Institute of Fundamental Technological Research

In this work, a new, simple method is presented, which enables identifcation of material properties of solids basing on the digital image correlation (DIC) measurements. It may be considered as a simplifed alternative of low computational complexity for the well-known fnite element model updating (FEMU) method and virtual felds method (VFM). The idea of the introduced sub-global equilibrium (SGE) method is to utilize the fundamental concept and defnition of internal forces and its equilibrium with appropriate set of external forces. This makes the method universal for the use in the description of a great variety of continua. The objective function is the measure of imbalance, namely the sum of squares of residua of equilibrium equations of external forces and internal forces determined for fnite-sized part of the sample. It is then minimized with the use of the Nelder–Mead downhill simplex algorithm. The efciency of the proposed SGE method is shown for two types of materials: 310 S austenitic steel and carbon-fber-reinforced polymer (CFRP). The proposed method was also verifed based on FE analysis showing error estimation.

Identifcation of material constant,Digital image correlation,Nelder–Mead downhill simplex algorithm,Finite element analysis,Optimization,Linear elasticity

This study presents the novel peridynamic constitutive relations formulated in order to predict the plastic deformation and damage evolution in irradiated materials. The plastic behaviour of the material in which radiation induced defects contribute to the defined peridynamic porosity is described by the Gurson-Tvergaard-Needleman (GTN) yield criterion with irradiation hardening. The definition of peridynamic porosity is proposed as a volume of discontinuities created in the volume of peridynamic particles. The new constitutive relations for irradiation hardening based on the dilatational part of elastic strain energy are formulated. The physical relevance of coupling the porosity with the nonlinear irradiation hardening is discussed. The expressions for the yield function, kinetics of evolution of radiation induced porosity, irradiation hardening and plastic flow rule are derived in terms of the peridynamics variables. The peridynamic predictions are calibrated based on the experimental data obtained during the advanced experimental campaigns dedicated to irradiated materials to verify the validity of the proposed constitutive model. Ion irradiation campaigns were carried out to mimic the effects of neutron irradiation. A series of indentation experiments were conducted to elucidate the effects of material structure modification and assess the hardening effect originating from radiation defects.

Peridynamics,Constitutive modeling,Radiation induced damage,Peridynamic porosity,Gurson yield function,Irradiation hardening,Ion irradiation,Nano-indentation test

The paper concerns the experimental analysis of the energy conversion process during uniaxial tension of 310S austenitic steel. The plastic work distributions were obtained taking into account the influence of strain rate and plastic anisotropy based on the displacement gradient determined experimentally using Digital Image Correlation (DIC) method. On the other hand, the energy dissipated as heat was obtained by the calculation of heat sources from the transient heat conduction equation basing on both the evolution of the temperature field determined by Infrared Thermography and mechanical field provided by DIC. It was shown that the proportions between the terms of the heat conduction equation and between the particular components of the energy dissipated as heat are significantly different for various process durations. As a measure of energy conversion the energy storage rate was used. At the beginning of the plastic deformation, the values are in the range from 0.4 to 0.6 depending on the strain rate and then decrease monotonically up to the level of around 0.15 with the increasing strain. Moreover, just before the end of the process the values decrease significantly and become close to 0 or even negative, which means that the material loses its ability to store the energy.

digital image correlation, infrared thermography, energy conversion, transient heatconduction equation, heat sources, energy storage rate

This paper discusses the issue of a lap joint in the form of a thin film attached to a rigid base with the use of a layer of flexible adhesive exhibiting a non-linear constitutive relation between shear stress and distortional strain, which is approximated by the second-order power law. Similarity theory is used to perform a qualitative analysis of the influence of magnitude of non-linearity on the performance of the system. The introduced similarity numbers are proposed to be used in formulation of simple design tools. The analysis is performed by solving the derived governing equations for characteristic cases in a numerical way combining the fourth-order Runge-Kutta algorithm and iterative shooting ruled by a steepest descent method. The results are compared with the results of the plane stress finite element analysis. It can be observed that within considered models the influence of the material non-linearity is of minor importance and in some cases it may be almost entirely surpassed by local effects resulting from boundary conditions. For relatively small load intensity it becomes negligibly small.

