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1

Modeling of temperature-dependent cyclic performance of superelastic NiTi shape memory alloy

Xiao Yao, Ju Shuangyan, Lin Jianping

Computer Methods in Materials Science

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2022

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Vol. 22, No. 1

13--22

EN

In this paper, a three-dimensional micromechanical-based constitutive model is proposed to describe the temperature-dependent performance of a cyclic deformed superelastic NiTi shape memory alloy. The dominant texture of the specimen is prescribed as <111> direction along the longitudinal direction. Apart from martensitic transformation, various mechanisms regarding superelastic degradation are taken into consideration. In order to be extended from the single-crystal scale to the polycrystalline version, the constitutive model is implemented into finite element software. It is verified that the measured cyclic response of a superelastic NiTi is well reproduced by the presented approach. Furthermore, the predicting capability of the proposed model is verified by simulating the mechanical behavior of NiTi tube subjected to cyclic bending.

2

Fluid solid interactions – a novelty in industrial applications

Ochrymiuk Tomasz, Banaszkiewicz Mariusz, Lemański Marcin, Kowalczyk Tomasz, Ziółkowski Paweł, Ziółkowski Piotr J., Hyrzyński Rafał, Stajnke Michał, Bryk Mateusz, Kraszewski Bartosz, Kruk-Gotzman Sylwia, Froissart Marcin, Badur Janusz

Archives of Thermodynamics

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2022

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Vol. 43, no 2

75--96

EN

The article deals with a current state-of-art of fluid solid interaction (FSI) – the new branch of continuum physics. Fluid-solid interaction is a new quality of modeling physical processes of continuum mechanics, it can be described as the interaction of various (so far treated separately from the point of view of mathematical modeling) physical phenomena occurring in continuous media systems. The most correct is the simultaneous application of the laws of the given physical disciplines, which implies that fluid solid interaction is a subset of multi-physical applications where the interactions between these subsets are exchanged on the surface in interconnected systems. Our purpose is to extend the fluid solid interaction aplications into new phenomena what follow from the industrial needs and inovative thechnologies. Selecting the various approaches, we prefer the arbitraty lagrangean-eulerian description within the bulk of fluid/solid domain and a new sort of advanced boundary condition on a surface of common contact.

3

Shape and packing effects in particulate composites: micromechanical modelling and numerical verification

Majewski Michał, Wichrowski Michał, Hołobut Paweł, Kowalczyk-Gajewska Katarzyna

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e86, 1--22

EN

The aim of this study is to analyse the joint effect of reinforcement shape and packing on the effective behaviour of particulate composites. The proposed semi-analytical modelling method combines the Replacement Mori-Tanaka scheme, by means of which the concentration tensors for non-ellipsoidal inhomogeneities are found numerically, and the analytical morphologically representative pattern approac to account for particle packing. Five shapes of inhomogeneities are selected for the analysis: a sphere, a prolate ellipsoid, a sphere with cavities, an oblate spheroid with a cavity as well as an in homogeneity created by three prolate spheroids crossing at right angles. Semi-analytical estimates are compared with the results of numerical simulations performed using the finite element method and with the outcomes of classical mean-field models based on the Eshelby solution, e.g. the Mori–Tanaka model or the self-consistent scheme.

4

On speeding up nano- and micromechanical calculations for irregular systems with long-range potentials

Rybarska-Rusinek L., Rejwer E., Linkov A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 2

337--344

EN

Irregular systems with long-range interactions and multiple clusters are considered. The presence of clusters leads to excessive computational complexity of conventional fast multipole methods (FMM), used for modeling systems with large number of DOFs. To overcome the difficulty, a modification of the classical FMM is suggested. It tackles the very cause of the complication by accounting for higher intensity of fields, generated by clusters in upward and especially in downward translations. Numerical examples demonstrate that, in accordance with theoretical estimations, in typical cases the modified FMM significantly reduces the time expense without loss of the accuracy.

5

Elastic properties of self-compacting concrete modified with nanoparticles: Multiscale approach

Stefaniuk D., Niewiadomski P., Musial M., Lydzba D.

