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Ultra-high-strength steels (UHSS), for instance, dual phase (DP) and martensitic steels, get growing challenges in strip metal forming processes of car industry manufacturing to achieve lightweight and improve passenger security. Predict and compensate for springback is still a major problems to be solved in cold roll forming (CRF) for complex section materials. In this study, the springback performance UHSS in cold roll forming is discussed by simulation and experimental methods. At the same time, one 3D FEA model was established to analyze the CRF process by COPPA RF and MSC MARC, in which planar swift’s model, anisotropic Hill’s 48 model, and Yid2000-2d model in the company with Yoshida-Uemori kinematic hardening pattern were investigated. Automobile threshold section CRF experiment and springback evaluation carried out through the comparison of numerical results. Considering Yoshida-Uemori kinematic hardening, the anisotropic Yid2000-2d model improves the springback prediction accuracy in CRF car threshold section in comparison with other models. The improved model is used to compensate the springback of product. A new method is proposed, which takes into account angle overbending compensation (AOC), small radius compensation (SRC), and revere-bending compensation (RBC) based on roll shape design. The method, which we call “USTB-Durable Integration of Springback Control (UDI),” is general for it considers the fact radius and angle would occur during springback. Compared with the AOC, SRC, and RBC method, the new method has higher precision especially for the springback compensation of ultra-high-strength complex section in CRF. The researchers are expected to conduct design engineer to calculate and compensate the springback trend before applying roller design to actual production.

Structural integrity plays an important role in any industrial activity, due to its capability of assessing complex systems against sudden and unpredicted failures. The work here presented investigates an unexpected new mechanism occurring in structures subjected to monotonic and cyclic loading at high temperature creep condition. An unexpected accumulation of plastic strain is observed to occur, within the high-temperature creep dwell. This phenomenon has been observed during several full inelastic finite element analyses. In order to understand which parameters make possible such behaviour, an extensive numerical study has been undertaken on two different notched bars. The notched bar has been selected due to its capability of representing a multiaxial stress state, which is a practical situation in real components. Two numerical examples consisting of an axisymmetric v-notch bar and a semi-circular notched bar are considered, in order to investigate different notches severity. Two material models have been considered for the plastic response, which is modelled by both Elastic-Perfectly Plastic and Armstrong-Frederick kinematic hardening material models. The high-temperature creep behaviour is introduced using the time hardening law. To study the problem several results are presented, as the effect of the material model on the plastic strain accumulation, the effect of the notch severity and the mesh element type and sensitivity. All the findings further confirm that the phenomenon observed is not an artefact but a real mechanism, which needs to be considered when assessing off-design condition. Moreover, it might be extremely dangerous if the cyclic loading condition occurs at such a high loading level.

Numerical solution to the problem of the springback of thick wall tubes is investigated with consideration of nonlinear kinematic hardening model. Also, the effects of different types of loading and their sequences on the springback of these pipes have been investigated. In the employed approach in this research, the precision of the springback forecast has increased, which will reduce the cost and time for assembly of materials. Considering the effects of loading, it is possible to take steps to reduce springback. In addition, the problem is simulated by finite element method, in addition to modeling this problem, its results can be used to validate the numerical solution of the problem. It is shown when the bending loading rate increases, the bending springback angle decreases and with increasing torsional loading rate compared to the bending loading, the torsional springback angle decreases. Also, by changing the loading sequence, for example, bending and then fixing the bending radius and increasing the torsional angle (torsional loading) can significantly reduce bending springback angles.

Tension levelling is used in the steel industry to remove shape defects present in cold rolled strip. This technology is increasingly being employed by steel makers to level AHSS steels, because conventional roll levelers are not able to correct explicit local errors like wavy edges and central buckles. In this study, the influence the hardening law has on the simulation of tension levelling processes using FEM is studied. Tension-compression tests have been performed in a DP1000 steel using several reversal cycles and a mixed nonlinear kinematic hardening law has been fitted to the experimental data using different amount of backstress tensors. It is observed that numerical results are influenced by the introduced hardening law and thus is an important input when simulating the tension levelling process.

