Institute of Fundamental Technological Research

This paper focuses on the development of the atomistic framework for determining the lower scale mechanical parameters of single components of a metal matrix composite for final application to a micromechanical damage model. Here, the deformation and failure behavior of NiAl–Al2O3 interfaces and their components, metal and ceramic, are analyzed in depth using molecular statics calculations. A number of atomistic simulations of strength tests, uniaxial tensile, uniaxial compressive and simple shear, have been performed in order to obtain a set of stiffness tensors and strain–stress characteristics up to failure for 30 different crystalline and amorphous systems. Characteristic points on the strain–stress curves in the vicinity of failure are further analyzed at the atomistic level, using local measures of lattice disorder. Numerical results are discussed in the context of composite damage at upper microscopic scale based on images of the fracture surface of NiAl–Al2O3 composites.

Metal-matrix composites (MMCs), Fracture, Computational modeling, Mechanical testing, Molecular statics

The paper presents a comprehensive investigation of the influence of the main process parameters of spark plasma sintering on the mechanical and microstructural properties of nickel-silicon carbide composites at various scales. Microstructure analysis performed by scanning and transmission electron microscopy revealed a significant interfacial reaction between nickel and silicon carbide due to the decomposition of silicon carbide. The chemical interaction of the matrix and reinforcement results in the formation of a multicomponent interphase zone formed by silicides (Ni31Si12 or/and Ni3Si) and graphite precipitates. Furthermore, several types of structure defects were observed (mainly nano/micropores at the phase boundaries). These significantly influenced the mechanical response of nickel-silicon carbide composites at different levels. At the macroscopic scale, uniaxial tensile tests confirmed that applying a 1000 oC sintering temperature ensured that the manufactured composite was characterised by satisfactory tensile strength, however, with a considerable reduction of material elongation compared to pure nickel. Moreover, the fractography study allowed us to identify a significant difference in the damage mode for certain nickel-silicon carbide samples. Secondly, the interface of the nickel matrix and silicate interphase was tested by bending with microcantilevers to evaluate its deformation behaviour, strength, and fracture characteristics. It was confirmed that a diffusive kind of interface, such as Ni-NiSi, demonstrates unexpected bonding properties with a relatively large range of plastic deformation. Finally, the nanoindentation of three main components of the nickel-silicon carbide composite was executed to evaluate the evolution of nanohardness, Young’s modulus, and elastic recovery due to the application of various spark plasma sintering conditions.

nickel-based composite,silicon carbide,spark plasma sintering,multiscale characterization,mechanical properties,nanoindentation,bending of microcantilevers

This work aims to revise and apply an original discrete element model (DEM) to evaluate effective thermal conductivity of sintered porous materials. The model, based on two-particle sintering geometry, calculates inter-particle neck using Constant Volume (CV) criterion. The model was validated using experimental measurements on sintered porous NiAl. For DEM simulations, heterogeneous samples with real particle size distribution and different densities were obtained by simulation of hot pressing. Neck size evaluated using Coble’s and CV models were compared to show that commonly used Coble’s model overestimates neck size and conductivity. The proposed model was improved by neck-size correction to compensate for non-physical overlaps at higher densities and by adding grain-boundary resistance to account for porosity within necks. Resistance contribution from grain boundaries was shown to decrease with increasing density. Thermal conductivity obtained from the improved model was close to experimental results, suggesting validity of the model.

Discrete element method,Effective thermal conductivity,Porous materials,Sintering,Heat conduction simulation

This paper aims to analyse electrical conduction in partially sintered porous materials using an original resistor network model within discrete element framework. The model is based on sintering geometry, where two particles are connected via neck. Particle-to-particle conductance depends on neck size in sintered materials. Therefore, accurate evaluation of neck size is essential to determine conductance. The neck size was determined using volume preservation criterion. Additionally, grain boundary correction factor was introduced to compensate for any non-physical overlaps between particles, particularly at higher densification. Furthermore, grain boundary resistance was added to account for the porosity within necks. For numerical analysis, the DEM sample was generated using real particle size distribution, ensuring a heterogeneous and realistic microstructure characterized by a maximum-to-minimum particle diameter ratio of 15. The DEM sample was subjected to hot press simulation to obtain geometries with different porosity levels. These representative geometries were used to simulate current flow and determine effective electrical conductivity as a function of porosity. The discrete element model (DEM) was validated using experimentally measured electrical conductivities of porous NiAl samples manufactured using spark plasma sintering (SPS). The numerical results were in close agreement with the experimental results, hence proving the accuracy of the model. The model can be used for microscopic analysis and can also be coupled with sintering models to evaluate effective properties during the sintering process.

Discrete element method, Effective electrical conductivity, Porous materials, Sintering, Resistor network model

The presented paper concerns the technological aspects of the interface evolution in the nickel-silicon carbide composite during the sintering process. The goal of our investigation was to analyse the material changes occurring due to the violent reaction between nickel and silicon carbide at elevated temperatures. The nickel matrix composite with 20 vol pct SiC particles as the reinforcing phase was fabricated by the spark plasma sintering technique. The sintering tests were conducted with variable process conditions (temperature, time, and pressure). It was revealed that the strong interaction between the individual components and the scale of the observed changes depends on the sintering parameters. To identify the microstructural evolution, scanning electron microscopy, energy dispersive spectroscopy, transmission electron microscopy, X-ray diffraction, and Raman spectroscopy were used. The silicon carbide decomposition process progresses with the extension of the sintering time. As the final product of the observed reaction, new phases from the Ni-Si system and free carbon were detected. The step-by-step materials evolution allowed us to reveal the course of the reaction and the creation of the new structure, especially in the reaction zone. The detailed analysis of the SiC decomposition and formation of new components was the main achievement of the presented paper.

