crack growth.
• An inverse method has been developed that
  requires only 2 forward runs and is independent
  of the number of spatially varying search
  parameters.
• These 3 methods are being combined to provide
  improved techniques for determining CZM
  parameters and, in turn, provide a method to
  reconcile experiment with MD simulation of crack
  growth.

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