flexible adhesives, non-linear elasticity, lap joint, strengthening films

This paper deals with the numerical simulation of the dynamic failure of an aluminium plate under air-blast loading. Constitutive modelling based on the fractional viscoplasticity is used. The material model is non-local due to the properties of the applied fractional differential operator and is implemented as user material in the engineering finite element computation code ABAQUS. It is important that the numerical simulations are contrasted with experiments. Numerical outcomes clearly show the applicability of the adopted modelling for the description of salient stages of dynamic structural failure.

fractional viscoplasticity, rate sensitivity, plastic anisotropy, non-locality, damage mechanics

This paper focuses on the experimental determination of the distribution of material, lattice and plastic rotation during deformation of crystalline aggregate. The proposed methodology uses standard electron backscattering diffraction technique combined with 3D digital image correlation data. The presented approach is used for analysis of rotations during deformation of aluminium multicrystal.

image analysis, electron backscattering diffraction, plastic deformation, misorientation, plastic rotation

The paper considers the plastic strain localization phenomenon in the framework of the fractional viscoplasticity. As an illustrative example, full spatial modelling of a tension test under extreme dynamic conditions is presented. The modelling assumes adiabatic conditions including isotropic work hardening-softening effects induced by plastic strains, temperature and damage (scalar). Special attention is paid to additional, compared to the classical Perzyna viscoplasticity, model parameters resulting from application of fractional calculus in the evolution law for plastic strains. It is shown that the proposed formulation allows for high flexibility of modelling of the localization zone with a limited number of model parameters.

fractional viscoplasticity, strain localization, extreme dynamics

The paper presents experimental and numerical characterization of damage evolution for ion-irradiated materials subjected to plastic deformation during nano-indentation. Ion irradiation technique belongs to the methods where creation of radiation-induced defects is controlled with a high accuracy (including both, concentration and depth distribution control), and allows to obtain materials having a wide range of damage level, usually expressed in terms of displacements per atom (dpa) scale. Ion affected layers are usually thin, typically less than 1 micrometer thick. Such a low thickness requires to use nano-indentation technique to measure the mechanical properties of the irradiated layers. The He or Ar ion penetration depth reaches approximately 150 nm, which is sufficient to perform several loading-partial-unloading cycles at increasing forces. Damage evolution is reflected by the force-displacement diagram, that is backed by the stress–strain relation including damage. In this work the following approach is applied: dpa is obtained from physics (irradiation mechanisms), afterwards, the radiation-induced damage is defined in the framework of continuum damage mechanics to solve the problem of further evolution of damage fields under mechanical loads. The nature of radiation-induced damage is close to porosity because of formation of clusters of vacancies. The new mathematical relation between radiation damage (dpa) and porosity parameter is proposed. Deformation process experienced by the ion irradiated materials during the nano-indentation test is then numerically simulated by using extended Gurson–Tvergaard– Needleman (GTN) model, that accounts for the damage effects. The corresponding numerical results are validated by means of the experimental measurements. It turns out, that the GTN model quite successfully reflects closure of voids, and increase of material density during the nano-indentation.

radiation-induced damage, evolution of vacancy clusters, nano-indentation test, ion irradiation, radiation hardening

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

The aim of this work was to determine the stress distribution during plastic deformation, based on the displacement field obtained using the digital image correlation (DIC) method. To achieve stress distribution, the experimentally measured displacement gradient and the elastoplastic material model with isotropic hardening were used. The proposed approach was implemented in the ThermoCorr program. The developed procedure was used to determine stress fields for uniaxial tension and simple shear processes, carried out on samples made of austenitic steel 304L. Both material parameters, such as the Young's modulus, Poisson's ratio, yield stress, and parameters of the hardening curve, were acquired experimentally. The macroscopic force obtained from the DIC-based stresses and its finite element analysis (FEA) equivalent were compared with that measured during the experiment. It was shown that the DIC-based approach gives more accurate results with respect to FEA, especially for a simple shear test, where FEA significantly overestimates the value of experimentally obtained macroscopic force.