The main objective of this paper was to investigate the heat transfer of modified lightweight refractory concrete at the microscopic scale. In this work, such material was treated as a porous composite based on the compound of calcium aluminate cement and aluminosilicate cenospheres. The presence of air inclusions within the cenospheres was an essential factor in the reduction in thermal performance. Due to the intricacy of the subject investigated, our research employed numerical, theoretical, and experimental approaches. Scanning electron microscopy (SEM) imaging was performed to study the composite microstructure with a special focus on geometry, dimensions, and the distribution of cenospheres. Based on the experimental analysis, simplified geometrical models were generated to reproduce the main features of the composite matrix and cenospheres. A finite element framework was used to determine the effective thermal conductivity of such domains as well as the thermal stresses generated in the sample during the heat flow. A considerable difference in thermal properties was revealed by comparing the simulation results of the pure composite matrix and the samples, indicating a varying arrangement of cenosphere particles. The numerical results were complemented by a theoretical study that applied analytical models derived from the two-phase mixture theory—parallel and Landauer. A satisfactory agreement between numerical and theoretical results was achieved; however, the extension of both presented approaches is required.

thermal conductivity,heat transfer,finite element method,thermal stress,microstructure,calcium aluminate cement,cenosphere,refractory concrete

The paper presents the experimental, numerical, and theoretical investigation of the microstructure of nickel aluminide samples manufactured by spark plasma sintering using electron backscatter diffraction and computer assisted software. The aim of the work was to reveal the evolution of the microscopic and macroscopic parameters related to the microstructure of the material and its dependence on the applied sintering parameters—temperature and pressure. The studied porous samples with different relative density were extracted from various planes and then tested by electron backscatter diffraction to evaluate the crystallographic orientation in every spot of the investigated area. On this foundation, the grain structure of the samples was determined and carefully described in terms of the grain size, shape and boundary contact features. Several parameters reflecting the grain morphology were introduced. The application of the electric current resulting in high temperature and the additional external loading leads to the significant changes in the structure of the porous sample, such as the occurrence of lattice reorientation resulting in grain growth, increase in the grain neighbours, or the evolution of grain ellipticity, circularity, grain boundary length, and fraction. Furthermore, the numerical simulation of heat conduction via a finite element framework was performed in order to analyse the connectivity of the structures. The numerical results related to the thermal properties at the micro- and macroscopic scale—local heat fluxes, deviation angles, and effective thermal conductivity—were evaluated and studied in the context of the microstructural porosity. Finally, the effective thermal conductivity of two-dimensional EBSD maps was compared with those obtained from finite element simulations of three-dimensional micro-CT structures. The relationship between the 2D and 3D results was derived by using the analytical Landauer model.

This work presents a comprehensive analysis of heat transfer and thermal conductivity of porous materials manufactured by spark plasma sintering. Intermetallic nickel aluminide (NiAl) has been selected as the representative material. Due to the complexity of the studied material, the following investigation consists of experimental, theoretical and numerical sections. The samples were manufactured in different combinations of process parameters, namely sintering temperature, time and external pressure, and next tested using the laser flash method to determine the effective thermal conductivity. Microstructural characterisation was extensively examined by use of scanning electron microscopy and micro-computed tomography (micro-CT) with a special focus on the structure of cohesive bonds (necks) formed during the sintering process. The experimental results of thermal conductivity were compared with theoretical and numerical ones. Here, a finite element framework based on micro-CT imaging was employed to analyse the macroscopic (effective thermal conductivity, geometrical and thermal tortuosity) and microscopic parameters (magnitude and deviation angle of heat fluxes, local tortuosity). The comparison of different approaches toward effective thermal conductivity evaluation revealed the necessity of consideration of additional thermal resistance related to sintered necks. As micro-CT analysis cannot determine the particle contact boundaries, a special algorithm was implemented to identify the corresponding spots in the volume of finite element samples; these are treated as the resistance phase, marked by lower thermal conductivity. Multiple simulations with varying content of the resistance phase and different values of thermal conductivity of the resistance phase have been performed, to achieve consistency with experimental data. Finally, the Landauer relation has been modified to take into account the thermal resistance of necks and their thermal conductivity, depending on sample densification. Modified theoretical and finite element models have provided updated results covering a wide range of effective thermal conductivities; thus, it was possible to reconstruct experimental results with satisfactory accuracy.

thermal conductivity, porous materials, spark plasma sintering, micro-computed tomography, nickel aluminide, finite element modelling, tortuosity

This work presents a 3D extension of the deformable discrete element method (DDEM) developed previously for 2D problems. The 3D formulation employs spherical particles. The particle deformation is made up of a global and local deformation mode. The global mode is assumed to be produced by uniform stress due to the contact forces. Particle deformability yields a nonlocal contact model, in which one contact between particles is influenced by contacts with other particles. It also leads to the formation of new contacts in the particle assembly. The DDEM affects the behavior of the granular material at the macroscopic level and gives new possibilities in material modeling by the discrete element method (DEM). The new algorithm is verified on a unconfined uniaxial compression test of a cuboid specimen discretized with equal‐size bonded particles aligned in a simple cubic pattern using an analytical solution. Enhanced modeling capabilities are presented by simulating cylindrical specimens discretized with a nonuniform size of bonded particles. The micro–macro relationships for elastic parameters are obtained. It is shown that the DDEM extends the range of the Poisson's ratio achievable with the DEM. Additional simulations are performed to determine the stability limits of the DDEM.

average stress, deformable particles, discrete element method, elastic constants, micro–macro relationships, nonlocal contact model

Experiments were conducted to investigate, within the framework of a multiscale approach, the mechanical enhancement, deformation and damage behavior of copper–silicon carbide composites (Cu–SiC) fabricated by spark plasma sintering (SPS) and the combination of SPS with high-pressure torsion (HPT). The mechanical properties of the metal–matrix composites were determined at three different length scales corresponding to the macroscopic, micro- and nanoscale. Small punch testing was employed to evaluate the strength of composites at the macroscopic scale. Detailed analysis of microstructure evolution related to SPS and HPT, sample deformation and failure of fractured specimens was conducted using scanning and transmission electron microscopy. A microstructural study revealed changes in the damage behavior for samples processed by HPT and an explanation for this behavior was provided by mechanical testing performed at the micro- and nanoscale. The strength of copper samples and the metal–ceramic interface was determined by microtensile testing and the hardness of each composite component, corresponding to the metal matrix, metal–ceramic interface, and ceramic reinforcement, was measured using nano-indentation. The results confirm the advantageous effect of large plastic deformation on the mechanical properties of Cu–SiC composites and demonstrate the impact on these separate components on the deformation and damage type.

copper–silicon carbide composite, high-pressure torsion, metal–matrix composites, multiscale analysis, nano-indentation, small punch test

