Application of MesoMicroNano Scale

1
Application of Meso/Micro/Nano Scale Heterogeneous
Materials for Impact and Blast Resistance
NAMAS CHANDRA Department of Mechanical
Engineering Florida State/Florida AM
University Tallahassee FL 32310 August 24 2005
2
Impact and Blast
Material selection under high velocity impact
should

• Absorb high energy in a contained manner
• Be light weight

Composite Armored Vehicle
Composite face-sheet
Ceramic tile
Rubber pad
Composite back-plate
Composite Integral Armor (for the hull of a tank)
3
Other Blast Situations?
4
Armor and Anti armor materials
5
Key Issues in Macro composites

• Key issues of ballistic impact response of
  engineering composites

• Effects of material inelasticity and damage
  evolution
• Effects of wave scattering and propagation

• Problem idealizations (at the scale of a lamina)

Planar interface
Periodically planar layered system
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Periodically Layered System Under Impact Loading

• Plate impact is a standard diagnostic test
  configuration used to characterize
• the impact response of materials

• Uniaxial strain state in the center

• Stress history and particle velocity history
  Wave profiles

7
The stress wave profile of a monolithic metallic
material

• A wave profile contains rich information about
  the dynamic material behavior

• Structured three portions rise, pulse duration
  and unloading

• Task the structural response of layered systems
• Effects of material heterogeneity on wave
  interactions at interfaces
• Structure of the stress wave profiles

8
Wave scattering at interfaces

• Exact solution - dispersion explicitly accounted
  for by tracing all wave
• reflections and transmissions

• In elastic regime, wave scattering is
• determined by material heterogeneity
• factors

• Impedance mismatch

• Interface density number of wave interactions.

• Thickness ratio the wave train patterns in a
  periodic layered system.

N. Chandra, X. Chen and A. Rajendran, Journal
of Composites Technology and Research, 24 (4),
232-238, 2002.
9
Approach of the analytical solution to plate
impact problem
X. Chen, N. Chandra and A. Rajendran,
International Journal of Solids and Structures,
41, 4635-4659, (2004).
10
Stress Boundary condition of the target plate in
plate impact problem
Wave trains reaching impact plane sequentially

• Stepwise stress increments (with time delays)

Step 1
Step 2
where
Step 3
or
or

Stress boundary condition at the impact plane
keeps varying due to wave scattering!
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Formulation

• Equation of Motion

• Velocity continuity

• Constitutive relation

Unit step loading
Idealized plate impact

• Stress and velocity continuity at all interfaces

Where

• Stress Boundary condition

(unit step loading)
(plate impact loading)
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Dispersion Relations

• Floquets theory ODEs with periodic
  coefficients

• Dispersion relation Effective wave speed as a
  function of frequency

• Zero frequency limit wave speed Let

Equilibrium Wave speed
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Analytical Elastic Solution

• Effective stress boundary condition

• Superimpose the first n steps

• Solution for plate impact problem when n4

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Far Field (late time) solution

• Characteristic distance for far-field
  solution ( )

Head wave dies out
Identify
Low interface density, small I large

• Effect of number of steps N

• For systems with big I, N1 is applicable

Equivalent loading condition
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Shock Waves Regime

• Hydrodynamic treatment

s
HEL (Hugoniot Elastic Limit)
Shear stress is neglected

• Fundamental requirement for the
• establishment of a shock wave

• Equation of State (EOS)

Incident stress upon impact
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shock waves in periodic bilaminates

• Structural response of periodically layered
  systems in elastic and shock wave regime

• Similar wave scattering process
• Sustain steady state in the wave structure.

Shock response
Elastic response
Elastic analysis as a special case of shock
analysis
Obtain the approximate solution by corrections
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Experimental Validation

• Structure of the stress wave profiles is
  captured by analytical solution by

• Incorporating EOS
• Explicitly considers wave scattering at
  interfaces.

• Homogenization based theories predict vertical
  rise and smooth plateau.

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Quantitative wave structure analysis

• Analytical solution

where

• Measured wave speed of layered systems based on
  arrival time is x dependent.

