Institute of Fundamental Technological Research

Kinetic model of polymorphic crystallization of uniaxially oriented amorphous poly(L-lactide) under isothermal conditions is formulated basing on the Hoffman-Lauritzen theory. Entire ranges of the crystallization temperatures and amorphous orientation factor are considered. The inverse transformation half-times of the amorphous phase to the individual polymorphs, between the unstable α’ and stable α polymorphs, as well as of the overall crystallization are discussed. The kinetic effects are assigned to the decrease in the amorphous phase entropy caused by deformation and orientation of the flexible chain macromolecules. The model predicts that crystallization to the stable α form is controlled by the rate of transformation of the amorphous phase to α’ Concentration of heterogeneous nuclei typical for commercial polymer is assumed and in this case the role of homogeneous nucleation in the transformation kinetics is negligible. The role of homogeneous ucleation at different hypothetical concentrations of heterogeneous nuclei is estimated vs. the Hermans amorphous orientation factor and crystallization temperature. Ranges of domination of heterogeneous and homogeneous nucleation are predicted as dependent on the heterogeneous nuclei concentration. The increase of the overall oriented crystallization rate is predicted for the entire crystallization temperature range as resulting from the increase of the amorphous-to-α′ transformation rate at increasing amorphous orientation. The model provides a view on the mechanisms for possible control of the development of α’/α composition by adjusting the crystallization time vs. orientation and temperature. composition by adjusting the crystallization time vs. orientation and temperature.

Modeling and simulation, Oriented crystallization

An in-situ nanoindenter with a flat tip was employed to conduct buckling tests of a single nanowire with simultaneous SEM imaging. A series of SEM images allowed us to calculate deflection. The deflection was confronted with the mathematical model of elastica. The post-buckling behaviour of nanowires is conducted in the framework of the nonlinear elasticity theory. Results show the significant effect of geometrical parameters on the stability of buckled nanowires.

post-buckling, nanowire, nanomechanics

Development of polymorphic composition during isothermal crystallization of unstressed amorphous PLLA is considered in the introduced model. The model analysis of the overall crystallization half-time indicates involvement of both α′ and α polymorphs in the crystallization kinetics at substantial impact of the α′ form strongly dependent on temperature. Above 120 ◦C effective creation of α form takes place at much slower amorphous-to-α transformation and proceeds via α′ -to-α transformation which occurs through orders of magnitude faster direct solid-to-solid transition mechanism. The model allows to predict development of indi-vidual α′ and α phases during isothermal crystallization of PLLA basing only on the overall temperature-dependent crystallization half-time, t1/2. The predictions are in good agreement with the experimental data reported by different authors in the literature. The model indicates that the transformation degrees to the individual α′ and α polymorphs vs. crystallization temperature, as well as the overall transformation degree are independent of the nuclei concentration in terms of the multiples of the crystallization half-time, because the concentration of nuclei is directly involved in t1/2.

modeling of crystallization,crystallization kinetics,polymorphic crystallization of PLLA

The subject of the study is the deformation of the oxygen-free high conductivity copper. The copper sample is given in the form of a foam. The sample undergoes an impact into an elastic wall. The strain rate hardening effect is investigated. The numerical model of the open-cell foam skeleton is prepared in the framework of the peridynamics method. The dynamic process of compression with different impact velocities is simulated. It has been found that the strain rate hardening effect is essential for the load-carrying capacity of the material under study. Taylor impact test of solid cylinder analysis precedes the analysis of the metallic foam.

cellular materials, OFHC copper, elastic-viscoplastic model, strain rate hardening, peridynamics, foam skeleton

The aim of the paper is to formulate physically well founded yield condition for initially anisotropic solids revealing the asymmetry of elastic range. The initial anisotropy occurs in material primarily due to thermo-mechanical pre-processing and plastic deformation during the manufacturing processes. Therefore, materials in the "as-received" state become usually anisotropic. After short account of the known limit criteria for anisotropic solids and discussion of mathematical preliminaries the energy-based criterion for orthotropic materials was formulated and confronted with experimental data and numerical predictions of other theories. Finally, possible simplifications are discussed and certain model of isotropic material with yield condition accounting for a correction of shear strength due to initial anisotropy is presented. The experimental verification is provided and the comparison with existing approach based on the transformed-tensor method is discussed.

energy-based yield condition, orthotropic solids, initial anisotropy, strength differential effect, numerical simulation

Closed-form analytical formulas describing kinetics of oriented crystallization under constant or variable amorphous orientation and isothermal or non-isothermal conditions are derived, valid in the whole range of orientation. Master relation for the deformation free energy vs. orientation factor, or tensile stress, is derived accounting for non-linear effects of finite chain extensibility. The Avrami-Evans model is expanded to account for the effects of orientation in thermodynamic driving force of nucleation and crystal growth. Involvement of predetermined and spontaneous nucleation varies strongly with the orientation and leads to domination of spontaneous nucleation at high orientations. Crystallization half-time involving separated or coexisting predetermined and spontaneous nucleation is discussed. A formula predicting equal contribution of both nucleation modes vs. orientation factor and temperature is derived and ranges of domination of the modes are discussed. Example computations illustrate the model predictions for an example polymer (PLLA) and are in good agreement with the experimental results.

amorphous orientation, oriented crystallization kinetics, nucleation rate

Laser-assisted tube bending is a promising manufacturing process which enables production of forms and shapes that cannot be obtained by purely mechanical bending. It is particularly suitable for high hardness and brittle materials, such as nickel alloys, ceramics and cast iron. In the current paper, mechanical loading and simultaneous heating by a moving laser beam are used in a controlled manner to obtain the required deformation. Experimental investigation of the Inconel 718 (IN718) alloy provides the basis for identification of parameters of two constitutive models, which encompass softening phenomena and the coupling of temperature and strains. Numerical simulations are conducted to provide more insight into the laser-assisted bending process of the IN718 thin-walled tubes. Temperature, stress and deformation fields are determined in sequentially coupled thermomechanical analyses using the FE code ABAQUS. Laser beam is modeled as a surface heat flux using the dedicated DFLUX procedure. The temperature field is used as a thermal load in the static general step, together with an external mechanical load. The process of tube bending is controlled by the displacement of the piston rod of the actuator, while the thrust force is the resulting value.

laser-assisted bending of tubes, identification of material parameters, numerical simulations

Obliczono i przedyskutowano wpływ orientacji molekularnej oraz temperatury na szybkość nukleacji i wzrostu kryształów ze wskazaniem na rolę entropii w kinetyce krystalizacji polimerów. W celu określenia efektów entropowych w całym zakresie orientacji molekularnej wywołanej naprężeniami rozciągającymi zastosowano dwa przybliżenia statystyki molekularnej. Badania doświadczalne kinetyki krystalizacji orientowanej przeprowadzono dla orientowanej włókniny z polilaktydu (PLLA) oraz nieorientowanego granulatu PLLA jako przykładowego polimeru, z wykorzystaniem różnicowego kalorymetru skaningowego DSC. Przedstawiono znaczny wpływ orientacji molekularnej na szybkość nukleacji, wzrostu kryształów i szybkość krystalizacji, wynikający ze spadku entropii fazy amorficznej w warunkach orientacji. Ujęte jest to w rozszerzonych modelach Hoffmana i Lauritzena oraz Avramiego i Evansa dla orientowanej krystalizacji i w eksperymentalnych wynikach badań kalorymetrycznych DSC.
Effect of mol. orientation and temp. on the nucleation and crystal growth rates of polymers were calcd. and discussed to indicate the role of entropy in the kinetics of its crystn. Two approximations of mol. statistics were used to det. the entropic effects in the entire range of mol. orientation produced by tensile stresses. The exp. investigations on the oriented crystn. kinetics of polylactide nonwoven fibres and unoriented pellets were carried out by differential scanning calorimetry. High effects of the mol. orientation in the entropy strongly affecting the nucleation and crystal growth rates, as well as the crystn. rate were shown based on the Hoffman-Lauritzen and Avrami-Evans models.

In the last 20 years, a new meshless computational method has been developed that is called peridynamics. The method is based on the parallelized code. The subject of the study is the deformation of open-cell copper foams under dynamic compression. The computational model of virtual cellular material is considered. The skeleton structure of such a virtual cellular material can be rescaled according to requirements. The material of the skeleton is assumed as the oxygen free high conductivity (OFHC) copper. The OFHC copper powder can be applied in additive manufacturing to produce the open-cell multifunctional structures, e.g., crush resistant heat exchangers, heat capacitors, etc. In considered peridynamic computations the foam skeleton is described with the use of an elastic-plastic model with isotropic hardening. The dynamic process of compression and crushing with different impact velocities is simulated.

virtual cellular material, metallic foams, OFHC copper, elastic-plastic model, numerical methods, peridynamics, crushing process

The thermoplastic polymers present amorphous or semi-crystalline structures which are very important factors in describing volumetric shrinkage. The thermoplastic materials are commonly used for production of daily life products, industrial or as the prototypes. Different techniques of manufacturing polymer structures are considered like: injection molding, extrusion, milling, additive manufacturing (AM). AM is a very fast developing field in the manufacturing and research. Unfortunately, components or prototypes made using the thermoplastic semi-crystalline materials in 3D techniques have quite low mechanical strength compared to the parts made by injection molding processes. It is caused by porosity obtained during the processing, as well as by fraction of crystallinity in the volume of the components. Additionally, the volumetric shrinkage is hard to predict without knowledge of its origin. Therefore, it is necessary to consider crystallization kinetics and the melting of the analysed materials. The investigations presented in this work concern the crystallization and melting model to be implemented in the finite element (FE) analyses. With use of the model, one can predict development of the structure during the real processes and, in the future, to control the warpage of the manufactured components.

additive manufacturing, Avrami model, crystallization, differential scanning calorimetry (DSC), glass transition temperature, Hoffman-Lauritzen theory, melting, PA2200, van Krevelen empirical model

An analytical formula is derived for the oriented crystallization coefficient governing kinetics of oriented crystallization under uniaxial amorphous orientation in the entire temperature range. A series expansion approach is applied to the free energy of crystallization in the Hoffman-Lauritzen kinetic model of crystallization at accounting for the entropy of orientation of the amorphous chains. The series expansion coefficients are calculated for systems of Gaussian chains in linear stress-orientation range. Oriented crystallization rate functions are determined basing on the 'proportional expansion' approach proposed by Ziabicki in the steady-state limit. Crystallization kinetics controlled by separate predetermined and sporadic primary nucleation is considered, as well as the kinetics involving both nucleation mechanisms potentially present in oriented systems. The involvement of sporadic nucleation in the transformation kinetics is predicted to increase with increasing amorphous orientation. Example computations illustrate the dependence of the calculated functions on temperature and amorphous orientation, as well as qualitative agreement of the calculations with experimental results.

modeling and simulation, kinetics of oriented crystallization, amorphous orientation, sporadic nucleation, predetermined nucleation

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.