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 4

1150--1162

EN

Advances in cementitious composites and nanotechnologies have led to the development of self-compacting concrete (SCC) modified with nanoparticles. SCC with Al2O3 nanoparticles was used in this study. In addition, a reference sample of SCC without an addition of nanoparticles was investigated. First, the micro-mechanical properties of each phase of the composites were examined using the statistical nanoindentation techniques and deconvo-lution. Then, the interfacial transition zone (ITZ) was investigated using line indentation and X-ray microCT. The results indicated that the ITZ played no significant role in the compo-sites. Subsequently, modified Mori–Tanaka and self-consistent homogenization schemes, accounting for random variability of constituent properties, were applied to evaluate the overall elastic properties of the composites. Then, macroscale laboratory (uniaxial compres-sion) tests were carried out to verify the adopted approach. The results of the micro- and macroscale tests showed that the proposed laboratory investigation procedure and homog-enization approach were proper. Finally, the modified Mori–Tanaka scheme was used to verify the influence of material composition on the effective elastic modulus of SCC with Al2O3 nanoparticles.

6

An analytical study on buckling behavior of CNT/polymer composite plates using the first order shear deformation theory

Peyyala P. K., Subba Rao V. V.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 1

71--79

EN

Most plates used in engineering structures such as aircraft wings, ship ducts and buildings, although quite capable of resisting tensile loads, are poor in withstanding compression. In order to avoid premature failure under compression, it is important to know buckling behavior of the plate. This article primarily deals with the analytical study of buckling behavior of a carbon nanotube reinforcing polymer composite plates based on the first order shear deformation theory by employing Mori-Tanaka micromechanics approach to obtain elastic properties. In this investigation, an attempt is made for evaluating the effect of plate thickness, CNT volume fraction, stacking sequence and CNT radii on the buckling of plates.

7

The Hardening in Alloys and Composites and Its Examination with a Diffraction and Self-Consistent Model

Gadalińska E., Baczmański A., Wroński S., Wróbel M., Scheffzük C.

Fatigue of Aircraft Structures

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2018

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Iss. 10

31--46

EN

The paper presents the results of diffraction stress measurement in Al/SiC composite and in 2124T6 aluminum alloy during the in situ tensile test. The main aim of the work is to observe the stress values for different stages of tensile test for the composite after applying two types of thermal treatment and for the alloy used as a matrix in this composite, to identify the type of hardening process. The experimental results were compared against the calculations results obtained from the self-consistent model developed by Baczmański [1] - [3] to gain the information about the micromechanical properties (critical resolved shear stress τcr and hardening parameter H) of the examined materials. This comparison allowed researchers to determine the role of reinforcement in the composite as well as the impact of the heat treatment on the hardening of the material.

8

Assessment methods of mechanical properties of composite materials

Kamocka M., Mania R. J.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 4

1005--1018

EN

The paper deals with a specific kind of imperfection in multilayered composite structures as thickness deviation. During manufacturing process the layers are laminated together with resin. Lack of accuracy or some errors during autoclaving process could contribute to thickness deviation when thin layer of resin remains between plies. This is particularly important in the case of hybrid laminates as Fibre Metal Laminates (FML). Therefore, the aim of this work is to determine the impact of thickness imperfection on the variation of effective mechanical properties of FML thin-walled panels. Two methods have been considered in the study: assumption of additional resin/matrix layer in a stacking sequence and a correction of fibre volume fraction in composite layers. A full 3-2 FML lay-up has been analyzed using Classical Lamination Plate Theory with connection to two micromechanical approaches: analytical (Rule of Mixture) and numerical (Finite Element Method). Results of calculations were verified by conducted experimental tests.

