Open Access Open Access  Restricted Access Subscription Access

Fracture Simulation in Polymer Nanocomposites Using Molecular Dynamics



The objective of this paper is to (a) investigate the validity of application of continuum-based linear elastic fracture mechanics (LEFM) methodology, which is often employed by researchers to model fracture processes at the “discrete” atomic scale, and (b) to study the effect of nanographene platelet size on the rupture strength of an edge-cracked polymer block. The material selected for this study is EPON 862 epoxy polymer with 85% cross-link density. Further, an atomistic J-integral is implemented as a nano-scale fracture metric to investigate flaw-tolerance at the nanoscale reported by many researchers, and to develop a methodology to predict the initiation fracture toughness of the material. For this purpose, a bond-order based potential (ReaxFF) available in LAMMPS , a molecular dynamics (MD) software, is utilized. Predictions obtained using the atomistic J-integral are compared with LEFM predictions for the case of a cross-linked epoxy polymer block with a center-crack under uniform far-field loading. Significant deviations from LEFM for crack-lengths below a certain critical crack-length threshold are observed. Further, far-field stress vs. strain plots are obtained for an edge-cracked epoxy polymer block with a single 14 nm graphene nanoplatelet embedded ahead of the crack tip and it is compared with stress vs. strain plot obtained for the same epoxy block with two 7 nm graphene nanoplatelets embedded ahead of the crack tip to study platelet size effect. Significant size effect was observed as shown in the results.


Full Text:



Zhang, P., Ma, L., Fan, F., Zeng, Z., Peng, C., Loya, P.E., Liu, Z., Gong, Y., Zhang, J., Zhang, X. and Ajayan, P.M., 2014. “Fracture toughness of graphene”. Nature communications, 5, p.3782.

Pugno, N.M. and Ruoff, R.S., 2004. Quantized fracture mechanics. Philosophical Magazine, 84(27), pp.2829-2845.

Gao, H., Ji, B., Jäger, I.L., Arzt, E. and Fratzl, P., 2003. Materials become insensitive to flaws at nanoscale: lessons from nature. Proceedings of the national Academy of Sciences, 100(10), pp.5597-5600.

Dewapriya, M.A.N., Rajapakse, R.K.N.D. and Phani, A.S., 2014. Atomistic and continuum modelling of temperature-dependent fracture of graphene. International Journal of Fracture, 187(2), pp.199-212.

Wang, L., Zhang, Z. and Han, X., 2013. In situ experimental mechanics of nanomaterials at the atomic scale. NPG Asia Materials, 5(2), p.e40.

Khare, R., Mielke, S.L., Paci, J.T., Zhang, S., Ballarini, R., Schatz, G.C. and Belytschko, T., 2007. Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Physical Review B, 75(7), p.075412.

Cheng, S.H. and Sun, C.T., 2013. Size-dependent fracture toughness of nanoscale structures: Crack-tip stress approach in molecular dynamics. Journal of Nanomechanics and Micromechanics, 4(4), p.A4014001.

Roy, S., Ryan, J., Webster, S. and Nepal, D., 2017. A Review of In Situ Mechanical Characterization of Polymer Nanocomposites: Prospect and Challenges. Applied Mechanics Reviews, 69(5), p.050802.

Eringen, A.C. and Edelen, D.G.B., 1972. On nonlocal elasticity. International Journal of Engineering Science, 10(3), pp.233-248.

Allegri, G. and Scarpa, F.L., 2014. On the asymptotic crack-tip stress fields in nonlocal orthotropic elasticity. International Journal of Solids and Structures, 51(2), pp.504-515.

Odegard, G.M., Clancy, T.C. and Gates, T.S., 2005. Modeling of the mechanical properties of nanoparticle/polymer composites. Polymer, 46(2), pp.553-562.

Jones, R.E., Zimmerman, J.A., Oswald, J. and Belytschko, T., 2010. An atomistic J-integral at finite temperature based on Hardy estimates of continuum fields. Journal of Physics: Condensed Matter, 23(1), p.015002.