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

The magnetorheological fluid is a functional material that is changing its rheological properties and finally solidifies in a magnetic field. The dynamic behaviour, tested with the use of the Split Hopkinson Pressure Bar is an important issue for description of this material, which is commonly used in different kinds of shock absorbers. This note presents a new idea how to modify the known SHPB set up in order to investigate dynamic properties of magnetorheological materials.

Split Hopkinson Pressure Bar (SHPB), Magnetorheological Fluid (MRF), dynamic behaviour, solidification in magnetic field, ferroelements

The subject of the study are the models based on digital microstructures, in particular open-cell metallic foams characterized with the skeleton formed of convex or re-entrant cells. Recently, the auxetic materials revealing negative Poisson's ratio have attracted increasing attention in the context of modern materials applications. Up to date, the research of auxetics is mainly concentrating on the cell structure design and the analysis of quasi-static response. The dynamic properties of such materials are less known. Impact compressions of the two kind of foams under high-velocity are numerically analyzed. To simulate the deformation processes the finite element program ABAQUS is used. The computer tomography makes the basis for the formulation of computational model of virtual foam and the finite element discretization of the skeleton. For numerical simulations the constitutive elasto-viscoplasticity model is applied that defines the dynamic behavior of oxygen-free high conductivity (OFHC) Cu using the experimental data reported in the literature. The numerical predictions of crushing force for velocity 50 and 300 m/s are discussed.

compression test, open-cell copper, convex cell, re-entrant cell, virtual cellular materials, metallic foams, numerical simulation

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.

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

Electron back-scattered diffraction (EBSD) studies carried out for the Cu/α−Al2O3 composites manufactured by pulsed laser deposition method and by the powder metallurgy enable to uncover a set of orientation relationships characteristic for materials of this type. The identified interfaces are categorized according to the bonding strength. Additionally, their microstructure is reproduced by molecular dynamic (MD) simulations. The obtained classification of the phase boundaries constitutes key information for effective composite design.

EBSD, Cu/α−Al2O3 composites, PLD, bonding strength, molecular dynamics simulation

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.

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

The biaxial compression test, based on the concept presented in [1] and on the technique of the channel-die test [2] and [3], is discussed as an experimental method allowing evolution of the friction conditions from the dry-film lubrication, by using MoS2 grease, to the dry conditions to be analysed. This article gives an outline of the experimental set-up, its validation and the technique of the test results analysis. The analysis of friction is based on the experimental data coupled with the numerical simulation of the performed tests and on the theoretical approach introduced in [4]. The Oxygen-Free High Conductivity (OFHC) copper in the ‘as-received’ state in contact with the 42CrMo4 steel are chosen as the materials used for the experimental investigation.

Biaxial compression, Friction modelling, OFHC copper

The present work concerns the description of the yield state of biodegradable materials. As examples, biodegradable polymers are chosen – cornpole CRP-M2, starch fatty acid ester, and PLA/PBAT, poly(lactic acid) (PLA) blended with poly(butylene adipate/terephthalate) (PBAT) [1, 2]. These biodegradable, plant-derived bioplastics are a promising alternative to petroleum-based plastics. To describe the onset of plasticity in the bioplastics under discussion, Burzyński ’s hypothesis of material effort has been applied [3, 4]. The applied criteria account for the differential strength effect and for the shear correction resulting from the difference between experimental and theoretical values, obtained as a result of the Huber-Mises approach [5, 6]. In general, these properties of yield state are characteristic for polymers. The description of yield state for bioplastics is an issue that has hardly been investigated, which illustrates the novel nature of this paper in which this topic is discussed

bioplastics, strength differential effect, shear correction, yield surface, Burzyński yield condition

This paper presents results of experimental studies of forming limit curves (FLC) for sheet forming under complex strain paths. The Nakazima-type formability tests have been performed for the as-received steel blank and for the blank pre-strained by13%. Prestraining leads to abrupt change of strain path in the blank deformation influencing the forming limit curve. The experimental FLC of the pre-strained blank has been compared with the FLC constructed by transformation of the as-received FLC. Quite a good agreement has been found out. The concept of strain-path independent FLCs in polar coordinates has been verified. Two types of the polar diagrams have been considered, the first one with the strain-path angle and effective plastic strain as the polar coordinates, and the second one originally proposed in this work in which the thickness strain has been used instead of the effective plastic strain as one of the polar coordinates. The second transformation based on our own concept has given a better agreement between the transformed FLCs, which allows us to propose this type of polar diagrams as a new strain-path in dependent criterion to predict sheet failure in forming processes.

sheet forming, formability, forming limit curve, complex strain-path

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.

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

In the paper a new proposition of limit state criteria for anisotropic solids exhibiting different strengths at tension and compression is presented. The proposition is based on the concept of energetically orthogonal decompositions of stress state introduced by Rychlewski. The concept of stress state dependent parameters describing the influence of certain stress modes on the total measure of material effort was firstly presented by Burzynski. The both concepts are reviewed in the paper. General formulation of a new limit criterion as well as its specification for certain elastic symmetries is given. It is compared with some of the other known limit criteria for anisotropic solids. General methodology of acquiring necessary data for the criterion specification is presented. The ideas of energetic and limit state orthogonality are discussed - their application in representation of the quadratic forms of energy and limit state criterion as a sum of square terms is shown

anisotropy, strength hypothesis, material effort, yield condition, plastic potential, strength differential effect, elasticity, plasticity

This paper presents numerical investigations of the influence of friction on sheet deformation in Nakazima type formability tests. Numerical simulations have been performed using the authors’ own explicit dynamic finite element program. Numerical results have been compared with experimental data. Location of fracture was of major interest in this work. The studies confirmed that the fracture location near the center of the specimen as required by the standards can be obtained for low values of the friction coefficient. Numerical simulation combined with the inverse analysis has been used to estimate a real value of the friction coefficient in the Nakazima formability test.

formability test, explicit FE method, friction, fracture location

W artykule przedstawiono analizę numeryczną wpływu tarcia na rozkład odkształceń uzyskanych w próbach tłoczności przeprowadzonych metodą Nakazimy. Symulacje numeryczne zostały przeprowadzone w autorskim programie opartym na metodzie elementów skończonych z jawnym całkowaniem ruchu względem czasu. Wyniki numeryczne porównano z danymi eksperymentalnymi. Główną uwagę zwrócono na lokalizację miejsca pęknięcia. Badania potwierdziły, że miejsce pęknięcia w pobliżu środka próbki, zgodnie z wymaganiami norm, można uzyskać przy małych wartościach współczynnika tarcia. Symulacja numeryczna, w połączeniu z analizą odwrotną, została wykorzystana do oszacowania rzeczywistej wartości współczynnika tarcia w przeprowadzonych próbach tłoczności metodą Nakazimy.

próba tłoczności Nakazimy, wpływ tarcia, lokalizacja pękania, symulacje numeryczne MES, analiza odwrotna

This paper presents the results of numerical simulations of the formability tests carried out for a pre-stretched 1 mm thick DC04 steel sheet. Simulation consisted of the subsequent stages as follows: uniaxial stretching of the sheet, unloading and stress relaxation, cutting specimens out of the pre-stretched sheet and bulging the blank with a hemispherical punch. Numerical modeling has been verified by comparison of the simulation results with the experimental ones. Good concordance of the results indicates correct performance of the numerical model and possibility to use it in further theoretical studies.