Elastic wave
X. Chen and N. Chandra, Composites Science and
Technology, 64, 10-11, 1477-1493, (2004).
19
Comparison of mean stress in PC/GS systems

• Good agreement between numerical results and
  analytical solutions.
• Low experimental stress values when the impact
  velocity is low.

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Composites design for the application of armor

• Analytical solution vs. material heterogeneity
  factors

Material heterogeneity factors
Analytical solution

• Material heterogeneity factors vs. composites
  design variables

Material heterogeneity factors
Basic variables in composites
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Parameter Based Design

• Mean stress and peak stress are governed by
  effective impedance

Low effective density
and low effective wave velocity
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Impedance mismatch I of various combinations
0
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Meso/Macro Composite Designs

• Geometry variables design

2. Volume fractions (thickness ratio)

• Overall fiber volume fraction
• Fiber yarn packing density

3. Lamina size (interface density)
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Role of Nanoscale Heterogeneous Materials
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The Scale of Things -- Nanometers and More
Things Natural
Things Manmade
MicroElectroMechanical devices 10 -100 mm wide
Red blood cells
Pollen grain
Zone plate x-ray lensOutermost ring spacing
35 nm
Atoms of silicon spacing tenths of nm
Office of Basic Energy Sciences Office of
Science, U.S. DOE Version 03-05-02
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Carbon Nanotubes (CNTs)

• CNTs can span 23,000 miles without failing due to
  its own weight.
• CNTs are 100 times stronger than steel.
• Many times stiffer than any known material
• Conducts heat better than diamond
• Can be a conductor or insulator without any
  doping.
• Lighter than feather.

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Local elastic moduli of CNT with defects

• Type I defect ? E 0.62 TPa

• Type II defect ? E0.63 Tpa

• Reduction in stiffness in the presence of defect
  from 1 Tpa
• -Initial residual stress indicates additional
  forces at zero strain
• -Analogous to formation energy

Namilae and Chandra, Chem.. Phy. Letters 387,
4-6, 247-252, (2004)
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Functionalized Nanotubes

• Change in hybridization (SP2 to SP3)
• Experimental reports of different chemical
  attachments
• Application in composites, medicine, sensors
• Functionalized CNT are possibly fibers in
  composites

• How does functionalization affect the elastic and
  inelastic deformation behavior and fracture

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Functionalized nanotubes

• Increase in stiffness observed by functionalizing

Vinyl and Butyl Hydrocarbons T77K and
3000K Lutsko stress
N. Chandra, S. Namilae, and C. Shet, Physical
Review B, 69, 094101, (2004).
Stiffness increase is more for higher number of
chemical attachments Stiffness increase higher
for longer chemical attachments
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Local Stiffness of functionalized CNTs
 

• Stiffness increase is more for higher number of
  chemical attachments
• Stiffness increase higher for longer chemical
  attachments

 
Namilae and Chandra, Chem. Phy. Letters 387,
4-6, 247-252, (2004)
31
Atomic simulation of CNT pullout test

• Simulation conditions
• Corner atoms of hydrocarbon attachments fixed
• Displacement applied as shown 0.02A/1500 steps
• T300K

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Interfacial shear
Interfacial shear measured as reaction force of
fixed atoms
Max load
Typical interface shear force pattern. Note zero
force after Failure (separation of chemical
attachment)
After Failure
250,000 steps
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Debonding and Rebonding of Interfaces
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Debonding and Rebonding
Matrix
Matrix

• Energy for debonding of chemical attachment 3eV
• Strain energy in force-displacement plot 20 4
  eV
• Energy increase due to debonding-rebonding

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Buckling Behavior-Neat CNT
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Buckling of CNT composites
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Cohesive zone model for interfaces

• Assumptions
• Nanotubes deform in linear elastic manner
• Interface character completely determined
• by traction-displacement plot

Chandra et. a., IJSS, 39, 2827-2855, (2002)
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Cohesive zone Models for nanoscale interfaces
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Finite element simulation

• ABAQUS with user element for cohesive zone model
• Linear elastic model for both matrix and CNT
• About 1000 elements and 100 elements at interface
  

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Parametric studies
Variation of CNT content for different interface
strengths
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Parametric studies
Variation of matrix stiffness for different
interface strengths
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Parametric studies
Variation of fiber stiffness for different
interface strengths
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Summary

• Heterogeneous materials will play a key role in
  mitigating impact and blasts
• Finite Element method/analytical methods can be
  used at macro scale.
• We see that composite material and geometric
  parameters can be optimized at the meso levels.
• Novel ideas include the use of atomic level
  phenomena to achieve orders of magnitude
  improvements.
• Use atomic processes for multiple purposes.

