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...
This work focuses on assessment of real fiber and matrix volume ratios of unidirectional fiber composites which will be used while designing corresponding micromodels. Scanning electron microscopy (SEM) was employed on samples with polished cross-sections. Obtained images of various parts of the composite cross-sections are analyzed by convolution with a circular binary mask and a suitably chosen spatial function using Matlab and its Image processing toolbox. The output of this analysis are center positions and radii of all fibers. Subsequently, the fiber and matrix volume ratios are easily determined.
Material parameters for elastic, plastic and damage behavior of low-molecular-weight epoxy resin CHS-EPOXY 520 hardened with CHS-P 11 are identified in the paper. Uniaxial cyclic static tests were performed on specimens in line with the ASTM standard D638 -10 using a Zwick Roell/Z050 test machine with a BTC-Exaclbi.001 clip-on biaxial extensometer. Poisson's ratio and tensile strength were calculated directly from the test results. Other parameters were identified using a combination of a one-dimensional material model, which assumes the infinitesimal strain theory and takes into account elastic, plastic and damage behavior and the optimization method. The model is coded in Python and the values of the material parameters are identified using the optiSLang optimization software. The optimization process uses simple design improvement and gradient-based algorithms with the goal to minimize the difference between the force-elongation curves recorded during the tests and those calculated with the proposed model. Keywords: epoxy, identification, optimization, elasticity, plasticity, damage V~lanku so opredeljeni parametri epoksi smole z majhno molekulsko maso CHS-EPOXY 520, utrjeno z CHS-p 11, pri elasti~nem, plasti~nem obna{anju in pri po{kodbi. Enoosni stati~ni cikli~ni preizkusi so bili izvedeni na vzorcih, ki ustrezajo ASTM standardu D638-10, z uporabo Zwick Roell/Z050 preizkusnega stroja z name{~enim dvoosnim ekstenziometrom BTC-Exaclbi.001. Poissonov koli~nik in natezna trdnost sta bili izra~unani neposredno iz rezultatov preizkusov. Drugi parametri so ugotovljeni s kombinacijo enodimenzijskega modela materiala, ki predpostavlja infinitezimalno teorijo napetosti in ki upo{teva obna{anje v elasti~nem, plasti~nem in ob po{kodbi ter metodo optimizacije. Model je kodiran v Pythonu in vrednosti parametrov materiala so ugotovljene z uporabo optiSLang programske opreme za optimizacijo. Proces optimizacije uporablja enostavno izbolj{anje oblike in algoritme, ki temeljijo na gradientu, s ciljem po zmanj{anju razlike med krivuljo silaraztezek zabele`ene med preizkusom in izra~unane z uporabo predlaganega modela.
This work focuses on an assessment of the real fiber and matrix volume ratios of unidirectional fiber composites that can be used for the design of corresponding numerical models on the micro-scale. Samples with polished cross-sections were prepared from three composite plates and they were previously analyzed using scanning electron microscopy (SEM). All the plates were manufactured from the same prepreg material using autoclave technology. Each plate consisted of a different number of plies. Images of the various parts of the composite cross-sections obtained with SEM are analyzed using several image-processing techniques programmed in Matlab, its Image Processing Toolbox, and C code. The results of this analysis are the center positions and radii of all fibers within the image. The fiber and matrix volume ratios are determined subsequently and mutually compared for different locations across the plates' thicknesses. Keywords: composite, unidirectional, micromechanics, constituents, image, detection, microscopy, cross-section Delo je osredoto~eno na oceno realnih vlaken in volumenskega dele`a v osnovi, v enosmernih kompozitih iz vlaken, ki jih je mogo~e uporabiti za postavitev ustreznih numeri~nih modelov na mikropodro~ju. Pripravljeni vzorci, s poliranim presekom, iz treh kompozitnih plo{~, so bili pregledani s pomo~jo vrsti~nega elektronskega mikroskopa (SEM). Vse plo{~e so bile izdelane iz enakega, v avtoklavih izdelanega, predimpregniranega materiala. Vsaka plo{~a je bila sestavljena iz razli~nega {tevila plasti. Posnetki razli~nih delov preseka kompozita, dobljeni s SEM, so bili analizirani z ve~tehnikami za obdelavo slik, programiranimi v Matlab, Image Processing Toolbox in C-kodo. Rezultati teh analiz so pozicije sredine in radiji vseh vlaken na posnetku. Pozneje so bili dolo~eni, in medsebojno primerjani, volumenski dele`i vlaken na razli~nih lokacijah preko debeline plo{~e.
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