Sheet forming, Formability, Forming limit diagram, Pre-stretching, Numerical simulation

In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński [3] and on the concept of decomposition of elastic energy density introduced by Rychlewski [18]. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.

linear elasticity, anisotropy, material effort hypotheses, limit state criteria

W artykule przedstawiono propozycję nowego kryterium plastyczności dla blach ortotropowych wykazujących różnicę wytrzymałości przy rozciąganiu i ściskaniu. Nowe kryterium bazuje na energetycznym warunku stanu granicznego dla materiałów anizotropowych zaproponowanym przez Rychlewskiego [2] i łączy się z wprowadzoną przez Burzyńskiego [3] koncepcją zależnych od charakteru stanu naprężenia funkcji określających udział poszczególnych składników rozkładu głównego gęstości energii sprężystej w całkowitej mierze wytężenia materiału. Podano specyfikację kryterium dla wszystkich płaskich symetrii sprężystych. Zaprezentowano ogólną metodę pozyskiwania danych niezbędnych do wyznaczenia parametrów kryterium na podstawie wyników prostych prób wytrzymałościowych - rozciągania, ściskania i ścinania. Wskazano na szczególne konsekwencje w opisie deformacji plastycznej blach w przypadku przyjęcia prawa płynięcia plastycznego stowarzyszonego z zaprezentowanym warunkiem plastyczności.

blachy walcowane, anizotropia, asymetria zakresu sprężystego, kryterium plastyczności, hipotezy wytężenia

W pracy przedstawiono wyniki symulacji numerycznej próby tłoczności wstępnie wyprężonej blachy ze stali DC04 o grubości 1 mm. Symulacja obejmowała kolejno następujące etapy: wyprężanie blachy, odciążenie, wycięcie wykrojki z blachy wyprężonej oraz próbę wybrzuszania półkulistym stemplem. Wyniki numeryczne porównano z wynikami doświadczalnymi. Uzyskana zgodność wyników wskazuje na prawidłowe działanie modelu numerycznego oraz możliwość wykorzystania go do dalszych badań teoretycznych.

blacha wstępnie wyprężona, próby tłoczności, symulacja numeryczna

The classical J2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure-sensitive yielding or plastic dilatancy. Another difficulty is the so-called strength differential effect (SD), leading to the asymmetry of the elaasstic range. The Burzyński yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto-plastic constitutive equations for the paraboloid case of Burzyński yield condition is frmulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial FE code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plasticity theory with the paraboloid case of Burzyński's yield condition describes adequately the strength diffrential effect, which is present in many kinds of materials significant for recent applications.

metal matrix, mechanical, plastic behaviour, Burzyński paraboloid yield condition, strength differential effect

Ultrafine grained (UFG) and nanocrystalline metals (nc-metals) are studied. Experimental investigations of the behaviour of such materials under quasistatic as well as dynamic loading conditions related with microscopic observations show that in many cases the dominant mechanism of plastic strain is a multiscale development of shear deformation modes. The comprehensive discussion of these phenomena in UFG and nc-metals is given in M.A. Meyers, A. Mishra and D.J. Benson [Mechanical properties of nanocrystalline materials, Progr. Mater. Sci. 51 (2006), pp. 427–556], where it has been shown that the deformation mode of nanocrystalline materials changes as the grain size decreases into the ultrafine region. For smaller grain sizes (d < 300 nm) shear band development occurs immediately after the onset of plastic flow. Significant strain-rate dependence of the flow stress, particularly at high strain rates, was also emphasized. Our objective is to identify the parameters of Perzyna constitutive model, a new description of viscoplastic deformation, which accounts for the observed shear banding. The viscoplasticity model proposed earlier by Perzyna [Fundamental problems in viscoplasticity, Adv. Mech. 9 (1966), pp. 243–377] was extended in order to describe the shear banding contribution in Z. Nowak, P. Perzyna, R.B. Pecherski [Description of viscoplastic fow accounting for shear banding, Arch. Metall. Mater. 52 (2007), pp. 217–222]. The shear banding contribution function, which was introduced formerly by Pe¸cherski [Modelling of large plastic deformation produced by micro-shear banding, Arch. Mech. 44 (1992), pp. 563–584] and applied in continuum plasticity accounting for shear banding in R.B. Pecherski [Macroscopic measure of the rate of deformation produced by micro-shear banding, Arch. Mech. 49 (1997), pp. 385–401] plays pivotal role in the viscoplasticity model. The derived constitutive equations were identified and verified with the application of experimental data provided in the article by D. Jia, K.T. Ramesh and E. Ma [Effects of nanocrystalline and ultrafne grain sizes on constitutive behavior and shear bands in iron, Acta Mat. 51 (2003), pp. 3495–3509], where quasistatic and dynamic compression tests with UFG and nanocrystalline iron specimens of a wide range of mean grain size were reported. Numerical simulation of the compression of the prismatic specimen was made by the ABAQUS FEM program with UMAT subroutine. Comparison with experimental results proved the validity of the
identified parameters and the possibilities of the application of the proposed description for other high strength metals.

Ultra fine grained metals, nanocrystalline metals, viscoplastic deformation, shear banding, shear banding contribution function, numerical simulation of compression test, identification of the model parameters

The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condtion is analyzed and possible applications and comparison with the results known in the literature are discussed.

Burzyński yield condition, strength differential effect, pressure sensitivity, Lode angle, third invariant of stress tensor deviator

In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński [3] and on the concept of decomposition of elastic energy density introduced by Rychlewski [18]. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.

linear elasticity, anisotropy, material effort hypotheses, limit state criteria

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.

Kompozyty metalowo-ceramiczne, pianki ceramiczne, modelowanie, symulacje MES

The aim of our study is to discuss a new methodology to account for the effect of strain rate on ductile fracture phenomena. Theory of inelastic materials accounting for the effects of microshear bands and microdamage is presented. The influence of microshear bands is explained by means of a function describing the instantaneous contribution of shear banding in the total rate of plastic deformation. The experimental investigations of the effect of strain rate on ductile fracture with use of the results of a dynamic double shear test of DH-36 steel with thermographic observations are reported. The registration of temperature evolution during the deformation process can provide additional data for the identification of the shear banding contribution function and the onset of ductile fracture.

Effect of strain rate, ductile fracture, dynamic double shear test, DH-36 steel, thermographic observation

The main idea of energy-based hypothesis of material effort proposed by Burzyński is briefly presented and the resulting failure criteria are discussed. Some examples, based on the own studies, which depict applications of these criteria are discussed and visualisations of limit surfaces in the space of principal stresses are presented.

Burzyński yield condition, yield surface, strength differential effect, energy-based yield criteria

Using the results of High Resolution Transmission Electron Microscopy studies on epitaxial layers fcc metal/corundum we have proposed atomistic model of the interfacial structure of the Al2O3-Ni composite.

High Resolution Transmission Electron Microscopy, epitaxial layers, fcc meta/corundum, CTIP+EAM model, strength of the interface

The aim of the paper is to apply the energy-based criterion of limit elastic states for the assessment of the material effort of anisotropic materials. The linear elastic anisotropic materials in the plane state of stress are considered. The theory of elastic eigen states determined by the symmetry of the Hooke elastic tensors (stiffness and compliance tensors) and the energy-based criterion of elastic limit states for anisotropic materials is used according to the theory proposed by Jan Rychlewski. Experimental data for paperboard and the results of atomic calculations were applied. The common feature of aforementioned materials is the strength differential effect related to the asymmetry of the elastic range. Often, to determine the degree of this asymmetry one uses the ratio of the experimentally measured limit of elasticity (yield) in compression to the limit of elasticity in tension. Also, the failure criterion of P.S. Theocaris is mentioned within the discussion of the possibility of the extension of the criterion proposed by Rychlewski for anisotropic materials revealing asymmetry of elastic range anfd the related strength differential effect.

strength differential effect, Rychlewski criterion, anisotropic materials, asymmetruy of elastic range

The paper contains a short presentation of main idea of energy-based hypothesis of material effort proposed by Burzyński with discussion of the resulting failure criteria. Some examples illustrating applications of these criteria are discussed and visualisations of limit surfaces in the space of principal stresses are presented.

Burzyński yield condition, yield surface, strength differential effect, energy-based yield criteria

In this paper, the thermo-viscoplastic behaviour of DH-36 and Weldox-460-E steels is analyzed at wide ranges of strain rates and temperature. These materials are commonly used for naval applications. Thus, the may be subjected to a wide range of exploitation temperature and at the same time to high strain rates due to accidental impact or explosion. The thermo-viscoplastic behaviour of these materials has been modeled by application of RK (Rusinek-Klepaczko) constitutive relation. The comparison with other models well known in the literature has been studied.

constitutive modelling, thermo-viscoplasticity, DH-36 steel, Weldox-460-E steel, impact processes, FE numerical simulations, perforation process

In this paper the thermo-visco-plastic behaviour of six high strength steels is analyzed in a wide range of strain rates and temperature. The steels belong to two well-known versions of steels: three ferritic steels: HSLA-65, DH-36 and Wedox 460-E and three austenitic steels: Nitronic-50, Uranus B66 and Al-6XN.
Micro-mechanism of plastic deformation in the case of ferritic steels is dominated by dislocation's gliding. In the case of austenitic steels the twinning appears that modifies the material's plastic properties. In the present paper the RK (Rusinek-Klepaczko) constitutive relation is evaluated for modelling of the plastic behaviour of six steels which represent these two different deformation mechanisms.

ferritic steels, austenitic steels, RK Rusinek - Klepaczko model, dislocation glide, twining, thermo-visco-plasticity

In this paper an extension of the Rusinek-Klepaczko (RK) constitutive relation is presented. The new formulation proposed, allows defining the phase transformation effect observed on macroscopic scale using a phenomenological approach. The key point is to introduce in the original formulation of RK model a new stress component based on evolution of martensite, which takes into account strain, strain rate and temperature effects. Analytical predictions of the xtended constitutive relation are compared with experimental results for 301Ln2B steel.

RK model, phase transformation, austenitic steel

The rigid-plastic crystal plasticity model accounting for the effect of micro-shear banding mechanism on the reduction of the global strain hardening rate is presented. The instantaneous contribution of micro-shear bands in the rate of plastic deformation is described by means of the constitutive function that depends on the type of strain path specified by the current direction of strain rate tensor. The capabilities of the model are explored by studying the strain-stress behavior of polycrystalline material together with the crystallographic texture evolution in the polycrystalline element

Crystallographic texture, Anisotropic material, Crystal plasticity, Polycrystalline material, Micro-shear banding

The paper is written in accompaniment of the publication of English translation of W. Burzyński's paper [1], which deals with the yield criterion for materials revealing the sensitivity of yield strength to pressure derived by W. Burzyński during preparation of his doctor thesis in 1927 [2]. More recently the dependence of yield strength on pressure is related to the so-called strength differential (SD) effect, i.e. asymmetry of elastic range, cf. e.g. [3,4]. Therefore, the original Burzyński's energy-based approach in the literature is reported and his main achievement in ths field concerning the recent studies is discussed.