9

High ductile behavior of a polyethylene fiber-reinforced one-part geopolymer composite: A micromechanics-based investigation

Nematollahi B., Sanjayan J., Qiu J., Yang E. H.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 3

555--563

EN

This study investigates the tensile performance a one-part strain hardening geopolymer composite (SHGC) reinforced by ultra-high-molecular-weight polyethylene (PE) fibers. The developed composite as a “dry mix” uses a small amount of solid activator rather than large quantities of commonly used alkaline solutions and eliminates the necessity for heat curing. The quantitative influences of curing condition (heat and ambient temperature curing) and type of fiber (poly vinyl alcohol (PVA) and PE fibers) on the macroscale properties of the matrix and composite including workability, density, compressive strength, and uniaxial tensile performance were evaluated. A micromechanics-based investigation was performed to explain the experimentally observed macroscopic high tensile ductility of the developed one-part PE-SHGCs. The investigation involved determination of the matrix fracture properties and the fiber–matrix interface properties using fracture toughness tests and single-fiber pullout tests, respectively. The fiber-bridging constitutive law of the composites was computed via a micromechanics-based model to link the material microstructures to macroscopic composite tensile performance. The results indicated that the ambient temperature curing increased the compressive and tensile strengths, but reduced the tensile ductility of the one-part PE-SHGCs. The one-part PE-SHGCs exhibited lower compressive and tensile strengths, but higher tensile ductility compared to the one-part PVA-SHGC.

10

Microscopically based calibration of the cohesive model

Gałkiewicz J.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 2

477--485

EN

In this paper, the calibration of a cohesive zone model in front of a crack is presented. It is based on the behavior of a cell containing a void. The sizes of the cell and the void are assumed to be representative for a chosen material. The cell is located at the crack tip. The loading conditions of the cell take into account the constraint level ahead of the crack tip. The influence of the constraint on the cohesive model parameters is investigated.

11

Determination of material parameters for microbuckling analysis of fiber reinforced polymer matrix composites

Romanowicz M.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 2

373--383

EN

This research focuses on studying the effect of the constitutive law adopted for a matrix material on the compressive response of a unidirectional fiber reinforced polymer matrix composite. To investigate this effect, a periodic unit cell model of a unidirectional composite with an initial fiber waviness and inelastic behavior of the matrix was used. The sensitivity of the compressive strength to the hydrostatic pressure, the flow rule and the fiber misalignment angle were presented. The model was verified against an analytical solution and experimental data. Results of this study indicate that a micromechanical model with correctly identified material parameters provides a useful alternative to theoretical models and experimentation.

12

Failure criterion for brick masonry: a micro-mechanics approach

Kawa M.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 3

37--48

EN

The paper deals with the formulation of failure criterion for an in-plane loaded masonry. Using micro-mechanics approach the strength estimation for masonry microstructure with constituents obeying the Drucker–Prager criterion is determined numerically. The procedure invokes lower bound analysis: for assumed stress fields constructed within masonry periodic cell critical load is obtained as a solution of constrained optimization problem. The analysis is carried out for many different loading conditions at different orientations of bed joints. The performance of the approach is verified against solutions obtained for corresponding layered and block microstructures, which provides the upper and lower strength bounds for masonry microstructure, respectively. Subsequently, a phenomenological anisotropic strength criterion for masonry microstructure is proposed. The criterion has a form of conjunction of Jaeger critical plane condition and Tsai-Wu criterion. The model proposed is identified based on the fitting of numerical results obtained from the microstructural analysis. Identified criterion is then verified against results obtained for different loading orientations. It appears that strength of masonry microstructure can be satisfactorily described by the criterion proposed.

13

Numerical identification of material parameters for microbuckling analysis of fiber reinforced polymer matrix composites

Romanowicz M.

Computer Methods in Materials Science

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2014

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Vol. 14, No. 2

108--113

EN

This research focuses on studying the effect of material parameters upon the compressive response of a unidirectional fiber reinforced polymer matrix composite. To investigate this effect, the finite element method and a periodic unit cell model of unidirectional composite with an initial fiber waviness and inelastic behavior of the matrix were used. The sensitivity of the compressive strength to the hydrostatic pressure, the flow rule and the fiber misalignment angle were presented. The model was verified against an analytical solution and experimental data. The results of this study indicate that a micromechanical model with correctly identified material parameters provides a useful alternative to theoretical models and experimentation.