Metal dampers have been widely used to improve the seismic performance of the building structure. However, conventional metal dampers only possess one yield point and cannot protect the structure efficiently under earthquakes of different intensities. A new type of metal damper composed of two annular metal dampers with different sizes is proposed in this paper. It is a graded yield metal damper having two yield points, which can be used to reduce the responses of the structure efficiently under earthquakes of different intensities. Firstly, the mechanical properties of single annular metal damper, such as the failure mechanism, hysteretic behavior and anti-fatigue performance, are investigated by cyclic loading tests. The test results show that the annular metal dampers possess large deformation capacity and energy-dissipation capacity as well as excellent anti-fatigue performance. The calculation formulae are derived to determine major mechanical parameters of the damper. The theoretical results obtained by using the proposed calculation formulae are in good agreement with experimental results. Cyclic loading tests are carried out on the graded yield metal damper. The yielding process of the graded yield metal damper is simulated using the ABAQUS program. The trilinear kinematic hardening model is adopted to simulate the hysteretic behavior of the damper. Nonlinear time history analyses are carried out to compare the responses of a conventional reinforced concrete (RC) moment-resisting frame structure with that of the structure installed with the graded yield metal dampers under three levels of earthquakes using SAP2000. The results indicate that the seismic performance of the structure installed with the graded yield metal dampers under all levels of earthquakes is improved significantly. The graded yield metal dampers are more effective in displacement control of reinforced concrete moment-resisting frame structure in comparison with single yield point metal dampers.

The Hardening Soil model, an elasto-plastic second-order hyperbolic isotropic hardening model, in Plaxis has seen many applications in finite element analysis of various earth structures. This technical note presents a protocol for determination of the model parameters of the Hardening Soil model from a set of triaxial compression tests. The technical note also describes details about how to determine the Mohr-Coulomb strength parameters c and ϕ for well-compacted fills (with and without cohesion), of which the failure envelopes are typically curved. The motivation for preparing this technical note came from a study on analysis of field-scale soil–geosynthetic composites in which the soil model and model parameters deduced from triaxial tests were able to predict with very good accuracy “all” measured results of five field-scale soil–geosynthetic composites under increasing applied vertical loads up to 1000 kPa (approximately five times the load level commonly used in design of reinforced soil bridge abutments). The model parameters were determined by a well-defined protocol. The protocol should be of value to researchers and engineers who use the soil model for sophisticated finite element analysis and design of earth structures.

Ratcheting simulation for steel material is of importance especially when it is subjected to asymmetrical cyclic loading. A strategy to fast determine the Chaboche elasto-plastic model parameters is proposed by considering the ratcheting effect. First, one cyclic ascend experimental test with an equal strain increment of ±0.1% after each twenty-cycle loading phase up to ±1.2% is performed to observe the Masing effect. Then, a strain-controlled fatigue test is conducted at a strain range of ±0.8% to identify the parameters of Chaboche combined hardening model. Besides, a ratcheting test with stress variation from −361.6 MPa to 441.6 Mpa is executed. Based on these experiments, two computational programs are carried out to simulate the cyclic stress-strain response and ratcheting, respectively. In the parameters identification process, a pseudo-percent allocation method is developed to reduce the stress overestimation. Results indicate that: (i) 304SS presents Masing effect when the strain range is bound within ±0.9%, and it follows the previous experimental results about the serrated flow and ratcheting; (ii) The Armstrong-Frederick rules reverse in a small strain when the isotropic hardening considered, so the predicted ratcheting strains for the first few cycles are inevitably underestimated; (iii) Not only the third Armstrong-Frederick hardening rule, but the second Armstrong-Frederick hardening rule has also an effect on the ratcheting simulation.

This study examines the previous experimental results of ratcheting behavior of elbow pipe made of Z2CN18.10 austenitic stainless steel subjected to constant internal pressure and reversed in-plane bending by Chen-Jiao-Kim (CJK) kinematic hardening model as a user subroutine of ANSYS. A set of more precise CJK model parameters were determined. Based on the new model parameters, the evolutions of ratcheting behavior of pressurized elbow pipe were made under two sets of different loading paths. The paths consist of the alternation of internal pressure and bending moment, and bending-torsion combination under constant internal pressure. The preliminary results claim that different loading paths have a significant effect on ratcheting behavior of pressurized elbow pipe.

Modeling of material behaviour under strain-controlled and stress-controlled loading for cyclically stable materials (CSMs) is generally done using kinematic hardening, neglecting the isotropic hardening component. Although this approach is able to simulate the hysteresis loops, the quantitative ratcheting characteristics are often not of the desired accuracy; thus earlier investigators have introduced different modifications in the kinematic hardening component for case to case basis to obtain better agreement to the experimentally observed cyclic-plastic behaviour. Combined hardening models, though used for cyclic softening/hardening materials, have not been used for cyclically stable materials to the best knowledge of the authors. The primary aim of this study is to improve the ratcheting predictions for CSMs considering the well-known Chaboche's combined hardening model using a new generalized methodology. The initial estimates of the hardening components are obtained from symmetric strain-controlled tests subjected to their refinement by genetic algorithm based optimization technique. The Chaboche's parameters have been evaluated using the proposed methodology for available reported experimental data on cyclically stable steels to demonstrate the response of materials under stress-controlled and strain-controlled loading conditions.

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.