Burzyński yield condition, strength differential effect, asymmetry of elastic range, hypotheses of material effort

The rigid-plastic crystal plasticity model with single yield surface of 2n-degree is applied to simulate the polycrystalline behaviour and the crystallographic texture development under non-proportional deformation paths. The role of two controlling parameters: the amplitude and frequency for the processes of tension or compression assisted by cyclic torsion of thin-walled tubes made of copper is analysed. The effect of micro-shear bands on the reduction of global hardening rate is described by means of the contribution function of shear banding in the rate of plastic deformation. The conclusions drawn from the study can find also application in the extension of the analysis for high strength and hard deformable materials.

micromechanics, modelling of materials, rigid-plastic solids, crystal plasticity, texture, cyclic torsion, non-proportional deformation path, micro-shear bands

The subject of the study is concerned with ultra fine grained (ufg) and nanocrystalline metals (nc-metals). Experimental investigations of the behaviour of such materials under quasistatic as well as dynamic loading conditions related with microscopic observations show that in many cases the dominant mechanism of plastic strain is multiscale development of shear deformation modes – called shear banding. The comprehensive discussion of these phenomena in ufg and nc-metals is given in [1], [2] and [3], where it has been shown that the deformation mode of nanocrystalline materials changes as the grain size decreases into the ultrafine region. For smaller grain sizes (d < 300 nm) shear band development occurs immediately after the onset of plastic flow. Significant strain-rate dependence of the flow stress, particularly at high strain rates was also emphasized. Our objective is to propose a new description of viscoplastic deformation, which accounts for the observed shear banding. Viscoplasticity model proposed earlier by P e r z y n a [4], [5] was extended in order to describe the shear banding contribution. The shear banding contribution function, which was introduced formerly by P ę c h e r s k i [6], [7] and applied in continuum plasticity accounting for shear banding in [8] and [9] as well as in [10] and [11] plays pivotal role in the viscoplasticity model. The derived constitutive equations were identified and verified with application of experimental data provided in paper [2], where quasistatic and dynamic compression tests of ufg and nanocrystalline iron specimens of a wide range of mean grain size were reported. The possibilities of the application of the proposed description for other ufg and nc-metals are discussed.

Viscoplastic flow, shear banding, micro-shear bands, nanocrystalline metals, nc-metals, ultra fine grain (ufg) metals

Technological metal forming processes of extrusion, forging and rolling with imposed cyclic torsion or shear deformation have been recently studied in view of their advantages with respect to monotonic loading processes, cf. Bochniak and Korbel [2–4]. The present work is aimed to analyze such process in the case of simple tension or compression of a cylindrical tube with imposed cyclic torsional deformation. The material element response is assumed to be rigid-perfectly plastic or elastic-perfectly plastic. For these models, the analytical solutions can be provided for the steady cyclic responses and the effect of two process parameters, namely the ratio of shear and axial strain rates η and the amplitude of shear strain γm, can be clearly demonstrated. Three different regimes of cyclic response can be visualized in the plane η, γm. The cyclic response of a cylinder under combined axial compression and cyclic torsion is predicted by considering a simplified model of a set of concentric tubes and neglecting their radial stress interaction. The axial force and torsional moment are then specified by averaging the responses of consecutive tubes. The cyclic response diagrams for the cylinder are then generated in terms of axial force and torsional moment related to axial deformation and angle of twist

cyclic torsion, plastic deformation of cylinders, elastic-perfectly plastic model, rigid-perfectly plastic model, analytical solutions of cyclic response of a cylinder

Results of static and dynamic compression tests for two types of glass fibrereinforced polypropylene composites are presented. Stress-strain curves showing the influence of the strain rate on the composite mechanical properties have been obtained.
A three-dimensional description of the material behavior during the deformation has been developed. The material constitutive parameters have been calculated.
Specification of the parameters and description of the methods used for their identification have been worked out. The results are discussed in terms of the deformation processes and the material non-homogeneity.

static and dynamic compression tests, glass fibrereinforced polypropylene composites, Stress-strain curves, constitutive model, three-dimensional description

The rigid-plastic model for the single grain is developed in which the velocity gradient is split into two parts connected with crystallographic slip and micro-shear bands respectively. For crystallographic slip the regularized Schmid law proposed by Gambin is used. For the micro-shear bands the model developed by Pęcherski, which accounts for the contribution of this mechanism in the rate of plastic deformation by means of a function fms is applied. Different constitutive equations for the plastic spin due to two considered mechanisms of plastic deformation are used. The present model is applied to simulate crystallographic texture evolution in the polycrystalline element.

crystallographic texture, modelling of texture, micro-shear bands, regularized Schnid law, plastic spin

W pracy przedyskutowano aktualne problemy modelowania własności mechanicznych metali o strukturze nanometrycznej. Omówiono możliwości opisu deformacji sprężysto-plastycznej i lepkoplastycznej materiałów o bimodalnym rozkładzie ziarn. Przedstawiono wyniki badań sprężystych własności nanoziarn oraz identyfikacji ich spręzystych stanów granicznych z zastosowaniem kwantowo-mechanicznych obliczeń z pierwszych zasad (ab initio) na przykładzie idealnego kryształu miedzi. Wskazano na możliwości dalszych badań zmierzających do opracowania przesłanek potrzebnych do projektowania nanomateriałów.

nanometale, obliczenia ab initio, kryształ miedzi, modelowanie własnosci mechanicznych, sprężyste stany graniczne

Metallic open-cell foams have excellent potential characteristics as impact energy absorbers due to their ability to deform over a long stroke at an almost constant load. Under intensive dynamic load, the compaction waves travelling through the material cause a strength and energy absorption enhancement. The subject of the study is the model of virtual metallic foam with the skeleton formed of convex cells.The computed tomography make the basis for the numerical model and and the finite element discretization of the skeleton. The goal of the presented investigations is to study the propagation of compaction waves, the impact limits and absorption energy of open-cell copper foam.The shock state variables derived from analytical Hugoniot relation and the conservation laws can be used for comparison with FEM simulations. The primary outcome of the research is the assessment of the crushing force in the open-cell metallic foams that is obtained on the basis of virtual material concept with use of the known shock waves theory.

open-cell copper foams, shock wave theory, crushing force, finite element calculations

The study of modern cellular materials due to complexity of their internal structure requires the application of efficient computational methods. One of such methods developed in the last 10 years is peridynamics. This approach resulted in the parallelized code that is used in presented analysis. The subject of the study are alumina foams produced by gelcasting method and metallic cellular materials that can be produced in the process of additive manufacturing. The results of microtomoraphy are used to create numerical model reconstructing the structure of foam skeleton. In this way an example of virtual cellular material is obtained. The peridynamic modelling is applied to investigate dynamic damage process under axial compression.

virtual cellular material, peridynamic modelling, cellular skeleton, deformation and damage simulations, alumina foams, additive manufacturing

The results of experimental and numerical investigations concerning the influence of strain rate on mechanical properties of pure tantalum and VP159 high nitrogen austenitic steel are presented. Experiments were carried out using Split Hopkinson Pressure Bar (SHPB) and Direct Impact Compression Test (DICT) technique. The Perzyna elasto-viscoplasticity theory was applied to predict the dynamic compression yield strength of the tantalum at strain rates from 1.0x10-3 s−1 to 0.5x106 s−1. In the case of the VP159 high nitrogen austenitic steel the experimental results were used to calibrate the Rusinek-Klepaczko model. There are still no sufficient data on the flow stress at higher strain rates than 1.0x105s−1, in particular for large strains. The experimental identification of material parameters required for constitutive modelling are not sufficiently reported. This paper is an attempt to supplement our knowledge in this area. The impact resistance of material in question is analysed numerically with use of ABAQUS/Explicit finite element program. The Huber-Mises-Hencky yield criterion and Perzyna viscoplasticity model with adiabatic conditions are used.

Dynamic tests, Direct Impact Compression Test, Hopkinson bar, punching effect

The metallic materials undergo various manufacturing operations such as forming, forging, extrusion, machining, and cold working. Experimental investigations of the behaviour of high strength metallic materials under quasistatic and dynamic loading conditions related to microscopic
observations show that in many cases, the dominant mechanism of plastic strain is multiscale development of shear deformation modes–called shear banding [1]. The Viscoplasticity model with the overstress function proposed earlier by Perzyna [2] was extended to describe the new
mechanism of inelastic deformation [1, 3, 4]. The paper aims to study the application of the new description of viscoplastic deformation,
which accounts for the observed shear banding phenomena. The numerical simulations of the deformation processes of metallic specimens in the channel-die test are performed

The paper‘s subject is the formulation accounting for shear bands in fine-grained metals [2] in terms of peridynamics. The formulation stands for an extension of the viscoplasticity model [1]. Several experimental investigations prove that plastic deformation's main mechanism is developing shear bands in prevailing cases. An influence of the rapid shear banding generation on the cumulated plastic strain field is investigated. The model is valid for finite strains. The primary interest is focused on impact analysis. The numerical models of the Taylor bar are shown. A complex structure, such as copper open-cell foam, were presented in [3]. The numerical examples given in [3] are enriched with the newly developed formulation.

