Cyclic Plasticity Model Research Articles

Damage-coupled ratcheting behaviors of SA508 Gr.3 steel at room and elevated temperatures: Experiments and simulations

A series of experiments subjected to uniaxial and non-proportionally multiaxial cyclic loadings were performed to investigate the ratcheting responses of SA508 Gr.3 steel at room and elevated temperatures. The influences of different stress levels and nonproportional loading paths on the damage-coupled ratcheting responses were discussed. From experimental results, cyclic softening characteristic and dynamic strain aging can be observed under cyclic loadings. Moreover, the steel exhibits an obvious nonproportional path-dependence of the damage evolution under multiaxial loading paths. To numerically simulate the ratcheting responses under uniaxial and multiaxial loadings with the extended cyclic plastic model, the damage-coupled variable was introduced into the classic isotropic and nonlinear kinematic hardening rules. Corresponding material parameters could be calibrated from experimental data, and comparisons between experimental and simulated results were performed to validate the proposed model.

Stability of immersed tunnel in liquefiable seabed under wave loadings

This paper presents a robust modeling method for fully coupled effective stress analyses of wave–induced liquefaction scenarios around immersed tunnels. The method is based on the Biot consolidation theory, and special emphasis is placed on modeling the high–strain behavior of the liquefiable seabed and the evolving boundary conditions at the tunnel–seabed interface. Motivated by the experimental results, the existing Masing model is extended to the high–strain regime in the cyclic plasticity framework to capture the liquefaction–induced nonlinear behavior of the sand. In particular, a newly–observed shear–volume coupling model is implemented into plastic flow rule to realize volumetric compaction by cyclic shearing and exercise as the source term for residual excess pore pressure accumulation in the Biot’s equation. Subsequently, the proposed cyclic plasticity model is implanted into an explicit time matching finite difference analysis platform, permitting a comprehensive simulation of the intensive response of the immersed tunnel in the seabed experiencing the excess pore pressure accumulation and residual liquefaction. Moreover, a model calibration procedure is presented based on the cyclic laboratory sample test data and prescribed loading paths. Finally, the liquefaction–induced uplift of an immersed tunnel under progressive wave action is studied numerically. The obtained results provide the cause of liquefaction and the resulting consequences for tunnel uplift in ocean wave environments.

Towards Deterministic Computation of Internal Stresses in Additively Manufactured Materials under Fatigue Loading: Part I.

The ongoing studies of the influence of internal defects on fatigue strength of additively manufactured metals adopted an internal crack or notch-like model at which the threshold stress intensity factor is the driving mechanism of fatigue failure. The current article highlights a shortcoming of this approach and offers an alternative based on X-ray microcomputed tomography and cyclic plasticity with a hybrid formulation of Chaboche and Armstrong–Frederick material laws. The presented tessellation and geometrical transformation scheme enabled a significantly more realistic morphological representation of internal defects that yielded a cyclic strain within 2% of the experimental values. This means that cyclic plasticity models have an accurate prediction of mechanical properties without repeating a full set of experiments for additively manufactured arbitrary microstructures. The coupling with a material law that is oriented towards the treatment of cyclic hardening and softening enabled more accurate computation of internal stresses under cyclic loading than ever before owing to the maturity of tessellation and numerical tools since then. The resulting stress–strain distributions were used as input to the Fatemi–Socie damage model, based on which a successful calculation of fatigue lifetime became possible. Furthermore, acting stresses on the internal pores were shown to be more than 450% concerning the applied remote stress amplitude. The results are a pretext to a scale bridging numerical solution that accounts for the short crack formation stage based on microstructural damage.