To predict fracture initiation in ductile material under nonproportional loadings, an approach considering combined hardening and a fatigue-rule-based damage accumulation law was investigated. Eleven complex nonproportional experiments, including torsion-tension tests, compression-torsion tests, and uniaxial tension-compression cyclic tests were performed. Finite element analysis was conducted on the experimental data to extract information on essential local fractures, such as stress triaxiality and the Lode parameter. The Chaboche combined hardening model was tuned to capture the material hardening characteristics, ensuring a reliable description of the hardening behavior compared with the isotropic hardening assumption. In addition, the inclusion of fracture locus was proposed to determine the predeformation effect on damage evolution. Combined with the fatigue-rule-based damage accumulation laws, the damage evolution can consider the variable strain history. Thus, fatigue-rule-based damage accumulation, together with the combined hardening law, considerably improved the ability to predict fracture onset in cases of torsion-tension loading with respect to the integral-based damage accumulation law.

The integration of forming in the fatigue modelling of cold-formed components significantly improves the predictive accuracy of the estimated life. The current study investigated the fatigue behaviour of a bent specimen made from a 5 mm thick, S900MC high strength steel plate. Because of its superior static and dynamic strength, this grade is progressively used for hollow cold-formed sections in mobile applications. However, it exhibits a strong stress saturation as well as limited formability. In this regard, a finite element modelling framework was adopted from previous research and further developed to integrate bending in the fatigue modelling and life estimation procedure. However, this framework currently ignores the possible influence of kinematic hardening and associated Bauschinger effect. For this reason, a numerical study was performed that compares isotropic with kinematic hardening for this specific application. First, the characteristic behaviour of these models was verified in a virtual tension-compression test. Subsequently, they were implemented in forming simulation followed by fatigue loading. Herein, the stress-strain evolution was investigated and a multi-axial fatigue criteria was used to map the sensitivity of the estimated life to the type of hardening. In general, the stress that entered the fatigue calculation was at least 21% lower for the kinematic model. As a result, a significant increase of 65% was observed for the estimated fatigue life, yielding a better comparison with experimental data.

Numerical models of structural components that deteriorate primarily due to geometric instabilities under multiaxis cyclic loading are sensitive to both the assumed geometric imperfections and the nonlinear material model assumptions. Therefore, the accuracy of the constitutive model is a desirable feature in finite-element simulations. However, the classic Voce-Chaboche metal plasticity model, ubiquitous among commercial finite-element software, is found to underestimate the initial yield stress in structural steels by about 10%-30% when calibrated to minimize the overall difference in strain energy between the model and test data of load protocols representative of earthquake loading. This paper proposes a refined version of the Voce-Chaboche material model. When compared with the original model, the updated one improves the prediction of the initial yield stress, can simulate initial yield plateau behavior, and better estimates experimental cyclic stress-strain data. Constraints on the model parameters are established, a calibration procedure is developed, and model parameters are proposed for nine structural steels used worldwide. Source code for the material model is also made publicly available. A case study demonstrates that steel component behavior is sensitive to subtle differences in the material response that arise between the Voce-Chaboche and the proposed material models. (C) 2021 American Society of Civil Engineers.

This work proposes an elasto-plastic study of SAE 1045 steel through a stress versus cyclic deformation curve, which was the basis for calculating the material’s hardening parameters, defining the isotropic hardening value as null and kinematic hardening value as 415.05 MPa. Therefore, due to the wide use of SAE 1045 steel in structures and elements that undergo cyclical stresses, the parameters defined in the present work are highly relevant for the analysis of structures based on this material, making it easier to meet the needs during research, diagnostics, or sizing using this steel. The mathematical model used proved to be efficient in generating results compatible with those expected based on the bibliography.

Fatigue damage models based on the continuum damage mechanics have been proposed to predict fatigue life of specimens under uniaxial and multiaxial loadings. In this research the fatigue damage model of Chaboche is used to predict the fatigue life under different proportional and non-proportional strain controlled loadings paths. The nonlinear kinematic hardening model of Chaboche is used and it is coupled by nonlinear fatigue damage model. S-N curves of 7075-T6 and 6061-T6 alloys are modeled by applying the fatigue damage model of Chaboche. Constants of the models are determined from S-N curves of two different stress ratios and cyclic uniaxial tests. Ten different loading paths are considered and modeled. Modeling of the multiaxial loading paths is carried out by the obtained constants. Fatigue life is predicted and compared with the experimental results. The experimental and numerical results consist of high and low cycle fatigue tests. Maximum stress in each cyclic strain loops are also obtained by the present models and compared with the experimental results. The present research evaluates the capabilities of the used fatigue damage model.