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Acknowledgement
Nanomechanics Group Professors A. Srinivasan, U.
Chandra Dr. S. Namilae, C. Shet S. Guan, M.
Naveen, Girish, Yanan, J. Kohle, Jason Montgomery
Nanomechanics Group Dr. Bruce Lamattina and
Rajendran, ARO and US Army
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Further References
MD Papers N. Chandra, S. Namilae, and C. Shet,
Local elastic properties of carbon nanotubes in
the presence of Stone -Wales defects, Physical
Review B, 69, 094101, (2004). S. Namilae, N.
Chandra, and C. Shet, Mechanical behavior of
functionalized nanotubes, Chemical Physics
Letters 387, 4-6, 247-252, (2004) N. Chandra and
S. Namilae, Multi-scale modeling of
nanocystalline materials, Materials Science
Forum, 447-448, 19-27, (2004).. C. Shet, N.
Chandra, and S. Namilae, Defect-defect
interaction in carbon nanotubes under mechanical
loading, Mechanics of Advanced Materials and
Structures, (2004) (in print). C. Shet, N.
Chandra, and S. Namilae, Defect annihilations in
carbon nanotubes under thermo-mechanical loading,
Journal of Material Sciences , (in print). S.
Namilae, C. Shet, N. Chandra and T.G. Nieh,
Atomistic simulation of grain boundary sliding in
pure and magnesium doped aluminum bicrystals,
Scripta Materialia 46, 49-54 (2002). S. Namilae,
C. Shet, N. Chandra and T.G. Nieh, Atomistic
simulation of the effect of trace elements on
grain boundary of aluminum, Materials Science
Forum, 357-359, 387-392, (2001). C. Shet, H. Li
and N. Chandra, Interface Models for grain
boundary sliding and migration, Materials Science
Forum 357-359, 577-586, (2001). N. Chandra and P.
Dang, Atomistic Simulation of Grain Boundary
Sliding and Migration, Journal of Materials
Science, 34, 4, 656-666 (1998). N. Chandra,
Mechanics of Superplastic Deformations at Atomic
Scale, Materials Science Forum, 304, 3, 411-419
(1998).
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Further References
Cohesive Zones C. Shet and N. Chandra, The
effect of the shape of the cohesive zone curves
on the fracture responses, Mechanics of Advanced
Materials and Structures, 11(3), 249-276,
(2004). N. Chandra and C. Shet, A
Micromechanistic Perspective of Cohesive Zone
Approach in Modeling Fracture. Computer Modeling
in Engineering Sciences, CMES, Computer
Modeling in Engineering and Sciences, 5(1),
21-34, (2004)) H. Li and N. Chandra, Analysis of
Crack Growth and Crack-tip Plasticity in Ductile
Material Using Cohesive Zone Models,
International Journal of Plasticity, 19, 849-882,
(2003). N. Chandra, Constitutive behavior of
Superplastic materials, International Journal for
nonlinear mechanics, 37, 461-484, (2002). N.
Chandra, H. Li, C. Shet and H. Ghonem, Some
Issues in the Application of Cohesive Zone Models
for Metal-ceramic Interface. International
Journal of Solids and Structures, 39, 2827-2855,
(2002). C. Shet and N. Chandra, Analysis of
Energy Balance When Using Cohesive Zone Models to
Simulate Fracture Process, ASME Journal of
Engineering Materials and Technology, 124,
440-450, (2002). N. Chandra, Evaluation of
Interfacial Fracture Toughness Using Cohesive
Zone Models, Composites Part A Applied Science
and Manufacturing, 33, 1433-1447, (2002). C.
Shet, H. Li and N. Chandra, Interface Models for
grain boundary sliding and migration, Materials
Science Forum 357-359, 577-586, (2001).
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Further References
Interface Mechanics N. Chandra and H. Ghonem,
