Staff

Abstract:
The interest in the Spark Plasma Sintering (SPS) technique has continuously increased over the last few years. This article shows the possibility of the development of an SPS device used for material processing and synthesis in both scientific and industrial applications and aims to present manufacturing methods and the versatility of an SPS device, presenting examples of processing Arc-Melted- (half-Heusler, cobalt triantimonide) and Self-propagating High-temperature Synthesis (SHS)-synthesized semiconductor (bismuth telluride) materials. The SPS system functionality development is presented, the purpose of which was to broaden the knowledge of the nature of SPS processes. This approach enabled the precise design of material sintering processes and also contributed to increasing the repeatability and accuracy of sintering conditions.

Keywords:
spark plasma sintering, arc melting, semiconductor materials, half-Heusler, bismuth telluride, cobalt triantimonide, SHS, SPS

Abstract:
This paper presents an extension of the authors’ previously developed interface coupling technique for 2D problems to 3D problems. The method combines the strengths of the Discrete Element Method (DEM), known for its adeptness in capturing discontinuities and non-linearities at the microscale, and the Boundary Element Method (BEM), known for its efficiency in modelling wave propagation within infinite domains. The 3D formulation is based on spherical discrete elements and bilinear quadrilateral boundary elements. The innovative coupling methodology overcomes a critical limitation by enabling the representation of discontinuities within infinite domains, a pivotal development for large-scale dynamic problems. The paper systematically addresses challenges, with a focus on interface compatibility, showcasing the method’s accuracy through benchmark validation on a finite rod and infinite spherical cavity. Finally, a model of a column embedded into the ground illustrates the versatility of the approach in handling complex scenarios with multiple domains. This innovative coupling approach represents a significant leap in the integration of DEM and BEM for 3D problems and opens avenues for tackling complex and realistic problems in various scientific and engineering domains.

Keywords:
Interface coupling, Concurrent multi-scale coupling, Boundary element method (BEM), Discrete element method (DEM) , Staggered time integration, Dynamic wave propagation, Infinite domain

Abstract:
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.

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

Abstract:
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.

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

Abstract:
This paper presents a novel and highly efficient approach for coupling the Discrete Element Method (DEM) and the Boundary Element Method (BEM) for time-domain simulations of dynamic problems, utilising multi-scale staggered time integration. While the DEM captures phenomena with discontinuous behaviours, such as fracturing and granular flow, the BEM excels in accurately modelling seismic wave propagation in infinite domains. By separately solving the governing equations of the DEM and BEM at different time instants, the proposed scheme considerably enhances computational efficiency compared to conventional monolithic coupling schemes. The incorporation of non-conforming interfaces enables larger time steps in the BEM, thereby reducing computational costs and memory usage. Moreover, an innovative coupling of DEM rotations with the BEM displacement field is introduced, leading to more accurate and realistic modelling of complex dynamics. Numerical experiments are conducted to demonstrate the superior accuracy and efficiency of the proposed method, establishing its potential for modelling a wide range of dynamic problems.

Keywords:
BEM-DEM coupling,Multi-scale time integration,Rotational degrees of freedom,Seismic wave propagation,Infinite domain

Abstract:
This work presents a novel scheme to couple the Boundary Element Method (BEM) and the Discrete Element Method (DEM) in the time domain. The DEM captures discontinuous material behaviour, such as fractured and granular media. However, applying the method to real-life applications embedded into infinite domains is challenging. The authors propose a solution to this challenge by coupling the DEM with the BEM. The capability of the BEM to model infinite domains accurately and efficiently, without the need for numerical artifices, makes it the perfect complement to the DEM. This study proposes a direct monolithic interface-based coupling method that resolves any incompatibilities between the two methods in two dimensions. The benchmark results show that the proposed methodology consistently produces results that align with analytical solutions. The final example in the paper showcases the full potential of this innovative methodology, where the DEM models a fracturing process, and the BEM evaluates its far-field effect.

Keywords:
Discrete Element Method (DEM), Boundary Element Method (BEM), Discontinuous materials, Wave propagation, Infinite domain, Monolithic coupling

Abstract:
The problem of high-rate elastic-plastic deformation of micro-sized copper particles impacting against a copper substrate was investigated by applying the continuum-based formulation and finite element thermomechanical analysis. Comparative study of selected plasticity models was performed. The aim of the paper was to study strain rate-dependant plasticity for a wide range of strain rates. The strain-rate-dependant Johnson-Cook and Cowper-Symonds models were studied by comparing displacements, velocities, strains, strain rates, stresses, contact forces, and temperatures and their contribution to material yield stress. The study shows the importance of the high-strain rate yielding model and its adequacy for experimental data. Both models complement each other and may be regarded as soft and hard bounds of the solution. A new, combined, two-function model, containing two independent functions for each of the two ranges, is suggested. The proposed model describes a low strain rate sensitivity range using the Johnson-Cook expression, while allows fitting of the model for experimental results in a high strain rate sensitivity range, using a modified Cowper-Symonds expression. This combination is capable of describing both low and high strain rate regimes, giving the minimum deviation from experimental results.