In this work, dynamic mechanical properties of amorphous silicon and scale effects were investigated by the means of nanoindentation. An amorphous silicon sample was prepared by plasma-enhanced chemical vapor deposition (PECVD). Next, two sets of the samples were investigated: as-deposited and annealed in 500 °C for 1 hour. A three-sided pyramidal diamond Berkovich's indenter was used for the nanoindentation tests. In order to determine the strain rate sensitivity (SRS), indentations with different loading rates were performed: 0.1, 1, 10, 100 mN/min. Size effects were studied by application of maximum indentation loads in the range from 1 up to 5 mN (penetrating up to approximately one-third of the amorphous layer). The value of hardness was determined by the Oliver-Pharr method. An increase of hardness with decrease of the indentation depth was observed for both samples. Furthermore, the significant dependence of hardness on the strain rate has been reported. Finally, for the annealed samples at low strain rates a characteristic "elbow" during unloading was observed on the force-indentation depth curves. It could be attributed to the transformation of (β-Sn)-Si to the PI (pressure-induced) a-Si end phase.

In this paper, the discrete element method framework is employed to determine and analyze the stresses induced during and after the powder metallurgy process of particle-reinforced composite. Applied mechanical loading and the differences in the thermal expansion coefficients of metal/intermetallic matrix and ceramic reinforcing particles during cooling produce the complex state of stresses in and between the particles, leading to the occurrence of material defects, such as cracks, and in consequence the composite degradation. Therefore, the viscoelastic model of pressure-assisted sintering of a two-phase powder mixture is applied in order to study the stress field of particle assembly of intermetallic-ceramic composite NiAl/Al2O3. The stress evaluation is performed at two levels: macroscopic and microscopic. Macroscopic averaged stress is determined using the homogenization method using the representative volume element. Microscopic stresses are calculated both in the body of particles and in the contact interface (necks) between particles. Obtained results are in line with the cooling mechanism of the two-phase materials.

sintering, discrete element method, residual stress, particle-reinforced composites

In this work, (W,Ti)B2 films with different stoichiometric ratio Ti/W deposited on silicon and 304 stainless steel by radio frequency magnetron sputtering are presented. The coatings were deposited from plasma spark sintered targets obtained from the mixture of pure boron, tungsten and titanium powders. It is shown that during plasma spark sintering process using overstoichiometric boron and a low content of titanium change the WB2 to WB4 phase with almost no secondary phases. Subsequently, the impact of titanium content on the films properties is investigated systematically, including the chemical and phase composition, crystalline structure, surface and cross-section morphology. Simultaneously, nano-indentation test and ball-on-disk tribometery are performed to analyse the hardness and tribological properties of the films. It is shown that deposited films with titanium content of 3.6 and 5.5 at.% are formed in the zone T of the Thornton's Structural Zone Model. In opposite to α-WB2 magnetron sputtered coatings they are more flexible and hard nanocomposite coatings. The results show that the addition of titanium is apparently changing the film structure from nanocrystalline columnar to amorphous, very dense and compact structure with the addition of TiB2 phase. That films are simultaneously hard (H > 37.5 GPa), have high hardness to effective Young's modulus ratio values (H/E* > 0.1) and elastic recovery (We > 60%) appropriate for tough and resistant to cracking materials. The presented (W,Ti)B2 films exhibit also tribological and corrosion properties better than unalloyed coatings.

superhard films, ternary tungsten borides, RF magnetron sputtering, wear resistance, corrosion

This work investigates numerical properties of the algorithm of the discrete element method employing deformable circular discs presented in an earlier authors' publication. The new formulation, called the deformable discrete element method (DDEM) enhances the standard discrete element method (DEM) by introducing an additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. An accurate computation of the contact forces would require an iterative solution of the implicit relationship between the contact forces and particle displacements. In order to preserve efficiency of the DEM, the new formulation has been adapted to the explicit time integration. It has been shown that the explicit DDEM algorithm is conditionally stable and there are two restrictions on its stability. Except for the limitation of the time step as in the standard DEM, the stability in the DDEM is governed by the convergence criterion of the iterative solution of the contact forces. The convergence and stability limits have been determined analytically and numerically for selected regular and irregular configurations. It has also been found out that the critical time step in DDEM remains unchanged with respect to standard DEM.

discrete element method, deformable particles, iterative solution, convergence criterion, explicit scheme, stability

This paper presents a numerical and experimental analysis of manufacturing of intermetallic ceramic composites by powder metallurgy techniques. The scope of the paper includes the formulation and development of an original numerical model of powder metallurgy of two-phase material within the framework of the discrete element method, simulations of powder metallurgy processes for different combinations of process parameters, and a verification of the numerical model based on own experimental results. Intermetallic-based composite NiAl–Al2O3 has been selected as representative material for experimental and numerical studies in this investigation. Special emphasis was given to the interactions between the intermetallic and ceramic particles by formulating the special model for adhesive contact bond. In order to properly represent a real microstructure of a two-phase sintered body, a discrete element specimen was generated using a special algorithm. Numerical validation showed the correct numerical representation of a sintered two-phase composite specimen. Finally, micromechanical analysis was performed to explain the macroscopic behavior of the sintered sample. The evolution of the coordination number, a number of equilibrium contacts, and the distribution of the cohesive neck size with respect to time are presented.

powder metallurgy, sintering, discrete element method, modeling, intermetallic matrix composites

The present work is aimed to investigate the capability of the discrete element method (DEM) to model properly wave propagation in solid materials, with special focus on the determination of elastic properties through wave velocities. Reference micro–macro relationships for elastic constitutive parameters have been based on the kinematic hypothesis as well as obtained numerically by simulation of a quasistatic uniaxial compression test. The validity of these relationships in the dynamic analysis of the wave propagation has been checked. Propagation of the longitudinal and shear wave pulse in rectangular sample discretized with discs has been analysed. Wave propagation velocities obtained in the analysis have been used to determine elastic properties. Elastic properties obtained in the dynamic analysis have been compared with those determined by simulation of the quasistatic compression test.

discrete element method, wave propagation, elastic properties, micro–macro relationships

