Research Papers

Estimating the Cohesive Zone Model Parameters of Carbon Nanotube–Polymer Interface for Machining Simulations

[+] Author and Article Information
Lingyun Jiang

Department of Mechanical Engineering,
University of Illinois at Urbana–Champaign,
1206 W. Green Street,
Urbana, IL 61801
e-mail: ljiang10ui@gmail.com

Chandra Nath

Post Doctorate Research Associate
Department of Mechanical Engineering,
University of Illinois at Urbana–Champaign,
1206 W. Green Street,
Urbana, IL 61801
e-mail: nathc2@asme.org

Johnson Samuel

Assistant Professor
Department of Mechanical Nuclear and
Aerospace Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: samuej2@rpi.edu

Shiv G. Kapoor

Department of Mechanical Engineering,
University of Illinois at Urbana–Champaign,
1206 W. Green Street,
Urbana, IL 61801
e-mail: sgkapoor@illinois.edu

1Corresponding author.

Manuscript received October 4, 2012; final manuscript received May 10, 2013; published online March 26, 2014. Assoc. Editor: Donggang Yao.

J. Manuf. Sci. Eng 136(3), 031004 (Mar 26, 2014) (8 pages) Paper No: MANU-12-1292; doi: 10.1115/1.4024941 History: Received October 04, 2012; Revised May 10, 2013

