TY - JOUR

T1 - Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

AU - Hamdia, Khader M.

AU - Silani, Mohammad

AU - Zhuang, Xiaoying

AU - He, Pengfei

AU - Rabczuk, Timon

N1 - Funding information: The authors gratefully acknowledge the support for this research provided by the Deutsche Forschungsgemeinschaft (DFG).

PY - 2017/8

Y1 - 2017/8

N2 - 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.

AB - 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.

KW - Computational mechanics

KW - Fracture toughness

KW - Interphase

KW - Polymeric nanoparticle composites

KW - Sensitivity analysis

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85018707902&partnerID=8YFLogxK

U2 - 10.1007/s10704-017-0210-6

DO - 10.1007/s10704-017-0210-6

M3 - Article

AN - SCOPUS:85018707902

VL - 206

SP - 215

EP - 227

JO - International Journal of Fracture

JF - International Journal of Fracture

SN - 0376-9429

IS - 2

ER -