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Advanced simulations are needed in the industry nowadays for reliable design of various machine parts. A complex computation is presented here to describe the whole manufacturing process, apart from the machining, of forged spur gear for a reverse transmission from a car gearbox. A coupled thermomechanical analysis was realized through the explicit finite element method, while the stress–strain analysis was conducted in all phases of the production with time- and temperature-dependent constitutive law. The influence of process parameters was assessed, and the magnitudes of forging load were compared for selected dimensions of intermediate product (blank) and its initial temperature (preheating). The numerical simulation was finished with the flash trimming along the circumference, so the temperature-dependent ductile failure criterion proposed by Johnson and Cook was accounted for as well.

The ductile fracture has been observed in large as well as small scales. Three chosen Lode and pressure dependent phenomenological ductile fracture criteria with cut-offs were calibrated for aluminium alloy EN AW 2024-T351 using an enhanced hybrid experimental–numerical technique. It consisted of calibrating all the material constants of fracture criteria altogether. This enabled ready determination of the cut-off related constant for one of those criteria. Moreover, a non-quadratic Lode dependent plasticity model was coupled with the ductile failure criteria to form the damage plasticity approach in the numerical analysis. The fracture criteria were calibrated using the standard – large – sized specimens including a non-standard upsetting test. The specimens used for the calibration of failure criteria are usually ten times larger than that of a specimen for the small punch test. The transferability of calibrated parameters was tested and fair predictability was observed for all numerical models when applied to small scales.

Accurate material behaviour and its response to loading are needed for a reliable calibration of ductile failure criteria. Non-quadratic yield functions are often necessary for such a description. Nevertheless, it leads to the prediction of stress states that are inconsistent with the expected behaviour and deformations that are in contradiction with the experiments when the associated flow rule is adopted. These problems may be solved by applying a less restrictive non-associated flow rule. Therefore, an isotropic non-associated non-quadratic phenomenological plasticity model was developed as a function of the second and third invariants of deviatoric stress tensor. The yield function that is convex was proposed to allow for different yield stresses in tension, compression and shear. For simplicity, the same function was used for the plastic potential. Each of these functions is described by seven material parameters. The scheme of the so-called next increment corrects error method was adopted for the implementation of the proposed model within finite elements. Above that, three additional plasticity models were calibrated for 2024-T351 aluminium alloy. It is shown how the non-associated flow rule resolves the above-mentioned problems. Moreover, the possible extensions of the proposed yield function are described to include the hydrostatic stress dependence. Přesný popis chování materiálu a jeho odezva na zatěžování jsou potřeba pro věrohodnou kalibraci kritérií tvárného porušování. Pro takový popis jsou často potřeba nekvadratické funkce plasticity. To vede nicméně k predikci napěťových stavů, které nejsou konzistentní s očekávaným chováním a deformací, které jsou v rozporu s experimenty, pokud je přijatý sdružený zákon tečení. Proto byl vyvinut izotropní nesdružený nekvadratický fenomenologický model plasticity jako funkce druhého a třetího invariantu deviátoru tenzoru napětí. Funkce plasticity, která je konvexní, byla použita i pro plastický potenciál. Každá z těchto funkcí je popsána sedmi materiálovými parametry. Schéma takzvané metody další přírůstek koriguje chybu bylo přijato pro implementaci navrženého modelu v rámci konečných prvků. Navíc byly kalibrovány tři další modely plasticity pro slitinu hliníku 2024-T351. Je ukázáno, jak nesdružený zákon tečení řeší výše zmíněné problémy. Mimoto jsou popsána možná rozšíření funkce plasticity o zahrnutí závislosti na hydrostatickém napětí.

The plastic behavior of some polycrystalline metals exhibit the Lode dependence. There are many yield criteria, which are capable of such a description. Nevertheless, these criteria predict wrongly the deformation or the stress state or both in some cases. This paper focuses on the comparison of the deformation predicted by a classical von Mises yield criterion and advanced model, which covers the Lode dependence. The comparison was carried out using the tensile tests of two types of specimens manufactured from the aluminum alloy. The numerical simulations were conducted in the Abaqus/Explicit finite element commercial code and the material models were implemented using the user subroutine.