PL

W pracy badano wpływ parametrów materiałowych na wytrzymałość na wzdłużne ściskanie kompozytu jednokierunkowo wzmocnionego. W tym celu wykorzystano metodę elementów skończonych oraz komórkę elementarną kompozytu z początkową imperfekcją włókien i plastyczną matrycą. Analizowano zmianę krzywej ściskania kompozytu w wyniku zmiany tarcia wewnętrznego matrycy, prawa plastycznego płynięcia matrycy oraz początkowej imperfekcji włókien. W celu identyfikacji wymienionych parametrów materiałowych wykorzystano badania doświadczalne oraz istniejące modele analityczne. Wyniki badań pokazują, że model numeryczny jest skuteczną alternatywą w analizie mikro-wyboczenia kompozytów polimerowych wzmocnionych ciągłym włóknem.

14

Particle shape influence on elastic-plastic behaviour of particle-reinforced composites

Ogierman W., Kokot G.

Archives of Materials Science and Engineering

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2014

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Vol. 67, nr 2

70--76

EN

Particle-reinforced composite materials very often provide unique and versatile properties. Modelling and prediction of effective heterogeneous material behaviour is a complex problem. However it is possible to estimate an influence of microstructure properties on effective macro material properties. Mentioned multi-scale approach can lead to better understanding of particle-reinforced composite behaviour. The paper is focused on prediction of an influence of particle shape on effective elastic properties, yield stress and stress distribution in particle-reinforced metal matrix composites. Design/methodology/approach: This research is based on usage of homogenization procedure connected with volume averaging of stress and strain values in RVE (Representative Volume Element). To create the RVE geometry Digimat-FE software is applied. Finite element method is applied to solve boundary value problem, in particular a commercial MSC.Marc software is used. Findings: Cylindrical particles provide the highest stiffness and yield stress while the lowest values of stiffness and yield stress are connected with spherical particles. On the other hand stress distribution in spherical particles is more uniform than in cylindrical and prismatic ones, which are more prone to an occurrence of stress concentration. Research limitations/implications: During this study simple, idealised geometries of the inclusions are considered, in particular sphere, prism and cylinder ones. Moreover, uniform size and uniform spatial distribution of the inclusions are taken into account. However in further work presented methodology can be applied to analysis of RVE that maps the real microstructure. Practical implications: Presented methodology can deal with an analysis of composite material with any inclusion shape. Predicting an effective composite material properties by analysis of material properties at microstructure level leads to better understanding and control of particle-reinforced composite materials behaviour. Originality/value: The paper in details presents in details an investigation of influence of inclusion shape on effective elastic-plastic material properties. In addition it describes the differences between stress distributions in composites with various inclusion shapes.

15

Wear mechanisms of multilayer TiN/Ti/a-C:H coatings investigated by transmission electron microscopy technique

Major L.

Archives of Civil and Mechanical Engineering

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2014

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Vol. 14, no. 4

615--621

EN

Wear mechanisms of multilayer TiN/Ti/a-C:H coatings were investigated by transmission electron microscopy technique. Mechanical properties of the TiN/Ti/a-C:H multilayer coating were tested by a ball-on-disk. Microstructure of the coatings was analyzed after the mechanical treatment. Two types of wear mechanisms were discovered: cracking layer by layer remove and tribofilm formation. Cracking was performed by the ‘layers motion’ mechanism. After a one layer step movement they were fixed again. Tribofilm was built of two types of fractions. One was homogenous, the second one had layered structure. The qualitative chemical EDS analysis showed, that titanium oxide dominated in the homogenous area, while in the layered structure partial graphitization process was found. The graphite formation during the wear process, from the carbon phase presented in the coating, is a beneficial phenomenon due to the fact that graphite is a very good lubricant. The presence of the graphite phase in the tribofilm has been confirmed by the qualitative EDS chemical analysis, electron diffraction pattern and the high resolution technique. The article presents new ideas and techniques in materials science, especially in surface engineering, as well as in mechanics and mechanisms of wear of multilayer coatings.

16

Determination of effective properties of fiber-reinforced composite laminates

Skrzat A., Stachowicz F.

Advances in Science and Technology. Research Journal

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2014

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Vol. 8, nr 22

56--59

EN

The determination of effective mechanical properties of multi-layer composite is presented in this paper. Computations based on finite element method predicting properties of inhomogeneous materials require solving huge tasks. More effective is Mori-Tanaka approach, typical for micromechanics problems. For regularly distributed fibers closed-forms for effective composite material properties are possible to derive. The results of homogenization are used in strength analysis of the composite pressure vessel.