viscoplasticity, shear bands, peridynamics

In the last 20 years, a new rapidly developing method is applied to calculations of solid mechanics problems, [1]. It is a non-local method. The predecessors of the method that have been applied to crystals were developed in [2] and [3]. In the presentation, we show an application of the method for the evaluation of the viscoplasticity effects [4, 5] in the copper foams. The oxygen free high conductivity copper (OHFC) can be applied to produce the open-cell multifunctional structures, for example, heat exchangers, heat capacitors, using additive manufacturing [6]. We use the highly parallelized program Peridigm for the analysis, [7].
Figure 1(a) shows an exemplary impacting foam sample attacking with a velocity of 20 m/s an elastic block. The highest plastic strains are in the case of ideally elastic-plastic case (b). The equivalent plastic strains are higher when neglecting the strain rate hardening effects (d) than including both strain hardening and strain rate hardening effects (c). We provide dependences of the equivalent plastic strains on impact velocities and strain rate hardening exponents.
Literature;
1. S.A. Silling, Journal of Mechanics and Physics of Solids, 48, 175 (2000).
2. D. Rogula, Nonlocal theory of material media (Springer), 123 (1982).
3. A. Kunin, Elastic media with microstructure, one dimensional models (Springer), (1982).
4. J.A. Mitchell, A Nonlocal, Ordinary, State-Based Plasticity Model for Peridynamics (SANDIA ), (2011).
5. J.T. Foster, S.A. Silling, W.W. Chen, International Journal for Numerical Mechods in Engineering, 81,1242 (2010).
6. R.B. Pęcherski, M. Nowak, Z. Nowak, International Journal for Multiscale Computational Engineering, 15, 431 (2017).
7. M.L. Parks, D.J. Littlewood, J.A. Mitchell, S.A. Silling, Peridigm Users’ Guide (SANDIA), (2012).

metallic foams, composites, impact loading, peridynamics, parallel computing

A new physical model of multilevel hierarchy and evolution of shear bands is proposed with use of the analysis of recent state of the art of the investigations carried on different levels of observations: uni-axial and bi-axial mechanical tests enhanced with digital image correlation method and in-situ tests with use of electron microscopy as well as atom probe tomography in relation with ab initio and molecular dynamics computational simulations. Physical motivation and heuristic foundations of theoretical description are discussed with reference to known results in the literature. The difficulties with application of a direct multiscale integration scheme are discussed and an original idea of an extension of the representative volume element concept with use of the known theory of the propagation of the singular surfaces of microscopic velocity field is proposed. A new formulation of the description of rate of shear strain generated by multilevel hierarchy of shear bands is formulated in the workflow integration approach, in which information from molecular simulation at different levels flows into the decision process.

shear banding, viscoplasticity, strong discontinuity surface

Plastic deformation of solids: polycrystalline metals, polymers, and amorphous materials is often produced as an effect of micro-shear banding. The micro-shear bands are observed as concentrated shear zones in the form of layers of the thickness of the order 0.1 m, which form the clusters developing on multiple levels of observation. The identification and elucidation of physical mechanisms that are responsible for initiation, growth and evolution of micro-shear bands is of fundamental importance for understanding the macroscopic behaviour of many materials. Physical motivation and heuristic foundations of theoretical description are discussed with reference to known results in the literature. The difficulties with application of a direct multiscale integration scheme are discussed and an original idea of an extension of the representative volume element concept with use of the known theory of the propagation of the singular surfaces of microscopic velocity field is proposed. A new formulation of the description of rate of shear strain generated by multilevel hierarchy of shear bands is proposed and incorporated into theory of elastic/plastic or elastic/viscoplastic solids by means of the concepts of the instantaneous contribution function and volume fraction of shear banding.

multilevel hierarchy, shear banding, plasticity, viscoplasticity, shear banding contribution function, singular surface of velocity field

W ciągu ostatnich dwudziestu lat opracowano nową metodę bezsiatkową znaną jako perydynamika [1]. Metoda ta posługuje się zrównoleglonym kodem obliczeniowym [2]. Przedmiotem badań jest deformacja miedzianej pianki o strukturze otwartokomórkowej poddanej dynamicznemu ściskaniu, Rys. 1.
Model komputerowy szkieletu pianki otrzymano wykorzystując koncepcję materiału wirtualnego przedstawioną w pracy [3]. W zależności od potrzeb wymiary struktury szkieletu pianki można skalować. Materiałem pianki jest miedź beztlenowa o wysokiej przewodności cieplnej (OFHC), wykorzystywana do wytwarzania wielofunkcyjnych struktur komórkowych takich jak wymienniki lub kondensatory cieplne, itp. W obliczeniach zastosowano lepkoplastyczny model materiału szkieletu pianki, a symulacje przeprowadzono dla różnych prędkości uderzenia. Rezultaty metody perydynamiki porównano z obliczeniami MES podobnych problemów ściskania dynamicznego pianki. Obliczenia wykonano w ICM Uniwersytetu Warszawskiego na komputerze CRAY XC-40 oraz na klastrze HP w centrum TASK w Gdańsku.

Obciążenia uderzeniowe, pianka metaliczna, perydynamika

The analyses of the modern cellular materials due to complexity of their internal structure require efficient computer methods and codes. The new method that has been developed mostly in the last 10 years is peridynamics [1, 2]. The developments resulted in highly parallelized code [3] that we use in our analysis. The subject of the study are alumina foams produced by gelcasting method. The results of microtomography of alumina foams are used to create the numerical model reconstructing the structure of foam skeleton. 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. The 3D model of the foam structure is created. The detailed description of the model generation is presented in Nowak et al. [5]. The numerical models of real Al2O3 foam with porosity 96 %, and discussion of theirs mechanical properties have been presented. The method of the assessment of failure strength of real alumina foam produced by the gelcasting is proposed. We attempt to present the mechanism of damaging of a crushable foam under impact.

foams, damage, impact, peridynamics

Molecular deformation and orientation in the amorphous phase subjected to tensile stresses strongly accelerates crystallization of polymers by orders of the magnitude. Closed-form analytical formula is derived for the crystallization rate under high tensile stresses in the entire range of crystallization temperature and the temperature rates. Such formula, lacking in the literature, is needed for modelling of the dynamics of crystallizing polymers processing and predicting structure development in obtaining highly oriented materials of enhanced tensile modulus and tenacity. Rapid online crystallization strongly influences the rheological behaviour during the processing and introduces coupling of crystallization with the processing dynamics. Tensile stress affects the crystallization rate mainly by influencing the configurational entropy of the chain macromolecules in amorphous phase. None of the actually available models are capable to account for the effects of high molecular orientation in the crystallization kinetics. In the present approach, non-Gaussian chain statistics is considered to account for finite extensibility of real macromolecules in the amorphous phase under high tensile stresses which results in non-linear effects in the model. The Hoffman-Lauritzen model of crystallization kinetics is extended to account for free energy of deformation of the amorphous component under uniaxial molecular orientation produced by the tensile stresses. The crystallization rate is considered as controlled by predetermined and sporadic nucleation present in real systems. The involvement of both nucleation mechanisms in the crystallization kinetics varies strongly with the level of tensile stress and amorphous orientation, with domination of sporadic nucleation at high orientations. The closed-form analytical formulas are validated by computations. Example numerical calculations illustrate influence of amorphous orientation on the crystallization free energy and the crystallization rate function involving both nucleation mechanisms.

polymer crystallization, crystallization kinetics, molecular orientation, non-Gaussian chain statistics

Stacking faults are the special regions of the crystal structure that exhibit non-uniform structure and diversified stability. Energy of this defects determines configurations of dislocation cores and type of predominant plastic deformation mechanism. In this study we focus on the generalised stacking fault energy computations of multi-slip-system hexagonal Ti alloys in the context of solution strengthening effect and the atomic as well as electronic structure identification of the analysed planar defects. The far reaching goal is to provide the physical and theoretical basis to answer the still unresolved question concerning the initiation of a micro-shear band in metallic solid.

stacking faults, hexagonal Ti alloys, instability of crystal lattice, solution strengthening, micro-shear band

Due to their finely balanced strength and density, hexagonal close-packed (hcp) metals such as Ti and Mg are perceived as potential prime elements for the production of new light, and strong alloys essential for the sustainable development of green technologies oriented towards a reduction in mass in all transport sectors. Nevertheless, the conscious design of materials requires information on the relationship between alloy elements and individual deformation mode activity. Such complex knowledge in the context of hcp systems remains a challenge, seriously hampering our ability to anticipate the strength and ductility of new materials developed. In general, hcp metals and alloys suffer from limited cold workability arising from reduced crystal symmetry (compared to cubic crystals) and from the geometrical relations between their dislocation glide planes. On the other hand, the unique properties of single phase hcp materials, such as great strength and reasonable ductility of α-Ti+O solutions and a pronounced solution softening of α-Mg+Y alloys demonstrate the great potential of this groups of materials. All these aspects provide incentive for exploring the physics of plastic deformation and solution strengthening theories.

Hexagonal Ti alloys, solid solution strengthening, Peierls barriers, screw dislocations, first principles calculations

Additive Manufacturing (AM) process is a very fast and promising technique to build various very complex prototypes and components directly in the industry. One can choose different techniques of AM like Selective Laser Sintering (SLS), Fused Filament Fabrication (FFF) dedicated for thermoplastic materials or Direct Laser Metal Sintering (DMLS) for powder metals, or Stereolitography Apparatus (SLA) for thermosets. One of the most common techniques in AM are SLS and FFF for thermoplastic materials. The complexity of the processes and the behaviour of the materials in specific environment have a strong influence on the quality, strength and warpage of the obtained structures. The state of the art of the studies indicates that morphology of the material and the crystallization processes influence the aforementioned characteristics of the created components. The knowledge on the crystallization kinetics of polymers is known since many years but it is still developing in order to get an adequate description of the behaviour of the materials in isothermal and non-isothermal conditions. Furthermore, it is needed to predict the warpage of manufactured components based on the virtual AM process in order to decrease the costs. The available tools dedicated for FE analyses allow to increase functionality and implementation of own material models and techniques to perform the customize simulations. Based on the theory and Differential Scanning Calorimetry (DSC) results it is possible to predict the behaviour of the materials and start working on simulation of the virtual AM process [1-4]. The extracted curves of the velocity of material crystallization in temperature domain with different cooling rate obtained in FE simulations are shown in Fig. 1. The simulated curves are confronted with the DSC experimental results.

