Chaboche Model Research Articles

Modeling the Hydrogen Effect on the Constitutive Response of a Low Carbon Steel in Cyclic Loading

Abstract Hydrogen-accelerated fatigue crack growth is a most severe manifestation of hydrogen embrittlement. A mechanistic and predictive model is still lacking partly due to the lack of a descriptive constitutive model of the hydrogen/material interaction at the macroscale under cyclic loading. Such a model could be used to assess the nature of the stress and strain fields in the neighborhood of a crack, a development that could potentially lead to the association of these fields with proper macroscopic parameters. Toward this goal, a constitutive model for cyclic response should be capable of capturing hardening or softening under cyclic straining or ratcheting under stress-controlled testing. In this work, we attempt a constitutive description by using data from uniaxial strain-controlled cyclic loading and stress-controlled ratcheting tests with a low carbon steel, Japanese Industrial Standard (JIS) SM490YB, conducted in air and 1 MPa H2 gas environment at room temperature. We explore the Chaboche constitutive model which is a nonlinear kinematic hardening model that was developed as an extension to the Frederick and Armstrong model, and propose an approach to calibrate the parameters involved. From the combined experimental data and the calibrated Chaboche model, we may conclude that hydrogen decreases the yield stress and the amount of cyclic hardening. On the other hand, hydrogen increases ratcheting, the rate of cyclic hardening, and promotes stronger recovery.

A novel finite element simulation of hot stamping process of DP780 steel based on the Chaboche thermomechanically hardening model

Advanced high-strength steels (AHSS) despite excellent properties with low weight and high strength have the concern of high springback occurrence. The amount of springback can be reduced by hot forming process. In this paper, the influence of temperature rises on the springback quantities generated potentially during a hot stamping process of the DP780 steel is investigated. To obtain a proper description for hardening behavior, a type of the Chaboche thermomechanically constitutive model has been used in conjunction with an anisotropic Yld2000-2D yield criterion. Since the elastic modulus of the AHSS during loading and unloading stages can make considerable influences on the springback, consideration of Young’s modulus as a function of equivalent plastic strain is necessary. Moreover, the process is simulated via ABAQUS software implementing UMAT and VUMAT user-defined subroutines as well as the forward Euler explicit integration scheme is applied to calculate the stress and strain at the end of time increments. The results demonstrate the efficiency of the novel temperature-dependent Chaboche model to predict the level of stresses and temperature during and after hot stamping process.

Ductile tearing simulation of STS410 pipe fracture test under load-controlled large-amplitude cyclic loading: Part II – effect of load amplitude and sequence

As a companion paper of Part I, this paper presents ductile tearing simulation results of STS410 through-wall cracked pipe test data with different amplitudes of load-controlled fully-reversed cyclic loading. The multiaxial fracture strain energy damage model is used with the Chaboche model. The simulated crack growths are not dependent on the ratcheting term in the Chaboche model, but deformations are slightly sensitive. Simulation results suggest that acceleration and retardation behavior in crack growth rates due to the load sequence may not occur under large-amplitude cyclic loading.

Ratcheting behavior of pressurized lateral nozzle of cylinder with local wall thinning under different loading paths

Ratcheting effect of pressurized lateral nozzle of cylinder with local wall thinning is studied using Chaboche model in ANSYS. Firstly, the influence of internal pressure, bending loading, loading path, loading history and the different defect sizes on ratcheting effect of pressurized oblique nozzle with local wall thinning is studied in this study. The results indicate that ratcheting strain increased with the increasing of internal pressure and bending moment and is affected by the different loading paths and loading history. Secondly, the effect of different defect sizes such as defect depth, depth length and defect hoop angle on ratcheting behavior of pressurized oblique nozzle with local wall thinning is studied. The results investigated that ratcheting strain of the lateral nozzle of cylinder with local inside wall thinning under cyclic bending increased with the increasing of defect depth, had no relationship with the increasing of defect length and ratcheting strain of the lateral nozzle of cylinder with local wall thinning under cyclic bending increased with the increasing of defect circumferential angle. Finally, the ratcheting boundary of pressurized lateral nozzle of cylinder with different defect size is determined by linear matching method. The results show that the increase of the defect depth could induce a remarkable increase of the reverse plasticity and the ratchet limits of the component, the defect length has a slight effect on the reverse plasticity and ratchet limits of the component and the increase of the defect circumferential angle could induce a remarkable increase of the reverse plasticity and the ratchet limits of the component.

