1. Constitutive modeling of viscoelastic behavior of CNT/Polymer composites K. Yazdchi 1, M. Salehi 2 1- Multi scale Mechanics (MSM), Faculty of Engineering Technology, University of Twente, Enschede, The Netherlands k.yazdchi@utwente.nl 2- Mechanical engineering Department, Amirkabir University of Technology, Tehran, Iran

2. Presentation Outline Geometric Structure, Mechanical Properties and Applications of SWCNTs Micromechanical analysis Predicting mechanical properties, using equivalent continuum model (ECM) Numerical results Conclusions

3. Geometric Structure of SWCNTs Source: http://www.photon.t.u-tokyo.ac.jp/~maruyama/agallery/agallery.html

4. Geometric Structure of SWCNTs O C Armchair Zigzag

5. Wrapping (10,0) SWNT (Zigzag) C h = (10,0)

6. Wrapping (10,10) SWNT (Armchair) C h = (10,10)

7. Wrapping (10,5) SWNT (Chiral) C h = (10,5)

8. Mechanical Properties of CNTs  High Elastic Modulus (1 TPa)  Strength 100 times greater than steel (up to 50 GPa) at one sixth the Weight  High Strain to Failure (10%-30%) igh Electrical and Thermal Conductivity igh Aspect Ratio (1000)  Excellent Resilience and Toughness xcellent Optical and Transport Properties  Low Density (1.3 g/cm^3)

9. CNTs Applications  Reinforcement Elements  Aerospace, Automobile, Medicine, or Chemical Industry  Sensors and Actuators pace Elevator  CNT Nano-Gear and Puncher NT Transistor  Defect and Junction Devices

10. Micromechanical analysis Representative Volume Element (RVE) MacroscaleMicroscale Zoom InclusionsVoids

11. Micromechanical analysis (Modeling Procedures) Step 1 Step 2 Step 3 Homogenization scheme

12. Micromechanical analysis (Stress & Strain Averages) Inclusions Matrix

13. Micromechanical analysis (Homogenized elastic operator) Assume that each phase of this RVE obeys Hooke’s law: On the other hand: ?

14. Micromechanical analysis (Voigt Assumption) Upper Bound

15. Micromechanical analysis (Reuss Assumption) Lower Bound

16. Micromechanical analysis (Mori Tanaka (M-T) scheme) The most popular For composites with moderate volume fractions of inclusions (25% - 30%) Takes into account the interaction between inclusions Heterogeneous RVE Step 1 Step 2 Associated Isolated Inclusion Medium For composites with transversely isotropic, spheroidal inclusions, unidirectional reinforcements Equivalent Homogeneous Medium

17. Micromechanical analysis (Mori Tanaka (M-T) scheme) Consistency condition Average inclusion

18. Micromechanical analysis (Viscoelasticity ) Dynamic Correspondence Principle (DCP): Elastic SolutionViscoelastic Solution Time DomainFrequency Domain LCT Inverse LCT

19. Numerical Results Straight NTs (Effects of Waviness is ignored) Perfectly aligned or completely randomly oriented nanotubes Matrix is linearly viscoelastic and isotropic and effective continuum fiber is elastic and transversely isotropic Perfect bounding between NT and polymer Assume a SWCNT, the non-bulk local polymer around the NT, and the NT/polymer interface layer collectively as an effective continuum fiber Mechanical properties of NT and polymer are independent from temperature

20. Numerical Results (Analytical Formulation) Transversely isotropic

21. Numerical Results (Modeling the interphase region) Bulk polymer Interphase CNT R Carbon fibers Carbon Nanotubes!!

22. Numerical Results (Modeling the interphase region) Multiscale modeling

23. Numerical Results (Modeling the interphase region)

24. Numerical Results (Completely randomly oriented nanotubes) Isotropic composites OR

25. Numerical Results (Perfectly aligned) Transversely isotropic composites

26. Numerical Results (Perfectly aligned) Transversely isotropic composites

27. Numerical Results (Perfectly aligned) Transversely isotropic composites

28. Numerical Results (Perfectly aligned) Transversely isotropic composites

29. Conclusions The parameters which affect the mechanical properties of NTRPCs are NT aspect ratio, volume fraction and orientation. For composites having unidirectionally aligned nanotubes (transversely isotropic), numerical results indicate that the increase of the nanotube aspect ratio and volume fraction significantly enhances their axial creep resistance but has insignificant influences on their transverse, shear and plane strain bulk creep compliances. The effect of the nanotube orientation on the shear compliances is negligibly small.

30. Conclusions For composites with aligned or randomly oriented nanotubes, all the compliances are found to decrease monotonically with the increase of the nanotube volume fraction. For composites having randomly oriented NTs (isotropic) with increasing the aspect ratio or NT volume fraction, the axial and shear creep compliances will decreases also the effect of aspect ratio in comparison with volume fraction is negligible. The model proposed in the foregoing is simple and very economical to employ, particularly in viscoelastic behaviour of nanocomposites, compared with other methods.

31. Suggestions  The effects of NT waviness and agglomeration and also temperature on the viscoelastic behavior of NTRPCs.  Find new methods in modeling the interphase region (such as MD, etc).  The effect of anisotropic properties of CNTs, 3D modelling, end caps and any possible relative motion between individual shells or tubes in a MWNT and an NT bundle Voids and Defects will be studied in the future.  Use other Micromechanical models and compare the results with experimental data.

32. Thank you for your attention Any Questions?