Keywords:
Finite element method, Thermomechanical analysis, High velocity particle impact, Continuum plasticity models, High strain-rate

Abstract:
The discrete element method (DEM) is the most dominant method for the numerical prediction of dynamic behaviour at grain or particle scale. Nevertheless, due to its discontinuous nature, the DEM is inherently unable to describe microscopic features of individual bodies which can be considered as continuous bodies. To incorporate microscopic features, efficient numerical coupling of the DEM with a continuous method is generally necessary. Thus, a generalised multi-scale PD–DEM framework is developed in this work. In the developed framework, meshfree discretised Peridynamics (PD) is used to describe intra-particle forces within bodies to capture microscopic features. The inter-particle forces of rigid bodies are defined by the DEM whereas a hybrid approach is applied at the PD–DEM interface. In addition, a staggered multi-scale time integration scheme is formulated to allow for an efficient numerical treatment of both methods. Validation examples are presented and the applicability of the developed framework to capture the characteristics mixtures with rigid and deformable bodies is shown.

Keywords:
Peridynamics (PD),Discrete element method (DEM),Contact coupling,Multi-scale modelling,Deformable particles

Abstract:
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.

Abstract:
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.

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

Abstract:
A discrete element thermal conductance model suitable for the modelling of heat flow between sintered particles has been proposed. The model is formulated using the sintering geometry consisting of two spheres connected with a cylindrical neck. The calculation of the neck size is based on the criterion of volume conservation. Therefore the neck obtained is more accurate than that of the popular Coble's model. The thermal conductance is determined for different neck sizes by the finite element simulations of the heat flow in half of the sintering geometry. The numerical results are fitted with a linear relationship which is the basis to determine the equivalent conductance between two sintered particles. The model can be used in the pipenetwork formulation of the discrete element method for simulation of heat conduction problems in powder sintering or in sintered porous materials.

Keywords:
sintering, particles, discrete element method, thermal conductance, pipe-network model, volume conservation, heat conduction

Abstract:
This work presents a novel scheme to couple the Discrete Element Method (DEM) and the Boundary Element Method (BEM) for the multi-scale modelling in the time domain. The DEM can model discontinuous material at micro scale very well, but it cannot represent infinite domains. Hence, coupling with the BEM is proposed. A formulation employing the DEM and BEM in different subdomains of the same body is presented. There is no overlap between the sub-domains, and the system of equations is derived based on strong equilibrium and compatibility conditions at the interface. The proposed coupling scheme is based on monolithic time integration. The conducted numerical experiments of one-dimensional wave propagation show excellent agreement with the analytical solution. Some spurious wave reflections are observed at the interface, but their effect is quantified and deemed not critical for infinite domains, which are of main interest. Even though the applications for one-dimensional wave propagation are of limited practical engineering interest, this work represents a significant theoretical breakthrough. This paper establishes a reference for future coupling schemes for two- and three-dimensional multi-scale analysis.

Keywords:
siscrete element method (DEM), boundary element method (BEM), infinite domain coupling, dynamic multi-scale analysis, stability of time integration, spurious wave reflection

Abstract:
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.

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

Abstract:
In this paper, we present a method that allows for the quick and efficient simulation of the comminution process in high-speed rotor mills. The method requires only the feed’s macroscopic material data and the geometry of the machine. Consisting of two stages, the method couples Computational Fluid Dynamics (CFD) with the Discrete Element Method (DEM) to obtain the collisional velocities and angles of a representative group of particles passing through the machine. Due to this coupling, any mill which relies on fluid forces acting on the ore particles can be simulated. After obtaining these values, the second stage commences wherein a single ore particle consisting of DEM elements collides against a rigid surface. The data obtained from this stage is then used to determine the minimum required working parameters of the chosen machine to achieve proper ore comminution. The proposed methodology was applied to analyse the novel concept of using beater mills for the comminution of copper ore.

Keywords:
CFD, DEM, comminution modelling, particle breakage, beater mill, sandstone, copper ore

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

Keywords:
contact, discrete element method, elastoplastic, spheres, unloading

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
This paper presents an investigation on the detection of strain localization in numerical simulation of sheet metal forming. Two methods to determine the onset of localized necking have been compared. The first criterion, newly implemented in this work, is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method, studied in the authors' earlier works, is determined by the maximum of the strain acceleration. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. This has allowed to construct numerical forming limit curves (FLCs). The numerical FLCs have been compared with the experimental one. Mesh sensitivity analysis for these criteria has been performed for the selected specimens. It has been shown that the numerical FLC obtained with the new criterion predicts formability limits close to the experimental results so this method can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.