This paper presents a new model for reproducing the elasto-plastic behavior of metals characterized by the presence of Bauschinger effect, taking as reference the case of autofrettaged cylinders. The paper is composed of an experimental part and of a numerical part. The experimental part consists of a set of tension-compression tests performed on AISI 4140 investigating the level of plastic strains typical of autofrettage: experiment arrangement, load cycles, measurement procedure and relevant results are presented. In the numerical part a multiaxial elasto-plastic model, derived from a combination of non-linear Kinematic hardening and non-linear Isotropic softening, is formulated and the key points for implementing it in a commercial Finite Element code are discussed. Then a fitting procedure for model parameters is proposed for reproducing the results obtained in experimental part. In the end the model has been implemented in ANSYS software and an example of application is presented for the case of an autofrettaged cylinder.

This paper focuses on the effects of prior cyclic loading on the subsequent monotonic tensile properties of low yield point (LYP) steels compared to that of virgin material. Carefully designed axial steel coupons machined from LYP steel plates were tested under various cyclic loading protocols to model seismic-induced damage and then monotonically tensioned until fracture to obtain their remaining mechanical properties. The experimental results indicate that a prior history of cyclic loading caused an increase in strength but a decrease in both ductility and stiffness of LYP steels. Moreover, significant cyclic hardening was observed in LYP steels, which could be characterized as combined isotropic and kinematic hardening, of which the former component played an overwhelmingly dominant role.

By analyzing the simulation results for stress relaxation with Chaboche model, the effect of loading history is discussed. It is revealed that the Chaboche model without static recovery term cannot demonstrate the influence of prior loading strain rates for drop stress during strain holding period. A modified model based on the Chaboche unified viscoplasticity theory is proposed to mainly focus on the remarkable features of the relaxation behavior of materials. Several numerical examples are discussed in detail to show some potential descriptions and the strong dependence on prior uploading strain rates for relaxation. The experiments of two materials Type 304 stainless steel and TIMETAL 21S are selected to verify the feasibility of proposed model. A series of consistent simulation and prediction results are obtained, including the dependence of drop stress on various prior loading strain rates, the effect of different peak stresses or holding strains with the same prior loading strain rate, multi-relaxation with relaxation histories, and cyclic plasticity. Finally, the principle of parameter determination is also discussed.

In this work, we investigate the numerical convergence of a set of plasticity models with different kinematic and directional distortional hardening rules under cyclic plastic loading. In particular, we revisit the results presented in Feigenbaum et al. (2012) in order to more robustly check for convergence during the numerical integration procedure, and show that the results presented in the previous work do not converge. We investigate the role of the step-size and numerical scheme on the convergence of these models when predicting ratcheting. By reducing step-sizes and using a forward Euler scheme during numerical integration, converged solutions are obtained. The new converged results lead to new conclusions. Results still suggest that directional distortional hardening can improve ratcheting predictions, however the addition of directional distortional hardening yields less improvements compared to kinematic hardening alone than previously thought. This new conclusion, strongly suggests the need for additional modeling developments in order accurately predict ratcheting strains under a wide variety of cyclic plastic loadings.

Numerical simulations of tube hydroforming process of hollow crankshafts were conducted by using finite element analysis method. Moreover, the modified model involving the integration of isotropic–kinematic hardening model with ductile criteria model was used to more accurately optimize the process parameters such as internal pressure, feed distance and friction coefficient. Subsequently, hydroforming experiments were performed based on the simulation results. The comparison between experimental and simulation results indicated that the prediction of tube deformation, crack and wrinkle was quite accurate for the tube hydroforming process. Finally, hollow crankshafts with high thickness uniformity were obtained and the thickness distribution between numerical and experimental results was well consistent.

The springback phenomenon plays a significant role in precision sheet metal bending. In an early attempt, Gardiner proposed an analytical solution for springback under pure bending with perfect elastoplasticity. Several studies expanded on Gardiner's research to provide improved solutions of springback. However, the fore-mentioned studies did not account for mechanical analysis considering deformation history in their improved solutions. Thus, the present study divides the deformation history of metal material bend-forming into three stages, namely a loading stage, a free unloading stage, and a non-free unloading stage. An elastoplastic analysis was performed by considering deformation history based on uniaxial stress state and plane section assumptions. The study also investigated the springback rule of bilinear kinematic hardening elastoplastic metal materials with uniform rectangular cross-section under pure bending. With respect to common metal materials, the study obtained an improved springback prediction solution in which the hardening component was considered, and its prediction results indicated a degree of agreement with the experimental data that exceeded those of the prediction results obtained by Gardiner's approximate solution when applied to the springback prediction of sheet metals.