Roy, S. and Nair, A., 2011. Concurrent multi-scale modeling of nano-particle reinforced polymers using statistical coupling of MD and GIMPM. In 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 19th AIAA/ASME/AHS Adaptive Structures Conference 13t (p. 1922).

Roy, S. and Akepati, A., 2014. Multi-scale Modeling of Failure in Nano-Particle Reinforced Polymers Using the Atomistic J-Integral. In 55th AIAA/ASMe/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference (p. 0106).

Roy, S. and Kumar, A., 2018. Modeling of toughness enhancement mechanisms in graphene nanocomposites. Mechanics of Advanced Materials and Structures, 25(14), pp.1197-1204.

Mielke, S.L., Belytschko, T. and Schatz, G.C., 2007. Nanoscale fracture mechanics. Annu. Rev. Phys. Chem., 58, pp.185-209.

Weiner, J.H., 2012. Statistical mechanics of elasticity. Courier Corporation.

Rice, J.R., 1968. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of applied mechanics, 35(2), pp.379-386.

Begley, J.A. and Landes, J.D., 1972. The J integral as a fracture criterion. In Fracture Toughness: Part II. ASTM International.

Mindess, S., Lawrence, F.V. and Kesler, C.E., 1977. The J-integral as a fracture criterion for fiber reinforced concrete. Cement and Concrete Research, 7(6), pp.731-742.

Jones, R.E. and Zimmerman, J.A., 2010. The construction and application of an atomistic J-integral via Hardy estimates of continuum fields. Journal of the Mechanics and Physics of Solids, 58(9), pp.1318-1337.

Eshelby, J.D., 1975. The elastic energy-momentum tensor. Journal of elasticity, 5(3-4), pp.321-335.

Inoue, H., Akahoshi, Y. and Harada, S., 1994. A fracture parameter for Molecular Dynamics method. International journal of fracture, 66(4), pp.R77-R81.

Jin, Z.H. and Sun, C.T., 2004. On J-integral and potential energy variation. International journal of fracture, 126(1), pp.L19-L24.

Hardy, R.J., 1982. Formulas for determining local properties in molecular‐dynamics simulations: Shock waves. The Journal of Chemical Physics, 76(1), pp.622-628.

Nakatani, K., Nakatani, A., Sugiyama, Y. and Kitagawa, H., 2000. Molecular dynamics study on mechanical properties and fracture in amorphous metal. AIAA journal, 38(4), pp.695-701.

Xu, Y.G., Behdinan, K. and Fawaz, Z., 2004. Molecular dynamics calculation of the J-integral fracture criterion for nano-sized crystals. International journal of fracture, 130(2), pp.571-583.

Latapie, A. and Farkas, D., 2004. Molecular dynamics investigation of the fracture behavior of nanocrystalline α-Fe. Physical Review B, 69(13), p.134110.

Roy, S. and Akepati, A., 2015. A Methodology for the Prediction of Fracture Properties in Polymer Nanocomposites. Advanced Computational Nanomechanics, p.175.

Roy, S. and Roy, A., A Computational Investigation of Length-Scale Effects in the Fracture Behaviour of a Graphene Sheet using the Atomistic J-Integral, Engineering Fracture Mechanics, Vol. 207, pp. 165-180 (2019).

Zhang, P., L. Ma, F. Fan, Z. Zeng, C. Peng, P. E. Loya, Z. Liu, Y. Gong, J. Zhang, X. Zhang, P. M. Ajayan, T. Zhu, and J. Lou, Fracture Toughness of Graphene, Nature Communications, Vol. 5, Article number: 3782 (2014).

Gao, H., and S. Chen, Flaw Tolerance in a Thin Strip Under Tension, Journal of Applied Mechanics, Vol. 72, no. 5, pp. 732-737 (2005).

Cheng, S., and C. T. Sun, Size-Dependent Fracture Toughness of Nanoscale Structures: Crack-Tip Stress Approach in Molecular Dynamics, J. Nanomech. Micromech., Vol. 4, no. 4, pp. A4014001 (2014).


  • There are currently no refbacks.