Inelastic Material Models of Type 316H for Elevated Temperature Design of Advanced High Temperature Reactors

In this paper, the inelastic material models for Type 316H stainless steel, which is one of the principal candidate materials for elevated temperature design of the advanced high temperature reactors (HTRs) pressure retained components, are investigated and the required material parameters are identified to be used for both elasto-plastic models and unified viscoplastic models. In the constitutive equations of the inelastic material models, the kinematic hardening behavior is expressed with the Chaboche model with three backstresses, and the isotropic hardening behavior is expressed by the Voce model. The required number of material parameters is minimized to be ten in total. For the unified viscoplastic model, which can express both the time-independent plastic behavior and the time-dependent viscous behavior, the constitutive equations have the same kinematic and isotropic hardening parameters of the elasto-plastic material model with two additional viscous parameters. To identify the material parameters required for these constitutive equations, various uniaxial tests were carried out at isothermal conditions at room temperature and an elevated temperature range of 425–650 °C. The identified inelastic material parameters were validated through the comparison between tests and calculations.

Fatigue crack growth determination based on cyclic plastic zone and cyclic J‐integral in kinematic–isotropic hardening materials with considering Chaboche model

AbstractFor many materials, plastic deformations under cyclic loadings differ from monotonic loading. Cyclic plastic zone with considering the strain hardening effects becomes complicated during unloading step. In this research, the effects of nonlinear kinematic and isotropic hardening behaviours on the cyclic plastic reaction around the crack tip for different conditions are investigated. For study of various hardening characteristics, as‐received and annealed copper are tested under same symmetric cyclic loadings. The results indicate considerable isotropic hardening behaviour in annealed material. A Chaboche nonlinear hardening model was used to determine the hardening parameters. The cyclic plastic zone around the crack tip in C(T) specimen was measured by back stresses. The cyclic plastic zones are specified via variations of the back stresses in a cycle. The cyclic plastic zones predicted by Chaboche model are smaller than those for Irwin model because of the hardening effects. Also, Irwin model for prediction of the cyclic plastic zone size is modified with considering the cyclic plastic effects. According to the results, the cyclic plastic zone around the crack tip is almost constant in the same load range, and load ratio (R) has a slight effect on this zone. Whereas, for constant load range, cyclic J‐integral (∆J) is different for various R values. For studying of the fatigue crack growth, two parameters of ∆J and cyclic plastic zone area were evaluated. These parameters can apply in fracture mechanics especially in elastic–plastic conditions with considering the cyclic plastic responses.

Experimental investigation and numerical modelling of 3D printed polyamide 12 with viscoplasticity and a crack model at different strain rates

This contribution presents an investigation of strain rate dependent behaviour for selective laser sintered polyamide 12. Two different cases are considered: a strain rate change within tensile loading and a relaxation test incorporating a strain rate change after each holding time section. For the simulation of material behaviour the material model of Bodner-Partom and Chaboche were used. The damage behaviour was considered by the Lemaitre crack model. Thereby it was determined which numerical model is more suitable to reproduce the strain rate-dependent behaviour. Tensile and relaxation tests at constant speeds served as the basis for these investigations.