The presented research investigation comprises the study of the mechanical properties of modified copper–silicon carbide composites at the micro- and macroscopic scale. The improvement of a copper–silicon carbide composite refers to the addition of a protective layer at the ceramic reinforcement in order to prevent the dissolution of silicon in the copper matrix. The macromechanical behaviour has been evaluated by the performance in a small punch test. The investigation has been carried out with samples with varying volume content of ceramic reinforcement and different protective layers of the silicon carbide particles. Moreover, the influence of temperature during the strength test has been studied. Next, the results have been referred to the interfacial bonding strength of Cu and SiC particles. SEM characterization of samples has been performed to link the composites' microstructure with the mechanical behaviour. Finally, the experimental results of the small punch test have been predicted via a numerical approach. Finite element analysis has been employed to reproduce the response of the composite specimen during the test. Satisfactory agreement with the experimental curve has been obtained.

metal matrix composites, silicon carbide, metallic layers deposition, small punch, interface strength, finite element method

This investigation examines the problem of homogenization in metal matrix composites (MMCs) and the methods of increasing their strength using severe plastic deformation (SPD). In this research MMCs of pure copper and silicon carbide were synthesized by spark plasma sintering (SPS) and then further processed via high-pressure torsion (HPT). The microstructures in the sintered and in the deformed materials were investigated using Scanning Electron Microscopy (SEM) and Scanning Transmission Electron Microscopy (STEM). The mechanical properties were evaluated in microhardness tests and in tensile testing. The thermal conductivity of the composites was measured with the use of a laser pulse technique. Microstructural analysis revealed that HPT processing leads to an improved densification of the SPS-produced composites with significant grain refinement in the copper matrix and with fragmentation of the SiC particles and their homogeneous distribution in the copper matrix. The HPT processing of Cu and the Cu–SiC samples enhanced their mechanical properties at the expense of limiting their plasticity. Processing by HPT also had a major influence on the thermal conductivity of materials. It is demonstrated that the deformed samples exhibit higher thermal conductivity than the initial coarse-grained samples.

copper, silicon carbide, high-pressure torsion, spark plasma sintering, thermal conductivity

This report presents the modeling of pressure-assisted sintering within the framework of a multiscale approach. Three individual numerical methods have been collectively applied to predict the behavior of a sintering body at three different scales. The appropriate solutions to connect each model/scale have been proposed. Molecular dynamics have been employed to evaluate the grain boundary diffusion coefficient at the atomistic scale. The obtained results of diffusive parameters have been transferred to the micromechanical model of sintering. Here, the discrete element method was used to represent the sintered material properties at the microscopic scale. Micromechanical based results have been validated by own experimental data of material density evolution, indicating the required coincidence. The transfer from micro- to the macroscopic model has been realized by determining the macroscopic viscous moduli from discrete element simulations and subsequently applying them to the continuum model of sintering. The numerical results from finite element simulations at the macroscopic scale have been compared with discrete element ones.

sintering, multiscale modeling, discrete element method, molecular dynamics, finite element method

A contact model for the normal interaction between elastoplastic spherical discrete elements has been investigated in the present paper. The Walton–Braun model with linear loading and unloading has been revisited. The main objectives of the research have been to validate the applicability of the linear loading and unloading models and estimate the loading and unloading stiffness parameters. The investigation has combined experimental tests and finite element simulations. Both experimental and numerical results have proved that the interaction between the spheres subjected to a contact pressure inducing a plastic deformation can be approximated by a linear relationship in quite a large range of elastoplastic deformation. Similarly, the linear model has been shown to be suitable for the unloading. It has been demonstrated that the Storåkers model provides a good evaluation of the loading stiffness for the elastoplastic contact and the unloading stiffness can be assumed as varying linearly with the deformation of the contacting spheres. The unloading stiffness can be expressed in a convenient way as a function of the Young's modulus and certain scaling factor dependent on the dimensionless parameter defining the level of the sphere deformation.

contact, discrete element method, elastoplastic, spheres, unloading

The study presents a detailed analysis of the impact of the coating type of silicon carbide particles and its share by volume on the microstructure and micromechanical properties of Cu-SiC composites. In order to protect the carbide from decomposition during the manufacturing of the composites, the surface of SiC was modified via a plasma vapour deposition technique with a layer of metals (W, Cr, Ti and Ni). Composites with a variable share of the ceramic phase (10–50 %vol.) were obtained at a temperature of 950 °C using spark plasma sintering. An analysis of the structures of the composites, especially in the metal-ceramic boundary region, was conducted with the use of scanning and transmission electron microscopy. The mechanical properties of the composites in the Cu-interface-SiC system were studied via a nanoindentation technique. The comparison of the results of hardness and Young's modulus studies were completed in relation to the actual structures of the materials, which in turn made it possible to determine the impact of the interfacial structure on the global properties of the composite materials.

copper-silicon carbide composites, nanoindentation, SPS, interface study

This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform-sized bonded particles. The numerical results have been verified by a comparison with equivalent finite elementmethod results and available analytical solutions. The micro-macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.

average stress, deformable particles, discrete element method, elastic constants, micro-macro relationships, nonlocal contact model

Self-diffusion parameters in stoichiometric B2-NiAl solid state crystals were estimated by molecular statics/dynamics simulations with the study of required simulation time to stabilise diffusivity results. An extrapolation procedure to improve the diffusion simulation results was proposed. Calculations of volume diffusivity for the B2 type NiAl in the 1224–1699 K temperature range were performed using the embedded-atom-model potential. The results obtained here are in much better agreement with the experimental results than the theoretical estimates obtained with other methods.

NiAl nickel–aluminium, diffusivity, molecular dynamics, molecular statics, embedded-atom method, sintering

The performance of the present-day scanning electron microscopy (SEM) extends far beyond delivering electronic images of the surface topography. Oxide dispersion strengthened (ODS) steel is on of the most promising materials for the future nuclear fusion reactor because of its good radiation resistance, and higher operation temperature up to 750°C. The microstructure of ODS should not exceed tens of nm, therefore there is a strong need in a fast and reliable technique for their characterization. In this work, the results of low-kV SEM characterization of nanoprecipitates formed in the ODS matrix are presented. Application of highly sensitive photo-diode BSE detector in SEM imaging allowed for the registration of single nm-sized precipitates in the vicinity of the ODS alloys. The composition of the precipitates has been confirmed by TEM-EDS.