Cyclic plasticity models for the description of the deformation characteristics of austenitic stainless steel 304 at a room temperature have been studied with the focus on its industrial use. The main objective of this work is to investigate the capabilities of the classical Chaboche model with four terms which is commonly used in practice, and to compare those capabilities with the same model enriched with the evolution of some kinematic hardening parameters. The incorporation of parameters evolution brings significant number of necessary parameters to be determined, compared to the classical Chaboche model with four terms. To overcome excessive number of necessary parameters, also two terms Chaboche model with parameters evolution is used. Presented paper evaluates the time and temperature independent modeling possibilities of Chaboche combined nonlinear kinematic hardening model and isotropic hardening model with von Mises yield criterion.

This paper deals with a small punch test and ductile failure prediction of austenitic stainless steel 316L. Comprehensive investigation of fracture surfaces was conducted as well as examination of δ-ferrite and σ-phase present in the material in order to reveal the reason of occurrence of nonstandard type of fracture. Three phenomenological ductile fracture criteria were selected for comparative simulations regarding the prediction of crack initiation and propagation during the SPT. These criteria were calibrated by using the fracture tests of smooth cylindrical specimens, notched cylindrical specimens, notched tube specimens and cylinders with spherical recess. The whole material model including the fracture criteria with von Mises plasticity and element deletion technique for simulation of the crack initiation was implemented by using the user subroutine Vectorised User MATerial into the commercial finite element code of Abaqus. Finally, the simulation results with three ductile fracture criteria are compared and discussed based on the experimental results. Only one of the failure criteria captured the displacement at fracture correctly.

Notched specimen was designed for testing in compression. It was manufactured from the aluminium alloy 2024-T351, which is widely used in the aerospace, aeronautical and automotive industry. The test, among others, was used for the calibration of three uncoupled ductile fracture criteria dependent on the first invariant of stress tensor and third invariant of deviatoric stress tensor. The yielding was described by three plasticity models dependent on the second invariant of deviatoric stress tensor – proposed by von Mises, dependent on the second and third invariants of deviatoric stress tensor, and the most complex yield criterion dependent on the first invariant of stress tensor and second and third invariants of deviatoric stress tensor. All models were implemented into Abaqus commercial finite element code using VUMAT user subroutine. The ductile fracture prediction was carried out by widely used element deletion technique for specimen under compression. In the aftermath, the results were compared to experiments to see the performance of complex plasticity models with uncoupled fracture criteria.

The paper provides extensive experiments on aluminium alloy 2024-T351. Those cover the uniaxial strain- and stress-controlled tests using cylindrical specimens. Then, multiaxial tests were conducted via strain- and stress-controlled tensile–torsional loading on tubular specimens, which also cover the following non-proportional test – the 3-step experiment carried out in order to document the additional hardening. The paper also provides a fractography using the scanning electron microscopy and the life assessment. A novel approach to fatigue life prediction is presented, based on replacing the plastic part of the strain-life curve by the non-linear term in order to provide more variability and approximation ability. The broad experimental base will serve as a basis for future calibration and simulation using advanced cyclic plasticity models within the finite elements.

The paper presents a complex material model which covers the elastic-plastic behavior, material deterioration and ductile fracture. The calibration of such model was conducted for Aluminum Alloy (AA) 2024-T351 using specimens with various geometries and loading which covers various stress states. The model was then applied to the simulations of tensile test of plates. The computations were carried out in Abaqus/Explicit using the user subroutine Vectorized User MATerial (VUMAT), where the crack initiation and subsequent propagation was realized using the element deletion technique. The results were compared to the experimental observation in the end.

The experimental program was designed and proportional tests carried out at a room temperature on aluminium alloy 2024-T351. These concerned tension, torsion and compression, in order to investigate the damage accumulation nonlinearity and to reliably calibrate new phenomenological ductile fracture criterion. This fracture model, KHPS2, expressed through the fracture strain, was dependent on the stress triaxiality and normalized third invariant of deviatoric stress tensor. The ductile fracture model was then coupled with the yield criterion, as in the continuum damage mechanics, using the material softening. The plasticity model was considered in the form of taking into account the Lode dependence for investigated material, through normalized third invariant of deviatoric stress tensor. The whole approach, fully applicable to multiaxial ductile fracture related problems, was implemented using the user subroutine into the commercial software, based on the explicit finite element method. In the end, the proposed approach was verified using chosen realized fracture tests, which were used in the calibration, and newly designed KHPS2 criterion along with an existing one—modified Hosford–Coulomb model. The latter model showed better performance in simulations despite worse approximation ability, which can be attributed to its micromechanically-motivated formulation. Keywords: Al–Mg–Cu alloy, Failure, Finite element, Elastic–plastic material, Weakening, Polycrystalline material

Two alternative methods for the stress–strain curve determination in the large strains region are proposed. Only standard force–elongation response is needed as an input into the identification procedure. Both methods are applied to eight various materials, covering a broad spectre of possible ductile behaviour. The first method is based on the iterative procedure of sequential simulation of piecewise stress–strain curve using the parallel finite element modelling. Error between the computed and experimental force–elongation response is low, while the convergence rate is high. The second method uses the neural network for the stress–strain curve identification. Large database of force–elongation responses is computed by the finite element method. Then, the database is processed and reduced in order to get the input for neural network training procedure. Training process and response of network is fast compared to sequential simulation. When the desired accuracy is not reached, results can be used as a starting point for the following optimization task.