Plasticity modeling for a metastable austenitic stainless steel with strain-induced martensitic transformation under cyclic loading conditions

In the present paper, the strain-induced martensitic transformation and the cyclic plasticity model of a metastable austenitic steel AISI 348 under multi-axial cyclic loadings were studied. Cyclic loading tests under different stress triaxialities and strain amplitudes were carried out and used to verify the material model. Based on the Santacreu model, a kinetics model for evolution of martensitic transformation under multi-axial cyclic loading conditions was obtained by defining a threshold of equivalent plastic strain for phase transformation. The model can degenerate into a simplified form to describe strain-induced martensite evolution under monotonic loadings. The prediction of martensite content by the model matched well with experiments. By correlating the effect of martensitic transformation into isotropic hardening, a modified Ohno–Wang model was obtained and verified. The stress–strain response along the different loading paths and histories was well described by the introduced model.

Strain Range Dependent Cyclic Hardening of 08Ch18N10T Stainless Steel-Experiments and Simulations.

This paper describes and presents an experimental program of low-cycle fatigue tests of austenitic stainless steel 08Ch18N10T at room temperature. The low-cycle tests include uniaxial and torsional tests for various specimen geometries and for a vast range of strain amplitude. The experimental data was used to validate the proposed cyclic plasticity model for predicting the strain-range dependent behavior of austenitic steels. The proposed model uses a virtual back-stress variable corresponding to a cyclically stable material under strain control. This internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. A modification is presented that enables the cyclic hardening response of 08Ch18N10T to be simulated correctly under torsional loading conditions. A comparison is made between the real experimental results and the numerical simulation results, demonstrating the robustness of the proposed cyclic plasticity model.

An Isotropic Model for Cyclic Plasticity Calibrated on the Whole Shape of Hardening/Softening Evolution Curve

This work presents a new isotropic model to describe the cyclic hardening/softening plasticity behavior of metals. The model requires three parameters to be evaluated experimentally. The physical behavior of each parameter is explained by sensitivity analysis. Compared to the Voce model, the proposed isotropic model has one more parameter, which may provide a better fit to the experimental data. For the new model, the incremental plasticity equation is also derived; this allows the model to be implemented in finite element codes, and in combination with kinematic models (Armstrong and Frederick, Chaboche), if the material cyclic hardening/softening evolution needs to be described numerically. As an example, the proposed model is applied to the case of a cyclically loaded copper alloy. An error analysis confirms a significant improvement with respect to the usual Voce formulation. Finally, a numerical algorithm is developed to implement the proposed isotropic model, currently not available in finite element codes, and to make a comparison with other cyclic plasticity models in the case of uniaxial stress and strain-controlled loading.

Modeling the Strain-Range Dependent Cyclic Hardening of SS304 and 08Ch18N10T Stainless Steel with a Memory Surface

This paper deals with the development of a cyclic plasticity model suitable for predicting the strain range-dependent behavior of austenitic steels. The proposed cyclic plasticity model uses the virtual back-stress variable corresponding to a cyclically-stable material under strain control. This new internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. First, the proposed model was validated on experimental data published for the SS304 material (Kang et al., Constitutive modeling of strain range dependent cyclic hardening. Int J Plast 19 (2003) 1801–1819). Subsequently, the proposed cyclic plasticity model was applied to our own experimental data from uniaxial tests realized on 08Ch18N10T at room temperature. The new cyclic plasticity model can be calibrated by the relatively simple fitting procedure that is described in the paper. A comparison between the results of a numerical simulation and the results of real experiments demonstrates the robustness of the proposed approach.

New formulation of nonlinear kinematic hardening model, Part II: Cyclic hardening/softening and ratcheting

The second part of the study presents development of the Dirac delta functions framework to modelling of cyclic hardening and softening of material during cyclic loading conditions for the investigated in Part I low carbon S355J2 steel. A new criterion of plastic strain range change is formulated. This provides more certainty in the cyclic plasticity modelling framework compared to classical plastic strain memorization modelling. Two hardening parameters from the developed kinematic hardening rule are written as functions of both plastic strain range and previously accumulated plastic strain. This representation of hardening parameters is able to accurately match experimental results with different types of loading programs including random loading conditions and considering initial monotonic behaviour with yield plateau deformation. Ratcheting behaviour is simulated by the developed cyclic plasticity framework by considering an approximated form of the Dirac delta function for modelling the deviation effect and introducing an additional supersurface for better prediction of ratcheting rate. The proposed cyclic plasticity model requires up to 21 material constants, depending on application. A clear and straightforward calibration procedure, where sets of material constants are determined for each plasticity phenomenon considered, is presented. Application of the model to different materials under various tension-compression and non-proportional axial-torsion cycles shows very close agreement with test results.