17

Numerical homogenization of fiber-reinforced composites with complex microstructural features

Romanowicz M.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 4

883--890

EN

A micromechanical model for solution of the problem of transverse stiffness of unidirectional fiber reinforced composites taking into account the presence of the interphase and a random distribution of fibers over the transverse cross-section has been developed. The influence of interphase properties on the elastic modulus in the transverse direction of glass/epoxy composites has been investigated. It has been found that numerical computations of transverse Young’s modulus obtained from the unit cell models for different fiber volume fractions are in a good agreement with experimental data.

18

Parallel identification of voids in microstructure using BEM and bioinspired algorithm

Kuś W., Górski R.

Computer Methods in Materials Science

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2013

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Vol. 13, No. 2

251--257

EN

The problem of identification of the size of a void in a microscale on the basis of the homogenized material parameters is studied in this work. A three-dimensional unit-cell model of a porous microstructure is modelled and analyzed by the boundary element method (BEM). The method is very accurate and for the considered problem requires discretization only the outer boundary of models. The algorithm used for identification is characterized by a hierarchical structure which allows for parallel computing on three different levels. The parallel algorithm is used for evolutionary computations. The solution of boundary value problems by the BEM and the determination of effective material properties by numerical homogenization method are also parallelized. The computation of the compliance matrix for a porous microstructure is shown. The matrix is used to formulate the objective function in identification problem in which the size of a void is searched. The scalability tests of the algorithm are performed using a server consisting of eight floating point units. As a result of using the hierarchical structure of the identification algorithm and the BEM, a significant computation speedup and the accuracy are achieved.

PL

W pracy przedstawiono zagadnienie identyfikacji rozmiaru pustki w skali mikro, na podstawie zhomogenizowanych parametrów materiałowych. Trójwymiarowy model komórki jednostkowej mikrostruktury porowatej modelowany i analizowany jest metodą elementów brzegowych (MEB). Metoda jest bardzo dokładna i dla rozważanego zadania wymaga jedynie dyskretyzacji zewnętrznego brzegu modeli. Zastosowany algorytm do identyfikacji charakteryzuje się hierarchiczną budową pozwalającą prowadzić obliczenia w sposób równoległy na trzech różnych poziomach. Wykorzystano równoległy algorytm do obliczeń ewolucyjnych. Zrównoleglono także rozwiązywanie zadań brzegowych za pomocą MEB oraz wyznaczanie zastępczych własności materiałowych metodą numerycznej homogenizacji. Pokazano sposób wyznaczania macierzy podatności mikrostruktury porowatej. Macierz jest wykorzystana do sformułowania funkcji celu w zagadnieniu identyfikacji, w którym poszukiwany jest rozmiar pustki. Przeprowadzono testy skalowalności algorytmu z użyciem serwera zawierającego osiem jednostek zmiennoprzecinkowych. Jako rezultat zastosowania algorytmu o budowie hierarchicznej oraz MEB uzyskano znaczne przyśpieszenie i dokładność obliczeń.

19

Prediction of elastic properties of polyurethane-infiltrated carbon foams

Janus-Michalska M.

Mechanics and Control

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2012

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Vol. 31, no. 3

97--101

EN

This paper presents micromechanical approach to assessment of elastic properties of composite polyurethane-carbon foams. Analysis is based on specific choice of RVE combined with micro-macro transition. It leads to evaluation of strength and elastic constants of a composite. Foam behaviour is investigated numerically. Solid skeleton part shape is based on the tetrahedron cut out with spheres. 3D unit cell model is FE discetized. Calculations are performed for foams of selected densities using ABAQUS system. The comparison shows good agreement between the theoretical approach and experimental data. The presented method may be applied to design novel materials such as graphitized foam and nano composites and tailoring these materials for desired elastic properties.