ODS steels, scanning electron microscopy, spark plasma sintering

The purpose of this paper is to elaborate on mechanical alloying conditions for a composite powder consisting of copper and brittle aluminium oxides. Detailed analysis of the Cu-Al2O3 powder mixture structure obtained in the mechanical alloying process allows for the study of the homogenization phenomena and for obtaining grains (in composite form) with a high degree of uniformity. The Cu-5 vol.%Al2O3 composites were obtained by means of the spark plasma sintering technique. The results presented herein were studied and discussed interms of the impact of using a different form of aluminium oxide powder and a different shape of copper powder on composite properties. Research methodology included microstructure analysis as well as its relation to the strength of Cu-Al2O3 interfaces. It transpires from the results presented below that the application of electrocor undum as a reinforcement phase in composites decreases poro sity in the ceramic phase, thus improving thermal properties and interfacial strength.

metal matrix composites, spark plasma sintering, thermal conductivity, interfacial strength

In the presented paper a coating of SiC particles with a metallic layer were used to prepare copper matrix composite materials. The role of the layer was to protect the silicon carbide from decomposition and dissolution of silicon in the copper matrix during the sintering process. The SiC particles were covered by chromium, tungsten and titanium using Plasma Vapour Deposition method. After powder mixing of components, the final densification process via Spark Plasma Sintering (SPS) method at temperature 950C was provided. The almost fully dense materials were obtained (> 97.5%). The microstructure of obtained composites was studied using scanning electron microscopy as well as transmission electron microscopy. The microstructural analysis of composites confirmed that regardless of the type of deposited material, there is no evidence for decomposition process of silicon carbide in copper. In order to measure the strength of the interface between ceramic particles and the metal matrix, the micro tensile tests have been performed. Furthermore, thermal diffusivity was measured with the use of the laser pulse technique. In the context of performed studies, the tungsten coating seems to be the most promising solution for heat sink application. Compared to pure composites without metallic layer, Cu-SiC with W coating indicate the higher tensile strength and thermal diffusitivy, irrespective of an amount of SiC reinforcement. The improvement of the composite properties is related to advantageous condition of Cu-SiC interface characterized by well homogenity and low porosity, as well as individual properties of the tungsten coating material.

metal matrix composites, silicon carbide, metallic layers deposition, thermal conductovity, interface strength

This paper presents the numerical and experimental analysis of hot pressing of NiAl powder with an emphasis on the best possible representation of its main stages: initial powder compaction and pressure-assisted sintering. The numerical study has been performed within the discrete element framework. In the paper, an original viscoelastic model of hot pressing has been used. In order to ensure that the applied values of material parameters in numerical simulations are appropriate, the reference literature has been reviewed. It produced the relations and equations to estimate the values of all required sintering material parameters of the considered viscoelastic model. Numerical simulations have employed the geometrical model of the initial dense specimen generated by a special algorithm which uses the real grain distribution of powder. The numerical model has been calibrated and validated through simulations of the real process of hot pressing of intermetallic NiAl material. The kinetics of compaction, sintering and cooling stage indicated by the evolution of density, shrinkage and densification rate have been studied. The comparison of numerical and experimental results has shown a good performance of the developed numerical model.

Powder metallurgy, Hot pressing, Sintering, Simulation, Discrete element method, Nickel aluminide

This paper presents the numerical modelling of initial powder compaction and pressure-assisted sintering performed by original viscoelastic discrete element model. The research is focused on the influence of the type of the model representing an elastic part of interparticle force. Two elastic contact models—linear and nonlinear Hertz model—have been implemented and used to analyse interaction of NiAl powder particles during compaction and sintering process. Numerical models have been validated using own experimental results. Microscopic effects (particle penetration) and macroscopic changes (relative density) have been compared. It has been shown that although both models represent properly macroscopic behaviour of the material at the sintering process, the Hertz model produces the results closer to the real experimental ones during the initial compaction stage. Evaluation of macroscopic quantities enables implementation of the discrete element model in the framework of the multiscale modelling framework which is currently developed for sintering processes.

powder metallurgy, sintering, initial compaction, elasticity, discrete element method

This paper analyses the technological aspects of the interface formation in the copper-silicon carbide composite and its effect on the material's microstructure and properties. Cu-SiC composites with two different volume content of ceramic reinforcement were fabricated by hot pressing (HP) and spark plasma sintering (SPS) technique. In order to protect SiC surface from its decomposition, the powder was coated with a thin tungsten layer using plasma vapour deposition (PVD) method. Microstructural analyses provided by scanning electron microscopy revealed the significant differences at metal-ceramic interface. Adhesion force and fracture strength of the interface between SiC particles and copper matrix were measured. Thermal conductivity of composites was determined using laser flash method. The obtained results are discussed with reference to changes in the area of metal-ceramic boundary.

copper matrix composites, silicon carbide, interface, thermal conductivity, adhesion

The presented paper investigates the relationship between the microstructure and thermal properties of copper–silicon carbide composites obtained through hot pressing (HP) and spark plasma sintering (SPS) techniques. The microstructural analysis showed a better densification in the case of composites sintered in the SPS process. TEM investigations revealed the presence of silicon in the area of metallic matrix in the region close to metal ceramic boundary. It is the product of silicon dissolving process in copper occurring at an elevated temperature. The Cu-SiC interface is significantly defected in composites obtained through the hot pressing method, which has a major influence on the thermal conductivity of materials.

metal matrix composites, silicon carbide, interface, spark plasma sintering, thermal conductivity

A two-scale modeling framework for sintering processes has been presented. Formulation of the micromechanical model of sintering developed in the discrete element method and basic relationships in the macroscopic model of sintering have been briefly reviewed. The methodology to determine macroscopic quantities–stress, strains, and constitutive viscous properties-from the discrete element simulations has been presented. This methodology has been applied to modeling of NiAl sintering. First, the discrete element model (DEM) has been calibrated by fitting the numerical densification curve to the experimental data. The DEM model with calibrated parameters has been used in simulations specially conceived to give macroscopic viscous moduli of the sintered material. Using the averaging procedures macroscopic stresses and strains have been calculated. Strain rates have been obtained differentiating the strain curves with respect to time. Finally, the viscous constitutive properties of the sintered material have been determined. The dependence of the shear and volumetric viscous moduli on the relative density (or equivalently) on the porosity has been obtained. It has been found that the numerical simulations predict a similar dependence as that assumed in the phenomenological macroscopic models. Thus, the validity of the micro-macro relationships obtained from the discrete element simulations of powder sintering has been confirmed. The proposed methodology allows us to use the discrete element model in the framework of multiscale modeling of sintering.

