Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by d...

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Published in	International journal of fracture Vol. 206; no. 2; pp. 215 - 227
Main Authors	Hamdia, Khader M., Silani, Mohammad, Zhuang, Xiaoying, He, Pengfei, Rabczuk, Timon
Format	Journal Article
Language	English
Published	Dordrecht Springer Netherlands 01.08.2017 Springer Nature B.V
Subjects	Alloys Automotive Engineering Characterization and Evaluation of Materials Chemistry and Materials Science Civil Engineering Classical Mechanics Concentration (composition) Crack propagation Energy consumption Fillers Finite element method Fracture mechanics Fracture toughness Material properties Materials Science Mathematical models Mechanical Engineering Modulus of elasticity Nanocomposites Nanoparticles Original Paper Parameter uncertainty Polymers Polynomials Probability theory Propagation (polymerization) Reinforcement Sensitivity analysis Stochastic models Two dimensional models Variance analysis Uncertainty quantification Computational mechanics Sensitivity analysis Interphase Polymeric nanoparticle composites Fracture toughness
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Abstract	The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.
AbstractList	The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.
Author	Hamdia, Khader M. Silani, Mohammad Zhuang, Xiaoying He, Pengfei Rabczuk, Timon
Author_xml	– sequence: 1 givenname: Khader M. orcidid: 0000-0001-9898-8421 surname: Hamdia fullname: Hamdia, Khader M. organization: Duy Tan University, Institute of Research & Development, Institute of Structural Mechanics, Bauhaus-Universität Weimar – sequence: 2 givenname: Mohammad surname: Silani fullname: Silani, Mohammad organization: Department of Mechanical Engineering, Isfahan University of Technology – sequence: 3 givenname: Xiaoying surname: Zhuang fullname: Zhuang, Xiaoying organization: Tongji University – sequence: 4 givenname: Pengfei surname: He fullname: He, Pengfei organization: Tongji University – sequence: 5 givenname: Timon surname: Rabczuk fullname: Rabczuk, Timon email: timon.rabczuk@uni-weimar.de organization: Duy Tan University, Institute of Research & Development, Institute of Structural Mechanics, Bauhaus-Universität Weimar
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Keywords	Uncertainty quantification Computational mechanics Sensitivity analysis Interphase Polymeric nanoparticle composites Fracture toughness
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Snippet	The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers...
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SubjectTerms	Alloys Automotive Engineering Characterization and Evaluation of Materials Chemistry and Materials Science Civil Engineering Classical Mechanics Concentration (composition) Crack propagation Energy consumption Fillers Finite element method Fracture mechanics Fracture toughness Material properties Materials Science Mathematical models Mechanical Engineering Modulus of elasticity Nanocomposites Nanoparticles Original Paper Parameter uncertainty Polymers Polynomials Probability theory Propagation (polymerization) Reinforcement Sensitivity analysis Stochastic models Two dimensional models Variance analysis
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Title	Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions
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