The failure mechanisms encountered during the machining of carbon nanotube (CNT) polymer composites are primarily governed by the strength of the CNT–polymer interface. Therefore, the interface should be explicitly modeled in microstructure-level machining simulations for these composites. One way of effectively capturing the behavior of this interface is by the use of a cohesive zone model (CZM) that is characterized by two parameters, viz., interfacial strength and interfacial fracture energy. The objective of this study is to estimate these two CZM parameters of the interface using an inverse iterative finite element (FE) approach. A microstructure-level 3D FE model for nanoindentation simulation has been developed where the composite microstructure is modeled using three distinct phases, viz., the CNT, the polymer, and the interface. The unknown CZM parameters of the interface are then determined by minimizing the root mean square (RMS) error between the simulated and the experimental nanoindentation load–displacement curves for a 2 wt. % CNT–polyvinyl alcohol (PVA) composite sample at room temperature and quasi-static strain state of up to 0.04 s−1, and then validated using the 1 wt. % and 4 wt. % CNT–PVA composites. The results indicate that for well-dispersed and aligned CNT–PVA composites, the CZM parameters of the interface are independent of the CNT loading in the weight fraction range of 1–4%.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Lu, J. P., 1997, “Elastic Properties of Carbon Nanotubes and Nanoropes,” Phys. Rev. Lett., 79, pp. 1297–1300. [CrossRef]
Peng, B., Locascio, M., Zapol, P., Li, S., Mielke, S. L., Schatz, G. C., and Espinosa, H. D., 2008, “Measurements of Near-Ultimate Strength for Multiwalled Carbon Nanotubes and Irradiation-Induced Crosslinking Improvements,” Nat. Nanotechnol., 3, pp. 626–631. [CrossRef] [PubMed]
Stewart, R., 2004, “Nanocomposites: Microscopic Reinforcement Boost Polymer Performance,” Plast. Eng., 60, pp. 22–29.
Endo, M., Hayashi, T., Kim, Y. A. K., and Muramatsu, H., 2006, “Development and Application of Carbon Nanotubes,” Jpn. J. Appl. Phys., 45, pp. 4883–4892. [CrossRef]
Eklund, P., Ajayan, P., Blackmon, R., Hart, A. J., Kong, J., Pradhan, B., Rao, A., and Rinzler, A., 2007, “International Assessment of Research and Development on Carbon Nanotubes Manufacturing and Application” World Technology Evaluation Center (WTEC) Panel Report.
Dikshit, A., Samuel, J., DeVor, R. E., and Kapoor, S. G., 2008, “Microstructure–Level Machining Simulation of Carbon Nanotube–Reinforced Polymer Composites–Part I: Model Development and Validation,” ASME J. Manuf. Sci. Eng., 130, p. 031114. [CrossRef]
Dikshit, A., Samuel, J., DeVor, R. E., and Kapoor, S. G., 2008, “Microstructure–Level Machining Simulation of Carbon Nanotube–Reinforced Polymer Composites—Part II: Model Interpretation and Application,” ASME J. Manuf. Sci. Eng., 130, p. 031115. [CrossRef]
Dikshit, A., Samuel, J., DeVor, R. E., and Kapoor, S. G., 2008, “A Microstructure–Level Material Model for Simulating the Machining of Carbon Nanotube–Reinforced Polymer Composites,” ASME J. Manuf. Sci. Eng., 130, p. 031110. [CrossRef]
Samuel, J., DeVor, R. E., Kapoor, S. G., and Hsia, K. J., 2005, “Experimental Investigation of the Machinability of Polycarbonate Reinforced with Multi-Walled Carbon Nanoutbes,” ASME J. Manuf. Sci. Eng., 128, pp. 465–473. [CrossRef]
Samuel, J., DeVor, R. E., Kapoor, S. G., and Hsia, K. J., 2010, “Effect of Microstructural Parameters on the Machinability of Aligned Carbon Nanotube Composites,” ASME J. Manuf. Sci. Eng., 132, p. 051012. [CrossRef]
Ortiz, M., and Pandolfi, A., 1999, “Finite–Deformation Irreversible Cohesive Elements for Three-Dimensional Crack-Propagation Analysis,” Int. J. Numer. Methods Eng., 44, pp. 1267–1282. [CrossRef]
Camanho, P. P., Davila, C. G., and de Moura, M. F., 2003, “Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials,” J. Compos. Mater., 37, pp. 1415–1438. [CrossRef]
Golestanina, H., and Shojaie, M., 2010, “Numerical Characterization of CNT-Based Polymer Composites Considering Interface Effects,” Comput. Mater. Sci., 50, pp. 731–736. [CrossRef]
Shokrieh, M. M., and Rafiee, R., 2010, “On the Tensile Behavior of an Embedded Carbon Nanotube in Polymer Matrix With Non-Bond Interphase Region,” Compos. Struct., 92, pp. 647–652. [CrossRef]
Strus, M. C., Cano, C. I., Pipes, R. B., Nguyen, C. V., Raman, A., 2009, “Interfacial Energy Between Carbon Nanotubes and Polymers Measured From Nanoscale Peel Test in the Atomic Force Microscope,” Compos. Sci. Technol., 69, pp. 1580–1586. [CrossRef]
Frankland, S. J. V., Harik, V. M., Odegard, G. M., Brenner, D. W., and Gates, T. S., 2003, “The Stress-Strain Behavior of Polymer–Nanotube Composite from Molecular Dynamic Simulation,” Compos. Sci. Technol., 63, pp. 1655–1661. [CrossRef]
Cooper, C. A., Cohen, S. R., Barber, A. H., and Wagner, H. D., 2002, “Detachment of Nanotube From Polymer Matrix,” Appl. Phys. Lett., 81, pp. 3873–3875. [CrossRef]
Liu, K., VanLandinghamM. R., and OvaertT. C., 2009, “Mechanical Characterization of Soft Viscoelastic Gels via Indentation and Optimization-Based Inverse Finite Element Analysis,” J. Mech. Behav. Biomed. Mater., 2, pp. 355–363. [CrossRef] [PubMed]
Pavia, M. C., Zhou, B., FernandoK. A. S., LinY., KennedyJ. M., and SunY.-P., 2004, “Mechanical and Morphological Characterization of Polymer-Carbon Nanocomposites From Functionalized Carbon Nanotubes,” Carbon, 42, pp. 2849–2854. [CrossRef]
Zhao, B., Wang, J., Li, Z., Liu, P., Chen, D., Zhang Y. 2008, “Mechanical Strength Improvement of Polypropylene Threads Modified by PVA/CNT Composite Coatings,” Mater. Lett., 62, pp. 4380–4382. [CrossRef]
Pradhan, B., KohlmeyerR. R., and ChenJ., 2010, “Fabrication of In-Plane Aligned Carbon Nanotube-Polymer Composite Thin Films,” Carbon, 48, pp. 217–222. [CrossRef]
Lichinchi, M., and Lenardi, C., 1998, “Simulation of Berkovich Nanoindentation Experiments on Thin Films Using Finite Element Method,” Thin Solid Films, 312, pp. 240–248. [CrossRef]
Yu, M. F., Lourie, O., Dyer, M. J., Moloni, K., Kelly, T. F., and Ruoff, R. S., 2000, “Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load,” Science, 287, pp.637–640. [CrossRef] [PubMed]
Hou, Y., Tang, J., Zhang, H., Qian, C., Feng, Y., and Liu, J., 2009, “Functionalized Few-Walled Carbon Nanotubes for Mechanical Reinforcement of Polymeric Composites,” ACS Nano, 3, pp. 1057–1062. [CrossRef] [PubMed]
Oliver, W. C., and Pharr, G. M.1992, “An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments,” J. Mater. Res., 7, pp. 1564–1583. [CrossRef]
Lohnert, S., and Wriggers, P., 2003, “Homogenization of Microheterogneous Materials Considering Interfacial Delamination at Finite Strains,” Tech. Mech., 23, pp. 167–177.
Calzada, K. A., Kapoor, S. G., DeVor, R. E., Samuel, J., and Srivastava, A. K., 2011, “Modeling and Interpretation of Fiber Orientation-Based Failure Mechanisms in Machining of Carbon Fiber–Reinforced Polymer Composites” Trans. North Am. Manuf. Res. Inst. SME, 39, pp. 332–341.
Xu, X. P., and Needleman, A., 1994, “Numerical Simulations of Fast Crack Growth in Brittle Solids,” J. Mech. Phys. Solids, 42, pp.1397–1434. [CrossRef]
van den Bosch, M. J., Schreurs, P. J. G., and Geers, M. G. D., 2006, “An Improved Description of the Exponential Xu and Needleman Cohesive Zone Law for Mixed-Mode Decohesion,” Eng. Fract. Mech., 73, pp. 1220–1234. [CrossRef]
Wang, J., Piechna, J., Yume, J. A. O., and Muller, N., 2012, “Stability Analysis in Wound Composite Material Axial Impeller,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 226, pp. 1162–1172. [CrossRef]
McMinisJ., Crombez, R., Montalvo, E., and Shen, W., 2007, “Determination of the Cross-Sectional Area of the Indenter in Nano-Indentation Test,” Phys. B: Condens. Matter, 391, pp. 118–123. [CrossRef]