discrete element method, sintering, simulation, micro-macro relationships, multiscale modeling

Molecular statics/dynamics estimation of constitutive parameters for a micromechanical NiAl sintering model is reported in this paper. The parameters include temperature-dependent diffusion coefficients, surface energy, and linear thermal expansion. These parameters define material behavior during sintering and are used in the sintering particle model implemented in the discrete element model. The investigated material, the NiAl intermetallic, belongs to novel materials characterized by advantageous mechanical properties. Various machine elements are manufactured from a pure NiAl powder or from powder mixtures containing the NiAl using the sintering technology. It is well known that sintering is governed by diffusion. Therefore diffusive properties are important parameters of the micromechanical model of sintering. Numerical estimation of the model parameters by simulations at the lower scale is a powerful tool alternative to experimental methods. Molecular statics and dynamics models for NiAl have been created using the embedded atom model potential. Numerical simulations have allowed us to estimate the volume, surface, and grain-boundary diffusivity for the B2-type NiAl in the 1573 to 1673 K temperature range. Dependence of the diffusion coefficients on temperature has been determined and validity of the Arrhenius-type temperature dependency has been assessed. The parameters evaluated numerically have been compared with available experimental data as well as with theoretical predictions obtained with other methods. Many of the results presented in this paper have a pioneer character and are not known in the literature.

NiAl, sintering, diffusivity, molecular dynamics, molecular statics, nanoparticles

This paper constitutes an analysis of the effect of heat treatment time on the properties of Cr-Re-Al2O3 composite materials. It was found that as a result of sintering, rhenium is dissolved in chromium to create chromium-rhenium solid solution. This process is time-dependent, therefore as the time extends, the structure of material becomes homogenous, which improves its mechanical properties. Within the frame of herein presented studies, a series of technological tests have been carried out for a constant sintering temperature (1450°C) and pressure (30 MPa), with the use of a variable holding time in the maximum temperature. As a result, changes in the structure of Crsingle bondRe matrix have been determined and the resulting changes in the properties of composite. Based on those tests, optimal conditions of the sintering process have been determined from the point of view of obtaining a homogenous structure and the most beneficial properties of Cr-Re-Al2O3 composites.

Metal-matrix composites (MMCs), Mechanical properties, Mechanical testing, Sintering

This paper comprises the results of studies of the changes in the structure of Cr-Re-Al2O3 metal matrix depending on heat treatment time in sintering temperature. The density of material with the following composition: 95%(75%Cr-25%Al2O3)+5%Re was increased using the technique of sintering under pressure (30MPa) at the temperature of 1450°C. As a result, materials characterized by a high relative density (< 97% of theoretical density) were obtained. Next, they were subjected to structural tests including scanning and transmission electron microscopy as well as X-ray diffraction. Changes in the phase composition, grains size and parameters of crystallographic structure depending on heat treatment time were analysed. It was found that during sintering rhenium is dissolved in the chromium matrix and Cr-Re solid solution is formed. When sintering time is extended to 120 min, the matrix of the composite becomes completely homogenous, which results in an increased strength of the composite.

Metal matrix composites, Rhenium, Hot pressing, Microstructure analysis, XRD

W niniejszym artykule zaprezentowano wyniki modelowania zagęszczania proszku stanowiącego wstępny etap procesu prasowania na gorąco. Modelowanie numeryczne zrealizowano metodą elementów dyskretnych z wykorzystaniem kulistych cząstek. Analizę skoncentrowano na badaniu mechanizmów zagęszczania proszku przy ciśnieniu do 50 MPa oraz poszukiwaniu modeli odpowiednich przy zastosowanych warunkach realizacji procesu. Symulacje numeryczne wykonano wykorzystując dwa modele oddziaływania cząstek proszku: sprężysty model Hertza-Mindlina-Deresiewicza oraz plastyczny model Storåkersa. Wyniki numeryczne zostały porównane z wynikami laboratoryjnymi prasowania proszku NiAl. Otrzymano dużą zgodność wyników eksperymentalnych i numerycznych.

This paper presents the results of discrete element simulation of powder compaction which is the initial stage in the hot pressing process. Numerical simulation has been performed by discrete element method with using spherical particles. The research has been focused on densification mechanisms under pressure 50 MPa and models appropriate for these conditions. Numerical simulations have been carried out for two contact models: elastic Hertz-Mindlin-Deresiewicz and plastic - Storåkers. Numerical results and results from laboratory test of the uniaxial pressing of NiAl powder have been compared. The obtained results of numerical simulation and laboratory tests showing a good agreement.

metoda elementów dyskretnych, prasowanie proszków, materiały intermetaliczne, discrete element method, powder compaction, intermetallics

This paper presents numerical studies of powder compaction in cold uniaxial pressing. The powder compaction in this work is considered as an initial stage of a hot pressing process so it is realized with relatively low pressure (up to 50 MPa). Hence the attention has been focused on the densification mechanisms at this range of pressure and models suitable for these conditions. The discrete element method employing spherical particles has been used in the numerical studies. Numerical simulations have been performed for two different contact models—the elastic Hertz–Mindlin–Deresiewicz model and the plastic Storåkers model. Numerical results have been compared with the results of laboratory tests of the die compaction of the NiAl powder. Comparisons have shown that the discrete element method is capable to represent properly the densification mechanisms by the particle rearrangement and particle deformation.