The ductile failure predictions have been an issue in many engineering applications. It begins with a design of machines and tools, continues with an evaluation of manufacturing processes, and last but not least ends with the assessment of various structures. The paper deals with a predictability of used criteria for a random structure of aluminum alloy 2024-T351, which was performed under the conditions of room temperature three-point bending. The bi-failure mode creates a space for the numerical studies of various approaches and gives an insight into the model performance. The plasticity was described by Lode-dependent yield criterion, which was coupled with several pressure and Lode-dependent fracture models to form a continuum damage mechanics approach via the material weakening. It was incorporated through a nonlinear damage accumulation, which was finally implemented using Fortran 77 subroutine into abaqus/explicit. All the models exhibited a good ability of crack onset prediction in terms of the force responses and realistic predictability of the crack propagation. The field of deformations was successfully compared with experimental data obtained by an optical method.

A new finite element formulation, aimed at the modeling of cross roll straightening of circular bars is presented. It is based on Eulerian description of elastoplastic material flow through a stationary finite element mesh, which is fixed in space and coupled with the multi-roller straightening machine. This approach leads to extremely effective computational algorithm which provides the relation between input parameters like curvature, diameter and material of the bar, straightening rollers geometry and intermeshing on one hand and output bar curvature and residual stress distribution on the other. Using this strategy, multiple repetition of the straightening process analysis for variable intermeshing scheme is a feasible task, aimed to optimization of roller intermeshing. Basic features of the algorithm are described, some verification results presented and compared with real experiments realized in industrial conditions. The industry was also a motivation for the optimization study, presented in the last part of paper. The results prove that the suggested solution strategy is a mighty tool for effective analysis of cross roll straightening and show a great potential for other types of straightening processes as well.

The performance of ductile fracture criteria often depends on the accuracy of material constants identification. Calibration process of three uncoupled phenomenological models was analysed. All of them contain the strain hardening exponent which is related to material plasticity as one of the fracture criteria parameter. More flexibility, better approximation of the fracture locus and more convenient shape of the fracture envelope might be reached when the strain hardening exponent is considered as another independent parameter of the fracture criteria in the identification process. Results are illustrated on the example of two structural steels, AISI 316L and AISI 1045, respectively.

The cutting process is now combined with machining, milling, or drilling as one of the widespread manufacturing operations. It is used across various fields of engineering. From an economical point of view, it is desirable to maintain the process in the most effective way in terms of the fracture surface quality or minimizing the burr. It is not possible to manage this experimentally in mass production. Therefore, it is convenient to use numerical computation. To include the crack initiation and propagation in the computations, it is necessary to implement a suitable ductile fracture criterion. Uncoupled ductile fracture models need to be calibrated first from fracture tests when the test selection is crucial. In the present article, there were selected widespread uncoupled ductile fracture models calibrated with, among others, an extremely low-stress triaxiality test realized through the compression of a cylinder with a specific recess. The whole experimental program together with the cutting process experiment were carried out on AISI 1045 carbon steel. After the fracture models were calibrated and the cutting process was simulated with their use, fracture surfaces and force responses from computations were compared with those experimentally obtained and concluding remarks were made.

The aluminium alloy 2024-T351 and AISI 1045 carbon steel was examined in scope of uncoupled ductile fracture criteria calibration using newly designed specimen. Its novel geometry allowed to reach extremely low stress triaxialities. The analysis of fracture envelopes was carried out with comparison of each criteria cut-off regions after the calibration where one novel criterion, KHPS, has been introduced. Ductile fracture criteria implemented into the commercial finite element code Abaqus through user subroutine VUMAT were applied to simulation of compression of newly designed cylinder with specific recess to show the crack prediction ability using the element deletion technique. Crack initiation loci together with force responses were compared to experimental observations.