International audience; The aim of this work is to propose a Gurson-type model for ductile porous solids exhibiting isotropic and kinematic hardening. The derivation is based on a " sequential limit-analysis " of a hollow sphere made of a rigid-hardenable material. The heterogeneity of hardening is accounted for by discretizing the cell into a finite number of spherical layers in each of which the quantities characterizing hardening are considered as homogeneous. A simplified version of the model is also proposed, which permits to extend the previous works of Leblond et al. (1995) and Lacroix et al. (2016) for isotropic hardening to mixed isotropic/kinematic hardening. The model is finally assessed through comparison of its predictions with the results of some micromechanical finite element simulations of the same cell. First, the numerical and theoretical overall yield loci are compared for given distributions of isotropic and kinematic pre-hardening. Then the predictions of the model are investigated in evolution problems in which both isotropic and kinematic hardening parameters vary in time. A very good agreement between model predictions and numerical results is found in both cases.

Based on the pseudo-strain method, a computational modeling technique coupling with Armstrong-Frederick type nonlinear kinematic hardening rule (Jiang-Sehitoglu model) is developed to calculate the multiaxial stress-strain responses of notched components. The pseudo-strain-true notch stress curve is determined using Neuber’s rule. The material constants in Jiang-Sehitoglu model are calculated using the Ramberg-Osgood curve. The presented method is applied to simulate the notch-tip deformations of circumferentially notched 1070 steel and S460N steel shafts subjected to various loadings, including box, circle, V-shape, zigzag-shape, and butterfly-shape loading paths. The calculated strain loops are in accord with experimental data and show reasonable accuracy.

Crash box design as one of the passive safety components in a vehicle had been developed to enhance energy absorption. Initial fold on the crash box is set to facilitate folding during the crash. The aims of this study is to investigate the initial folded crash box with length to thickness ratio subjected to frontal test. The frontal test is modelled by using finite element analysis. Through computer simulation using 9 models, the obtained result was used to provide the better design of crash box. The variations in this study were length to thickness ratio of crash box with length of tube (L) = 115; 132.5; 150 mm and the thickness of tube (t) = 1.6; 2.0; 2.5 mm. The crash box material was assumed as bilinear isotropic hardening material. The velocity used in the simulations was 7.67 m/s with impact mass of 103 kg. Based on the results, it can be shown that 1st model to 8th model produce deformation pattern as concertina mode and 9th model has diamond mode. The 3rd model has the largest energy absorption with value 18.29 kJ.

A topology optimization approach for designing structures with maximum energy absorption capacity under cyclic loads is proposed. To simulate the Bauschinger effect in materials under cyclic loads, Prager and the Armstrong-Frederick kinematic hardening rules are considered together with the von Mises plasticity in the optimization process. Path-dependent sensitivities are derived analytically using the adjoint method, which are further verified by the central difference method. Effectiveness of the proposed approach is demonstrated on several examples. Results show that the optimized designs with kinematic hardening are remarkably different from the ones obtained with isotropic hardening and are highly dependent on the loading patterns.

This paper seeks to use Lemaitre’s Continuum Damage Model to obtain fatigue life estimates under multiaxial proportional and non-proportional loadings. Initially, the Lemaitre’s mathematical model is presented, by formulating the necessary constitutive relations. Chaboche’s model was chosen to describe the kinematic hardening law. Then, the numerical model necessary to solve the constitutive relations is developed, utilizing the Chaboche’s law with 3 terms and Euler’s implicit discretization. Then, the material parameters are identified for 304 and S460N steels and 6061-T6 aluminum alloy. The model is implemented in a FORTRAN routine, which is submitted to uniaxial and proportional and non-proportional multiaxial loading histories. The fatigue life data obtained from Lemaitre’s damage model is compared to experimental data. Then, a stress amplitude analysis is conducted and the numerical stresses are compared to experimental data. Damage evolution curves are also obtained for each material and loading. The results show that Lemaitre’s damage model describes adequately the behavior of the analyzed materials under low cycle fatigue, when low strain amplitudes are being applied to the specimen.

Material nonlinearity is of great importance in many engineering problems. In this paper, we exploit NURBS-based isogeometric approach in solving materially nonlinear problems, i.e. elastoplastic problems. The von Mises model with linear isotropic hardening and kinematic hardening is presented, and furthermore the method can also be applied to other elastoplastic models without any loss of generality. The NURBS basis functions allow us to describe exactly the curved geometry of underlying problems and control efficiently the accuracy of approximation solution. Once the discretized system of non-linear equilibrium equation is obtained, the Newton-Raphson iterative scheme is used. Several numerical examples are tested. The accuracy and reliability of the proposed method are verified by comparing with results from ANSYS Workbench software.