Keywords:
Sheet forming, Formability, Forming limit diagram, Strain localization, Numerical simulation

Abstract:
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool–rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.

Keywords:
rock cutting, disc cutters, TBM, numerical model, discrete/finite element method, simulation

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
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.

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

Abstract:
The general objective of the present paper is to improve the understanding of micromechanical mechanisms in granular materials and their representation in numerical models. Results of numerical investigations on micro–macro relationships in the discrete element model of granular material are presented. The macroscopic response is analysed in a series of simulations of the triaxial compression test. The numerical studies are focused on the influence of microscopic parameters on the initial response. The effect of the contact stiffness and friction coefficient on the effective elastic moduli is investigated. Numerical results are compared with the analytical estimations based on the kinematic Voigt's hypothesis as well as with selected numerical results of other authors. The comparisons show that a better agreement between the numerical and analytical results is observed for particle assemblies with higher coordination numbers. Higher coordination numbers are related to more compact specimens and for a given specimen can be associated with low values of the contact stiffness and a higher confining pressure.

Keywords:
Discrete element method, Granular material, Triaxial test, Micro–macro relationship, Voigt hypothesis

Abstract:
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.

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

Abstract:
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.

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

Abstract:
In the present paper, a possibility of an approximation of elastic particulate composite with a network of elastic springs that undertake only axial forces is considered. It is assumed that the springs are equivalent to two hemispheres interacting through a weaker interface member. In a frame of the suggested approach, the description of the composite is limited to translational degrees of freedom, therefore, only a normal interaction between the spheres was considered. The methodology for calculation of the axial stiffness of the elastic springs and obtained solutions of the stiffness in explicit form are the main novelty of the article. A comparison of the stiffnesses of the springs obtained by the proposed methodology and by the three dimensional Finite Element Method (FEM) has shown a good agreement between them in a wide range of the ratio of the modulus of elasticity of the particles and matrix at four different distances between surfaces of the particles. A possibility of the approximation of particulate composite by springs was tested and discussed in details by comparing results of a mechanical response of a sample (under three different loading cases) modelled as a three dimensional solid and as a system comprised of the springs. The solutions were obtained by the FEM.

Keywords:
Spring network model, Lattice model, Particulate composites, Heterogeneous materials, Finite element modelling

Abstract:
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.

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

Abstract:
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.

Keywords:
sintering, modeling, discrete element method, macroscopic stresses

Abstract:
This paper presents results of numerical simulations of the Nakazima test with determination of formability without using the forming limit curve. The onset of localized necking has been determined using the criterion based on analysis of the major principal strain and its first and second time derivatives in the most strained zone. The strain localization has been determined by the maximum of strain acceleration which corresponds to the inflection point of the strain velocity versus time. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering a whole range of the strain paths typical for sheet forming processes. This has allowed us to construct the numerical FLC. The numerical FLC has been compared with the experimental one. It has been shown that the numerical FLC predicts higher formability limits but the differences are not large so the method can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.

Keywords:
sheet forming, formability, forming limit curve, numerical simulation

Abstract:
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.

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

Abstract:
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.

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

Abstract:
The NUMPRESS System has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. The program consists of (i) an analytical module for analysis of forming processes with the finite element method, (ii) an optimization module controlling execution of the analytical module and performing optimization with respect to selected process parameters, in both deterministic and robust formulation, (iii) a reliability analysis module controlling execution of the analytical module to assess how random distribution of design parameters affects forming results, and (iv) a graphical user interface enabling communication between modules and easy definition of design parameters and optimization criteria. The analytical module consists of two independent programs up to the user's choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic and elastic-viscoplastic shells. Both programs are interfaced to a well-known commercial graphical pre- and postprocessor GiD. Fundamentals of formulations employed in the system and numerical examples are presented in the paper.

Keywords:
sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Abstract:
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

Keywords:
Lagrangian analysis, Multiscale particulate flows, Particle finite element method

Abstract:
The paper presents a thermomechanical discrete element model of rock cutting process. The thermomechanical formulation of the discrete element method considers mechanical and thermal phenomena and their reciprocal influence. The thermal model developed for transient heat conduction problems takes into account conductive heat transfer at the contact between particles and convection on the free surface. The thermal and mechanical problems are coupled by consideration of: (1) heat generated due to friction which is calculated in the mechanical problem and passed to the thermal solution, (2) influence of thermal expansion on mechanical interaction between particles. Estimation of temperature dependent wear has been included into the contact model. The coupled problem is solved using the staggered scheme.The thermomechanical algorithm has been implemented in a discrete element program and applied to simulation of rock cutting with single pick of a dredge cutter head. Numerical results confirm good performance of the developed algorithm.

