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

• 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
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-017-0210-6

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.