Grahic Jump Location
Fig. 1

The optimization-based inverse iterative finite element approach

Grahic Jump Location
Fig. 2

SEM image of the cross-section of a typical 2 wt. % CNTs–PVA composite film (The highlighted region of 4 μm × 2 μm contains an average of 16 CNTs across all samples)

Grahic Jump Location
Fig. 3

Experimental load–displacement curves of the pure PVA, and the 2 wt. % CNT–PVA composite

Grahic Jump Location
Fig. 4

Schematic diagram of (a) the Berkovich indenter and (b) the equivalent cone indenter

Grahic Jump Location
Fig. 5

Parameterization of CNTs

Grahic Jump Location
Fig. 6

Schematic of distribution of the CNTs in the composite sample (cross-sectional area)

Grahic Jump Location
Fig. 7

Simulated and exprimental load–displacement curves for PVA

Grahic Jump Location
Fig. 8

Representation of the cohesive zone model for the interface between the CNT and the PVA in composite (a) top view and (b) cross-sectional view

Grahic Jump Location
Fig. 9

Traction–separation curve for the interface

Grahic Jump Location
Fig. 10

(a) 3D microstructure model for nanoindentation simulation and (b) close-up view of a CNT-integrated cohesive zone with finite element mesh

Grahic Jump Location
Fig. 11

Simulated and exprimental load–displacement curves for 2 wt. % CNT–PVA composite

Grahic Jump Location
Fig. 12

Simulated microstructure for the 2 wt. % CNT–PVA composite at the indentation depth of (a) 100 nm and (b) 200 nm. The shear stress along the CNT is captured in (c) and the plastic recovery of the microstructure after unloading the indenter is shown in (d).

Grahic Jump Location
Fig. 13

Simulated and exprimental load–displacement curves for the 1 wt. % CNT–PVA composite

Grahic Jump Location
Fig. 14

Simulated and exprimental load–displacement curves for the 4 wt. % CNT–PVA composite




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In