Instytut Podstawowych Problemów Techniki

Streszczenie:

This paper discusses the science of material effort from the historical viewpoint. Two gen eral scientific tools: the geometrical descriptive method of Mohr, and the energetic method of Huber are compared and evaluated from the very beginning. Three appropriate stress invariants are taken into account: stress intensity, stress triaxiality and stress shearness. Es pecially, much attention is devoted to explanation of the stress shearness invariant, which aims at describing the Lode parameter in a more analytical manner. Two different tools of finding a proper yield surface which contains the above mentioned three stress invariants are discussed in the literature perspective. In particular, the three-parameter yield surface, called the Burzyński-Pęcherski hypothesis is researched and explained from this new of point view.

Słowa kluczowe:

Tresca-Mohr hypothesi, Beltrami-Huber, Mises, Burzyński Hypothesis, Lode parameter

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The impact resistance behaviour of the plate made of the AM60 magnesium alloy at the low velocity impact perforation mode is here investigated at room temperature using a numerical approach based on experimental results. Dynamic tests were performed using an impact digital tower on the 10.0 mm thick AM60 magnesium alloy plates using cylindrical impactors with conical-nose shapes of a nominal diameter of 12.0 mm, and a nominal mass of 5.77 kg. The plates were impacted with velocities ranging from 7 to 16 m/s. During the experiments, the failure of the target plates was evaluated. Finite element (FE) model was validated using experimental results. FE simulations of the conducted experiments were performed with ABAQUS software. In simulations the strain rate dependent Johnson–Cook yield criterion with a strain hardening law was accompanied with either the ductile fracture criterion or stress triaxiality-dependent JC fracture criterion to describe the target material properties. The stress and strain distributions for different impactor velocity considered were calculated using initial impact velocity data obtained from the experiments. A range of parameters, like element size, the fracture initiation strain, friction coefficient, etc. which play an important role in the simulation, were studied. The results of numerical simulation were compared with those from the experiment obtained. A good agreement between them was achieved. The failure process of AM60 target-plate revealed that in the case of the conical-nose impactor, the ductile hole enlargement occurs during the initial stage of the impact, and subsequently, a through-thickness fracture develops causing its shear plugging failure.

Słowa kluczowe:

AM60 magnesium alloy, Room temperature impact drop-weight tower experiment, Conical-shape impactor, Numerical study of perforation process, Elastic-viscoplastic numerical analysis

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Laser thermal forming is an application of laser heating without any intentional use of external forces. Force-assisted laser bending and laser-assisted bending are hybrid techniques, which combine the use of external forces and local heating to increase the effectiveness of forming. A quantitative description of bending deformation induced by concurrent laser heating and mechanical loading is proposed in this study. Mechanical loading is expressed by the bending moment while the curvature is used to describe the resulting deformation. The contribution of a relatively less known mechanism of laser thermal bending in the hybrid process is identified. The mechanism is able to produce the so-called convex deformation, i.e., bending away from the incident laser beam. Experimental and numerical analysis is performed with thin-walled beams made of Inconel 718 nickel-based superalloy in the factory-annealed state. The Johnson–Cook constitutive material model is used in numerical simulations validated by experimental results.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

laser forming, laser-assisted bending, numerical modelling

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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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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The order of the internodes, and their geometry and mechanical characteristics influence the capability of theEquisetumstem to vibrate, potentially stimulating spore liberation at the optimum stress setting along the stem. Equisetum hyemale L. plants represent a special example of cellular solid construction with mechanical stability achieved by a high second moment of area and relatively high resistance against local buckling. We proposed the hypothesis that the order of E. hyemale L. stem internodes, their geometry and mechanical characteristics influence the capability of the stem to vibrate, stimulating spore liberation at the minimum stress setting value along the stem. An analysis of apex vibration was done based on videos presenting the behavior of an Equisetum clump filmed in a wind tunnel and also as a result of excitation by bending the stem by 20°. We compared these data with the vibrations of stems of the same size but deprived of the three topmost internodes. Also, we created a finite element model (FEM), upon which we have based the 'natural' stem vibration as a copy of the real object, 'random' with reshuffled internodes and 'uniform', created as one tube with the characters averaged from all internodes. The natural internode arrangement influences the frequency and amplitude of the apex vibration, maintaining an equal stress distribution in the stem, which may influence the capability for efficient spore spreading.

Słowa kluczowe:

mechanical properties, plant biomechanics, segmented structure, stem vibration, stress distribution, wind

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This paper is concerned with numerical modeling of deformation and fracture of a metal ligament bridging the crack faces in ceramic-metal composites, as a prerequisite for the determination of the J integral for composites with interpenetrating microstructure. A finite element model is proposed of an elasto-plastic crack-reinforcing fiber undergoing large plastic deformations and progressive debonding from the elastic matrix through a cohesive matrix-fiber interface. The σ-u relationships are derived first in the case of pullout of an elasto-plastic fiber embedded in an elastic matrix and then in uniaxial tension of the elasto-plastic fiber bridging the crack faces in elastic matrix. The obtained numerical results are discussed and compared with the theoretical predictions reported by other authors.