A novel extension of the basis reduction method for kinematic hardening shakedown problem is presented. Firstly, the basis reduction method is implemented based on the modified Newton–Raphson (N-R) method. Then a new technique for the construction of back stress field is introduced, where the simultaneous influence of multiple load corners in shakedown is taken into consideration. Finally, two typical numerical examples are investigated. The results compared with previous works in literatures demonstrated that the proposed method is accurate and the performance in reducing of computation time is significant.

Cyclic hardening of metals is considered as one of the most important features that affects extremely the hysteresis behavior of steel structures. One approach to study this characteristic is dividing it into two components, including isotropic hardening and kinematic hardening, and defining any of these components for any type of metals by calibrated data obtained from experiments. However, the lack of these calibrated data on metals, restricts this approach. Therefore, in this paper the isotropic and kinematic characteristics of five different steel grades from 100 to 485 MPa, under various strain ranges between ±1 and ±7% were proposed. Afterwards, four of these five grades were validated in order to find the appropriate combination of data for any of them, and to compare the result of this approach with those obtained from a well-known hardening model, Ramberg-Osgood. The results showed the high accuracy of the isotropic-kinematic hardening model in comparison to the Ramberg-Osgood method.

In this paper, we compare and contrast the performance of two analogous thermo-mechanical models. The first reference model assumes an energetic isotropic hardening mechanism – the conventional approach in literature. Additionally, we consider an alternative formulation where isotropic hardening is strictly dissipative. Mechanically, both models are identical. The only difference lies in their respective heat conduction equations, where a heat source term associated with isotropic hardening manifests itself for the dissipative-based model. The predictions from the two models for different cyclic loading conditions are benchmarked against available experimental data for 316L stainless steel. While the energetic-based model is able to reasonably capture the material responses for simple load cases, its inadequacy for the more complex cases is easily observed. The superior performance of the dissipative-based model is furthermore demonstrated for a series of cyclic loading conditions. The results suggest that a dissipative isotropic hardening mechanism may be more appropriate for cyclic loadings.

На базі методу скінченних елементів розроблено числові методики для розв’язання нелінійної пружно-пластичної задачі з врахуванням ізотропного зміцнення за двома алгоритмами. Програмна реалізація числової методики виконана на мові програмування CAD-системи Mathcad та базується на програмному коді для розв’язання тривимірних задач статичної пружності. За допомогою розробленого програмного забезпечення отримано результати числових експериментів під час навантаження внутрішнім тиском товстостінного сталевого циліндра та виконано їх зіставлення з даними числового аналізу, одержаного з використанням програмних продуктів ANSYS Mechanical APDL. Встановлено, що максимальне значення похибки визначення фізичних полів не перевищує 3,62 % за алгоритмом 1 і 1,11 % – за алгоритмом 2., The modern analysis of the scientific publications shows that sometimes the works which are dedicated to the numerical methods of solving the nonlinear elastoplastic problems lack the detailed algorithm description, intermediate calculations helping to obtain the main correlations and formulas. It complicates the coherence and the process of the appropriate program codes development. The given paper is considered as an attempt to solve these issues taking the elastoplastic problems with isotropic hardening as an example. The work is aimed to develop the numerical methodologies using 2 algorithm approaches when solving the nonlinear elastoplastic problem with isotropic hardening. The methodologies are based on the finite elements method. The formulated mathematical model of the elastoplastic problem is based on the mechanical motion balance equation in the incremental formulation using the mechanical model for the material with isotropic hardening according to bilinear law. The used step by step algorithm is based on the elastoplastic dependence between stress and deformation. The algorithm fulfills the condition of finding the intermediate solutions of the problem. The used reverse incremental algorithm is based on the usage of stress in order to find the equivalent plastic deformations using the reverse Euler's method. The numerical model is realized using the programming language of the CAD-system Mathcad and is based on the programming code for solving 3-dimensional problems of the static pressure. The results of the numerical experiments were compared with the application of the designed software with the data analysis obtained with the usage of the programming products of ANSYS Mechanical APDL. The comparison showed violation in the physical fields up to 3,62 % for the algorithm 1 and 1,11 % for the algorithm 2

In sheet metal formingprocess of automotive parts, springback effect is crucial, in particular, foradvanced high strength (AHS) steels. Most structural components of new vehiclesshow very complex shapes that require multi–step forming procedures.Therefore, finite element (FE)simulation has been often used to describe plasticdeformation behavior and springback occurrence of formed metal sheets.Recently, the kinematic hardening Yoshida–Uemorimodel has showed great capability for predicting elastic recovery of material. In this work, the AHSsteel grade JSC780Y wasinvestigated, in which tension–compressiontests were carried out. From resulted cyclic stress–strainresponses, material parameters were identified using different fitting methods.Determined model parameters were firstly verified by using simulations of 1–elementmodel. The most appropriate parameter set was thenobtained. Finally, a Hat-Shape forming test was performed and springback waspredicted and compared with experimental results.