Computational modeling of viscoplastic polymeric material response during micro-indentation tests

The computational modeling of instrumented indentation tests used to characterize material properties is challenging. It is mainly due to the computational techniques demanded to couple the complex physical mechanisms involved, such as, for example, the time-dependent inelastic material response to loads during contact. Therefore, this work aims to simulate the mechanical response of the poly vinylidene fluoride (PVDF) during a micro-indentation test considering a viscoplastic material model, and a prescribed load approach, using the finite element method. Further, model validation is performed based on experimental data measured during the contact between the indenter and the PVDF. Numerical analyses were performed using COMSOL Multiphysics finite element software considering the loading scheme of the experimental tests of 800 mN/min rate during loading and unloading, and a 400 mN constant load, held by 30 s. Finally, a viscoplastic Chaboche constitutive model is presented considering two cases: (1) a perfectly plastic behavior, and (2) a nonlinear isotropic hardening behavior based on Voce and Hockett–Sherby exponential laws. While the latter models exhibit some discrepancy in capturing the experimental behavior, the former one has shown excellent agreement with the load-depth curves obtained experimentally, achieving the best fitting for the set of Chaboche parameters: $$A=1\,{\mathrm{{s}}}^{-1}, {n}=4.62$$ and $$\sigma _\mathrm{{ref}}=132$$ MPa. Moreover, several phenomenological features of viscoplastic behavior such as rate dependence, plastic flow (or creep) and stress relaxation were accurately provided by the Chaboche model when describing the behavior of the PVDF material.

Optimization procedure for parameter determination of caboche kinematic hardening model

The ratcheting behavior and prediction of 316L stainless steel pipe was developed using numerical finite elementapproach. The Chaboche model parameters to be used in the numerical method were adopted from symmetric post monotonic teston the pipe. The significant property, the elastic limitof the material,was extracted using incremental cyclic uniaxial test. Comparison between two well-known optimization methods, Particle Swarm Optimization and Genetic Algorithm gave the former a slightly better correlation with experimental tests.The Chaboche model in ANSYS was utilized to predict the uniaxial ratcheting behavior of the pipe specimen. Theclose comparison of rate of ratcheting between finite element simulation and experimental test indicates that accurate elastic limit extraction from post monotonic test alone results in improved ratcheting prediction, with PSO method adopted to optimize ratcheting parameters.

Effects of Dwell Time on the Deformation and Fatigue Behaviour of A356-T7 Cast Aluminium Alloys Used in High Specific Power IC Engine Cylinder Heads.

The electrification of automotive powertrains in recent years has been driving the development of internal combustion engines towards reduced volumes with higher power outputs. These changes place extreme demands on engine materials. Engineers employ the computer-aided engineering approach to design reliable and cost-effective engines. However, this approach relies on accurate knowledge of the material deformation and fatigue characteristics during service-like loading. The present study seeks to investigate the effect of dwell times on the deformation and fatigue behaviour of the A356-T7 + 0.5 wt.% Cu alloy used to cast cylinder heads. In particular, we study the effect of dwell time duration at various temperatures. A combined fatigue-dwell testing procedure, with the dwell at the maximum compressive strain, replicates the service conditions. It is found that the material exhibits a stress relaxation behaviour with a decreasing relaxation rate. At lower temperatures, the load level influences the relaxation more than at elevated temperatures. However, the dwell does not significantly affect the hardening behaviour or the life of the tested alloy. Finally, we model the time-dependent material behaviour numerically. The Chaboche model, combined with a Cowper–Symonds power-law, is found to capture the visco-plastic deformation behaviour accurately.

The application of Chaboche model in uniaxial ratcheting simulations

Abstract This article presents the application of Chaboche nonlinear kinematic hardening model in simulations of uniaxial ratcheting. First, the symmetrical strain-controlled cyclic tension/compression tests for PA6 aluminum samples were done. Using the experimental stress–strain curve, initial material hardening parameters were determined by the ABAQUS software. The experimental curve was compared with the numerical one. For better fitting of both curves, the optimization procedure based on the least-square method was applied. Using the determined hardening parameters, numerical simulations of the ratcheting were done by the finite element analysis software. Numerical results were then compared with the experimental data obtained in the stress-controlled cyclic loading test.