Low-Cycle-Fatigue (LCF) behavior and cyclic plasticity modeling of E250A mild steel

A series of strain-controlled fully-reversed uni-axial tension-compression Low-Cycle-Fatigue (LCF) tests are carried out on IS 2062:E250A (Fe410W-A) mild steel specimens with strain amplitudes upto ±1.2%, to study the cyclic in-elastic material behavior. Accordingly, parameters of Cyclic-Stress-Strain (CSS) and Basquin-Coffin-Manson relationships are derived using the LCF test results. Further, the calibration of Non-Linear Combined (isotropic-kinematic) Hardening Material (NLCHM) model of cyclic plasticity is illustrated based on the experimental hysteresis response data. Finally, the efficiency of the calibrated NLCHM model parameters is substantiated by accurately simulating the material response from the tests conducted, using a non-linear FE software, Abaqus.

Considering cyclic plasticity to predict residual stresses in laser cladding of Inconel 718 multi bead samples

A thermo-mechanical finite element model is developed to accurately predict residual stresses of the multiple beads laser cladding process, incorporating the cyclic plasticity into the analysis by utilizing the nonlinear kinematic hardening behavior. Finite Element results are presented for Inconel 718, a material for which the laser cladding process is widely used. The FE results are compared with the results of incremental center hole drilling conducted on three specimens with different clad beads to evaluate the effect of cyclic plasticity modeling on the residual stresses. The results indicate that incorporating the nonlinear kinematic hardening model into the analysis can reduce the difference between its estimated residual stresses and the experimental results by about fifty percent comparing with the analyses without considering the kinematic hardening. The results also indicate that the nonlinear cyclic plasticity modeling provides the opportunity to capture important phenomena of hardening and stress relaxation in the laser cladding process.

Evaluation of a phenomenological elastic‐plastic approach for magnesium alloys under multiaxial loading conditions

AbstractMagnesium alloys are greatly appreciated due to their high strength to weight ratio, stiffness, and low density; however, they can exhibit complex types of cyclic plasticity like twinning, de‐twinning, or Bauschinger effect. Recent studies indicate that these types of cyclic plastic deformations cannot be fully characterized using the typical tools used in cyclic characterization of steels and aluminium alloys; thus, it is required new approaches to fully capture their cyclic deformation and plasticity. This study aims to propose and evaluate a phenomenological cyclic elastic‐plastic approach designed to capture the cyclic deformation of magnesium alloys under multiaxial loading conditions. Series of experimental tests were performed to characterize the cyclic mechanical behaviour of the magnesium alloy AZ31BF considering proportional loadings with different strain amplitude ratios and a nonproportional loading with a 45° phase shift. The experimental results were modulated using polynomial functions in order to implement a cyclic plasticity model for the AZ311BF based on the phenomenological approach proposed. Results show good correlations between experiments and estimates.

Fretting wear modelling incorporating cyclic ratcheting deformations and the debris evolution for Ti-6Al-4V

Abstract In the fretting wear process, wear particles are referred to as the third-body flow in the contact region. During cyclic slip motions, a part of particles are ejected out of the contact region after a certain number of fretting cycles. The rest particles are attached to contact surfaces and consolidated to form a debris layer, which plays an important role in the fretting wear process. In the present work, a fretting wear model incorporating the evolution of the debris layer is proposed within the framework of finite element analysis to predict the wear profile under different fretting conditions. In order to describe the evolution of the debris layer, the dynamic volume fraction of ejected particles is related to the accumulation of trapped debris volume. Furthermore, the Ohno–Wang cyclic plasticity model is employed to describe the cyclic plastic deformation of Ti-6Al-4V alloy. The major contribution of the present work is to study the influence of the accumulative ratcheting deformation and debris layer on the wear profile. Different wear configurations are considered in the simulations to validate the predictive ability of the proposed wear model. The simulation results show that the proposed approach is able to provide a reasonable prediction of the wear profiles in different wear configurations.