Keywords:
Discrete element method, Thermomechanical, Coupling, Rock cutting, Wear

Abstract:
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.

Keywords:
Powder sintering, Simulation, Discrete element method, Viscoelastic model

Abstract:
In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain.

Keywords:
Discrete element method, Initial stress conditions, Virgin stresses, Discrete/continuum modeling

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

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

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

Keywords:
formability test, explicit FE method, friction, fracture location

Abstract:
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

Keywords:
Powder Sintering, Simulation, Discrete Element Method

Abstract:
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.

Keywords:
sintering, composite, residual stresses, discrete element method

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

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

Abstract:
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.

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

Abstract:
Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test. Two cylindrical specimens with particle size distributions yielding different degree of heterogeneity have been used. Macroscopic response produced by different discrete element models has been compared. The main difference between the compared models consists in the evaluation of micromechanical constitutive parameters. Two approaches are compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. The size dependent contact parameters are calculated as functions of geometric parameters characterizing each contacting particle pair. As geometric scaling parameters, the arithmetic and harmonic means, as well as the minimum of the radii of two contacting particles are considered. Two different models with size dependent contact parameters are formulated. The performance of these models is compared with that of the discrete element model with global uniform contact parameters. Equivalence between the models with size dependent and uniform contact parameters has been checked. In search of this equivalence, different methods of evaluation of global uniform parameters have been studied. The contact stiffness has been evaluated in terms of the average radius of the particle assembly or in terms of the averages of the arithmetic and harmonic means of the contact pair radii, the geometric parameters used in the evaluation of the contact stiffness in the size-dependent models. The uniform contact strengths have been determined as functions of the averages of radii squares, squares of arithmetic radii means or squares of minimum radii of the contacting pairs.

For the more homogenous specimen, the models with local size dependent parameters and models with global uniform parameters give similar response. The models with uniform parameters evaluated according to the averages of the geometric parameters used in the evaluation of local parameters ensure better agreement with the respective models with size-dependent parameters than the models with uniform parameters evaluated according to the particle radii. Simulations using the more heterogenous specimen reveal differences between the considered models. There are significant differences in stress–strain curves as well as in the failure pattern. The models with local size-dependent parameters are more sensitive to the change of heterogeneity than the model with global uniform parameters.

Keywords:
Discrete element method, Brittle, Compression, Contact, Heterogeneity, Modelling

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

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

Abstract:
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.

Keywords:
materiały dwufazowe, metalurgia proszków, spiekanie, metoda elementów dyskretnych

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

Keywords:
blacha wstępnie wyprężona, próby tłoczności, symulacja numeryczna

Abstract:
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, which is suitable to study problems of multiple material fracturing such as those involved in rock cutting. Both 2D and 3D models are considered in this work. The paper presents a brief overview of the theoretical formulation and calibration of the discrete element model by a methodology combining the dimensional analysis with simulation of the unconfined compressive strength (UCS) and indirect tension (Brazilian) tests. The rock cutting process with roadheader picks, which is typical for underground excavation, has been simulated. The results of the 2D and 3D analyses have been compared with one another, and numerical results have been compared with the available experimental data.

Keywords:
Rock cutting, Roadheader, Discrete element method, Simulation, Numerical model

Abstract:
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.

Keywords:
powder sintering, powder metallurgy, simulation, discrete element method

Abstract:
Wsady spawane laserowo (WSL) stanowią wysoko zaawansowane technologicznie wsady przeznaczone do kształtowania w procesach tłoczenia. Wsady tego rodzaju powstają poprzez połączenie pasów blach składowych techniką spawania laserowego. Elementy tłoczone, wykonane z tego rodzaju wsadów, znajdują zastosowanie głównie w konstrukcji pojazdów. Wytwarzanie z WSL wymaga opanowania technik spawania laserowego blach cienkich różnego gatunku i grubości, o różnym rodzaju pokrycia powierzchni. Uzyskanie spoiny laserowej o zaprojektowanych właściwościach mechanicznych wymaga rozwiązania wielu problemów związanych z inicjacją wiązki i stabilizacją doczołowo łączonych pasów blach lub rur szczelinowych. Natomiast do właściwej oceny podatności do kształtowania wytworzonych WSL wymagana jest analiza plastycznego płynięcia blach składowych oraz WSL z nich wykonanych, w próbach podstawowych i technologicznych oceny tłoczności. Potrzeba wytwarzania szerokiego asortymentu wytłoczek uzasadnia zastosowanie symulacji numerycznych do prognozowania wyników tłoczenia WSL i stanowi nowoczesne narzędzie ułatwiające pracę projektanta i technologa. Kompleksowa analiza rozkładów odkształceń lokalnych wybranych wytłoczek laboratoryjnych oraz analiza wyników symulacji MES procesów tłoczenia wytłoczek laboratoryjnych pozwoliły na opracowanie wytycznych tłoczenia WSL.