crystallization kinetics, Differential Scanning Calorimetry (DSC), polyamide 2200, additive manufacturing, FE analysis

Experimental observations show that inelastic deformation of metals is often produced as an effect of competing mechanisms of crystallographic glide, twinning and micro-shear banding. The micro-shear bands are observed as concentrated shear zones in the form of transcrystalline layers of the thickness of the order 0.1 µm. It has been observed that the change of the mechanism of inelastic deformation has strong influence on ductile failure processes in different length scales. Therefore, the identification and elucidation of physical mechanisms that are responsible for initiation, growth and evolution of micro-shear bands is of fundamental importance for understanding the macroscopic behaviour of metallic materials. A new physical model of multilevel hierarchy and evolution of shear bands is proposed with use of the analysis of recent state of the art of the investigations carried on different levels of observations: uni-axial and bi-axial mechanical tests enhanced with digital image correlation method and in-situ tests with use of electron microscopy as well as atom probe tomography in relation with ab initio and molecular dynamics computational simulations. The difficulties with application of a direct multiscale integration scheme are discussed and an original idea of an extension of the representative volume element concept with use of the known theory of the propagation of the singular surfaces of microscopic velocity field is proposed. A new formulation of the description of rate of shear strain generated by multilevel hierarchy of shear bands is formulated in the workflow integration approach, in which information from molecular simulation at different levels flows into the decision process.

shear banding, multilevel hierarchy of shear bands, viscoplastic flow, failure

Przedstawiono zagadnienie efektu skali występującego w nieliniowej teorii sprężystości. Omówiono uwzględnienie efektu skali do badań stateczności jednowymiarowych nanostruktur na przykładzie nanoprętów i nanorurek węglowych. Przedstawiono problematykę zjawiska utraty stateczności w ujęciu nieliniowym oraz zaprezentowano, wynikające z wyprowadzonych zależności, postacie postbifurkacyjne (elastyki) z wykorzystaniem oprogramowania Wolfram Mathematica. Omówiono analizę zachowania jednowymiarowego ciała pod wpływem obciążenia ściskającego oraz samodzielne wyprowadzone wzory na krzywiznę nanopręta z uwzględnieniem efektu skali. Porównano wyniki teorii nieliniowej z uwzględnieniem efektu skali oraz bez jego uwzględnienia i przedstawiono je w postaci wykresów wygenerowanych w programie Wolfram Mthematica. Przedyskutowano możliwe zastosowania otrzymanych wyników w technicznych problemach nanotechnologii.

jednowymiarowe struktury, nanopręty, nanorurki węglowe, nieliniowy problem statecznosci, efekt skali, elastyka

Celem pracy jest upowszechnienie oryginalnej koncepcji hipotezy wytężenia, opierającej się na podstawowych założeniach i prawach fizyki ciała stałego, która została zaproponowana blisko pół wieku temu przez ucznia Włodzimierza Burzyńskiego - Jerzego Zawadzkiego. Zawadzki wyprowadził, na gruncie równań fizyki metali oraz fizyki polimerów, miarę wytężenia jako przyrost właściwej energii swobodnej. Daje to możliwość uwzględnienia zmian entropii w czasie procesu odkształcenia, co dla polimerów jest szczególnie istotne. Przewodnią myśl Zawadzkiego można przedstawić następująco. Jeżeli ciało odkształcalne zostaje obciążone, wzrasta jego energia sprężysta w wyniku zmian odległości między atomami lub molekułami. Innymi słowy, dla ciał izotropowych, energia zmian postaciowych i objętościowych ulega zmianie. Nie jest to jedyna zmiana, gdyż w także energia drgań atomów wokół położeń równowagi także się zwiększa, co w konsekwencji może powodować przejście ze stanu sprężystego w stan odkształcenia plastycznego. Ten trafny argument znalazł swoje potwierdzenie w rozwiniętej w późniejszych latach teorii termicznie aktywowanego ruchu dyslokacji jako fizykalnego mechanizmu odpowiedzialnego za proces deformacji lepkoplastycznych.Rozważania przytoczone w pracy Zawadzkiego doprowadziły do wyprowadzenia różnych form energetycznej hipotezy wytężenia. Autor przedyskutował także szczegółowo porównanie własnych kryteriów sprężystych stanów granicznych z tymi, które były dyskutowane wcześniej przez Hubera, Hubera i Beltramiego jak również Burzyńskiego oraz Schleichera.

energetyczna miara wytężenia, przyrost właściwej energii swobodnej jako miara wytężenia, fizyka metali, fizyka polimerów

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.

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

Metal foams in view of their structural strength and mechanical energy absorption capability under high speed impact can be utilized as energy absorbers. It is important to understand the propagation of compaction waves in the foams. Most commercially available metal foams are made of aluminium, nickel, copper, and metal alloys. Two kinds of foams exist, namely the open-cell and the closed-cell foams. Typically, the pore density of uncompressed open-cell foams varies between 5 to 100 PPI (pores per inch), while the porosity is in the range from 70% to 95%. Literature provides several examples of metal foams solutions for energy absorption applications, dealing with both experimental, numerical and analytical studies. The subject of the study are the models based on digital micro-structures, in particular open cell metallic foams characterized with the skeleton formed of convex or re-entrant cells. The re-entrant materials revealing negative Poisson's ratio have attracted increasing attention in the context of modern materials applications, [3]. The goal of the presented investigations is to study the impact limits and absorption energy of these two kind of open cell metallic foams. To simulate the deformation processes the finite element program ABAQUS is used. The computer tomography made the basis for the formulation of computational model of the foam and the finite element discretization of the skeleton. From each reconstructed volume, a representative cubic volume element was extracted. For numerical simulations the constitutive elasto-viscoplasticity model is applied that defines the dynamic behaviour of oxygen-free high conductivity (OFHC) Cu using the experimental data reported in the literature. The chosen material model for the numerical simulation is the Cowper-Symonds model. The model is able to predict the mechanical behaviour of the materials under different loading conditions and it is implemented in many FEM codes in order to investigate and describe problems such as ballistic impacts or problems in which the strain-rates component are relevant. In numerical simulations the bottom displacements in the impact direction are fixed and initial velocity V0 on the top surface and general contact (steel wall-Cu foam and selfcontact Cu foam) with the friction coefficient 0.35 is assumed. The numerical predictions of axial force (crushing force) within the wide range of velocity: from 50 to 300 m/s are discussed. The shock state variables derived from Hugoniot relation and the conservation laws are used for comparison with FEM simulations.

copper open-cell foams, compaction waves, shock waves, crushing force, elasto-viscoplasticity model

The subject of the study is the models based on digital microstructure, in particular open-cell metallic materials with the skeleton of convex or re-entrant cells. Recently, the auxetic materials have attracted increasing attention in the context of modern materials applications. The dynamic properties of such materials are less known. Impact compressions of the two kind of cellular materials under high-velocity are numerically analysed, [1]. To simulate the deformation processes the finite element program ABAQUS is used. The computer tomography makes the basis for the formulation of computational model and finite element discretization of the skeleton of virtual cellular material. For numerical simulations the constitutive elasto-viscoplasticity equations are applied that describe the dynamic behaviour of OFHC Cu. The numerical predictions of compression kinematics of the skeleton and crushing force for velocity 50 and 300 m/s are discussed. The results of computations are completed with the analysis of shock wave propagation.

virtual cellular material, dynamic loading, crushing force, auxetic material, OFHC Cu, shock vaves

The magnethoreological material is based on the ferroparticles immersed in carrying fluid. The acting magnetic field is forcing ferroelements to connect into characteristic structure - braids. Behaviour of the magnethoreological material at the high strain rates will be described by Perzyna model. The created model will be verified with use of dedicated laboratory set up.

magnethoreological material, viscoplasticity model, dynamic behaviour, ferroelements.

Obserwacje doświadczalne wykazują, że deformacja plastyczna metali jest często efektem konkurujących ze sobą mechanizmów krystalograficznych poślizgów, bliźniakowania oraz mikropasm ścinania. Te ostatnie przejawiają się jako koncentracje odkształcenia postaciowego w formie cienkich transkrystalicznych warstewek o grubości rzędu 0,1 µm. Mikropasma ścinania współdziałają z aktywnymi mechanizmami krystalograficznego poślizgu lub bliźniakowania, kontrolując w różnym stopniu proces plastycznej deformacji. Na podstawie analizy aktualnego stanu badań prowadzonych na różnych poziomach obserwacji: wspomagane cyfrową korelacją obrazu badania mechaniczne – próby jedno- i dwuosiowe, badania in-situ przy użyciu mikroskopii elektronowej, badania tomografii atomowej w połączeniu z obliczeniami ab initio oraz dynamiki molekularnej, zaproponowano fizyczny obraz wielopoziomowej hierarchii oraz ewolucji pasm ścinania. Przedstawiono motywację fizykalną i heurystyczne podstawy opisu teoretycznego. Odniesiono się do znanych wyników z literatury, [2]. Przedyskutowano trudności z zastosowaniem prostego wielkoskalowego sposobu uśredniania oraz oryginalną koncepcję rozszerzenia pojęcia reprezentatywnego elementu objętości z wykorzystaniem znanej teorii propagacji powierzchni osobliwych jako fal silnej nieciągłości mikroskopowego pola prędkości. Przedstawiono nowe sformułowanie opisu prędkości odkształcenia postaciowego generowanego przez wielopoziomową hierarchię pasm ścinania z uwzględnieniem decyzyjnego procesu wyboru kluczowych efektów przepływu informacji dla poszczególnych poziomów obserwacji. ********* Experimental observations show that plastic deformation of metals is often produced as an effect of competing mechanisms of crystallographic glide, twinning and micro-shear banding. The micro-shear bands are observed as concentrated shear zones in the form of trans crystalline layers of the thickness of the order 0.1 µm. They cooperate with active mechanisms of crystallographic glide and/or twinning controlling to various degrees process of plastic flow. It has been observed that the change of the mechanism of plastic deformation has strong influence on mechanical properties of material under consideration. Therefore, the identification and elucidation of physical mechanisms that are responsible for initiation, growth and evolution of micro-shear bands is of fundamental importance for understanding the macroscopic behaviour of metallic materials. Basing on the analysis of recent state of the art of the investigations carried on different levels of observations: uni-axial and bi-axial mechanical tests enhanced with digital image correlation method, in-situ tests with use of electron microscopy, atom probe tomography in relation with ab initio and molecular dynamics computational simulations, certain physical model of multilevel hierarchy and evolution of shear bands is proposed. Physical motivation and heuristic foundations of theoretical description are discussed with reference to known results in the literature, [2]. The difficulties with application of a direct multiscale integration scheme are discussed and an original idea of an extension of the representative volume element concept with use of the known theory of the propagation of the singular surfaces of microscopic velocity field is proposed. A new formulation of the description of rate of shear strain generated by multilevel hierarchy of shear bands is formulated in the workflow integration approach, in which information from molecular simulation at different levels flows into the decision process.