Prediction of plastic deformation and wear in railway crossings – Comparing the performance of two rail steel grades

Railway crossings are subjected to a severe load environment leading to damage and degradation of rail profiles. The damage is the result of the high magnitudes of contact pressure and slip generated in the wheel–rail contacts during each wheel transition between wing rail and crossing nose. In this paper, numerical predictions of the long-term accumulation of plastic deformation and wear are presented and compared for two rail grades used in crossings. The comparison is performed using a framework that includes simulations of dynamic vehicle–track interaction, wheel–rail contact and rail damage. A load sequence generated by means of Latin hypercube sampling, taking into account variations in worn wheel profile, vehicle speed and wheel–rail friction coefficient, is considered. A Hertzian-based metamodel for wheel–rail normal contact accounting for inelastic material response is used for the simulation of wheel–rail contact. The methodology is demonstrated by calculating the plastic deformation for one cross-section of the crossing nose using an Ohno-Wang cyclic plasticity model, while wear is predicted by means of the Archard model for sliding wear. For the studied conditions and after the simulation of 41400 load cycles, representing an accumulated traffic load of 0.8 MGT, it is concluded that the fine-pearlitic rail grade R350HT experiences half of the ratchetting strain compared to the austenitic hot-rolled manganese steel Mn13. Based on a wear model calibrated for Mn13, the maximum wear of the studied cross-section is about 2% of the maximum plastic deformation.

Cyclic Fractional Plastic Model for Granular Soils

Granular soils, e.g., sand, ballast and rockfill, usually experience dynamic loads in the field. Traditional constitutive models for monotonic loading conditions cannot be used for advanced characterisation of the complex loading behaviour of granular soils. In this study, a simple fractional plastic model is developed, based on the generalized fractional plastic flow rule which considers the loading and unloading differences under triaxial compression and extension conditions. The model is further validated against a series of cyclic loading behaviour of different granular soils, where a good predicting performance is observed.

Automated calibration of advanced cyclic plasticity model parameters with sensitivity analysis for aluminium alloy 2024-T351

The plasticity models in finite element codes are often not able to describe the cyclic plasticity phenomena satisfactorily. Developing a user-defined material model is a demanding process, challenging especially for industry. Open-source Code_Aster is a rapidly expanding and evolving software, capable of overcoming the above-mentioned problem with material model implementation. In this article, Chaboche-type material model with kinematic hardening evolution rules and non-proportional as well as strain memory effects was studied through the calibration of the aluminium alloy 2024-T351. The sensitivity analysis was performed prior to the model calibration to find out whether all the material model parameters were important. The utilization of built-in routines allows the calibration of material constants without the necessity to write the optimization scripts, which is time consuming. Obtaining the parameters using the built-in routines is therefore easier and allows using the advanced modelling for practical use. Three sets of material model parameters were obtained using the built-in routines and results were compared to experiments. Quality of the calibration was highlighted and drawbacks were described. Usage of material model implemented in Code_Aster provided good simulations in a relatively simple way through the use of an advanced cyclic plasticity model via built-in auxiliary functions.

Experimental and Numerical Investigations of Cyclic Plastic Deformation of Al-Mg Alloy

In this work, low-cycle fatigue (LCF) tests are performed on as-received and solution-treated Al-Mg alloy (AA 5754). Solution heat treatment of the as-received alloy is performed at 530 °C for 2 h and then quenched in water at room temperature. The low-cycle fatigue response of the as-received and solution-treated alloy is evaluated at five different strain amplitudes from 0.2 to 0.6%. The strain rate of 0.5 × 10−3 s−1 is kept constant in all the LCF tests. The LCF behavior of AA 5754 is modeled by finite element method (FEM) using Chaboche kinematic hardening cyclic plasticity model. Hardening behavior or fatigue life of as-received and solution-treated alloy is successfully simulated using this model. The results obtained by FEM simulations are compared with those obtained by LCF experiments. Microstructural studies are also performed for as-received and solution-treated alloy. The fracture surfaces obtained from LCF tests are analyzed by scanning electron microscopy.