Ratcheting assessment of low yield point steel BLY160: Experimental analysis and constitutive modelling

In this study, the ratcheting behaviour of low-yield-point steel BLY160 is evaluated via experimental investigation and constitutive modelling. A set of uniaxial asymmetrical cyclic loading tests in the strain- and stress-controlled modes is conducted to analyse the ratcheting response and stress relaxation, respectively. The effect of cyclic hardening and dependence on loading path are discussed to characterize the ratcheting behaviour. BLY160 steel is observed to exhibit a multi-stage evolution of ratcheting response with a significant cyclic hardening effect. However, the traditional Chaboche model calibrated according to the symmetric cyclic straining tests is observed to overestimate the cyclic hardening when predicting ratcheting, and might lead to an elastic shakedown under asymmetric cyclic stressing simulation. To overcome this disadvantage, a modified model based on the combined hardening rule is proposed; which introduces a new internal variable to distinguish the strain hardening under different loading paths. Hence, the interaction between the cyclic hardening and ratcheting behaviour can be accurately described. The accuracy of the modified model is validated by the close agreement between the simulation results and the experimental responses. The results verify that the proposed model is capable of simulating cyclical hardening, ratcheting, and stress relaxation behaviours for the test cases.

Cyclic loading tests on welded connections of stainless-clad bimetallic steel and modelling

Bimetallic steel is an advanced high-performance (HP) laminated steel that may balance well performance against production cost, and has great potential for practical use in structural engineering, particularly for stainless-clad (SC) ones. Welding is the most important connection technique for fabrication of such steel members because preparation of holes within the steel plate for mechanical fasteners may expose the substrate and thus destroy the corrosion resistance. The present paper aims to clarify mechanical performance of butt welded connection of the SC bimetallic steel that requires special welding configurations, particularly under seismic loadings. The butt welded connections are firstly tested for welding procedure qualification. Based on subsequent monotonic and cyclic test results, failure modes are clarified, and their mechanical properties are analysed in terms of cyclic and envelop curves. It is indicated that welded connections of the SC bimetallic steel plate are adequate for structural usage under earthquake; their cyclic hardening effects are remarkable, and the envelop curves can be well described by using the Ramberg-Osgood (R-O) model. An adapted cyclic constitutive model based on the Chaboche model is proposed with parameters being determined through non-linear fitting of cyclic test results, and its accuracy and adequacy are verified. Additionally, the butt welded connections exhibit more significant isotropic and kinematic hardening effects compared with the SC bimetallic steel plate. Research findings herein provide important evidence for adequacy of the SC bimetallic steel welded connections applied in seismic regions, and also provide accurate constitutive models for predicting their cyclic behaviour.

Uniaxial and biaxial ratcheting behavior of pressurized AISI 316L pipe under cyclic loading: Experiment and simulation

Ratcheting defined as the progressive accumulation of plastic strain occurring during cyclic loading in the presence of the mean stress is one of the most prevalent failure modes in engineering structures. Experimental studies were conducted to characterize the uniaxial and biaxial ratcheting responses of an AISI 316L pipe. Experimental results show that an obvious cyclic hardening occurs in the AISI 316L pipe under uniaxial strain loading. Uniaxial ratcheting rate obtained from the axial cyclic experiment reaches a quasi-steady rate after a certain number of loading cycles. Moreover, using a designed four-point bending experimental setup, different axial stress amplitudes in the presence of the constant hoop stress were considered to characterize the biaxial ratcheting response of the material. The ratcheting strain and ratcheting strain rate in the hoop direction increase with increasing axial stress amplitudes under the constant hoop stress. To simulate the uniaxial and biaxial ratcheting behavior of the AISI 316L pipe, the Chaboche nonlinear kinematic hardening model was used. Using the Particle Swarm Optimization (PSO) technique, parameters of the Chaboche model were identified efficiently from the monotonic response of a cold-worked sample. The elastic limit of the material was measured using a very careful quasi-static cyclic compression experiment. The procedure to calibrate the material parameters for the Chaboche model and finite element simulation results were validated well with experimental data for the AISI 316L pipe. It is shown that the Chaboche model with the suitably-calibrated parameters from the experimental study can be applied to rigorously predict the ratcheting behavior of the AISI 316L pipe under cyclic uniaxial and biaxial loading conditions.

