Modeling Atomic Scale Interfaces Using CZM in Carbon Nanotube Based Composites

1. Modeling Atomic Scale Interfaces Using CZM in Carbon Nanotube Based Composites NAMAS CHANDRA Department of Mechanical Engineering Florida State/Florida A&M University Tallahassee FL 32310 Santa Fe, New Mexico AFOSR Contract Review Meeting August 30- September 2, 2005

2. The Scale of Things -- Nanometers and More 1 cm 10 mm 10-2 m Head of a pin 1-2 mm 21st Century Challenge 1,000,000 nanometers = 10-3 m Ant ~ 5 mm 1 millimeter (mm) Microwave Dust mite 200 mm 0.1 mm 100 mm 10-4 m Fly ash ~ 10-20 mm Human hair ~ 10-50 mm wide The Microworld 0.01 mm 10 mm 10-5 m Infrared Red blood cells with white cell ~ 2-5 mm 1,000 nanometers = 10-6 m 1 micrometer (mm) Visible 0.1 mm 100 nm 10-7 m Combine nanoscale building blocks to make novel functional devices, e.g., a photosynthetic reaction center with integral semiconductor storage Ultraviolet 0.01 mm 10 nm The Nanoworld 10-8 m Nanotube transistor Nanotube electrode ~10 nm diameter ATP synthase 10-9 m 1 nanometer (nm) Soft x-ray DNA ~2-1/2 nm diameter 10-10 m 0.1 nm Carbon nanotube ~2 nm diameter Quantum corral of 48 iron atoms on copper surface positioned one at a time with an STM tip Corral diameter 14 nm Things Natural Things Manmade MicroElectroMechanical devices 10 -100 mm wide Red blood cells Pollen grain Zone plate x-ray “lens”Outermost 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

3. Note on Molecular Dynamics Given for one instance an intelligence which would comprehend all forces by which nature is animated and the respective situation of beings who compose it ……… Nothing would be uncertain and the future , as the past, would be present to its eyes Laplace, 1814 Limitations Given a geometric configuration of atoms, we can compute all the future configurations if we can compute the motion of each atom as a function of time if we know how the atoms will move under mutually interacting forces • Interacting forces given by potential energy functions; Right function or series of functions critical • Space scale • 1 μm3 of Al contains about 1010 atoms • Time Scale • 1 step= 1fs : For simulation of 1μs need 109 steps AMML

4. 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. AMML

5. High strength composites Functional composites Nano electronics Energy storage Carbon Nanotubes (CNT) • Carbon Nanotubes: Graphite sheet rolled into a tube • Single wall and Multiwall nanotubes • Zigzag, armchair and chiral nanotubes • Length ~ 100 nm to few m Diameter~ 1 nm Applications E ~ 1 TPa Strength ~150 GPa Conductivity depends on chirality Nano sensors Medical applications Do these properties extend to CNT reinforced composites ? AMML

6. Do we realize the potentials of CNT in PMC? Parallel model Upper Bound Answer is No-We do not Series model Lower Bound AMML

7. Factors affecting interfacial properties Asperities Interfacial chemistry Mechanical effects Origin:Surface irregularities inherent in the interface Issues: Affects interface fracture process through mechanical loading and friction Approach: Incorporate roughness effects in the interface model; Study effect of generating surface roughness using: Sinusoidal functions and fractal approach; Use push-back test data and measured roughness profile of push-out fibers for the model. Residual stress Origin:Chemical reaction during thermal-mechanical Processing and service conditions, e.g. Aging, Coatings, Exposures at high temp.. Issues: Chemistry and architecture effects on mechanical properties. Approach: Analyze the effect of size of reaction zone and chemical bond strength (e.g. SCS-6/Ti matrix and SCS-6/Ti matrix ) Origin:CTE mismatch between fiber and matrix. Issues: Significantly affects the state of stress at interface and hence fracture process Approach: Isolate the effects of residual stress state by plastic straining of specimen; and validate with numerical models. Metal/ ceramic/ polymer Interface CNTs Properties affected Trans. & long. Stiffness/strength Fatigue/Fracture Thermal/electronic/magnetic AMML

8. Critical Scientific Issues • Critical issues in nanotube composites • Alignment • Dispersion • Load Transfer • Load transfer and to some extant Dispersion affected by interfaces • Interface  Bounding surface with physical / chemical / mechanical discontinuity • CNT-matrix interfaces • Vanderwall’s forces • Mechanical interlocking • Chemical bonding AMML

9. Some issues in Elastic Modulii computation • Energy based approach • Assumes existence of W. Then, • Validity of W based on potentials questionable under conditions such as temperature, pressure • Value of E depends on selection of strain. • Stress –Strain approach • Circumvents the above problems • Evaluation of local modulus for defect regions possible AMML

10. Stress Measures Virial stress BDT stress Lutsko stress

11. Strain calculation in nanotubes • Defect free nanotube  mesh of hexagons • Strain calculated using displacements and derivatives shape functions in a local coordinate system formed by tangential (X) and radial (y) direction of centroid and tube axis • Area weighted averages of surrounding hexagons considered for strain at each atom • Similar procedure for pentagons and heptagons Updated Lagrangian scheme is used in MD simulations

12. Elastic modulus of defect free CNT -Defect free (9,0) nanotube with periodic boundary conditions -Strains applied using conjugate gradients energy minimization • All stress and strain • measures yield a Young’s • modulus value of 1.002TPa • Values in literature range • from 0.5 to 5.5 Tpa. Mostly • around 1Tpa

13. Effect of Diameter stiffness values of defects for various tubes with different diameters do not change significantly Stiffness in the range of 0.61TPa to 0.63TPa for different (n,0) tubes Mechanical properties of defect not significantly affected by the curvature of nanotube stress strain curves for different (n,0) tubes with varying diameters.