The Anisotropic Distortional Yield Surface Constitutive Model Based on the Chaboche Cyclic Plastic Model.

Considering the cross effect in the evolution of subsequent yield surfaces for metals, an anisotropic distortional yield surface constitutive model is developed. By introducing an anisotropic distortional hardening function into the isotropic hardening part of the classical Chaboche rate-dependent constitutive model, the plastic-deformation-induced distortional and anisotropic hardening behaviors of subsequent yield surfaces are characterized. The experimental data of distortional yield surfaces for T2 pure copper under three different loading paths, including pre-tension, pre-torsion, and pre-tension-torsion proportional loading of 45-degree, are simulated by implementing the models into a numerical user defined material (UMAT) procedure based on the ABAQUS finite element package. To validate the anisotropic plastic model, the simulated yield surfaces are compared with experimental observations and predicted results for a crystal plasticity model and good agreement are noted. The simulations demonstrate that the proposed model can accurately capture the characteristics of the distortional yield surface and the anisotropic hardening process of the yield surface. Moreover, the distortional shapes of experimental subsequent yield surfaces in loading direction and opposite direction can be better revealed by the anisotropic plastic constitutive model than the crystal plastic constitutive model.

Cyclic mean stress relaxation behaviour of P91 steel: Experiments and constitutive modeling

In the present study effect of mean strain on cyclic plastic deformation characteristics of P91 steel is experimentally evaluated and compared with results of finite element simulation considering cyclic plasticity models. P91 steels being used in various components in fossil fired and nuclear power plants are subjected to cyclic loading with mean strains/stresses. Symmetrical and asymmetrical strain controlled tests of P91 steel conducted at room temperature revealed cyclic softening nature during the fatigue cycling process. The influence of mean strain imposed showed strong dependence on stress relaxation behavior and fatigue life of P91 steel. Tensile mean stress was found to relax steeply in initial cycles followed by stabilization during the asymmetric strain cycling. A reduction in fatigue life is observed with increase in mean strain for particular strain amplitude. An attempt has also been made to simulate asymmetric strain controlled behavior of P91 steel through cyclic plastic modeling in the framework of rate independent plasticity theory. Ohno-Wang material model is employed to predict the influence of mean strain on stress relaxation behavior of the investigated steel. The simulated results depicted that Ohno-Wang model captures the cyclic plastic deformation behavior of P91 steel reasonably well.

Basic Kinematic Hardening Rules Applied to 304 Stainless Steel and the Advantage of Parameters Evolution

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.

Experimental and numerical investigations of low cycle fatigue behavior of cryorolled AA 5754

The objective of the present work is to study the influence of cryogenic forming on low cycle fatigue (LCF) properties of Al-Mg (AA 5754) alloy. AA 5754 is rolled at liquid nitrogen temperature (cryorolling) for maximum of 40% thickness reduction. Post-annealing heat treatment (PAHT) at 250oC for 2 hours is adopted to enhance the mechanical and fatigue properties of the cryorolled alloy. A series of uniaxial strain controlled LCF tests are executed at three different strain amplitudes from 0.4% to 0.6% for cryorolled (CR) and annealed cryorolled (ACR) AA 5754 alloy. PAHT significantly improves the tensile strength as well as ductility of CR alloys. LCF tests reveal that cryorolled alloys show mild hardening in the initial cycles followed by noticeable cyclic softening at all strain amplitudes. In contrast, only cyclic hardening behavior is depicted by ACR specimens at all strain amplitudes. The extended finite element method (XFEM) has been utilized to simulate the tensile behavior of the specimen. Finite Element Method (FEM) coupled with Chaboche kinematic hardening cyclic plasticity model is used for simulating hysteresis loop obtained during LCF test. The present study exhibits good match between simulations and experimental results.