pasma ścinania, hierarchia pasm ścinania, powierzchnia osobliwa, cyfrowa korelacja obrazu (DIC), shear bands, multilevel hierarchy of shear bands, singulatity surface, digital image correlation (DIC)

Badania doświadczalne efektu Portevin - Le Chatelier w Inconelu 718 przeprowadzono na płaskich próbkach. Do pomiarów zastosowano metodę cyfrowej korelacji obrazu (DIC), która jest efektywna i praktyczna dzięki bezkontaktowym pomiarom i dużej dokładności w ustalaniu charakterystycznych cech przestrzenno-czasowych deformacji próbki. Określenie takich cech zlokalizowanych pasm ścinania jest konieczne do zaproponowania modelu konstytutywnego dla metali wykazujących ten typ plastycznej niestabilności. Opracowany model konstytutywny pozwoli na numeryczne symulacje w pełnej skali 3D fizycznych testów z użyciem programu ABAQUS. Głównym celem pracy jest przedstawienie możliwości wykorzystania pomiarów uzyskanych techniką cyfrowej korelacji obrazu do wykrywania i charakteryzowania przestrzenno-czasowych cech efektu PLC w dostępnym komercyjnie stopie Inconel 718.
An experimental investigation of the Portevin–Le Chatelier effect in the Inconel 718 alloy is undertaken in this study through flat specimen geometries. Measurements based on digital image correlation (DIC) is an effective and practical optical technique due to the advantages of easy operation, non-contact, full field optical measurement, high accuracy and high computational efficiency for investigating the PLC effect and its spatio-temporal characteristics. The localization band characteristics are required to develop the constitutive relations for metals exhibiting this type of plastic instability, based on available material tests. The constitutive model can be used in full-scale 3D numerical simulations of the physical tests using the explicit solver of the finite element code ABAQUS. The objective of this paper is to show how DIC techniques are readily able to detect and characterize spatio-temporal features of the PLC behaviour of a commercial available Inconel 718 alloy.

stop Inconel 718, efekt Portevin-Le Chatelier, cyfrowa korelacja obrazu, Inconel 718 alloy, Portevin-Le Chatelier effect, Digital Image Correlation (DIC)

In the paper the results of experimental and numerical investigations concerning an influence of strain rate on mechanical properties of pure tantalum are presented. Experiments were carried out using Direct Impact Compression Test (DICT) technique (Malinowski et al. [2007]). The Perzyna elasto-viscoplasticity theory (Perzyna [1966]) was applied to predict the dynamic compression yield strength of the tested material at strain rates from 1.0 x10-3 s−1 to 0.5 x106 s−1.

The results of experimental and numerical investigations concerning an influence of strain rate on mechanical properties of pure tantalum are presented. Experiments were carried out using Direct Impact Compression Test (DICT) technique. The miniaturization concept of the experimental setup for the dimensions of specimen (diameter dS = 1.5 mm and thickness lS = 0.50 mm), Hopkinson transmitter bar diameter (dH = 3.0 mm) and the striker (diameter dI = 11.5 mm and the length lI =12 mm), together with application of a novel optical arrangement for measurement of striker velocity, enabled compression tests to be executed at strain rates from 1.0 x103 s−1 to 0.5 x106 s−1. The Perzyna elasto-viscoplasticity theory is applied to predict the dynamic compression yield strength of the tested material at different strain rates. In the course of specimens deformation by means of the DICT technique, it was observed that the peak force obtained from the strain gauge mounted on the transmitter Hopkinson bar was lower than the peak force obtained within the framework of the uniaxial stress wave analysis. An explanation of this discrepancy is provided due to the analysis of the localization of deformation in the tested specimens considered as three-dimensional body subjected to high strain rate loading and the resulting stress wave attenuation as it propagates within the specimen.

direct impact test, numerical simulations, tantalum

Recent investigations reveal that interface bonding strength is dependent on the relative orientation of crystallites of the both phases [2]. The experimental, theoretical and computational investigations confirm this observation in the case of Cu/Al2O3 system, [3], [4]. It is shown that the statistical distribution of the values of interface strength for different relative orientations of bonded phases should be included in the phenomenological model of the damage initiation in nanocomposites. The novelty of the presented study is the combination of different experimental techniques: HRTEM, EBSD and molecular dynamics simulations with phenomenological theory of damage development in nanocomposites due to debonding at the interphase boundary [5], [6], [7]. A class of new models with the yield condition determined by one of quadric surfaces, in particular paraboloid or ellipsoid one is considered and the comparison with popular Gurson approach is discussed, [8].

nanocompistes, strength, interface, bonding, HRTEM, EBSD, molecular dynamics

The composition of metal with ceramics is applied to many devices, structural elements of machines as well as their equipment. Therefore, evaluating the strength of interfaces of this type becomes an important scientific issue of fundamental character. Numerous attempts are made to solve the posed problem, both experimental and theoretical ones. The presented approach enables local, more precise determining the mechanical properties of interfaces. The basis of conducted calculations is the geometry of the interface strongly preferred by the considered system of materials. It is defined by the mutual orientation of crystallites of two phases and the position of the plane boundary. The combination of two advanced research methods: electron back-scatter diffraction (EBSD) and high resolution transmission electron microscopy (HRTEM) enables identification of this crucial characteristics. The second of them additionally reveals a representative microstructure of the interface in the form of a projection. We reconstruct it in three dimensions by means of molecular dynamics (MD) simulations. In this way, we identify deformation mechanisms that enable the formation of the bonding between the metallic phase and ceramic one.

nanocomposites, deformation in interface, HRTEM

The microsized (~10µm) ferroelements build the structure of magenthoreological (MR) fluid. This two phase material in neutral state behaves as a fluid but in magnetic field becomes a solid and has properties of elasto-viscoplastic material. This is due to the skeleton made by ferrolements connected into braids. The aim of the paper is to identify the physical mechanisms of deformation of such a structure with use of own set up for in situ microscopic observations.

magnethoreological solids, viscoplasticity, ferroelements, compression test, shear banding

The design of new multifunctional foams as well as metal-ceramic and polymer-ceramic composites of ceramic foam structure, which can be applied as lightweight wear resistant elements, fire resistant or fire retardant parts, piezoelectric actuators etc., requires the solution of the following questions:
- in what way to fabricate polyurethane, metallic or ceramic foams and preforms of assumed skeleton structure,
- how to produce tomograms, i.e. 3D virtual volume reconstructions of real foam structure [1],
- how to elaborate methods of numerical simulations of fabrication processes of auxetic foams with use of the tomograms.
Depending on manufacturing method the cells obtain convex or concave shape. The materials with convex cell structure reveal positive Poisson's ratio. The complex structure of the foam related with reentrant cells produce the oposite effect - the negative Poisson's ratio is observed and such foams become auxetic. The aim of the presented study is to tackle the third question related with numerical simulation of fabrication processes of auxetic foams.

auxetic foam, micro-tomography, negative Poisson’s ratio, numerical simulation, metallic foam, open-cell foam, fabrication

Przedmiotem badań niniejszej pracy jest numeryczna rekonstrukcja struktur rzeczywistych pianek otwartokomórkowych w celu wygenerowania reprezentatywnego elementu objetości. Analizowane są dwa rodzaje pianek (ceramiczna i polimerowa), których porowatość wynosi odpowiednio 90% i 94%. Oba rodzaje pianek zostały przebadane z użyciem mikrotomografu komputerowego. Uzyskane dane zostały zaimportowane do programu ScanIP, przy pomocy którego przeprowadzono cyfrową obróbkę uzyskanych obrazów oraz wydzielono fazę reprezentującą szkielet pianki.

numeryczna rekonstrukcja, struktury otwartokomórkowe, pianki metaliczne, mikrotomografia komputerowa

W pracy dokonano analizy wielkości sił zgniatania, energii dyssypacji oraz sposobów deformowania się dwóch typów metalicznych pianek otwartokomórkowych sciskanych dynamicznie z różnymi prędkościami. Zbadano pianki o strukturze wypukłej oraz o komórkach wklęsłych, które charakteryzują się ujemnym wspołczynnikiem Poissona.

dynamiczna analiza, procesy zgniatania, pianki metaliczne, struktury otwarokomórkowe

Magnetorheological materials are commonly used in technical devices because of specific behaviour in magnetic field. The magnetoactive particles are immersed in the carried fluid. The material becomes solid under the influence of magnetic field. The structure of solid material consists of the chains of the particles lying along the direction of magnetic field and the material under the stress is deforming as a solid body. The present studies are focused on the microscopic and phenomenological models of non-newtonian fluid. However, the mechanisms of deformation in solidified material under magnetic field require further investigations. The aim of the paper is to present the experimental visualization of the rearrangements of the particles in the activated by magnetic field chains. Basing on microscopic observations, the hypothesis is formulated that the mechanism of micro-shear banding is responsible for inelastic deformation of magnetorheological material. The discussed physical model makes the basis of the material description within the framework of the Perzyna viscoplasticity theory.