Słowa kluczowe:

ceramic–metal composites, fracture modeling, crack bridging, fiber pullout, cohesive interface, fiber debonding, finite element simulations

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This paper presents a simple way of using X-ray micro-computed tomography (micro-CT) in numerical modeling of material properties of metal-ceramic composites. It shows step by step the proposed methodology with details of the finite element mesh creation, so that it can easily be reproduced by interested researchers. Two case studies are considered to show the proposed approach at work: i) determination of processing-induced residual stresses in hot pressed Cr/Al2O3 and NiAl/Al2O3 particulate composites and ii) determination of J-integral for an interpenetrating phase composite made of porous alumina preform infiltrated with molten copper. The method is straightforward and effective but has its limitations that are pointed out.

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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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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The main objective of the present paper is the description of the behaviour of the ultrafine- grained (UFG) titanium by the constitutive model of elasto-viscoplasticity with the development of the identification procedure. We intend to utilize the constitutive model of the thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals presented by Perzyna [21]. The identification procedure is based on experimental observation data obtained by JIA et al. [11] for ultrafine-grained titanium and by Wang et al. [25] for nanostructured titanium. Hexagonal close-packed (hcp) ultrafine-grained titanium processed by sever plastic deformation (SPD) has gained wide interest due to its excellent mechanical properties and potential applications as biomedical implants

Słowa kluczowe:

elasto-viscoplasticity, nanocrystalline titanium, uniaxial compression

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Streszczenie:

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

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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The aim of the paper is to determine the phenomenological model to characterize the stress-strain relation and to simulate the behaviour of solid polyurethane (PUR) rubbers used in civil engineering, as well as to present the process of identification of model parameters for such materials. For the material studied the strain energy density function was established and a general constitutive relationship for the second-order tensor of Piola–Kirchhoff stress for elasticity is determined. Constitutive relationships for engineering stress in terms of the principal stretches are also specified. The paper presents the method of identification of parameters for constitutive models of hyperelasticity and hypoelasticity for the accessible experimental data. The applied identification procedure is based on the feature of two-phase structure of polyurethane material and is supported by the experimental data from uniaxial quasi-static tension and compression tests. In the analysis, the material behaviour was considered both for the case of incompressible deformation and also for the case of slightly compressible, nonlinearly elastic materials that are homogeneous and isotropic. The change of volume was admitted too, in range of large deformations in a tension and compression test. The attempt of description of stress-softening phenomenon was undertaken in rubber-like materials, for a given level of strain, under unloading (the Mullins effect) caused by the damage of microstructure of this material. Different descriptions of the stress-softening phenomenon were already proposed in the literature but they fail to give fully satisfactory conformity of experimental data with theoretical predictions. The phenomenological model by Elias–Zúñiga and Beatty, A new phenomenological model for stress-softening in elastomers, ZAMP, 53, 794–814, 2002, for such materials was modified by different softening functions and a simplified version of this model was identified, based on the experimental data. In the proposed model, the damage of microstructure was described by a new exponential function, which depends on the current magnitude of intensity of strain and its earlier maximum value during the process of material loading. In this paper, a suitable analysis of existent models and their verification based on experimental data for polyurethane rubber is presented for uniaxial experiments. It is shown that the magnitude of stress-softening varies with strain and this phenomenon increases with the magnitude of the pre-strain and the type of loading: monotonic tension, compression or cyclic loading. The obtained results are presented graphically for uniaxial tension and compression.

Słowa kluczowe:

Rubber-like material, hyperelastic constitutive model, damage of polyurethane rubber

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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.

Słowa kluczowe:

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

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In the paper we investigate the robust identification approach to identify the material parameters in the augmented Gurson model for the elasto-plastic porous media. We consider the robust loss function given by Huber [9], Beaton and Tuckey [38] and the loss function based on the l1–norm. The resulting minimization problem is solved by means of our own implementation of the Boender et al. global minimization method. Our aim is to compare the results with our earlier standard least squares estimates. In the paper, the effects of nucleation and growth of voids in the plastic porous media are investigated. Three different forms of the model are considered: the augmented Gurson model (total porosity model) with variable nucleation and growth material function, the same model with constant growth material function and the separated porosity model. The identification of the material functions parameters is based on Fischer’s experimental data set for axisymmetric tension of steel specimens.

Słowa kluczowe:

Gurson model, elasto-plastic porous media, robust identification, Huber loss function, Beaton and Tuckey loss function, l1–norm loss function

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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Additive manufacturing (AM) is revolutionizing production with its ability to rapidly create complex designs while minimizing material waste. The influence of the SLM parameters on mechanical properties of two sets of open cell lattices (Set A and Set B) made of IN718 was investigated. The purpose of using the modified parameters was to reduce the cost/time of manufacturing as well as to reduce microporosity in ligaments by increased exposure time (reduced laser scanning speed) or higher energy density based on increased exposure time. The researchers investigate ligament deformation and collapse in porous lattices, its impact on overall behavior, and how microstructure influences hardening under varying strain rates.

