Comparison of homogenization approaches used for the identification of the material parameters of unidirectional composites

Abstract

The paper is aimed at the identification of the material parameters of the constituents of unidirectional long-fiber carbon/epoxy composites. The ratios between the real fiber and the matrix volume of unidirectional fiber composites were identified from the images obtained with scanning electron microscopy (SEM). Fiber and matrix areas were analyzed using Matlab and its image-processing toolbox. Determined volume ratios were used to propose the geometry of a micromechanical representative volume element. An algorithm ensuring an irregular fiber distribution in the representative volume element cross-section and periodicity in the cross-section plane were used. A single-layer representative volume element with a mesh was built in Abaqus/CAE. Experimentally obtained force-elongation dependencies for the tensile tests of the specimens with different fiber orientations were processed and effective moduli were determined. In the first approach, the material parameters of phases were identified using the OptiSlang optimization software and finite-element code Abaqus. A periodically constrained representative volume element was loaded according to the experiments where specimens with different fiber orientations were loaded by tensile force. In the second approach, the SfePy software and asymptotic homogenization were used for the numerical computation on the microscopic scale, resulting in the homogenized material parameters that were afterwards used at the macroscopic level. The optimization function characterized the sum of the differences of the effective moduli and the difference of Poisson's ratios of the whole composite. Keywords: composite, unidirectional, micro-model, constituents, material parameters, cross-section, homogenization Namen~lanka je ugotavljanje materialnih parametrov sestavin epoksi kompozitov z enosmernim dolgimi ogljikovimi vlakni. Razmerje realnih vlaken in volumna osnove kompozitov z usmerjenimi vlakni je bilo dolo~eno iz slik, dobljenih na vrsti~nem elektronskem mikroskopu (SEM). Vlakna in podro~ja osnove so bili analizirani s pomo~jo Matlaba in njegovega orodja za obdelavo slik. Dolo~ena volumska razmerja so bila uporabljena za predlog geometrije reprezentativnih mikromehanskih volumskih elementov. Uporabljen je bil algoritem, ki zagotavlja neenakomerno razporeditev vlaken na preseku reprezentativnega volumskega elementa in periodi~nost na ravnini preseka. Plast reprezentativnega volumskega elementa z mre`o, je bila postavljena z Abaqus/CAE. Izvedeni so bili eksperimenti za dolo~anje odvisnosti sila-raztezek pri nateznih preizku{ancih z razli~no orientacijo vlaken in dolo~eni so bili efektivni moduli. V prvem pribli`ku so bili ugotavljani materialni parametri faz s pomo~jo OptiSlang programske opreme za optimizacijo in kodo kon~nih elementov Abaqus. Periodi~no omejen reprezentan~ni volumski element je bil obremenjen, skladno s preizkusi. Pri~emer so bili vzorci z razli~no orientacijo vlaken, obremenjeni z natezno silo. Pri drugem pribli`ku je uporabljena programska oprema SfePy in asimptot...

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Experimental and numerical characterization of thin woven composites used in printed circuit boards for high frequency applications

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