Abstract:
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. Efficient numerical models have been obtained using techniques of parallel computing and coupling the discrete element method with finite element method. The discrete element algorithm has been applied to simulation of different excavation processes, using different tools, TBMs and roadheaders. Numerical examples of tunnelling process are included in the paper, showing results in the form of rock failure, damage in the material, cutting forces and tool wear. Efficiency of the code for solving large scale geomechanical problems is also shown.

Keywords:
Coupling, Discrete element method, Finite element method, Parallel computation, Tunnelling

Abstract:
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized linear triangles and tetrahedra using finite calculus and a new procedure combining particle methods and finite element methods. Applications of the new numerical methods to casting, forging and other bulk metal forming problems and mixing processes are shown.

Keywords:
Bulk forming processes, Stabilized finite element method, Particle method, Particle finite element method, Mixing processes

Abstract:
This paper presents some advances of finite element explicit formulation for simulation of metal forming processes. Because of their computational efficiency, finite element programs based on the explicit dynamic formulation proved to be a very attractive tool for the simulation of metal forming processes. The use of explicit programs in the sheet forming simulation is quite common, the possibilities of these codes in bulk forming simulation in our opinion are still not exploited sufficiently. In our paper, we will consider aspects of bulk forming simulation. We will present new formulations and algorithms developed for bulk metal forming within the explicit formulation. An extension of a finite element code for the thermomechanical coupled analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. A new formulation based on the so-called split algorithm allows us to use linear triangular and tetrahedral elements in the analysis of large plastic deformations characteristic to forming processes. Linear triangles and tetrahedra have many advantages over quadrilateral and hexahedral elements. Linear triangles and tetrahedra based on the standard formulations exhibit volumetric locking and are not suitable for large plastic strain simulation. The new formulation allows to overcome this difficulty. New formulations and algorithms have been implemented in the finite element code Stampack developed at the International Centre for Numerical Methods in Engineering in Barcelona. Numerical examples illustrate some of the possibilities of the finite element code developed and validate new algorithms.

Keywords:
Explicit formulation, Forming simulation, Split algorithm

Abstract:
The present paper is the second part of the contribution by Rojek and Telega (2001). An alternative adhesion law was used to the study of bone-implant interface. Numerical scheme was developed and applied to the knee joint after arthroplasty. Influence of wear debris on this interface and currently used wear models were investigated.

Keywords:
unilateral contact, adhesion, friction, wear, knee joint after arthroplasty, FEM

Abstract:
This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences reported here have been gained during the development and use of our own explicit program Stampack. An original formulation of a triangular shell element without rotational degrees of freedom is reviewed combining the explicit sheet forming simulation with the implicit springback analysis as well as the parallelization of the explicit program described. An extension of a finite element code for coupled thermomechanical analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. Numerical examples illustrate some of the possibilities of the finite element code developed.

Keywords:
Metal forming, Sheet stamping, Finite element simulation, Explicit dynamic analysis, Thermomechanical analysis

Abstract:
This paper presents an investigation on the determination of forming limit curves (FLCs) by finite element simulations. The numerical FLCs are determined applying the criteria of strain localization in simulations of the Nakazima formability tests. Two methods to determine the onset of localized necking have been compared. The first criterion is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The onset of necking is assumed to occur at the point corresponding to a sudden change of the slope of the strain rate vs. time curve. The limit strain in the second method is determined by the maximum of the strain acceleration, which corresponds to the inflection point of the strain velocity vs. time curve. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. This has made it possible to construct numerical forming limit curves (FLCs). The numerical FLCs have been compared with the experimental one, showing quite a good agreement, especially in the case of the first criterion. This shows that finite element simulations can be used as a potential alternative tool to determine formability limits for sheet forming processes.

Keywords:
Sheet metal forming, Formability, Forming limit curve, Finite element simulation

Abstract:
This paper presents a comparison of two criteria of strain localization in experimental research and numerical simulation of sheet metal forming. The first criterion is based on the analysis of the through-thickness thinning (through thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method is determined by the maximum of the strain acceleration. Experimental and numerical investigation have been carried out for the Nakajima test performed for different specimens of the DC04 grade steel sheet. The strain localization has been identified by analysis of experimental and numerical curves showing the evolution of strains and their derivatives in failure zones. The numerical and experimental limit strains calculated from both criteria have been compared with the experimental FLC evaluated according to the ISO 12004-2 norm. It has been shown that the first method predicts formability limits closer to the experimental FLC. The second criterion predicts values of strains higher than FLC determined according to ISO norm. These values are closer to the strains corresponding to the fracture limit. The results show that analysis of strain evolution allows us to determine strain localization in numerical simulation and experimental studies.

