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Development of stochastic nonlinear multiscale computational method for short fiber reinforced composites to study the influence of microstructural variability on damage propagation (本文)

Hoang, Tien Dat 慶應義塾大学

2020.09.21

概要

The mechanical properties of fiber reinforced composite materials are scattered especially in the development of a new and cost-effective manufacturing process. The main reason lies in the microstructural variability expressed by physical parameters of constituent materials and geometrical parameters to express the morphology at microscale. The short fiber reinforced composite materials can be fabricated easily by injection molding method, but they have random microstructures. To solve the problem considering variability, there have been many studies on the stochastic finite element method. The first-order perturbation based stochastic homogenization (FPSH) method has been developed based on the multiscale theory and verified for porous materials and multi-phase composite materials considering the variability in physical parameters. However, its applications were limited to linear elastic problems. Therefore, this study aims at the development of a stochastic nonlinear multiscale computational method. In its application to short fiber reinforced composites, the final goal of this study is to clarify the important random factors in the microstructure that give significant influence on the damage propagation.

Firstly, the above FPSH method was extended for the stochastic calculation of microscopic strain. This theory enabled us to analyze the damage initiation and propagation in a stochastic way. Since huge scenarios exist in the nonlinear behaviors, however, a sub- sampling scheme was proposed in the analysis by FPSH method together with the sampling scheme for geometrical random parameters. Furthermore, to reduce the computational time for practical and large-scale analyses of stochastic damage propagation problems, a numerical algorithm to accelerate the convergence of element-by-element scaled conjugate gradient (EBE-SCG) iterative solver for FPSH method was developed. The efficiency was demonstrated for spherical particulate-embedded composite material considering the damage in the coating layer and the variability in physical parameter.

Finally, the developed computational method was applied to short fiber reinforced composite materials. The fiber length distribution, fiber orientation denoted by two angles and fiber arrangement were considered as the geometrical parameters in addition to a physical random parameter. 11 models were analyzed having different fiber orientation and fiber arrangement with variability. In the sub-sampling, 2 scenarios with 50% and 0.3% probabilities were analyzed, which resulted in totally 22 cases. The differences among 22 possible damage patterns were discussed deeply. It was figured out that very largely scattered degradation of homogenized macroscopic properties was mostly affected by the fiber arrangement rather than the fiber orientation. This finding was different from the result in linear elastic region. The physical random parameters were more influential on the macroscopic properties. Also in these analyses, the accelerated EBE-SCG method was again shown to be efficient.

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