Phenomenological ductile fracture criteria represent, among others, one of powerful tools for prediction of ductile fracture. These criteria are based on evaluating damage throughout the solid body as a response to straining. The damage is influenced by plasticity but not vice versa. Therefore, these criteria are often called uncoupled as they do not mutually couple the damage and plasticity. One of immense advantages of such criteria is a possibility not only to predict the crack initiation but also to follow the propagation based on the damage. Moreover, it is not restricted for one specific locus but the damage is evaluated in the entire solid body and one or more cracks can be tracked simultaneously or sequentially. Ductile fracture criteria are calibrated on the basis of several independent calibration tests under various stress states. One way how to verify calibrated model is to simulate numerically an experimental tests and follow the crack initiation and propagation. In the present study, selected phenomenological criteria were calibrated using various calibration tests. Then, selected calibration tests were simulated together with implemented ductile fracture criteria. In our case, the verification is carried out on tensile cylindrical specimens. Finally, computationally obtained results were compared to the experimentally observed ones and the prediction ability and reliability of selected phenomenological criteria is discussed.

Forward extrusion is a manufacturing process in which the cross section of product is reduced by forcing it through the die under high pressure. Cold extrusion is most often used in the mass produc...

Extended Mohr–Coulomb criterion which is uncoupled, therefore the plasticity is not influenced by the damage, was selected and calibrated. Experiments on the aluminum alloy 2024-T351 were carried out. Further, the impact of the damage rule proportionality was investigated. The damage exponent was sequentially held 1, 2 and 3, respectively. Therefore, the influence of the damage rate on the damage failure in finite element simulations was examined. Numerical simulations of the tensile test of smooth and notched cylindrical specimens and flat grooved specimen were performed. It is also shown that there is inability to predict slant fracture by uncoupled models for flat grooved specimen and in the final phase of tensile tests of cylindrical specimens.

This paper presents the calibration of three universal ductile fracture criteria with the stress triaxiality and the normalized third invariant of deviatoric stress dependence. Xue-Wierzbicki, Bai-Wierzbicki and Extended Mohr-Coulomb criteria are calibrated using butterfly specimen and newly designed notched tube specimen for an austenitic stainless steel. Different stress states necessary for successful calibration are generated by suitable combination of tension/compression-shear or tension/compression-torsion loading of both specimens, respectively. Suitability of the specimens for ductile fracture criteria calibration is evaluated comparing the range of reached stress states, the homogeneity of stress in process zone and appropriateness for the computational simulation of tests. Possible combination of above mentioned results with tensile testing of standard and notched cylindrical specimens is discussed, too.

Selected ductile fracture criteria are introduced and applied to prediction of chevron crack initiation and development during forward extrusion of long shafts. We present the calibration of selected criteria for carbon steel, simulate the process of forward extrusion and compare the simulation results with real experiments realized in a cooperating industrial company.

The paper deals with numerical analysis of the process of roller leveling of long products. The problem of multiple elastic plastic bending is solved by a program in Matlab, which is based on the Finite Element Method. The aim is to provide a simple, user friendly tool, capable of quick and reliable analysis of the process without the necessity to work with large multipurpose FEM packages. Direct solution of the problem is formulated, starting from the roll intermeshing and product geometry. Roller loading, product deflection, curvature and plastification are the output parameters of the program. With fast and reliable solution of the direct problem, optimal setting of the leveling process will be sought in an iterative process.

The paper deals with numerical simulation of Small Punch Test (SPT). SPT is a penetration test used to determine basic mechanical properties from a tiny piece of material. The testing procedure drew a great interest in the last decade, nevertheless there are no generally accepted standards for this type of testing until now. “Code of Practice” was created as a consequence of the CEN Workshop 2007, recommending both geometry, experiment performance and its basic evaluation. To obtain other mechanical properties like flow curve, yield stress, ductility and ultimate strength, it is necessary to realize a numerical simulation of the test to identify the mentioned material parameters. As the SPT results are generally influenced by many other parameters besides material behaviour, we try to quantify their relevance to make the material identification more rigorous.

The small punch testing technique under quasi-static loading was examined in the view of punch eccentricity role. It might arise especially when the ball is used as the penetrating tool, instead of hemispherical-ended punch. The austenitic stainless steel AISI 316L was chosen to execute several various “large scale” tests in order to calibrate the multi-linear stress–strain relationship along with the ductile fracture criterion KHPS. All the calibration procedure was performed without using the small punch testing. Then, the model was applied to small punch tests to observe the prediction ability when compared to real small punch experiments. Consequently, a numerical study was conducted to see the role of eccentricity in the case of 2 and 2.5 mm ball diameters used as the penetrating tool. The magnitude of eccentricity up to 0.3 mm was numerically tested. The results showed negligible role of eccentricity for 2 mm ball diameter and minor role for 2.5 mm diameter and studied material.