Interfacial Mechanics of push-out tests theory
and experiments, Composites Part A Applied
Science and Manufacturing, 32, 3-4, 575-584,
(2001). D. Osborne, N. Chandra and, H. Ghonem,
Interface Behavior of Ti Matrix Composites at
elevated temperature, Composites Part A Applied
Science and Manufacturing, 32, 3-4, 545-553,
(2001). N. Chandra, S. C. Rama and Z. Chen,
Process Modeling of Superplastic materials,
Materials Transactions JIM, 40, 8, 723-726
(1999). S. R. Voleti, C. R. Ananth and N.
Chandra, Effect of Fiber Fracture and Matrix
Yielding on Load Sharing in Continuous Fiber
Metal Matrix Composites, Journal of Composites
Technology and Research, 20, 4, 203-209,
(1998). C.R. Ananth, S. R. Voleti and N. Chandra,
Effect of Fiber Fracture and Interfacial
Debonding on the Evolution of Damage in Metal
Matrix Composites, Composites Part A, 29A,
1203-1211, (1998) S. Mukherjee, C. R. Ananth and
N. Chandra, Effect of Interface Chemistry on the
Fracture Properties of Titanium Matrix
Composites, Composites Part A, 29A, 1213-1219,
(1998) S. R. Voleti, C. R. Ananth and N.
Chandra, Effect of Interfacial Properties on the
Fiber Fragmentation Process in Polymer Matrix
Composites, Journal of Composites Technology and
Research, 20, 1, 16-26, (1998). S. Mukherjee, C.
R. Ananth and N. Chandra, Evaluation of Fracture
Toughness of MMC Interfaces Using Thin-slice
Push-out Tests, Scripta Materialia, 36, 1333-1338
(1997). C. R. Ananth, S. Mukherjee, and N.
Chandra, Effect of Time Dependent Matrix Behavior
on the Evolution of Processing-Induced Residual
Stresses in Metal Matrix Composites, Journal of
Composites Technology and Research 19, 3,
134-141, (1997). S. Mukherjee, C. R. Ananth and
N. Chandra, Effect of Residual Stresses on the
Interfacial Fracture Behavior of Metal Matrix
Composites, Composite Science and Technology, 57,
1501-112, (1997). C. R. Ananth and N. Chandra,
Elevated temperature interfacial behavior of MMC
a computational study, Composites Part A, 27A,
805-811 (1996). S. R. Voleti, N. Chandra and J
R. Miller, Global-Local Analysis of Large-scale
Composite Structures Using Finite Element
Methods, Composites Structures, 58, 3, 453-464,
(1996). C. R. Ananth and N. Chandra, Evaluation
of Interfacial Properties of Metal Matrix
Composites from Fiber Push-out Tests, Mechanics
of Composite Materials and Structures, 2, 309-328
(1995). Xie, Z.Y. and N. Chandra, Application of
GPS Tensors to Fiber Reinforced Composites,
Journal of Composite Materials, 29, 1448-1514,
(1995). S. Mukherjee, H. Garmestani and N.
Chandra, Experimental Investigation of Thermally
Induced Plastic Deformation of MMCs Using
Backscattered Kikuchi Method, Scripta
Metallurgica et Materialia, 33, 1, 93-99 (1995).
N. Chandra and C.R. Ananth, Analysis of
Interfacial Behavior in MMCs and IMCs Using Thin
Slice Push-out Tests', Composite Science and
Technology, 54, 1 , 87-100, (1995). C. R. Ananth
and N. Chandra, Numerical Modeling of Fiber
Push-Out Test in Metallic and Intermetallic
Matrix Composites-Mechanics of the Failure
Process', Journal of Composite Materials, 29, 11,
1488-1514, (1995). N. Chandra., C.R. Ananth and
H. Garmestani, Micromechanical Modeling of
Process-Induced Residual Stresses in
Ti-24Al-11Nb/SCS6 Composite', Journal of
Composite Technology and Research, 17, 37-46,
(1994). Z. Xie and N. Chandra, Application of
Equation Regulation Method to Multi-Phase
Composites', International Journal of Non-linear
Mechanics, 28, 6, 687-704, (1993).