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Multi-Scale Modeling of Fracture Properties for Nano-Particle Reinforced Polymers Using Atomistic J-Integral

[+] Author Affiliations
Samit Roy, Avinash Akepati

University of Alabama, Tuscaloosa, AL

Paper No. IMECE2014-36419, pp. V014T11A032; 7 pages
  • ASME 2014 International Mechanical Engineering Congress and Exposition
  • Volume 14: Emerging Technologies; Engineering Management, Safety, Ethics, Society, and Education; Materials: Genetics to Structures
  • Montreal, Quebec, Canada, November 14–20, 2014
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4963-7
  • Copyright © 2014 by ASME


The nano-scale interaction between polymer molecules and nanoparticle is a key factor in determining the macro-scale strength of the composite. In recent years numerous efforts have been directed towards modeling nanocomposites in order to better understand the reasons behind the enhancement of mechanical properties, even by the slight addition (a few weight percent) of nano-materials. In order to better understand the local influence of nano-particle on the mechanical properties of the composite, it is required to perform nano-scale analysis. In this context, modeling of fracture and damage in nano-graphene reinforced EPON 862 has been discussed in the current paper. Regarding fracture in polymers, the critical value of the J-integral (JI), where the subscript I denotes the fracture mode (I=1, 2, 3), at crack initiation could be used as a suitable metric for estimating the crack driving force as well as fracture toughness of the material as the crack begins to initiate. However, for the conventional macroscale definition of the J-integral to be valid at the nanoscale, in terms of the continuum stress and displacement fields and their spatial derivatives — requires the construction of local continuum fields from discrete atomistic data, and using these data in the conventional contour integral expression for atomistic J-integral. One such methodology is proposed by Hardy that allows for the local averaging necessary to obtain the definition of free energy, deformation gradient, and Piola-Kirchoff stress as fields (and divergence of fields) and not just as total system averages. Further, the atomistic J-integral takes into account the effect of reduction in J from continuum estimates due to the fact that the free energy available for crack propagation is less than the internal energy at sufficiently high temperatures when entropic contributions become significant. In this paper, the proposed methodology is used to compute J-integral using atomistic data obtained from LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). As a case study, the feasibility of computing the dynamic atomistic J-integral over the MD domain is evaluated for a graphene nano-platelet with a central crack using OPLS (Optimized Potentials for Liquid Simulations) potential. For model verification, the values of atomistic J-integral are compared with results from linear elastic fracture mechanics (LEFM) for isothermal crack initiation at 0 K and 300 K. Computational results related to the path-independence of the atomistic J-Integral are also presented. Further, a novel approach that circumvents the complexities of direct computation of entropic contributions is also discussed. Preliminary results obtained from the bond-order based ReaxFF potential for 0.1 K and 300 K are presented, and show good agreement with the predictions.

Copyright © 2014 by ASME



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