Keywords:
Sheet forming, Formability, Forming limit diagram, Strain localization, Numerical simulation

Abstract:
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.

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

Abstract:
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.

Abstract:
This work presents results of investigations on the determination of strain localization in sheet forming. Nakajima formability test has been chosen for the experimental studies and numerical analysis. The onset of localized necking has been determined using the criteria studied in the authors' earlier works, based on the analysis of the principal strains evolution in time. The first criterion is based on the analysis of the through-thickness thinning (through–thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method is determined by the maximum of the strain acceleration. Limit strains obtained from these criteria have been confronted with the experimental forming limit curve (FLC) evaluated according to modified Bragard method used in the ISO standard. The comparison shows that the first criterion predicts formability limits closer to the experimental FLC and second method predicts values of strains higher than FLC. These values are closer to the maximum strains measured before fracture appears in experiment. These investigations show that criteria based on the analysis of strain evolution used in numerical simulation and experimental studies allow us to determine strain localization.

Abstract:
This paper presents the investigation on detection of strain localization in experimental research and numerical simulation of sheet metal forming. Experimental tests and numerical simulations of the Nakazima test have been performed for the DC04 grade steel sheet. The onset of localized necking has been determined using the criterion based on analysis of the major principal strain and its first and second time derivatives in the most strained zone. The strain localization has been evaluated by the maximum of strain acceleration which corresponds to the inflection point of the strain velocity vs. time. The limit strains have been calculated numerically and experimentally for specimens undergoing deformation at different strain paths. It has been shown that the numerical model predicts formability limits close to the experimental results. Analyzed criterion can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.

Keywords:
sheet forming, formability, forming limit curve, numerical simulation

Abstract:
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.

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

Abstract:
The paper presents a two-stage simplified method for the simulation of comminution process which takes place in a beater mill. The first stage of the proposed method is a simulation of the flow of gas and ore particles through a mill based on a two-phase continuous-discrete model. It allows to capture the interaction between the fluid flow and embedded particles, to determine trajectories of their motion and average velocities and frequencies of their collisions against the flywheel and the mill's walls. The second stage of the proposed method is a discrete element method simulation of the process of comminution of a single ore particle. It allows to determine the size distribution of created smaller particles in terms of normal velocity and angle of impact and to estimate the global efficiency of the comminution process. The proposed simulation methodology is applied for the verification of the innovative concept of the pplication of high–speed beater mill for the comminution of the copper ore.

Abstract:
In this work a trajectory study of copper ore particles through a fan mill was performed with the use of a commercial CFD code, ANSYS Fluent, coupled with DEM (Discrete Element Method). Particles of different sizes were analysed. Results highlight ore behaviour, fluid flow conditions and mark places requiring geometrical improvements.

Keywords:
CFD, DEM, beater mill

Abstract:
Modelowanie i symulacje numeryczne są obecnie nieodłączną częścią projektowania i optymalizacji różnorodnych procesów technologicznych. Zastosowanie metod numerycznych w projektowaniu procesów mechanicznego urabiania i przeróbki rud metali jest w dalszym ciągu stosunkowo niewielkie. Procesy odspajania kawałków skały od calizny i ich rozdrobnienia z zastosowaniem różnego rodzaju maszyn, wiążą się silnie nieciągłymi zjawiskami zniszczenia materiału i są bardzo trudne do modelowania za pomocą standardowych metod numerycznych, takich jak metoda elementów skończonych, opartych na ciągłym sformułowaniu zagadnienia mechaniki ciała stałego. Duże możliwości w zastosowaniu do tych procesów ma intensywnie rozwijana w ostatnich latach metoda elementów dyskretnych, w której materiał jest reprezentowany przez liczny zbiór ziaren, oddziałujących między sobą poprzez siły kontaktu. Model ten w sposób naturalny uwzględnia materiał rozdrobniony. Uwzględnienie wiązań kohezyjnych między ziarnami oraz możliwości ich zrywania umożliwia modelowanie inicjacji i propagacji pęknięć w materiale. W niniejszej pracy zostaną przedstawione możliwości wykorzystania metody elementów dyskretnych do symulacji urabiania skał za pomocą noży stożkowych i dysków oraz do symulacji zachowania się materiału w młynie. Sprzężenie metody elementów dyskretnych z modelem przepływu płynu umożliwi modelowanie zawiesiny pyłowej rozdrabnianego materiału.