Discrete element method, Simulation, Powder compaction, Cold uniaxial pressing

Evolution of the density and the microstructure during hot pressing of NiAl/Al2O3 composite has been investigated in the present paper. In particular, the effect of the process parameters, viz. compacting pressure, sintering temperature and sintering time, on the evolution of the density of the intermetallic–ceramic composite has been studied. Evolution of the density has been related to microstructure changing. Porosity, pore structures and grains rearrangement have been analysed in microscopic observations.

hot pressing, sintering, intermetallic–ceramic composite, density evolution, microstructure

This paper presents investigation of macroscopic stresses in powder metallurgy process modelled with the discrete element method. The discrete element model belongs to the class of micromechanical models. In the DEM model the material is represented by an assembly of particles interacting by contact forces and the method is formulated in terms of forces and displacements. In order to evaluate macroscopic stresses a special upscaling procedure is necessary. The paper presents basic formulation of the discrete element method with special attention for the contact interaction models for powder compaction and sintering. A method to evaluate macroscopic stresses based on the two level averaging is presented. The discrete element model of sintering is verified using own experimental results. Macroscopic stresses are calculated for the whole process including loading, heating, sintering, cooling and unloading. It has been found out that the macroscopic stresses are consistent with changing process parameters. The procedure is suitable for multiscale modelling of sintering.

sintering, modeling, discrete element method, macroscopic stresses

The influence of hot pressing conditions on mechanical properties of nickel aluminide/alumina composite has been investigated in the present paper. In particular, effect of the process parameters, viz. compacting pressure, sintering temperature and sintering time on the evolution of density, elastic constants and tensile strength properties of the intermetallic-ceramic composite has been studied. Elastic constants, the Young's modulus and Poisson's ratio, have been evaluated using an ultrasonic testing method, and the tensile strength has been determined by a Brazilian-type splitting test. Microscopic observations of microstructure evolution complemented the experimental procedure. Experimental results have been confronted with theoretical models showing a good agreement between the data compared.

Hot pressing, sintering, intermetallic-ceramic composite, elastic properties, Brazilian test, tensile strength, ultrasonic method

It is commonly known that the properties of sintered materials are strongly related to technological conditions of the densification process. This paper shows the sintering behavior of a NiAl-Al2O3 composite, and its individual components sintered separately. Each kind of material was processed via the powder metallurgy route (hot pressing). The progress of sintering at different stages of the process was tested. Changes in the microstructure were examined using scanning and transmission electron microscopy. Metal-ceramics interface was clean and no additional phases were detected. Correlation between the microstructure, density, and mechanical properties of the sintered materials was analyzed. The values of elastic constants of NiAl/Al2O3 were close to intermetallic ones due to the volume content of the NiAl phase particularly at low densities, where small alumina particles had no impact on the composite’s stiffness. The influence of the external pressure of 30 MPa seemed crucial for obtaining satisfactory stiffness for three kinds of the studied materials which were characterized by a high dense microstructure with a low number of isolated spherical pores.

ceramics, composites, electron, intermetallic, metallic matrix, microscopy, powder metallurgy, sintering, structural

This paper presents an original viscoelastic model of powder sintering developed within the discrete element framework. The viscous model used by other authors has been enriched by adding a spring connected in series to the viscous rheological element. In this way elastic and viscous effects in the particle interaction during sintering are treated using the Maxwell viscoelasticity. The new numerical model has been verified through simulation of simple problems of free sintering and sintering under pressure. Sintering processes have been treated as isothermic. In order to accelerate the analysis an algorithmic mass scaling has been used allowing to use larger time steps in the explicit time integration scheme. The results obtained using the new model are consistent with the standard viscous model. At the same time, a much better efficiency of the new model in comparison to the standard viscous one has been found because the critical time steps required by the viscoelastic model are much larger than those required by the viscous model. The new model has been applied to the simulation of real process of sintering of NiAl powder. The kinetics of sintering indicated by the evolution of density has been studied. The comparison of numerical and experimental results has shown a good performance of the developed numerical model.

Powder sintering, Simulation, Discrete element method, Viscoelastic model

This paper presents numerical simulation of powder sintering. The numerical model introduced in this work employs the discrete element method which assumes that material can be modelled by a large assembly of discrete elements (particles) of spherical shape interacting among one another. Modelling of sintering requires introduction of the cohesive interaction among particles representing interparticle sintering forces. Numerical studies of sintering have been combined with experimental studies which provided data for calibration and validation of the model. In the laboratory tests evolution of microstructure and density during sintering have been studied. Comparison of numerical and experimental results shows a good performance of the numerical model developed

Powder Sintering, Simulation, Discrete Element Method

Sintering process is one of the major method of manufacture technology of composite materials with intermetallic matrix reinforced by ceramic particles. In the final stage of sintering, during cooling of material, the microcracks may occur due to appearance of significant residual stress at the grain boundaries, which leads to progressive degradation of the material. This paper presents numerical modeling of micro- and macroscopic stress during and after sintering process composite materials. The original thermo-viscoelastic model of discrete elements have been performed. Numerical simulations have been carried out on the example of the NiAl-Al2O3 composite. The obtained results confirm correct and efficient performance of the proposed numerical model.

sintering, composite, residual stresses, discrete element method

W technologii metalurgii proszków spiekanie, wraz z chłodzeniem, jest jednym z kluczowych etapów wytwarzania materiałów kompozytowych na osnowie metalicznej, podczas którego może dochodzić do pękania materiału na skutek występujących na granicach faz naprężeń rezydualnych. Prezentowana praca przedstawia wyniki modelowania numerycznego naprężeń mikro- oraz makroskopowych występujących w trakcie oraz po procesie metalurgii proszków materiałów kompozytowych. Do analizy procesów metalurgii proszków został użyty oryginalny termo-lepkosprężysty model elementów dyskretnych. Symulacje numeryczne zostały przeprowadzone na przykładzie kompozytu NiAl-Al2O3. Uzyskane wyniki potwierdzają poprawne oraz efektywne działanie zaproponowanego modelu numerycznego.

metoda elementów dyskretnych, symulacje numeryczne, spiekanie, metalurgia proszków, naprężenia rezydualne

W niniejszym artykule zostały przedstawione nowe wyniki modelowania procesu spiekania metodą elementów dyskretnych. W sformułowaniu teoretycznym dla części sprężystej zastosowano model kontaktu Hertza w celu lepszego odwzorowania oddziaływania elementów kulistych w trakcie prasowania. Sformułowanie i implementację modelu rozszerzono na przypadek spiekania materiałów dwufazowych. Na podstawie badań literaturowych wyznaczono parametry materiałowe procesu, które zostały następnie zweryfikowane za pomocą wyników eksperymentalnych. Wyniki numeryczne ewolucji gęstości próbki porównano z wynikami doświadczalnymi otrzymując dużą zgodność.

materiały dwufazowe, metalurgia proszków, spiekanie, metoda elementów dyskretnych

