1. Microstructural modelling of elastoplastic behaviour of nodular cast iron by reduced homogenization method
- Author
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Plavšić, Luka and Lesičar, Tomislav
- Subjects
Heterogeni materijal ,Heterogeneous material ,nodularni lijev ,Lippman-Schwingerova jednadžba ,k-means clustering ,LippmanSchwinger equation ,k-means klasteriranje ,homogenizacija s reduciranim brojem stupnjeva slobode ,TEHNIČKE ZNANOSTI. Strojarstvo ,reduced homogenization method ,nodular casting (ductile iron) ,TECHNICAL SCIENCES. Mechanical Engineering ,Inmould ,Tundish - Abstract
Većina materijala je heterogena, ovisno na kojoj se skali promatraju. Prema tome, može se reći da su i mehanička svojstva materijala uvelike ovisna o heterogenoj mikrostrukturi, odnosno međusobnom interakcijom različitih konstituenata na mikrostrukturnoj razini. U novije vrijeme dolazi do ubrzanog razvoja naprednih višerazinskih numeričkih algoritama uz pomoć kojih je moguće definirati direktnu vezu između mikrostrukture i konstitutivnog ponašanja materijala na makrorazini. Na taj je način moguće razviti materijal optimalnih svojstava manipulirajući raspodjelom, volumenskim udjelom i svojstvima mikrokonstituenata. U ovom radu razmatran je nodularni lijev oznake EN-GJS-400-18-LT proizveden tehnikama lijevanja Tundish i Inmould. Provedena je analiza postojećih mikrostruktura uz pomoć opisanih razdioba prema promjeru nodula grafita te njihove međusobne udaljenosti. Određena je najtočnija razdioba za obje varijable te je generirana mikrostruktura nodularnog lijeva za oba načina lijevanja. Metodom homogenizacije s reduciranim brojem stupnjeva slobode izračunate su vrijednosti materijalnih parametara feritne matrice nodularnog lijeva. Uz pomoć k-means algoritma klasteriranja koji se temelji na strojnom učenju, materijalne točke mikrostrukture su grupirane u elemente sa sličnim svojstvima, u kojima je vrijednost naprezanja i deformacija jednaka. Sve navedeno omogućuje metodi da proračunski model diskretizira s razmjerno malim brojem klastera što omogućuje značajnu uštedu vremena računanja. Nakon provedenog klasteriranja inkrementalno se rješavaju Lippmann-Schwingerova jednadžba. Na temelju numeričkih simulacija, određeni su koeficijenti potpunih polinoma drugog i trećeg reda koji definiraju elastoplastična svojstva feritne matrice prema Swiftovom zakonu očvršćenja, pomoću kojih su određene stvarne vrijednosti materijalnih parametara feritne matrice. Točnost same metode je demonstrirana usporedbom parametara izračunatih numeričkim simulacijama sa stvarnim vrijednostima preuzetima iz literature. Most materials are heterogeneous, depending on the scale at which they are observed. Therefore, it can be said that the mechanical properties of the material are largely dependent on the heterogeneous microstructure, i.e., on the mutual interaction of different constituents at the microstructural level. In recent times, there has been an accelerated development of advanced multilevel numerical algorithms with the help of which is possible to define a direct connection between the microstructure and the constitutive behavior of the material at the macrolevel. In this way, it is possible to develop a material with optimal properties by manipulating the distribution, volume fraction and properties of microconstituents. In this paper, nodular cast EN-GJS-400-18-LT produced by Tundish and Inmould casting techniques was considered. An analysis of the existing microstructures was carried out with the help of the described distributions according to the diameter of the graphite nodules and their mutual distance. The most accurate distribution for both variables was determined and the microstructure of ductile iron was generated for both methods of casting. The values of the material parameters of the ferrite matrix of nodular cast iron were calculated using the reduced homogenization method. With the help of the k-means clustering algorithm based on machine learning, the material points of the microstructure are grouped into elements with similar properties, in which the stress and strain values are equal. All of the above allows the method to discretize the computational model with a relatively small number of clusters, which enables a significant saving of computation time. After clustering, the Lippmann-Schwinger equation is solved incrementally. On the basis of numerical simulations, the coefficients of complete polynomials of the second and third order that define the elastoplastic properties of the ferrite matrix according to Swift's law of hardening were determined, by means of which the actual values of the material parameters of the ferrite matrix were determined. The accuracy of the method itself was demonstrated by comparing parameters calculated by numerical simulations with real values taken from the literature.
- Published
- 2023