Institute of Fundamental Technological Research

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

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

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

contact, discrete element method, elastoplastic, spheres, unloading

In this paper, small punch test (SPT) which is one of miniaturized samples technique, was employed to characterize the mechanical properties of carbon steel P110. The tests were carried out in the range of –175°C to RT. Results obtained for SPT were compared to those calculated for tensile and Charpy impact test. Based on tensile and SPT parameters numerical model was prepared. 8 mm in diameter and 0.8 mm in height (t) discs with and without notch were employed in this research. The specimens had different depth notch (a) in the range of 0.1 to 0.4 mm. It was estimated that α factor for comparison of Tsp and DBTT for carbon steel P110 is 0.55 and the linear relation is DBTT = 0.55TSPT. The numerical model fit with force - deflection curve of SPT. If the factor of notch depth and samples thickness is higher than 0.3 the fracture mode is transformed from ductile to brittle at -150°C.

small punch test, carbon steel P110, small samples, low temperature, mechanical properties

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.

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

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

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

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

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

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

This paper presents 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.

sheet forming, formability, forming limit curve, numerical simulation

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.

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

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

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

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

formability test, explicit FE method, friction, fracture location

We have developed software for computation of geometric characteristics and analysis of tangential stresses of prismatic bars with an arbitrary cross section in the stages of preprocessing, processing, and postprocessing of data in a finite-element analysis. Based on the principle of virtual works, we obtain variational functionals for the Saint-Venant problem of torsion of a prismatic bar and bending by a transverse force that does not cause torsion. These functionals are directly used to obtain resolving relations of the finite-element method. On the basis of the Betti reciprocal theorem, the coordinates of the center of bending are determined. We formulate all relations for the warping function, which enables us to avoid problems associated with ambiguity in the case of using the Prandtl function of stresses for a multiply connected domain.

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

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

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

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

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

blacha wstępnie wyprężona, próby tłoczności, symulacja numeryczna

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.

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

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.

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

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.

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.

sheet forming, formability, forming limit curve, numerical simulation

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

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

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.

Steel and aluminum structures

Sheet forming, formability, forming limit curie, numerical simulation

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

metoda elementów dyskretnych, modelowanie, zagęszczanie proszków, prasowanie

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

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

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.

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

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

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

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

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

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

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

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.

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

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