In terms of forming processes with complex stress histories, like operations with drawbeads, the implementation of a kinematic hardening rule can significantly improve the numerical prediction quality. However, the variety of mathematical formulations and the non-standardized identification methodology make a preliminary evaluation of the models with respect to their subsequent application necessary. The use of a cyclic bending test is a very flexible and robust technique to validate material models. In view of the bending-like load distribution during a drawing operation of an open shape, this test allows a process near emulation of the forming history. Within this contribution, the realization of a defined strain history - derived form a deep drawing process with draw beads - is presented. For the high-strength steel HCT780X and the aluminum alloy AA6014-T4 an isotropic hardening rule as well as the extension with a kinematic hardening model according Chaboche and Rousselier are evaluated. The result’s transferability is finally analyzed on basis of the springback calculation of the deep drawing operation.

This paper presents a numerical investigation to describe ratchetting behaviour in rail steel under cyclic rolling-sliding contact state. The study numerically quantifies cyclic plastic strain accumulation in rail material. This study combines the Hertzian contact pressure, longitudinal tangential traction based on Carter's theory and heat flux distribution across the contact patch to simulate the wheel-rail contact problem. In the numerical procedure, the effective loading is translated on the rail surface for twelve wheel passes. Temperature dependent cyclic plasticity material model of Chaboche featuring non-linear kinematic hardening is employed that simulates the ratchetting behaviour of the rail material. Results are extracted in terms of plastic strain and stress-strain response. These results are able to augment the understanding of failure mechanisms in rail material that arise from friction based thermo-mechanical load at the dynamic wheel-rail contact interface. The knowledge evolved can provide useful information to the development and application of rail steels and the development of effective rail maintenance strategies in order to mitigate rail material degradation.

The paper summarizes the strength calculations made for the frame of the Tourist solar-powered vehicle. The peculiarities of the frame manufacture and its main characteristics were considered. Strength calculations were carried out in ANSYS, as it is a versatile software package that offers considerable functionality for core calculations. For the material model, the researchers picked a bilinear plasticity model with kinematic hardening; the plasticity condition was a von Mises criterion. The frame was rigidly fixed to the front wheel and rear suspension mounting points. A static load of 50–250 kg was set to the seat mounting points. According to these results, maximum static load is 172.5, as exceeding it will cause irreversible deformations. Static load capable of causing destabilization and destruction of the frame equals 228 kg. The obtained results mean it is recommendable to reinforce the lower frame in the seat mounting points in order to reduce the frame deflection. This requires either additional reinforcements or altering the frame configuration whatsoever. Further, research is required to find the most optimal solution.

The objective of the present paper emphasizes the investigation of the fatigue strength of materials containing surface defects and the development of a comprehensive analytical model, based on the response surface methodology (RSM), for correlating the interactive and higher-order influences of the various parameters such as the size of the defect, loading, and load ratio on the residual lifetime of these components. Firstly, a 3D-finite element analysis of a specimen containing a surface defect using ABAQUS commercial software is established to (i) simulate the distribution of the stress and the equivalent plastic deformation at the vicinity of the defect and (ii) to predict the fatigue life using the Smith-Watson-Topper SWT model. The non-linear kinematic hardening model, coupled with Lemaitre and Chaboche’s damage model, is used to characterize the material behavior. For this work, we used the experimental design technique to characterize the effects and the interactions between the defect size, the loading and the load ratio given by the Smith Watson Tooper model. Finally, using the surface response method, we have been able to develop an analytical model capable of predicting the fatigue response of steel 1045 considering defect size, loading and load ratio. Consequently, the finding results show a good agreement with those experimentally obtained.

For transmission of high-pressure corrosive fluids, it is required to pipe that with both anti-corrosive and high strength material. One of the economical and reliable approaches is the use of Tight Fit Pipe (TFP). Tight Fit Pipe is a double-walled pipe, where a corrosion-resistant alloy liner is fitted inside a carbon steel outer pipe through a thermal-hydraulic manufacturing process. TFP is manufactured under specified conditions for conducting this research. The most influential parameter to improve these pipes' structural response is the residual stress between the inner and outer pipes. In this study, finite element analysis and experimental method were utilized to calculate residual stress between the inner and outer pipes. A 2D finite-element model was performed in ABAQUS software to simulate the lined pipe with considering the effects of heat on the mechanical properties of the pipes and nonlinear isotropic/kinematic hardening material model. Analytical and experimental (Saw cut) methods were applied to measure residual stresses of two pipes to validate the numerical method's results. By comparing the simulation results with the experimental results, an appropriate agreement has been observed.

