×

A cohesive law for carbon nanotube/polymer interfaces based on the van der Waals force. (English) Zbl 1120.74324

Summary: We have established the cohesive law for interfaces between a carbon nanotube (CNT) and polymer that are not well bonded and are characterized by the van der Waals force. The tensile cohesive strength and cohesive energy are given in terms of the area density of carbon nanotube and volume density of polymer, as well as the parameters in the van der Waals force. For a CNT in an infinite polymer, the shear cohesive stress vanishes, and the tensile cohesive stress depends only on the opening displacement. For a CNT in a finite polymer matrix, the tensile cohesive stress remains the same, but the shear cohesive stress depends on both opening and sliding displacements, i.e., the tension/shear coupling. The simple, analytical expressions of the cohesive law are useful to study the interaction between CNT and polymer, such as in CNT-reinforced composites. The effect of polymer surface roughness on the cohesive law is also studied.

MSC:

74A50 Structured surfaces and interfaces, coexistent phases
74A60 Micromechanical theories
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ajayan, P.M.; Schadler, L.S.; Giannaris, C.; Rubio, A., Single-walled carbon nanotube-polymer composites: strength and weakness, Adv. mater., 12, 750-753, (2000)
[2] Bazant, Z.P., Concrete fracture models: testing and practice, Eng. fract. mech., 69, 2, 165-205, (2002)
[3] Breuer, O.; Sundararaj, U., Big returns from small fibers: a review of polymer/carbon nanotube composites, Polym. compos., 25, 630-645, (2004)
[4] Camacho, G.T.; Ortiz, M., Computational modelling of impact damage in brittle materials, Int. J. solids struct., 33, 2899-2938, (1996) · Zbl 0929.74101
[5] Deepak, S.; Wei, C.; Cho, K., Nanomechanics of carbon nanotubes and composites, Appl. mech. rev., 56, 2, 215-230, (2003)
[6] Elices, M.; Guinea, G.V.; Gomez, J.; Planas, J., The cohesive zone model: advantages, limitations and challenges, Eng. fract. mech., 69, 2, 137-163, (2002)
[7] Frankland, S.J.V.; Caglar, A.; Brenner, D.W.; Griebel, M., Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube-polymer interfaces, J. phys. chem. B, 106, 3046-3048, (2002)
[8] Frankland, S.J.V.; Harik, V.M.; Odegard, G.M.; Brenner, D.W.; Gates, T.S., The stress – strain behavior of polymer-nanotube composites from molecular dynamics simulation, Compos. sci. technol., 63, 1655-1661, (2003)
[9] Geubelle, P.H.; Baylor, J.S., Impact-induced delamination of composites: a 2D simulation, Compos. B, 29, 589-602, (1998)
[10] Gou, J.; Minaie, B.; Wang, B.; Liang, Z.; Zhang, C., Computational and experimental study of interfacial bonding of single-walled nanotube reinforced composites, Comp. mater. sci., 31, 225-236, (2004)
[11] Guo, Z.K.; Kobayashi, A.S.; Hay, J.C.; White, K.W., Fracture process zone modeling of monolithic al_{2}O3, Eng. fract. mech., 63, 2, 115-129, (1999)
[12] Harris, P.J.F., Carbon nanotube composites, Int. mater. rev., 49, 1, 31-43, (2004)
[13] Hong, S.S.; Kim, K.S., Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method, J. mech. phys. solids, 51, 7, 1267-1286, (2003) · Zbl 1077.74540
[14] Huang, Y.; Gao, H., Intersonic crack propagation, Part I: the fundamental solution. J. appl. mech., 68, 169-175, (2001) · Zbl 1110.74485
[15] Kubair, D.V.; Geubelle, P.H.; Huang, Y., Intersonic crack propagation in homogeneous media under shear-dominated loading: theoretical analysis, J. mech. phys. solids, 50, 1547-1564, (2002) · Zbl 1044.74038
[16] Kubair, D.V.; Geubelle, P.H.; Huang, Y., Analysis of a rate-dependent cohesive model for dynamic crack propogation, Eng. fract. mech., 70, 685-704, (2003)
[17] Lau, K.T.; Shi, S.Q., Failure mechanisms of carbon nanotube/epoxy composites pre-treated in different temperature environments, Carbon, 40, 2965-2968, (2002)
[18] Li, V.C.; Chan, C.M.; Leung, K.Y., Experimental determination of the tension-softening relations for cementitious composites, Cement concrete res., 17, 441-452, (1987)