Keywords:
modelowanie dyskretne, mechaniczne urabianie, rudy metali

Abstract:
This paper presents experimental and numerical studies of magnetorheological (MR) fluids. Experimental studies have been focused on the investigation of MR fluid flow in the valve mode. An experimental device operating in the valve mode has been built and used for testing. Numerical investigations h ave included analysis of magnetic field, continuum based analytical modelling of the valve mode as well as micromechanical discrete element simulation of MR fluid. Analytical studies of the MR flow have been carried out using the conventional Buckingham equation with constant yield stress across the valve gap and the modified Buckingham equation with nonlinear yield stress distribution across the channel according to the magnetic field distributionm determined numerically. The analytical results have been compared with experimental data. A better performance of the modified Buckingham model has been observed. A micromechanical model of MR fluids has been developed within the discrete element framework. The DEM model has been verified qualitatively on a test example of forming chains by magnetized particles after application of an external magnetic field.

Abstract:
The paper addresses discrete element (DEM) models of the heterogeneous particulate solids where the normal interaction between two deformable spherical particles bonded via weaker solid interface is considered. The integral interaction model aimed for evaluation of the bond stiffness was developed, where analytical expressions of the stiffness parameters reflecting individual contribution of the two particles and of the interface properties are derived. Application of the developed DEM model to particulate solid with many particles is considered. The accuracy and the suitability of this approach are evaluated by considering refined 3D Finite Element analysis.

Keywords:
Heterogeneous Solid, Particles Interaction, DEM, FEM

Abstract:
We present a new computational model for predicting the effect of blast loading on structures. The model is based in the adaptive coupling of the Finite Element Method (FEM) and the Discrete Element Method (DEM) for the accurate reproduction of multifracturing and failure of structures under blast loading. In the paper we briefly describe the basis of the coupled DEM/FEM technology and demonstrate its efficiency in its application to the study of the effect of blast loading on a masonry wall, a masonry tunnel and a double curvature dam.

Abstract:
W artykule przedstawiono badania doświadczalne oraz modelowanie numeryczne procesu spiekania proszków metalicznych. W części eksperymentalnej pracy badano ewolucję mikrostruktury oraz gęstości spieku w trakcie procesu spiekania. Jako metodę modelowania wybrano metodę elementów dyskretnych, w której zakłada się, że materiał jest reprezentowany przez liczny zbiór elementów dyskretnych (cząstek) o kształcie sferycznym oddziałujących między sobą. Modelowanie spiekania wymaga wprowadzenia oddziaływania kohezyjnego między cząstkami reprezentującego naprężenia powstające między ziarnami w trakcie spiekania. W artykule przedstawiono wstępne wyniki numeryczne pokazujące ewolucję naprężenia w trakcie spiekania między dwoma ziarnami spiekanego proszku.

Keywords:
spiekanie, metalurgia proszków, związki międzymetaliczne, modelowanie, metoda elementów dyskretnych

Abstract:
This paper deals with numerical aspects of nonlinear static analysis of a guyed mast of 649 m height. A concept of a new structure constructed of solid bars instead of tubes is analyzed. Due to decrease of member diameters the wind load declines, thus the horizontal displacements are smaller. A few structural variants of the proposed mast are calculated.

Keywords:
guyed mast, nonlinear analysis, tendons

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

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

Keywords:
wave propagation, elasticity, discrete element method,simulation

Keywords:
Elastic Wave Propagation, Deformability, Discrete Element Method

Keywords:
Discrete Element Method, Deformable Particles, Macroscopic Properties

Abstract:
This work presents an investigation on the determination of forming limit curves (FLCs) by finite element simulations and experimental approach. Nakajima formability test has been chosen for the experimental studies and numerical analysis. The onset of localized necking has been determined using the criteria studied in the authors’ earlier works, based on the analysis of the principal strains evolution in time. The criterion is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The onset of necking is assumed to occur at the point corresponding to a sudden change of the slope of the strain rate vs. time curve. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. Therefore, determined limit strains allowed us to construct experimental and numerical FLC determined using the presented algorithm. The FLCs have been compared with the conventional FLC determined according to the ISO 12004 standard, showing quite a good agreement. These results indicate that the used methodology of the limit strain determination can be used in finite element simulations as a potential alternative tool to determine formability limits for the sheet forming processes.

Keywords:
Steel and aluminum structures

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

Abstract:
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.

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

Abstract:
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.

Keywords:
discrete element method, deformable particles, soft contact

Abstract:
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.

Keywords:
sintering porcesses, numerical analysis, multiscale modelling

Abstract:
In this work a trajectory study of copper ore particles through a fan mill was performed with the use of a commercial CFD code, ANSYS Fluent, coupled with DEM (Discrete Element Method). Particles of different sizes were analysed. Results highlight ore behaviour, fluid flow conditions and mark places requiring geometrical improvements.