stress field determination, digital image correlation (DIC), finite element analysis (FEA), elastoplastic constitutive model, plastic work

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

The subject of the work is the analysis of thermomechanical bending process of a thin-walled tube made of X5CrNi18-10 stainless steel. The deformation is produced at elevated temperature generated with a laser beam in a specially designed experimental setup. The tube bending process consists of local heating of the tube by a moving laser beam and simultaneous kinematic enforcement of deformation with an actuator and a rotating bending arm. During experimental investigations, the resultant force of the actuator and temperature at the laser spot are recorded. In addition to experimental tests, the bending process of the tube was modelled using the finite element method in the ABAQUS program. For this purpose, the tube deformation process was divided into two sequentially coupled numerical simulations. The first one was the heat transfer analysis for a laser beam moving longitudinally over the tube surface. The second simulation described the process of mechanical bending with the time-varying temperature field obtained in the first simulation. The force and temperature recorded during experiments were used to verify the proposed numerical model. The final stress state and the deformation of the tube after the bending process were analyzed using the numerical solution. The results indicate that the proposed bending method can be successfully used in forming of the thin-walled profiles, in particular, when large bending angles and a small spring-back effect are of interest.

laser forming, laser-assisted bending, numerical modelling

This paper presents a general numerical scheme for the fractional plastic flow rule, dedicated to a wide class of materials manifesting the non-normality of plastic flow and induced plastic anisotropy. To determine the vector of the plastic flow, a special numerical procedure has been developed, which is applicable for any smooth and convex yield function. The obtained approximation is verified based on an analytical solution. The paper also presents a set of numerical results for the generalised Drucker–Prager model

Non-normality, Plastic anisotropy, Fractional calculus, Return mapping algorithm

The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme.

fractional viscoplasticity, rate dependence, plastic anisotropy, non-normality, directional viscosity, explicit/implicit non-locality

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 objective of the work is to develop numerical method for determining coupled thermo-mechanical fields based on experimental data obtained from two cameras working in the visible and infrared mode. The sequence of images recorded by the first camera is used to determine the displacement field on the sample surface using the 2D digital image correlation (DIC) method. The resulting field from DIC analysis in a form of a set of discrete points with the corresponding in-plane displacement vector is used as the input for the next step of analysis, where the coupled temperature field is computed. This paper provides a detailed description of the numerical procedures, that allow, to obtain coupled thermal and mechanical fields together with the specification of experimental data needed for calculations. The presented approach was tested on an experimental data obtained during uniaxial tension of the multicrystalline aluminum. The developed numerical routine has been implemented in dedicated software, which can be used for the testing of materials on both a macro and micro scales

Digital image correlation (DIC), Infrared thermography (IRT), Coupled thermo-mechanical fields, Aluminum multicrysta

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

Forming processes assisted by localised laser heating are studied in recent years. Heating is used to make it possible or facilitate forming of materials, which exhibit such adverse properties as: brittleness, effects of high work-hardening or a high elastic springback. The hereby presented investigations concern the hybrid thermo-mechanical forming of thin-walled parts using local heating of the material by the laser beam. The research is aimed at forming of parts from materials used in the aviation industry, such as the nickel-base super-alloys Inconel 625, Inconel 718, and also martensitic superalloys AISI 410 and AISI 325. Preliminary investigations are conducted using X5CrNil8-10 (1.4301) stainless steel. Experimental study and numerical simulations cover the behaviour of thin beams 1 mm thick, subjected to mechanical load in the cantilever arrangement and heated by the CO2 laser beam moving from the free end of the sample towards its fixture. The possibility of obtaining large bending deformations relatively easily due to the application of laser beam is demonstrated experimentally. Experimentally verified finite element numerical simulations show the intense plastic flow of the material layer heated by the laser beam. It is accompanied by a shift of the cross-section neutral axis of the beam. Bending of thin-walled tubes in a specially designed device is studied in the next step. It allows introducing mechanical loading in a controlled manner, heating the material by a moving laser beam and forcing the required deformation according to the kinematic scheme of the device.