[19] Li, C.Y.; Chou, T.W., Multiscale modeling of carbon nanotube reinforced polymer composites, J. nanosci. nanotechnol., 3, 5, 423-430, (2003)
[20] Liao, K.; Li, S., Interfacial characteristics of a carbon nanotube – polystyrene composite system, Appl. phys. lett., 79, 25, 4225-4227, (2001)
[21] Liu, Y.J.; Chen, X.L., Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element, Mech. mater., 35, 69-81, (2003)
[22] Lordi, V.; Yao, N., Molecular mechanics of binding in carbon-nanotube-polymer composites, J. mater. res., 15, 2770-2779, (2000)
[23] Maruyama, B.; Alam, H., Carbon nanotubes and nanofibers in composite materials, Sampe j, 38, 3, 59-70, (2002)
[24] Mohammed, I.; Liechti, K.M., Cohesive zone modeling of crack nucleation at bimaterials corners, J. mech. phys. solids, 48, 4, 735-764, (2000) · Zbl 0963.74503
[25] Namilae, S.; Chandra, N., Multiscale model to study the effect of interfaces in carbon nanotube-based composites, J. eng. mater. technol., 127, 222-232, (2005)
[26] Needleman, A., A continuum model for void nucleation by inclusion debonding, J. appl. mech., 54, 525-531, (1987) · Zbl 0626.73010
[27] Odegard, G.M.; Gates, T.S.; Nicholson, L.M.; Wise, K.E., Equivalent-continuum modeling of nano-structured materials, Compos. sci. technol., 62, 1869-1880, (2002)
[28] Odegard, G.M.; Gates, T.S.; Wise, K.E.; Park, C.; Siochi, E.J., Constitutive modeling of nanotube-reinforced polymer composites, Compos. sci. technol., 63, 1671-1687, (2003)
[29] Rapaport, D.C., The art of molecular dynamics simulation, (2004), Cambridge University Press Cambridge · Zbl 1098.81009
[30] Samudrala, O.; Huang, Y.; Rosakis, A.J., Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone, J. mech. phys. solids, 50, 1231-1268, (2002) · Zbl 1072.74540
[31] Samudrala, O.; Rosakis, A.J., Effect of loading and geometry on the subsonic/intersonic transition of a bimaterial interface crack, Eng. fract. mech., 70, 309-337, (2003)
[32] Schadler, L.S.; Giannaris, S.C.; Ajayan, P.M., Load transfer in carbon nanotube epoxy composites, appl, Phys. lett., 73, 26, 3842-3844, (1998)
[33] Shi, D.L.; Feng, X.Q.; Huang, Y.; Hwang, K.C.; Gao, H., The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites, J. eng. mater. technol., 126, 250-257, (2004)
[34] Tan, H.; Huang, Y.; Liu, C.; Geubelle, P.H., The mori – tanaka method for composite materials with nonlinear interface debonding, Int. J. plasticity, 21, 10, 1890-1918, (2005) · Zbl 1154.74318
[35] Tan, H.; Liu, C.; Huang, Y.; Geubelle, P.H., The cohesive law for the particle/matrix interfaces in high explosives, J. mech. phys. solids, 53, 8, 1892-1917, (2005)
[36] Tan, H., Liu, C., Huang, Y., Geubelle, P.H., 2006. The effect of nonlinear interface debonding on the constitutive model of composite materials. Int. J. Multiscale Comput. Eng. (in press).
[37] Thiagarajan, G.; Hsia, K.J.; Huang, Y., Finite element implementation of virtual internal bond model for simulating crack behavior, Eng. fract. mech., 71, 401-423, (2004)
[38] Thiagarajan, G.; Huang, Y.; Hsia, K.J., Fracture simulation using an elasto – viscoplastic virtual internal bond model with finite element, J. appl. mech., 71, 796-804, (2004) · Zbl 1111.74660
[39] Thostenson, E.T.; Ren, Z.F.; Chou, T.W., Advances in the science and technology of carbon nanotubes and their composites: a review, Compos. sci. technol., 61, 1899-1912, (2001)
[40] Thostenson, E.T.; Chou, T.W., On the elastic properties of carbon nanotube-based composites: modelling and characterization, J. phys. D-appl. phys., 36, 5, 573-582, (2003)
[41] Thostenson, E.T.; Li, C.Y.; Chou, T.W., Nanocomposites in context, Compos. sci. technol., 65, 3-4, 491-516, (2005)
[42] Wong, M.; Paramsothy, M.; Xu, X.J.; Ren, Y.; Li, S.; Liao, K., Physical interactions at carbon nanotube-polymer interface, Polymer, 44, 7757-7764, (2003)
[43] Zhang, P.; Klein, P.A.; Huang, Y.; Gao, H.; Wu, P.D., Numerical simulation of cohesive fracture by the virtual-internal-bond model, Comput. model. eng. sci., 3, 263-277, (2002) · Zbl 1066.74008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.