The paper deals with optimal setting of intermeshing parameters in multi roller cross roll straightening machine. The procedure is based on a fast algorithm of the straightening process simulation, which leads to an efficient analysis of the process for many combinations of intermeshing parameters, selected at random. Multi-objective optimization is then realized over the obtained response variables. Presented example shows the potential of the suggested solution strategy.

Large plastic deformation of cold formed metal is followed by its hardening, which can be experimentally evaluated by measuring hardness. To convert the measured hardness values into strain, the strain–hardness reference curves are used. Their evaluation is traditionally based on compression tests of cylindrical specimens. New procedure of reference curves evaluation is suggested here, based on an FE simulation of a forming process and direct relation of computed strain and measured hardness. The procedure is illustrated on the example of forward extrusion process and reference curves, obtained by classical and newly suggested procedure are compared.

In this paper, we describe the experience with cold forming of bolts, made of micro-alloyed steel, specially designed to enable elimination of thermal treatment. First, the flow stress curve and hardening of material are evaluated by compression testing. Next, cold forming of various geometrical versions of the bolts is numerically simulated to obtain and compare their strain distribution and formability exhaustion. The results are verified by hardness measurement of produced specimens. Final products are then subjected to tensile testing to evaluate basic mechanical characteristics of the bolts—yield and tensile strength and elongation at rupture.

Present study is aimed on the cutting process of circular cross-section rods where the fracture is used to separate one rod into two pieces. Incorporating the phenomenological ductile fracture model into the explicit formulation of finite element method, the process can be analyzed without the necessity of realizing too many real experiments which could be expensive in case of repetitive testing in different conditions. In the present paper, the steel AISI 1045 was examined and the tensile tests of smooth and notched cylindrical bars were conducted together with biaxial testing of the notched tube specimens to calibrate material constants of selected phenomenological ductile fracture models. These were implemented into the Abaqus/Explicit through user subroutine VUMAT and used for cutting process simulation. As the calibration process is based on variables which cannot be obtained directly from experiments, numerical simulations of fracture tests are inevitable part of the calibration. Finally, experiments regarding the cutting process were carried out and predictive capability of selected fracture models is discussed. Concluding remarks then make the summary of gained experience both with the calibration and application of particular ductile fracture criteria., {"references":["T. Wierzbicki, Y. Bao, Y.-W. Lee, and Y. Bai, \"Calibration and evaluation\nof seven fracture models,\" Int. J. Mech. Sci., vol. 47, pp. 719-743, 2005.","Y. Bai, and T. Wierzbicki, \"Application of extended Mohr–Coulomb\ncriterion to ductile fracture,\" Int. J. Frac., vol. 161, pp. 1-20, 2010.","Y. Bai, and T. Wierzbicki, \"A new model of metal plasticity and fracture\nwith pressure and Lode dependence,\" Int. J. Plast., vol. 24, pp. 1071-1096,\n2008.","J. Petruška, T. Navrat, and F. Šebek, \"A new model for fast analysis of\nleveling process,\" Adv. Mater. Res., vol. 586, pp. 389-393, 2012.","J. H. Hollomon, \"Tensile deformation,\" Trans. AIME, vol. 162, pp. 268-290,\n1945.","P. Kubík, F. Šebek, J. Petruška, J. Hůlka, J. R˚uˇziˇcka, M. ˇ Spaniel, J. Dˇzugan,\nand A. Prantl, \"Calibration of Selected Ductile Fracture Criteria Using\nTwo Types of Specimens\", Key Eng. Mater., vols. 592-593, pp. 258-261,\n2014.","J. Hůlka, Application of ductile fracture models in computational\nsimulation of manufacturing operations, Diploma Thesis, Brno University\nof Technology, 2008."]}

Numerical and experimental analysis of a stress state in the deformation zone during pass rolling is presented and compared. Obtained results are used for assessment of formability under given geometrical and thermodynamical conditions.

The problem of optimal design of pressure vessel heads to maximize limit load behaviour is presented. Incremental elasto‐plastic analysis is used and a formulation based on the finite element method is presented whereby an approximate design model is generated which can be optimized via sequential programming. Results are presented for torispherical head shapes and tables are provided in order to evaluate the influence of different geometrical forms on limiting pressure loads. The method is generally applicable and can be applied to the design of components which are required to exhibit limited plastification under increasing load.