Słowa kluczowe:

highly porous random open-cell lattice, additive manufacturing, direct impact Hopkinson pressure bar technique, Inconel 718

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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.

Słowa kluczowe:

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

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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

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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

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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.

Słowa kluczowe:

viscoplasticity, shear bands, peridynamics

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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).

Słowa kluczowe:

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

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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.

Słowa kluczowe:

Obciążenia uderzeniowe, pianka metaliczna, perydynamika

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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.

Słowa kluczowe:

foams, damage, impact, peridynamics

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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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

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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.

Słowa kluczowe:

direct impact test, numerical simulations, tantalum

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The motivation for research on interpenetrating phase composites and possible applications of these novel materials were given in [1]. A rationale behind designing an IPC is to achieve a highly durable material that would combine the most desirable properties of the constituent phases: the high hardness and wear resistance of ceramic and improved fracture toughness and thermal conductivity due to the metal content. The interpenetrating metal-ceramic composites may have remarkable applicability in different sectors of industry, e.g. automotive and aerospace. They should, thus, be carefully investigated in terms of processing routes, material properties and modeling of material response to service conditions.
A 3D FEM model in ABAQUS of the fracture parameters and crack growth in bi-continuous metal-ceramic composites with interpenetrating microstructure (IPC) is proposed. The crack is modeled using the extended finite element method (XFEM) [4]. The J-integral and fracture toughness KIc are determined for a real IPC microstructure obtained from micro-CT images. The fracture parameters (i.e. fracture toughness KIc, J integral, crack opening displacement) are key mechanical characteristics of IPC composites because of the brittleness of the ceramic phase. The main effects occurring in metal-ceramic IPC during fracture are described (cf. [2], [3]).

Słowa kluczowe:

Ceramic-metal composites, interpenetrating microstructure, fracture toughness, crack growth, numerical modeling, XFEM

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A 3D FEM model for crack growth in bi‐continuous metal‐ceramic composites with interpenetrating microstructure (IPC) is proposed. The results for the load‐displacements relationship in a plastically deformable reinforcing fibre computed by means of different material models will be shown. The J‐integral and fracture toughness will be determined for a simplified IPC microstructure with reinforcing ligaments modeled as axisymmetric fibres, and for real IPC microstructure obtained from micro‐CT images

Słowa kluczowe:

interpenetrating phase composites, bi‐continuous composites, metal‐ceramic composites, crack bridging, crack growth, fracture toughness, finite element method

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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.

Słowa kluczowe:

numeryczna rekonstrukcja, struktury otwartokomórkowe, pianki metaliczne, mikrotomografia komputerowa

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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.

Słowa kluczowe:

dynamiczna analiza, procesy zgniatania, pianki metaliczne, struktury otwarokomórkowe

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

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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Streszczenie:

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.

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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Streszczenie:

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.

Słowa kluczowe:

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

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The main objective of the present paper is the description of the behaviour of the ultrafine-grained (UFG) titanium by the constitutive model of elasto-viscoplasticity with the development of the identification procedure. We intend to utilize the constitutive model of the thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals presented by Perzyna (2010)[1]. The identification procedure is based on experimental observation data obtained by Jia et al. (2001)[4] for ultrafine-grained titanium and by Wang et al. (2007) [5] for nanostructured titanium. Hexagonal close-packed (hcp) ultrafine-grained titanium processed by sever plastic deformation (SPD) has gained wide interest due to its excellent mechanical properties and potential applications as biomedical implants.

Słowa kluczowe:

Elasto-viscoplasticity, ultrafine-grained titanium, uniaxial compression

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The paper is focused on modeling of the overall elastic properties and crack toughening mechanism by bridging in metal-ceramic interpenetrating phase composites (IPC). The Tuchinskii-Feng analytical model (Feng 2004) especially devised for IPC microstructures is further developed. Numerical FEM models of the effective elastic constants are implemented for the simplified 3-D cross microstructure and real microstructures based on micro-CT scans. The energy release rate increase due to crack bridging (Mataga 1989) is modeled numerically. The stress-displacement relationships in the reinforcing fibers undergoing large strains and delamination from the matrix materials are obtained and then applied as material models for the bridging reinforcements in compact-tension test specimen of the fracture toughness determination. The J integral for this specimen is calculated by FEM (Abaqus) with reinforcing ligaments modeled as truss and cohesive elements. The growth of a bridged crack is also modeled numerically.

Słowa kluczowe:

Effective elastic constants, Fracture toughness, Crack toughening, Crack bridging, Metal-ceramic composites, FEM

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

Słowa kluczowe:

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

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

Słowa kluczowe:

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

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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

Słowa kluczowe:

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

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