Extremely - low cycle fatigue fracture of Q235 steel at different stress triaxialities

This study presents an experimental and numerical investigation on the Extremely-Low Cycle Fatigue (ELCF) behavior of Q235 structural steel under different stress states and large strain amplitudes. A set of Q235 structural steel cylindrical specimens of different radii of curvature were selected to examine the effect of the triaxial state of stress on the fracture behavior. Cyclic axial tension-compression loading tests characterized by large strain amplitudes were conducted to obtain the hysteresis loops and the failure process by measuring both macroscopic and microscopic fracture morphologies. The results shows that, the failure behavior of Q235 steel in ELCF loading is a mixture of fatigue fracture and ductile fracture. Specimens with different stress triaxialities are characterized by different failure modes. A fracture criterion, namely the Combinatory Work Density Model (CWDM), was calibrated based on the test results. Furthermore, a cyclic plasticity constitutive model, i.e., the Chaboche model, was calibrated to describe the yield and cyclic hardening behaviors of the Q235 structural steel. Finite element (FE) simulations in the commercial software ABAQUS accounting the calibrated CWDM and Chaboche model were carried out to evaluate the fracture characteristics with different stress triaxialities and their stress-strain hysteretic curves under ELCF loading. The simulation results demonstrate that the developed FE model can reproduce the hysteretic characteristics and capture the failure process of Q235 structural steel. The proposed practical numerical tool can be used for the ELCF failure prediction in steel structures under complex stress state.

Investigation of Anisotropic Subsequent Yield Behavior for 45 Steel by the Distortional Yield Surface Constitutive Model.

The subsequent anisotropic yield behavior of 45 steel was predicted by the distortional yield surface constitutive model, which can describe the anisotropic subsequent yield and the cross effect of metal associating with loading history. The yield characteristics and plastic hardening behaviors of the 45 steel were simulated under three preloading paths including pre-torsion, pre-tension, and pre-tension–torsion. Based on the comparison between the experimental yield stresses and the simulation by the classical Chaboche model, the proposed model can describe the remarkable anisotropic yield behavior related to the loading history, which can effectively describe the sharp point of yield surface in pre-loading direction and the smaller curvature near its opposite direction. It was successfully simulated by the constitutive model proposed that the subsequent distortional yield surface defined by small offset strain and the degradation process of the distortion feature defined by large offset strain.

Fatigue–Creep Interaction of P92 Steel and Modified Constitutive Modelling for Simulation of the Responses

Fatigue–creep interaction (FCI) responses of P92 steel are investigated experimentally and numerically. A series of isothermal FCI experiments with tensile dwell time ranging from 60 to 600 s were conducted at two temperatures under strain-controlled trapezoidal waveform. The experimental responses demonstrate that the peak stress is influenced by temperature and dwell time. In other words, creep-mechanism-influenced stress relaxation during dwell time influences the peak stress and fatigue life (Nf). In addition, effects of strain range on peak stress and fatigue life under fatigue–creep loading are evaluated. Towards developing a simulation-based design methodology for high temperature components, first a conventional unified constitutive model is evaluated against the P92 steel experimental responses. Based on the simulation deficiency of the conventional model, a modified static recovery term incorporated in the kinematic hardening rule is proposed and satisfactory simulations of the P92 steel FCI responses are demonstrated. The experimental responses of P92 steel and strengths and deficiencies of the conventional and modified Chaboche models are elaborated identifying the important FCI phenomena and progress in constitutive model development for FCI response simulation.