14. Residual stress at zero strain • Stress is present at zero strain values. • This corresponds to stress due to curvature • It is found to decrease with increasing diameter • Basis for stress calculation  graphene sheet • Brenner et. al.1 observed similar variation in energy at zero strain 1 Robertson DH, Brenner DW and Mintmire 1992 N. Chandra et. al., Phys. Rev B 69, 09141 (2004)

15. CNT with 5-7-7-5 defect • Lutsko stress profile for (9,0) tube with type I defect shown below • Stress amplification observed in the defected region • This effect reduces with increasing applied strains • In (n,n) type of tubes there is a decrease in stress at the defect region Shet and Chandra, J. Mat. Sci, 40, 27-36 (2005) Shet, Chandra, Namilae, Mech. Adv. Mat. Str,,55-65, (2005).

16. Evolution of stress and strain Strain and stress evolution at 1,3,5 and 7 % applied strains Stress based on BDT stress

17. Local elastic moduli of CNT with defects • Type I defect  E= 0.62 TPa • Type II defect  E=0.63 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)

18. 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

19. Functionalized nanotubes • Increase in stiffness observed by functionalizing Vinyl and Butyl Hydrocarbons T=77K and 3000K Lutsko stress Stiffness increase is more for higher number of chemical attachments Stiffness increase higher for longer chemical attachments

20. 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)

21. Contour plots Stress contours with one chemical attachment. Stress fluctuations are present

22. Sp3 Hybridization here Radius variation • Increased radius of curvature at the attachment because of change in hybridization • Radius of curvature lowered in adjoining area

23. Defects Evolve Effect of functionalization on defect evolution Evolution of defects in tension • Defects Evolve at much lower strain of 6.5 % in CNT with chemical attachments • Onset of plastic deformation at lower strain. Reduced fracture strain

24. Different Fracture Mechanisms ? Fracture Behavior Different • Fracture happens by formation of defects, coalescence of defects and final separation of damaged region in defect free CNT • In Functionalized CNT it happens in a brittle manner by breaking of bonds Namilae and Chandra, Chem. Phy. Letters 387, 4-6, 247-252, (2004)

25. Compressive Behavior of CNT composites (weak) Weak Interfaces Compressive behavior of CNT in polymer matrix with Weak interface

26. Strong Interfaces Strong Interfaces • Deformation mechanism changes • Mechanical Response significantly altered Compressive Behavior of CNT composites (strong)

27. Effect of interstitial on tensile behavior of MWNTs Tensile simulation without functionalization Tensile simulation with functionalization Compressive response of (6,0)(15,0) nanotube with and without chemical bonding between the walls of nanotubes. Interstitial atoms increase the load transfer in tension, and both stiffness and strength increase Interstitial atoms in multiwall nanotubes Paper under review

28. Atomic simulation of CNT pullout test • Simulation conditions • Corner atoms of hydrocarbon attachments fixed • Displacement applied as shown 0.02A/1500 steps • T=300K

29. Simulation of pull-out test Energy for debonding of chemical attachment = 3eV

30. 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

31. Debonding Rebonding Failure Debonding and Rebonding of Interfaces

32. 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

33. Various types of Interface Behavior

34. d c b e a c b a Behavior of different lengths of interfaces • Increasing the length of attachment increases region ‘a’ • Decreasing the number of attachments extends region ‘b’

35. Temperature dependence of pullout tests • Force to failure decreases with increasing temperature • Debonding-rebonding behavior at higher temperatures • does not alter the energy dissipation

36. Cohesive zone model for interfaces Chandra et. a., IJSS, 39, 2827-2855, (2002) • Assumptions • Nanotubes deform in linear elastic manner • Interface character completely determined • by traction-displacement plot

37. Cohesive zone Models for nanoscale interfaces Namilae and Chandra JEMT, 222-232, (2005).

38. 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

39. Parametric studies Variation of CNT content for different interface strengths

40. Parametric studies Variation of matrix stiffness for different interface strengths

41. Parametric studies Variation of fiber stiffness for different interface strengths

42. Summary • Interfaces play a key role even at micro/nano scales. • Nanoscale effects can be effectively captured using molecular dynamics model (using the right potentials). • MD results can be integrated in an heirarchical model using CZM-Finite Element method • Using Atomistic scale we can determine atomic effect on macro effects. • Understanding the effects of nanoscale interfaces, and interface mechanics will be important in in a number of engineering applications. AMML

43. Acknowledgement Dr. Les Lee, AFOSR, Short Term Grant Nanomechanics Group: Prof. A. Srinivasan, U. Chandra Dr. S. Namilae, C. Shet S. Guan, M. Naveen, Girish, Yanan, J. Kohle, Jason Montgomery FuAlso contributed by ARO, NSF, FSURF AMML

44. 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 Materialia46, 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). AMML

45. 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, ASMEJournal 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). AMML

46. Further References Interface Mechanics: N. Chandra and H. Ghonem, Interfacial Mechanics of push-out tests: theory and experiments, CompositesPart 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, CompositesPart 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, CompositesPart 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 Research19, 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). AMML

47. Buckling Behavior-Neat CNT

48. Buckling Behavior-Functionalized CNT

49. Compressive loading of carbon nanotubes Using surface modified CNT in composites improves resistance to buckling

50. Thermal Stresses Thermal stress is higher for functionalized nanotube in polymer matrix