Keywords:
CFD, DEM, Beater mill

Keywords:
sintering, multiscale modelling

Keywords:
Sheet forming, formability, forming limit curie, numerical simulation

Abstract:
Fan mills, although generally used in coal comminution, show potential for the use with other minerals. They achieve high internal fluid velocities due to a spinning flywheel with its axis of revolutions normal to the flow. After hitting the flywheel, the ore is shed upward into a filter, where particles small enough are passed further on towards the next process stage. Particles considered too big are recirculated back onto the flywheel. In this work a trajectory study of copper ore particles through a fan mill was performed with the use of a commercial CFD code, ANSYS Fluent, coupled two-way with DEM (Discrete Element Method). Particles of different sizes were analysed. Results highlight ore behaviour, fluid flow conditions and mark places requiring geometrical improvements.

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

Keywords:
sintering, discrete element method, multi-scale modeling

Abstract:
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.

Keywords:
metoda elementów dyskretnych, modelowanie, zagęszczanie proszków, prasowanie

Keywords:
cohesive contact, discrete element method, viscoelasticity, sintering

Abstract:
A general objective of the paper is to improve understanding of micromechanical mechanisms in granular materials and their representation in numerical models. Results of numerical investigation on micro-macro relationship is the discrete element model of granular material are presented. The macroscopic response was analysed in a series of simulations of the triaxial compression test. Numerical studies were focused on the influence of microscopic parameters on the elastic response. The effect of the contact stiffness and the contact stiffness ratio on the effective elastic moduli, the Young’s modulus and Poisson’s ratio, were investigated. Numerical results were compared with the analytical estimations.

Keywords:
Discrete element method, granular material, triaxial test, micro-macro relationship, Voigt hypothesis, elastic moduli

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

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

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

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

Abstract:
This paper presents NUMPRESS System that has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. It seems undoubted that efficient design of an industrial sheet forming process requires reliable computer simulations and a tool for numerical optimization of the process parameters. It has to be also admitted that. among small and medium enterprises (SME) in this industrial branch, there are many who do not use any such numerical tools in their practice.
Computer simulation of sheet metal forming processes is a very specific branch of computational mechanics. Finite element systems dedicated strictly to this kind of processes are needed and actually present on the market. Commercial systems (like Autoform, PAM-Stamp, Stampack, etc.) are, due to their prices, usually beyond financial ability of SME.

Design of the drawing process and tools, i.e. choice of proper values of several design parameters, require efficient optimization strategy. In this process, random character of at least some of the parameters has to be taken into account. In view of this fact, the traditional, deterministic approach to optimization is insufficient and elements of robust design optimization techniques and reliability analysis have to be included in the formulation of the optimization problem. It has to be admitted that, even if some of the mentioned commercial simulation systems offer numerical optimization modules, not all of them reach beyond the deterministic concept of the optimization process.

Keywords:
sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Abstract:
This paper presents basic features of the NUMPRESS system and some examples ofuse. The system has been developed at IPPT PAN as a result of a project financially supported by European Regional Development Fund and is dedicated to small and middle enterprises (SME) dealing with sheet metal forming. The program consists of (i) an analytical finite element method module (ii) an optimization module, (iii) a reliability analysis module, and (iv) a graphical user interface enabling communication between modules. The analytical module consists of two independent programs up to the user’s choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic shells. Both programs are interfaced to a well-known commercial graphical pre-and postprocessor GiD.

Keywords:
sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Abstract:
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.

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

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

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

Abstract:
Numerical studies of effect of parameter evaluation on a failure mode in discrete element models of rock materials have been performed. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test using a cylindrical specimen with particle size distributions characterized by high degree of heterogeneity. Two different approaches to evaluation of micromechanical constitutive parameters have been compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. Significant differences in the failure pattern have been observed. The uniform constitutive parameters result in localized brittle-like fractures, while a distributed damage typical for a ductile failure is obtained for the model with local size-dependent parameters.

Keywords:
discrete element method, rock, modelling, failure mode, brittle, compression, contact

Abstract:
The failure probability estimation of FEM simulated sheet metal forming process is a computationally challenging task. The application of efficient gradient-based reliability techniques is very much limited due to the numerical noise introduced by the explicit dynamic algorithm used to perform the sheet stamping analysis and by the nonlinearity of the failure function. To cope with this difficulty, in the current study a two stage metamodel-based adaptive importance sampling method is employed. In order to assess the reliability of sheet metal forming operations the stochastic character of such parameters as friction, blankholding force, blank thickness, strain hardening parameters of the constitutive law as well as parameters defining the forming limit curve (FLC) are considered. Using the numerical example of a square cup deep drawing, the benchmark problem of the Numisheet’93 conference, it is investigated how the assumptions concerning the probabilistic distribution of the FLC location parameter affect the probability of sheet metal fracture.

Keywords:
Reliability, Metal forming

Keywords:
Friction, contact, metal sheet forming, Nakazima test, failure location