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Streszczenie:
The subject of the study are alumina foams produced by gelcasting method. The results of micro-computed tomography of the foam samples are used to create the numerical model reconstructing the real structure of the foam skeleton as well as the simplified periodic open-cell structure models. The aim of the paper is to present a new idea of the energy-based assessment of failure strength under uniaxial compression of real alumina foams of various porosity with use of the periodic structure model of the same porosity. Considering two kinds of cellular structures: the periodic one, for instance of fcc type, and the random structure of real alumina foam it is possible to justify the hypothesis, computationally and experimentally, that the same elastic energy density cumulated in the both structures of the same porosity allows to determine the close values of fracture strength under compression. Application of finite element computations for the analysis of deformation and failure processes in real ceramic foams is time consuming. Therefore, the use of simplified periodic cell structure models for the assessment of elastic moduli and failure strength appears very attractive from the point of view of practical applications.

Słowa kluczowe:
periodic cell structure, alumina open-cell foam, Young modulus, strength of alumina foams, Burzyński limit criterion

Streszczenie:
The aim of this paper is to apply the results of microtomography of alumina foam to create a numerical model and perform numerical simulations of compression tests. The geometric characteristics of real foam samples are estimated from tomographic and scanning electron microscopy images. The performance of the reconstructed models is compared to experimental values of elastic moduli. A preliminary analysis of failure strength simulations under compression of alumina foam is also provided.

Słowa kluczowe:
alumina open-cell foam, computed tomography microstructure, Young's modulus, compressive strength of alumina foams

Streszczenie:
The mechanical properties and numerical model of ceramic alumina open-cell foam, which is produced by the chemical method of gelcasting with different cell sizes (porosities) are presented. Geometric characteristics of real foam samples were estimated from tomographic and scanning electron microscopy images. Using this information, numerical foam model was proposed. A good agreement between the numerical model and the results elaborated from microtomography was obtained. To simulate the deformation processes the finite element program ABAQUS was used. The main goal of this computation was to obtain macroscopic force as a function of applied vertical displacement in compression test.

Słowa kluczowe:
mechanical properties of foams, alumina open-cell foam, Young modulus, strength of alumina foams

Streszczenie:
Recently, a new class of ceramic foams with porosity levels up to 90% has been developed as a result of the association of the gelcasting process and aeration of the ceramic suspension. This paper presents and discusses original results advertising sound absorbing capabilities of such foams. The authors manufactured three types of alumina foams in order to investigate three porosity levels, namely: 72, 88, and 90%. The microstructure of foams was examined and typical dimensions and average sizes of cells (pores) and cell-linking windows were found for each porosity case. Then, the acoustic absorption coefficient was measured in a wide frequency range for several samples of various thickness cut out from the foams. The results were discussed and compared with the acoustic absorption of typical polyurethane foams proving that the alumina foams with high porosity of 88-90% have excellent sound absorbing properties competitive with the quality of sound absorbing PU foams of higher porosity.

Słowa kluczowe:
Sound absorption, Porous materials, Alumina foams

Streszczenie:
In the present paper a finite element model was used to investigate the mechanical properties such as Young’s modulus of open-cell ceramic foam. Finite element discretization was derived from real foam specimen by computer tomography images. The generated 3D geometry of the ceramic foam was used to simulate deformation process under compression. The own numerical procedure was developed to control finite element mesh density by changing the element size. Several numerical simulations of compression test have been carried out using commercial finite element code ABAQUS. The size of the ceramic specimen and the density of finite element mesh were examined. The influence of type and size of finite element on the value of Young’s modulus was studied, as well. The obtained numerical results have been compared with the results of experimental investigations carried out by Ortega [11]. It is shown that numerical results are in close agreement with experiment. It appears also that the dependency of Young’s modulus of ceramic foam on density of finite element mesh cannot be ignored.

Słowa kluczowe:
foams, 3D image analysis, cellular ceramics, FE modeling, porous alumina, mechanical properties

Streszczenie:
Kompozyty metalowo-ceramiczne o strukturze infiltrowanej charakteryzują się unikatową przestrzenną strukturą wzajemnie przenikających się szkieletów fazy metalicznej i fazy ceramicznej. Najczęstszym sposobem wytwarzania tego typu kompozytów jest infiltracja roztopionego metalu do porowatej kształtki ceramicznej. W niniejszej pracy zastosowano piankowe kształtki korundowe (alfa-Al2O3), wytworzone nową metodą otrzymywania ceramiki porowatej, którą jest żelowanie spienionej zawiesiny (ang. gelcasting of foams). W projektowaniu właściwości mechanicznych pianek ceramicznych przeznaczonych do infiltracji roztopionym metalem, a także w badaniach właściwości mechanicznych kompozytów w postaci pianki ceramicznej infiltrowanej metalem powstaje potrzeba odtworzenia struktury ceramicznej szkieletu kompozytu.