PL

Artykuł przedstawia zastosowanie podejścia mikromechanicznego do oszacowania własności sprężystych kompozytowych pian poliuretanowo-węglowych. Analiza ośrodka sprężystego jest oparta na podejściu mikromechanicznym, które prowadzi do określenia własności sprężystych kontinuum, jakim jest materiał kompozytowy na podstawie reprezentatywnej komórki. Kształt szkieletu komórki jest oparty na czworościanie z wyciętymi sferami wypełnionymi innym materiałem. Obliczenia są przeprowadzone programem ABAQUS metodą elementów skończonych. Porównanie wyników numerycznych i eksperymentalnych dla wybranych gęstości pian wskazuje na dużą zgodność przewidywań teoretycznych z eksperymentem. Przedstawiona metoda może być użyta do projektowania pian kompozytowych o z góry zadanych własnościach sprężystych.

20

Mikromechaniczne modelowanie metali i stopów o wysokiej wytrzymałości właściwej

Kowalczyk-Gajewska K.

Prace Instytutu Podstawowych Problemów Techniki PAN

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2011

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nr 1

1-299

PL

Niniejsza rozprawa poświęcona jest mikromechanicznemu modelowaniu metali i stopów o wysokiej wytrzymałości właściwej. Metale i stopy charakteryzujace sie wysokim stosunkiem wytrzymałości i sztywności do gęstości materiału (np. stopy magnezu i tytanu, zwiazki miedzymetaliczne Ti-Al), wykazują zwykle niską ciągliwość i formowalność. Te niepożądane cechy ograniczają ich potencjalnie liczne zastosowania w przemyśle (Appel andWagner [6], Agnew et al. [2], Proust et al. [169], Mróz [141], Lasalmonie [110]). Wskazana kombinacja własności jest wynikiem mikrostruktury. W większości opisywanych materiałów mamy do czynienia z niską symetrią sieci (np. symetria heksagonalna A3 w przypadku stopów Mg i Ti lub symetria tetragonalna dla y-TiAl), a w konsekwencji z niewystarczajacą liczbą łatwych systemów poślizgu uruchamiajacych się podczas deformacji niesprężystych. W wielu przypadkach nie jest spełniony warunek Taylora, to znaczy liczba niezależnych łatwych systemów poślizgu, które są dostępne dla materiału, jest mniejsza od pięciu. Brak ten może być częściowo zrekompensowany przez inny mechanizm deformacji plastycznej - bliźniakowanie, Christian and Mahajan [36]. Analogiczny zespół zjawisk zachodzących na poziomie mikro jest obserwowany w przypadku stopów cyrkonu lub zwiazków miedzymetalicznych Fe-Al. Materiały te nie wykazują wysokiej wytrzymałości własciwej ale charakteryzują się wyjątkową odpornością na korozje. Dla wielu z wyżej wspomnianych metali i zwiazków miedzymetalicznych częste jest również występowanie substruktur lamelarnych powstałych na skutek obróbki termicznej, bądź tworzących się podczas bliźniakowania mechanicznego. Pojawienie się tego typu mikrostruktury wpływa na aktywność poszczególnych modów deformacji promując te sposród nich, które mają korzystną orientację względem geometrii laminatu (Lebensohn et al. [113], Proust et al. [169]). Oba fakty, to jest niespełnienie warunku Taylora przez zbiór możliwych łatwych systemów poślizgu oraz występowanie kierunkowych efektów typu Halla-Petcha związanych z istnieniem substruktury lamelarnej, wskazują na istnienie wiezów nałożonych na deformację niesprężysta na poziomie mikro pojedynczego ziarna. Na skutek powyższych cech omawianych materiałów, w procesach formowania wyrobów, np. walcowania, tworzą sią silne tekstury krystalograficzne, co na poziomie makroskopowym manifestuje się znaczącą anizotropią właściwości. Celem rozprawy jest opracowanie różnych metod mikromechanicznej analizy sprężysto-(lepko)plastycznych polikryształów metali i stopów o wysokiej sztywności i wytrzymałości właściwej. Oryginalne aspekty prezentowanych rezultatów to: - opis konstytutywny pojedynczego ziarna uwzgledniający sprzężenia zachodzące pomiędzy mechanizmami poślizgu i bliźniakowania, - opracowanie nowego schematu reorientacji ziarna na skutek bliźniakowania, słuzącego modelowaniu ewolucji tekstury krystalograficznej, - adaptacja zaproponowanego modelu pojedynczego ziarna deformującego się przez poślizg i bliżniakowanie w ramach różnych schematów przejścia mikro-makro i weryfikacja jego przewidywań pod względem makroskopowej odpowiedzi materiału oraz ewolucji tekstury krystalograficznej, - wykorzystanie niezmienników tensora IV-ego rzędu wynikających z rozkładów inwariantnych takiego tensora do znalezienia nowych zależności opisujących standardowe oszacowania właściwości makroskopowych (oszacowania Voigta i Reussa, Hashina-Shtrikmana, estymator wewnętrznie- zgodny), - sformułowanie warunków i dowód istnienia wewnętrznie-zgodnego oszacowania właściwości makroskopowych dla szerokiej klasy polikryształów z więzami nałożonymi na deformacje na poziomie lokalnym, w przypadku liniowych praw konstytutywnych, - numeryczne studium wpływu więzów nałożonych na deformację wynikających z niespełnienia warunku Taylora, jednokierunkowości mechanizmu bliźniakowania oraz występowania substruktur lamelarnych, na makroskopowa odpowiedz polikryształów metali opisanych nieliniowymi prawami konstytutywnymi, - sformułowanie trójskalowego modelu polikryształu o substrukturze lamelarnej w zakresie duzych deformacji niesprezystych, - opracowanie nowej metody przejscia mikro-makro dla sprezysto-lepkoplastycznych materiałów niejednorodnych bazujacej na zaproponowanej sekwencyjnej linearyzacji nieliniowej odpowiedzi materiału. Rozprawa składa sie z siedmiu rozdziałów. Rozdział pierwszy wskazuje motywacje do podjecia dyskutowanego zagadnienia, omawia cel i zakres podjętych badań oraz ich znaczenie, zawiera również uwagi dotyczące notacji zastosowanej w monografii. Ostatni rozdział podsumowuje najważniejsze rezultaty i płynące z nich wnioski oraz wskazuje kierunki możliwych dalszych badań. Praca uzupełniona jest trzema aneksami omawiającymi istotne narzędzia wykorzystane w modelowaniu: rozkład spektralny i harmoniczny tensora czwartego rzędu typu Hooke'a (Rychlewski [176, 178]) rozwiazanie Eshelby'ego oraz podstawy modelu wewnętrznie-zgodnego (self-consistent) ciał niejednorodnych (Eshelby [49], Hill [67], Li and Wang [120]), a także zagadnienia związane z implementacją numeryczną proponowanego podejścia. Monografię zamyka spis cytowanej literatury.