This paper presents numerical modelling of powder sintering. The numerical model introduced in this work employs the discrete element method which assumes that material can be modelled by a large assembly of discrete elements (particles) of spherical shape interacting among one another. Modelling of sintering requires introduction of the cohesive interaction among particles representing inter-particle sintering forces. Numerical studies of sintering have been supplemented with experimental studies which provided data for calibration and validation of the model. In the laboratory tests evolution of microstructure and density during sintering have been studied. Comparison of numerical and experimental results shows a good performance of the numerical model developed.

powder sintering, powder metallurgy, simulation, discrete element method

A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

This paper presents modelling of both single and double-phase powder sintering processes at the macroscopic level. In particular, its constitutive formulation, numerical implementation and numerical tests are described. The macroscopic constitutive model is based on the assumption that the sintered material is a continuous medium. The parameters of the constitutive model for material under sintering are determined by simulation of sintering at the microscopic level using a micro-scale model. Numerical tests were carried out for a cylindrical specimen under hydrostatic and uniaxial pressure. Results of macroscopic analysis are compared against the microscopic model results. Moreover, numerical simulations are validated by comparison with experimental results. The simulations and preparation of the model are carried out by Abaqus FEA - a software for finite element analysis and computer-aided engineering. A mechanical model is defined by the user procedure “Vumat” which is developed by the first author in Fortran programming language. Modelling presented in the paper can be used to optimize and to better understand the process.

Educational assessment, Hydrostatics, Computer simulation, Finite-element analysis, Programming languages, Sintering

This paper presents modeling of a sintering process at various scales. Sintering is a powder metallurgy process consisting in consolidation of powder materials at elevated temperature but below the melting point. Sintering models at the atomistic, microscopic and macroscopic scales have been presented. Sintering is a process governed by diffusion therefore the atomistic modeling using the molecular dynamics has been focused on investigation of the diffusion process. The micromechanical model has been developed within the framework of the discrete element method. It allows us to consider microstructure and its changes during sintering. The macroscopic model is based on the continuum phenomenological approach. It combines elastic, thermal and viscous creep deformation. The methodology to determine macroscopic quantities: stress, strains and constitutive viscous properties from the discrete element simulations has been presented. Possibilities of the developed models have been demonstrated by applying them to simulation of sintering of the intermetallic NiAl powder. Own experimental results have been used to calibrate and validate numerical models.

sintering, modeling, discrete element method, diffusion, molecular dynamics, macroscopic model

Cubic Crystal Structure, Deformable Discrete Element Method, Numerical Modeling, Numerical Homogenization, Elastic Properties

NiAl crystal, cubic anisotropy, Deformable Discrete Element Method, numerical modeling, mechanical properties

In the case of the sintering of composite materials exhibiting mutual solubility, intermediate phases with varying concentrations of elements may appear during the densification process. Microstructural and structural changes, especially in the area of the interface, strongly influence mechanical or thermal properties [1]. A good example of such materials is nickel – silicon carbide composites. At elevated temperatures nickel reacts with silicon carbide, which causes total SiC decomposition, and as a result, new Ni-Si phases are formed and free carbon is precipitated within the reaction zone. In this work, nickel-silicon carbide composites were obtained via the Spark Plasma Sintering method. The detailed microstructural analyses using X-ray diffraction, Raman spectroscopy, scanning electron microscopy and transmission electron microscopy revealed the material’s evolution during sintering. To investigate the correlation between microstructure and properties of obtained materials, the mechanical test at three different length scales (in macro-, micro- and nanoscale) was conducted. To evaluate the strength of Ni-SiC composites at a macroscopic scale the uniaxial tensile and compression tests were employed. The sample deformation and failure mechanism for different stages of sintering were analyzed. The strength of the nickel-silicon carbide interface was determined by bending tests of micro-cantilever beams. Nanoindentation was used to evaluate the hardness of each composite component. The conducted research revealed a strong relation between mechanical strength and sintering conditions.

wave propagation, elasticity, discrete element method,simulation

Discrete Element Method, Deformable Particles, Macroscopic Properties

Elastic Wave Propagation, Deformability, Discrete Element Method

Discrete Element Method, Deformable Particles, Nonlocal Contact Model, Poisson's Effect

This paper presents modelling of double-phase powder sintering processes at the macroscopic level. In particular, its constitutive formulation, numerical implementation and numerical simulations are described. Numerical tests were carried out for a cylindrical specimen under uniaxial pressure and are compared against the microscopic model results. The model has been developed within the framework of a MUSINT project which is carried on in Institute of Fundamental Technological Research, Warsaw, Poland. The overall objective of the MUSINT (Multiscale numerical modelling of sintering processes) is development of numerical models allowing us to analyse at various scales manufacturing processes employing sintering as the main technological stage.

finite element method, sintering, multiscale modelling, double-phase composite

This document presents modelling of single-phase powder sintering processes at the macroscopic level. In particular, its constitutive formulation, numerical implementation and numerical test are described. Numerical tests were carried out for a cylindrical specimen under hydrostatic and uniaxial pressure. Results of macroscopic analysis are compared against the microscopic model results.

sintering porcesses, numerical analysis, multiscale modelling

This work presents a new original formulation of the discrete element method based on the soft contact approach. The standard DEM has been enhanced by introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly.

discrete element method, deformable particles, soft contact

sintering, discrete element method, multi-scale modeling

Sintering, Powder Material, Ni-Al, Molecular Dynamics, Molecular Statics

W niniejszym artykule zaprezentowano wyniki modelowania, zagęszczania proszku stanowiącego wstępny etap procesu prasowania na gorąco, metodą elementów dyskretnych opisaną w [1]. Modelowanie numeryczne zrealizowano metodą elementów dyskretnych, z wykorzystaniem kulistych cząstek. Badania skoncentrowano na mechanizmach zagęszczania proszku przy ciśnieniu 50 MPa oraz modelach odpowiednich przy zastosowanych warunkach procesu. Numeryczne symulacje wykonano z wykorzystaniem dwóch modeli: pierwszy - elastyczny Hertz-Mindlin-Deresiewicz, drugi - plastyczny Storakers, opisanych w pracy [2]. Wyniki symulacji numerycznych zostały porównane z wynikami laboratoryjnymi zagęszczania proszku NiAl w matrycy. W rezultacie otrzymano dużą zgodność wyników eksperymentalnych i numerycznych.

metoda elementów dyskretnych, modelowanie, zagęszczanie proszków, prasowanie

sintering, multiscale modelling

cohesive contact, discrete element method, viscoelasticity, sintering