laser-assisted forming, finite element method, thin-walled structure

In this paper, an implementation of fractional plastic flow rule in the framework of implicit and explicit procedures is under consideration. The fractional plastic flow rule is obtained from a generalisation of the classical plastic flow rule utilising fractional calculus. The key feature of this new concept is that in general, the non-associative flow is obtained without necessity of additional potential assumption. If needed, the model can cover the anisotropy induced by plastic deformation. Illustrative examples showing the unusual flexibility of this model are also presented.

non-normality of plastic flow, fractional calculus, return mapping algorithm

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

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

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

Laser heating is industrially applied to facilitate plastic shaping, especially for materials difficult to form due to their high hardness or brittleness. The effects of thermal softening and thermal forming in the total plastic deformation of pre-stressed beams are investigated in the study. Laser-assisted bending experiments were performed using the moving CO2 laser beam and cantilever thin beams made of the factory-annealed Inconel 718 nickel-based superalloy. The deformation process is simulated numerically using the Finite Element Method and the Johnson–Cook constitutive material model. Curvature changes in thermo-mechanical bending are calculated numerically. Phenomenological moment–curvature relations for the laser-assisted bending process are formulated. The curvature in hybrid bending can be estimated as a sum of components resulting from the elastic deformation and inelastic deformations due to the pure thermal bending and thermally enhanced mechanical bending. For the effective hybrid bending, the external mechanical load should be applied consistently with the deformation effect of the heat source alone.

thermomechanics, curvature, laser-assisted bending, Johnson–Cook model, Inconel 718

The laser forming technique has an important disadvantage, which is the limitation of plastic deformation generated by a single laser beam pass. To increase the plastic deformation it is possible to apply external forces in the laser forming process. In this paper, we investigate the influence of external pre-loads on the laser bending of steel plate. The pre-loads investigated generate bending towards the laser beam. The thermal, elastic-plastic analysis is performed using the commercial nonlinear finite element analysis package ABAQUS. The focus of the paper is to identify how this pattern of the pre-load influence the final bend angle of the plate

Laser forming, Force-assisted laser forming, Laser-assisted bending, Thermo-mechanical simulations, Finite element analysis

Materials containing suspended micro- or nanomaterials are used extensively in multiple fields of research and industry. In order to understand the behavior of nanomaterials suspended in a liquid, the knowledge of particle stability and mobility is fundamental. For this reason, it is necessary to know the nanoscale solid-solid interaction and the hydrodynamic properties of the particles. In the presented research we used a hybrid Atomic Force Microscope coupled with Optical Tweezers system to measure the femtonewton scale interaction forces acting between single particles and the walls of a microchannel at different separation distances and environmental conditions. We show an important improvement in a typical detection system that increases the signal to noise ratio for more accurate position detection at very low separation distances.

Optical Tweezers, Atomic Force Microscopy, particle-wall interaction, colloid stability

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

image analysis, plastic deformation, misorientation, plastic rotation

Digital image correlation, Infrared thermography, Energy conversion, Heat sources, Transient heat conduction equation

The laser forming technique has an important disadvantage, which is the limitation of plastic deformation generated by a single laser beam pass. In order to increase the plastic deformation one has to repeat the process several times or use the alternative method. To increase the plastic deformation it is possible to add external forces during the laser forming process. In this paper, we investigate the influence of external pre-loads on the laser bending of steel plate. The pre-loads investigated generate bending towards the laser beam. The thermal, elastic-plastic analysis is performed using the commercial nonlinear finite element analysis package ABAQUS. The focus of the paper is to identify how this pattern of the pre-load influence the final bend angle of the plate.

laser forming, force-assisted laser bending, thermo-mechanical simulations, FEA

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 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

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

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

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

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