magnetorheological fluid, magnetorheological gel, Perzyna viscoplastic model

The extension of viscoplasticity Perzyna's model for the field of magnetorheological materials is proposed. The model is adopted to identify the mechanisms of microscopic rearrangement of ferroelements producing visible increase of material stiffness, in particular increase of shear modulus. The project of laboratory test stand is presented. It is based on Split Hopkinson Pressure Bar set-up equipped with container for magnetorheological fluid and coil to control it.

magnetorheological fluid, magnetorheological gel, Pezryna viscoplasticity model, Split Hopkinson Pressure Bar

The subject of te study are metallic open-cell foams. In particular, the foam of Cu skeleton is considered. To simulate the deformation process of such a material the finite element program ABAQUS is used. The tomogram reconstructing the 3D virtual volume of a real foam structure with the use of computed tomography is applied to formulate the finite element model of the convex open-cell foam cube of the edge of 800 voxels created with application of ABAQUS/CAE. The initial cube of convex open-cell skeleton is subjected to three-axial compression applied as uniform displacements normal to the surface of cube faces in order to simulate numerically auxetic foam fabrication process.

auxetic foam, micro-tomography, tomograms, negative Poisson's ration, numerical simulation, metallic foam, open-cell foam, foam fabrication

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.

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

The design of new multifunctional foams requires the solution of the following questions: in what way to fabricate metallic foams of assumed skeleton structure, how to produce tomograms, i.e. 3D virtual foam reconstructions of real foam structure [1], how to elaborate methods of numerical simulations of assumed processes in auxetic foams with use of the tomograms. Depending on manufacturing method the cells obtain convex or concave shape. The materials with convex cell structure reveal positive value of Poisson’s ratio, that is if a sample is stretching, then its cross-section is getting thinner. The complex structure of the foam related with reentrant cells produces the opposite effect during stretching of a sample, i.e. its cross-section is increasing. Then the negative Poisson’s ratio is observed and such foams become auxetic. The aim of the study is to study the third question. The motivation is given in [2], where it has been stressed that numerical simulations predicting a new material’s behaviour reduce laboratory costs and accelerates the trial and error procedure.

Metallic open-cell foam with the convex or concave cells, the foam of OFHC Cu skeleton, the foam structure with use of computer tomography images, numerical simulation of dynamic processes in metal foams

Metallic cellular materials have been widely acknowledged for their multifunctional applications related also with energy absorption capability in addition to their light weight. In recent years, the auxetic materials revealing negative Poisson’s ratio have attracted much attention. Up to date, the research of auxetics is mainly concentrating on the cell design and the static response, although the auxetic materials also demonstrate potential for energy absorption, fracture retardant, and high-velocity impacts resistance. In the paper, a comparative study is reported on the high-velocity impact responses of two type metallic cellular foams, that is, convex open cell foam and auxetic foam. The material of the skeleton of the virtual foam is assumed to be isotropic and elastic-plastic. For numerical simulations the constitutive relation is applied which defines the behaviour of oxygen-free high conductivity copper (OFHC) using the experimental data reported in Nemat-Nasser and Li (1998) and Rusinek at al. (2010). The impact limits and absorption energy of the two foams are obtained by means of explicit nonlinear finite element simulations using ABAQUS. It has been found that the auxetic foam is superior to the convex cell foam in impact resistance because of the material concentration at the impacted area due to the negative Poisson’s ratio effect.

Open-cell foams, the impact resistance of convex and auxetic copper (OFHC) foams

This paper presents numerical investigations of the influence of friction in the contact between sheet and a punch on sheet deformation in Nakazima type formabilitybtests. The Nakazima test [1] is one of the most comonnly used tests to study experimentally formability of metal sheets. It consits in stretching of a sheet specimen by means of a hemispherical punch until fracture occurs.
The aim of this study has been to numerically identify frictional conditions in a selected case of the Nakazima test and study numerically effect of change of friction on strain path and forming limit curve. (FLC). Numerical simulations have been performed assuming the data corresponding to own lboratory tests carried out for the steel grade HC380LA 1.5 mm thick.

formabilty of metal sheets, Nakazima test, numerical simulation, friction effects

Finite element method is an efficient numerical tool to analyse problems of the sheet metal forming processes including cup drawing and stamping. Proper description of material properties is crucial for accurate analysis. In particular, the anisotropy and asymmetry of elastic range, related with strength differential effect (SDE), of considered materials play an important role in finite element simulation. The paper presents a new yield criterion for the transversal isotropy of metal sheets under plane stress conditions which is an extension of the isotropic yield function proposed by Burzyński (1928) (Studium nad hipotezami Burzyński’s doctoral dissertation ”Study on material effort hypotheses”, Engng. Trans., 2009, t. 57, nr 3–4, s. 185–215). One additional coefficient has been introduced in order to allow a better representation of plastic behavior of metal sheets. The proposed yield condition includes the influence of first invariant of the stress tensor and also the strength differential effect. The system of equations describing the sheet metal forming process is solved by algorithm using the return mapping procedure. Plane stress constraint is incorporated into the Newton-Raphson iteration loop. The proposed algorithm is verified by performing a numerical test using shell elements in commercial FEM software ABAQUS/EXPLICIT with a developed VUMAT subroutine.

the strength differential effect, a new yield criterion for the transversal isotropy of metal sheets, numerical simulations of cup deep drawing process

Metallic materials are usually used in engineering applications in the as received state. In such a case, developing in in the course of manufacturing processes texture induces anisotropy of mechanical properties and produces often the so-called strength differential effect (SDE).The precise description of elastic properties and formulation of limit criterion requires application of the formalism used typically for anisotropic solids. It is a complex and difficult task related with
proper experimental characterisation of all material parameters. In some cases, however, a simple model of isotropic solid revealing possible strength differential effect and certain correction for the limit strength in shear can be proposed. It is in accord with the observation that developing texture influences mostly shear strength of metallic solids.

A simple model of isotropic solid, strength differential effect, the limit strength in shear

This paper presents experimental and numerical investigations of the influence of friction on sheet deformation in Nakazima type formability tests. Numerical simulations have been performed using the authors own explicit dynamic finite element program. Strain distribution obtained in numerical analyses has been compared with experimental data. Location of fracture was of major interest in this specimen as required by the standards can be obtained for low value of the friction coefficient. With the increase of the friction coefficient the fracture is displaced further from the center.

formability of metal sheets, Nakazima test, numerical simulation, friction effect, failure location

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.

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

The aim of the presentation is to discuss the classical problems of elastic limit criteria from the perspective of basic quantum mechanical approach [1]. In the case of metallic solids the multiscale mechanisms of plastic deformation and failure are analyzed [2]. In particular, the role of shear banding responsible for plastic flow is elucidated [3].

elastic limit criteria, metal/ceramic interface, copper/saphire nanocomposites, PLD, HRTEM, EBSD

This paper presents numerical investigations of the influence of friction in the contact between sheet and a punch on sheet deformation in Nakazima type formability tests. The Nakazima test [1] is one of the most commonly used tests to study experimentally formability of metal sheets. It consists in stretching of a sheet specimen by means of a hemispherical punch until occurrence of fracture.

formability, Nakazima test, influence of friction, numerical simulations, deformation of metal sheets

Finite element method is an efficient numerical tool to analyse problems of the sheet metal forming processes in particular cup drawing and stamping. Proper description of material properties is crucial for accurate analysis. In particular, the anisotropy and asymmetry of elastic range, which is related with strength differential effect (SDE), of considered materials play an important role in finite element simulation. For metal forming analysis with use of traditional models many experimental tests are usually needed to obtain the adequate description of anisotropic behaviour of metal sheets. Therefore, the search for new models, which are based on simplified description of the effects of anisotropy and SDE requiring less experimental tests seems to be justified.
The paper presents the application of a new yield criterion for the transversal isotropy of metal sheets under plane stress conditions. The proposed criterion is based on the study of yield criteria accounting for SDE and anisotropy nade by W. Burzyński [1]. The system of equations describing the sheet metal forming process is solved by the algorithm using the return mapping procedure. Plane stress constraint is incorporated into the Newton-Raphson iteration loop. The proposed algorithm is verified by performing the numerical calculations using shell elements of the commercial FEM sftware ABAQUS/EXPLICIT with own VUMAT subroutine.

metal sheet forming, metal cup deep drawing, FE numerical simulations, strength differential effect, anisotropy and asymmetry of elastic range, transversal isotropy

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.

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

The elastoplastic constitutive equations for materials under plane stress condition with new yield criterion have been proposed. This yield condition accounts for the effect of strength differential effect. The system of equations of sheet metal forming process is solved by algorithm using the return mapping procedure. Plane stress constrain is incorporated into the Newton-Raphson iteration loop. The proposed algorithm is verified by performing numerical tests using shell elements in commercial FEM software ABAQUS/EXPLICIT with developed VUMAT subroutine. It is shown that the proposed approach provides the satisfactory prediction of material behaviour, at least in the cases when the anisotropy effects are not so advanced.

anisotropic behaviour of metal sheets, strength differential effect, explicit finite element analysis, plane stress

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.

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 %

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.

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

The paper presents a new yield criterion for the transversal isotropy of metal sheets under plane-stress conditions which is an extension of the isotropic yield function proposed by Burzynski (Burzynski W. 1928). Studium nad hipotezami Burzynski's doctoral dissertation

elastic-plastic analysis, transversal isotropy, metal sheets, deep drawing process, FE simulations, Burzyński yield condition, strength differential effect