EN

The thesis reports the research effort aimed at the micromechanical description of various phenomena characteristic for elastic-viscoplastic deformations of polycrystalline materials. The attention has been focused on metals and alloys of high specific strength, in which the inelastic deformation at the local level is constrained by an insufficient number of easy deformation modes and the presence of lamellar substructure. The monograph consists of seven chapters. The first chapter has an introductory character. It outlines the motivation and scope of the thesis and indicates fields of applicability of the results obtained. In Chapter 2 a model of a single crystal deforming by slip and twinning is proposed, together with a new reorientation scheme formulated in order to account for appearance of twin-related orientations in polycrystalline aggregates. In the second part of the chapter an implementation of this model within known scale transition schemes is discussed. The validation of the proposed framework, when modelling the overall response and texture evolution for polycrystalline materials of high specific strength, is presented. In Chapter 3 a theoretical analysis of bounds and self-consistent estimates of overall properties of polycrystals of low symmetry, particularly those characterized by the constrained deformation at the local level, is performed. In the study two invariant decompositions of Hooke's tensors are employed. In Chapter 4 predictions of different extensions of the self-consistent method applicable to non-linear viscoplastic crystals of strong anisotropy are analysed. In Chapter 5 a micromechanical three-scale model of polycrystals of lamellar substructure is discussed, together with its extension to the large strain framework. An influence of the confinement effects induced by lamellar substructure on the overall response of polycrystals is evaluated. In Chapter 6 a new method of sequential linearisation of elastic-viscous response is presented. The procedure developed is applied to extend the self-consistent averaging scheme to elastic-viscoplastic heterogeneous materials. The last chapter recapitulates the most important conclusions and includes an outlook for future research employing the developed modelling tools.