Theoretical and experimental analysis of relation between entropy and tension–compression fatigue of aluminum 6061-T6

Fatigue life is one of the key parameters in investigating the elements which are under cyclic loading. It is known that during the fatigue loading, temperature of the specimen increases due to hysteresis heating which is referred to as the fatigue entropy. It has been also proven that when a metal experiences cyclic loading, the entropy at the failure point has a constant value. This research contains both analytical and experimental parts. A series of axial fatigue test are conducted on aluminum alloy 6061-T6 specimen, and temperature evolution is obtained under the fully reversed tension–compression cyclic loading. The variation of temperature in the material during loading is then used to compute the fatigue fracture entropy of the material. Then, the number of cycles to failure is calculated by using the relation between entropy and fatigue life. An empirical relation from tension–compression fatigue loading is derived which can link the temperature rise rate at the initial stage of the test with the number of cycles to failure. In the analytical part, the commercial finite-element software is used to find the temperature evolution under the fully reversed tension–compression cyclic loading by elastic plastic finite-element analysis. A combined hardening model of Chaboche is applied for estimating the material parameters. The comparison between the theoretical and experimental results is shown and discussed.

Tests and modelling on cyclic behaviour of stainless-clad bimetallic steel

In order to study the constitutive relation of stainless-clad (SC) bimetallic steel under earthquake actions, tests of 23 specimens prepared from 316L+Q235B SC bimetallic steel plate with a nominal thickness of 3 + 5 mm are carried out, in which tensile and compressive monotonic loadings as well as 15 different cyclic loading spectrums are incorporated. Based on the test results, monotonic and hysteretic behaviour, macro- and micro-failure characteristics are analysed. Through comparison and analyses, it is indicated that the envelope curves of the SC bimetallic steel under cyclic loadings are markedly higher than the monotonic tensile curves, which demonstrates that the cyclic hardening effect is significant. Both isotropic and kinematic hardening characteristics are observed, i.e. the cyclic behaviour of the SC bimetallic steel exhibits a typical combined hardening effect. In addition, it is found that envelope curves of the SC bimetallic steel may be described well by using the Ramberg-Osgood (R-O) three-parameter model, of which the parameters are updated though nonlinear fitting of the test data. To develop a constitutive model for simulating the cyclic behaviour of the SC bimetallic steel, the Chaboche plastic constitutive model is employed herein, and its relevant parameters are updated and calibrated. By using the adapted Chaboche model in finite element (FE) analyse through ABAQUS, the cyclic behaviour of all the test specimens are simulated. It is found that the simulated curves obtained from the FE model results agree well with the test curves, which demonstrates that the constitutive model proposed herein is adequate for evaluating the cyclic responses of the SC bimetallic steel. The research outcomes may provide an important basis for accurate analyses of structures fabricated from the SC bimetallic steel under earthquake actions.

Calibration of Chaboche Combined Hardening Model for Large Strain Range

Variable-loading path and large strain are two typical features in multistage plastic forming process. Material’s yield surface expands and translates simultaneously as the loading path changes, leading to certain transient phenomena such as Bauschinger effect. Chaboche combined hardening model is widely used in this kind of simulation due to its capability of characterizing the movement and expansion of yield surface. This study provides a parameter calibration method for Chaboche combined hardening model with 3 back stresses in a large strain range. Uniaxial tension-compression cyclic test with constant strain control was conducted for calibrating the Chaboche model firstly. Meanwhile, the flow curve obtained from uniaxial tension test (UT) associated with Swift extrapolation model were employed to provide the stress-strain relation at large strain level. Then, both theoretical analysis and optimal fitting using NSGA-II were used to determine the parameters in Chaboche model by using the data from the small strain cyclic test and the extrapolated UT curve at large strain simultaneously. The calibration result shows a good match with the experimental and extrapolated data, proving the efficiency of the parameter determination manner put forward in this study.