Fracture toughness of polymeric particle nanocomposites: Evaluation of models performance using Bayesian method

Abstract This study presents a methodology to evaluate the performance of different models used in predicting the fracture toughness of polymeric particles nanocomposites. Three analytical models are considered: the model of Huang and Kinloch, the model of Williams, and the model of Quaresimin et al. The purpose behind this study is not to recommend which of the three models to be adopted, but to evaluate their performance with respect to experimental data. The Bayesian method is exploited for this purpose based on different reference measurements gained from the literature. The models' performance is compared and evaluated comprehensively accounting for the parameter and model uncertainties. Based on the approximated optimal parameter sets, the coefficients of variation of the model predictions to the measurements are compared for the three models. Finally, the model selection probability is obtained with respect to the different reference data.

[1]  P. Sotta,et al.  Reinforcement of model filled elastomers: characterization of the cross-linking density at the filler–elastomer interface by 1H NMR measurements , 2003 .

[2]  L. Brinson,et al.  Interfacial and Substrate Effects on Local Elastic Properties of Polymers Using Coupled Experiments and Modeling of Nanoindentation , 2011 .

[3]  J. Tinsley Oden,et al.  Control of modeling error in calibration and validation processes for predictive stochastic models , 2011 .

[4]  Timon Rabczuk,et al.  A computational library for multiscale modeling of material failure , 2013, Computational Mechanics.

[5]  J. Beck,et al.  Model Selection using Response Measurements: Bayesian Probabilistic Approach , 2004 .

[6]  A. Argon,et al.  Toughenability of polymers , 2003 .

[7]  D. Long,et al.  Filler–elastomer interaction in model filled rubbers, a 1H NMR study , 2002 .

[8]  Khader M. Hamdia,et al.  Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling , 2015 .

[9]  Y. Mai,et al.  On fracture toughness of nano-particle modified epoxy , 2011 .

[10]  H. Steininger,et al.  The mechanical behaviour of ZnO nano-particle modified styrene acrylonitrile copolymers , 2015 .

[11]  Anthony J. Kinloch,et al.  Toughening mechanisms of nanoparticle-modified epoxy polymers , 2007 .

[12]  K. Masania,et al.  The toughness of epoxy polymers and fibre composites modified with rubber microparticles and silica nanoparticles , 2010 .

[13]  H. Steininger,et al.  Toughening by plastic cavitation around cylindrical particles and fibres , 2014 .

[14]  L. Schadler,et al.  Quantitative equivalence between polymer nanocomposites and thin polymer films , 2005, Nature materials.

[15]  K. Friedrich,et al.  Fracture behaviours of in situ silica nanoparticle-filled epoxy at different temperatures , 2008 .

[16]  P. Dittanet,et al.  Effect of silica nanoparticle size on toughening mechanisms of filled epoxy , 2012 .

[17]  A. Kinloch,et al.  The modelling of the toughening of epoxy polymers via silica nanoparticles: The effects of volume fraction and particle size , 2013 .

[18]  M. Quaresimin,et al.  A multi-scale and multi-mechanism approach for the fracture toughness assessment of polymer nanocomposites , 2014 .

[19]  David J. C. MacKay,et al.  Bayesian Interpolation , 1992, Neural Computation.

[20]  M. Cho,et al.  Multi-scale modeling of cross-linked epoxy nanocomposites , 2009 .

[21]  Gregory M. Odegard,et al.  Modeling of the mechanical properties of nanoparticle/polymer composites , 2005 .

[22]  M. Quaresimin,et al.  Mechanical behaviour of epoxy/silica nanocomposites: Experiments and modelling , 2015 .

[23]  P. Dittanet,et al.  Effect of bimodal particle size distributions on the toughening mechanisms in silica nanoparticle filled epoxy resin , 2013 .

[24]  R. Pearson,et al.  Toughening mechanisms in epoxy–silica nanocomposites (ESNs) , 2009 .

[25]  Timon Rabczuk,et al.  Efficient coarse graining in multiscale modeling of fracture , 2014 .

[26]  Khader M. Hamdia,et al.  Predicting the fracture toughness of PNCs: A stochastic approach based on ANN and ANFIS , 2015 .

[27]  Thomas Most.  Assessment of structural simulation models by estimating uncertainties due to model selection and model simplification , 2011 .

[28]  M. Quaresimin,et al.  Influence of interphase and filler distribution on the elastic properties of nanoparticle filled polymers , 2013 .

[29]  Holger Keitel,et al.  Selecting creep models using Bayesian methods , 2012 .

[30]  J. Jam,et al.  Fracture toughness of epoxy polymer modified with nanosilica particles: Particle size effect , 2013 .

[31]  Michele Zappalorto,et al.  An efficient RVE formulation for the analysis of the elastic properties of spherical nanoparticle reinforced polymers , 2015 .

[32]  Tsu-Wei Chou,et al.  Nanocomposites in context , 2005 .

[33]  A. Kinloch,et al.  Modelling of the toughening mechanisms in rubber-modified epoxy polymers , 1992, Journal of Materials Science.

[34]  A. Kinloch,et al.  Modelling of the toughening mechanisms in rubber-modified epoxy polymers , 1992, Journal of Materials Science.

[35]  J. Williams.  Particle toughening of polymers by plastic void growth , 2010 .

[36]  Timon Rabczuk,et al.  An adaptive multiscale method for quasi-static crack growth , 2014 .

[37]  M. Quaresimin,et al.  Influence of the interphase zone on the nanoparticle debonding stress , 2011 .

[38]  Klaus Friedrich,et al.  Epoxy nanocomposites ¿ fracture and toughening mechanisms , 2006 .

[39]  T. Rabczuk,et al.  Molecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture , 2013 .

[40]  Paul T. Bauman,et al.  A computational framework for dynamic data‐driven material damage control, based on Bayesian inference and model selection , 2015 .

[41]  L. Catherine Brinson,et al.  Simulation of interphase percolation and gradients in polymer nanocomposites , 2009 .

[42]  Jian-kang Chen,et al.  Size effect of particles on the damage dissipation in nanocomposites , 2007 .

[43]  B.E.A. Fisher,et al.  Why Use One Model? An Approach for Encompassing Model Uncertainty and Improving Best Practice , 2002 .

[44]  J. Oden,et al.  Calibration and validation of coarse-grained models of atomic systems: application to semiconductor manufacturing , 2014 .

[45]  Timon Rabczuk,et al.  Concurrent multiscale modeling of three dimensional crack and dislocation propagation , 2015, Adv. Eng. Softw..

[46]  M. Quaresimin,et al.  A multiscale model to describe nanocomposite fracture toughness enhancement by the plastic yielding of nanovoids , 2012 .

[47]  Zhongya Zhang,et al.  Property improvements of in situ epoxy nanocomposites with reduced interparticle distance at high nanosilica content , 2006 .

[48]  M. Quaresimin,et al.  Plastic shear bands and fracture toughness improvements of nanoparticle filled polymers: A multiscale analytical model , 2013 .

[49]  A. Kinloch,et al.  The mechanisms and mechanics of the toughening of epoxy polymers modified with silica nanoparticles , 2010 .