Słowa kluczowe:
Kompozyty metalowo-ceramiczne, pianki ceramiczne, modelowanie, symulacje MES

Streszczenie:
Three kinds of cellular materials are considered. Depending on geometry and physical properties of the skeleton, these are metallic cellular materials with convex or reentrant open cell structure. To the third group belong alumina foams produced by gel casting method. Finite element computations are used to analyse mechanical properties of a material volume. Such an analysis is usually related with big computational costs. Therefore, it is important to keep the size of the considered cellular material volume as small as possible. On the other hand, the validity of the continuum model requires the proper size of the RVE. The aim of the study is to estimate the sufficient size of representative volume element (RVE) in order to assess the validity of the elastic model of the considered cellular material. An array of cubes of virtual cellular material is used to compute the particular deformation modes providing elastic moduli, Young modulus E, shear modulus G and bulk modulus K as well as the resulting Poisson's ratio. Also the results of the microtomography of alumina foams are used to create the „virtual cellular material” i.e. the numerical model reconstructing the structure of real foam skeleton. The numerical simulations of compression test are performed. The results are compared with experimental data of elastic moduli and failure strength. The numerical simulations of failure strength under compression for alumina foams are performed. The calculations with use of the numerical model are time consuming. Therefore, the simplified method of the assessment of failure strength is proposed. It is based on the energy-based hypothesis on the equivalence of of elastic moduli and the resulting equivalence of the values of failure strength of real alumina foam and the cellular material with regular structure (e.g. fcc type). The justification of the hypothesis based on experimental data of compression of alumina foam are discussed and the range of validity as regards porosity values is studied.

Słowa kluczowe:
virtual cellular materials, convex skeleton, reentrant skeleton. representative volume element, numerical simulations

Streszczenie:
The aim of the paper is to apply the results of microtomography of alumina foam to create the numerical model and perform the numerical simulations of compression tests. The geometric characteristics of real foam samples are estimated from tomographic and scanning electron microscopy images. The performance of the reconstructed models is compared to experimental values of elastic moduli.

Słowa kluczowe:
Alumina open-cell foam, the computed tomography microstructure, Young modulus, the compressive strength of alumina foams

Streszczenie:
W pracy określono własności mechaniczne i przedstawiono model numeryczny ceramicznej pianki korundowej, otrzymanej metodą żelowania spienionej zawiesiny (gelcasting). Metoda ta pozwala wytwarzać pianki zawierające kmórki o różnej wielkości, a w konsekwencji otrzymywać pianki o różnej porowatości. Wielkości charakteryzujące geometrię rzeczywistych pianek ustalono z wykorzystaniem obrazów tomograficznych 3D oraz obrazów z mikroskopu skaningowego. Informacje te wykorzystano przy opracowaniu modelu numerycznego badanej pianki. Symulacje numeryczne procesów deformacji przeprowadzono z zastosowaniem programu elementow skończonych ABAQUS.

Słowa kluczowe:
pianki ceramiczne, metoda żelowania, porowatość, symulacje numeryczne procesów deformacji tomografia komputerowa, mikroskopia skaningowa

Streszczenie:
In this work a numerical model of real foam with different cell sizes is presented and its applications are discussed. Geometric characteristics of real foam samples were estimated from tomographic and scanning electron microscopy images. Using this information, numerical foam model was proposed. The examples of generated numerically structures are shown. A good agreement between numerical model and the results elaborated from microtomography was obtained.

Słowa kluczowe:
Alumina open-cell foam, foam with different cell sizes, numerical foam model based on tomographic and scanning electron microscopy images

Streszczenie:
New aeronautic materials are obtained by liquid metal infiltration into a ceramic foam, called a preform. Ceramic preforms are produced by a new method of manufacturing of porous ceramics foams known as gelcasting. Porous ceramics fabricated by this method is characterized by a continuous network of spherical cells interconnected by circular windows. The open porosity due to the presence of windows creates good hydro-dynamical properties for liquid metals infiltration. For better understanding mechanical properties of such composites a numerical model of ceramic foam is needed, see e. g. ref. [1-4]. Geometry of ceramic foams can be generated in two steps. First, the coordinates of the center point of the spherical bubbles and its diameter are produced by PYTHON scripts. The diameters of spherical bubbles were estimated from microtomography and scanning electron microscopy images. On the other hand, the coordinates of the center points are determined in such a way that the bubbles have to intersect with each other. Finally, the intersecting bubbles are subtracted from the bulk block of any shape. Using this information, numerical foam model was proposed and good agreement between numerical model and real foam structure from microtomography was obtained. In this work we present a numerical model of real foam of alumina with different cell sizes and discuss its mechanical properties using several examples. The numerical simulations of uniaxial compression test have been performed. As a result the compressive strength of the investigated foams with porosities changing from 60 to 95 % were determined.

Słowa kluczowe:
Porous ceramics foams produced by gelcasting, open-cell ceramic foam, the numerical simulations of uniaxial compression test, the compressive strength of alumina foams with porosities changing from 60 to 95 %

Streszczenie:
Celem pracy jest ocena granicznych ciśnień oraz temperatury procesu, dla których proces infiltracji zachodzi bez uszkodzenia pianki w skali makroskopowej. W pracy przedstawiono numeryczny model procesu wypełniania ceramicznej preformy o otwartej strukturze porów. W procesie wypełniania preformy ciekłym metalem lokalny wzrost naprężeń i kruchość materiału powodują pękanie części elementów pianki. Opracowano model numeryczny tego procesu, który zaimplementowano w programie ABAQUS. Dla określenia stanu naprężenia w piance użyto sprzężonej metody CEL (ang. the coupled Eulerian-Lagrangian method) w programie Abaqus/Explicit.

Słowa kluczowe:
Proces infiltracji ceramicznych pianek ciekłym metalem, ocena granicznych ciśnień oraz temperatury procesu