Elastoplastic design of process equipment in petrochemical and power generation industries requires the consideration of thermal ratcheting. Classical Bree diagrams assuming no strain hardening have been the basis in most of today's design Codes and Standards, which can be excessively conservative. In this study, three major kinematic hardening models by Pager, Armstrong and Frederick, and Chaboche are considered for modeling detailed thermal ratcheting behaviors and establishing Bree diagrams. It is found that the linear hardening model by Prager provides a reasonable upper bound ratcheting strain estimation while the perfect plastic assumption by Bree is adequate for the design diagram construction.

Present work is aimed at validation of existing popular cyclic plasticity material models and proposing an improved model for SA 333 Gr. 6 material. Recently reported in-house axial-torsion tests have been used for validation. Present analyses considered Chaboche’s non-linear kinematic hardening rule, Tanaka’s fourth order tensor and Meggiolaro’s non-proportionality considerations. The Chaboche-Tanaka-Meggiolaro model resulted in comparable assessments for stabilized loops under uniaxial, proportional and few non-proportional conditions. However, the axial stress response under most of non-proportional conditions was significantly under-predicted. The proposed modification in dynamic recovery term of kinematic hardening rule resulted in improved assessments for nearly all strain paths.

Author(s): Tsampras, G; Sause, R; Fleischman, RB; Restrepo, JI | Abstract: This paper presents experimental and numerical studies of a full-scale deformable connection used to connect the floor system of the flexible gravity load resisting system to the stiff lateral force resisting system (LFRS) of an earthquake-resistant building. The purpose of the deformable connection is to limit the earthquake-induced horizontal inertia force transferred from the floor system to the LFRS and, thereby, to reduce the horizontal floor accelerations and the forces in the LFRS. The deformable connection that was studied consists of a buckling-restrained brace (BRB) and steel-reinforced laminated low-damping rubber bearings (RB). The test results show that the force–deformation responses of the connection are stable, and the dynamic force responses are larger than the quasi-static force responses. The BRB+RB force–deformation response depends mainly on the BRB response. A detailed discussion of the BRB experimental force–deformation response is presented. The experimental results show that the maximum plastic deformation range controls the isotropic hardening of the BRB. The hardened BRB force–deformation responses are used to calculate the overstrength adjustment factors. Details and limitations of a validated, accurate model for the connection force–deformation response are presented. Numerical simulation results for a 12-story reinforced concrete wall building with deformable connections show the effects of including the RB in the deformable connection and the effect of modeling the BRB isotropic hardening on the building seismic response. Copyright © 2016 John Wiley a Sons, Ltd.

This paper proposes a cyclic plasticity model to describe the closure of a cyclic stress-strain hysteresis loop based on the Y-U model. In this model, the backstress moves in a cyclic memory surface following a newly proposed kinematic hardening law. For this model just the same Y-U parameters can be used, and no additional material parameters are needed. By using a supplementary rule, this model is also able to describe ratcheting.

In this work, the nonlinear kinematic hardening combined with Voce isotropic hardening was selected to characterize the material behavior of advanced high strength steel sheet samples subjected to a few reverse loading cycles. Multi-components of backstress were considered for the combined nonlinear kinematical hardening model, namely, one, two, and three backstress components. To calibrate the model, an inverse problem solution tool, so-called virtual fieldsmethod, which takes full advantage of full-field deformation measurement, was applied to identify the material constitutive parameters. First, finite element simulations of forward-reverse simple shear were performed to validate the proposed identification method. The influence of strain noise on the identification accuracy was also evaluated. Then, the proposed method was applied to three kinds of sheet metals (DP600, TRIP780 and TWIP980) tested under two cycles of forward-reverse simple shear for parameter identification. The identification results obtained with different number of backstress components were critically discussed.

The present study evaluates coupled kinematic hardening rules at which the calculation of plastic moduli is coupled with these models through the consistency condition of yield surfaces. The frameworks of the Ohno–Wang (O–W), McDowell, Jiang–Sehitoglu (J–S), Chen–Jiao–Kim (C–J–K) and Ahmadzadeh–Varvani (A–V) hardening rules and their incorporated dynamic recovery terms/coefficients were discussed for steel samples undergoing asymmetric stress cycles. Different hardening rules offered distinct procedures to determine terms/coefficients and to generalize hardening rule descriptions applicable for different materials and loading spectra. The progressive evolution of backstress over plastic deformation was attributed to the interaction of dislocations controlled by the dynamic recovery of the models. The predicted ratcheting curves through the C–J–K and A–V hardening rules closely agreed with ratcheting data of 1045 and 304 steel samples tested at different loading paths. The O–W, J–S and McDowell hardening rules showed some overprediction in ratcheting as compared with experimental data.