Chaboche Model Research Articles

Cyclic mechanical response of LPBF Hastelloy X over a wide temperature and strain range: Experiments and modelling

Additive manufacturing (AM) of high-temperature alloys through processes such as laser powder bed fusion (LPBF) has gained significant interest and is rapidly expanding due to its exceptional design freedom, which enables the fabrication of complex parts that contribute to the increased efficiency of aerospace and energy systems. The materials produced through this process exhibit unique microstructures and mechanical properties, which necessitate dedicated study and characterization. In this context, our research focuses on the experimental characterization of the isothermal cyclic viscoplastic mechanical response of Hastelloy X (HX) over the temperature range of 22 to 1000 °C and at various strain rates, addressing a current gap in the literature. Recognizing the need for material models that can accurately represent the cyclic mechanical response of LPBF HX across a broad temperature range, we developed a robust extension of the viscoplastic isotropic-kinematic hardening Chaboche model, intended for applications in the thermomechanical simulation of the LPBF process for the analysis of residual stress and distortion, as well as for assessing the mechanical integrity of LPBF components. The extension involves expressing the entire set of model parameters explicitly with analytical functions to account for their temperature dependence. Consequently, the model includes a relatively large number of parameters to represent the isotropic-kinematic hardening viscoplastic response of the alloy over a wide temperature range, and hence to overcome the endeavor of its systematic calibration, a dedicated calibration approach was introduced. The model ultimately demonstrated its capability to precisely represent the isothermal response of the alloy over the examined temperatures and strain rates. To evaluate the model’s predictiveness for non-isothermal conditions, out-of-phase thermomechanical cyclic experiments were also conducted as independent benchmark tests, where the model’s predictions were fairly consistent with the experimental results. As a part of this study, the derived material model has been integrated into the UMAT subroutine, complete with an analytical derivation of the consistent Jacobian matrix.

Advanced cyclic constitutive model and parameter calibration method for austenitic stainless steel

Austenitic stainless steel is recognized for its potential in improving structural seismic resistance due to its exceptional ductility. This study seeks to analyse the material characteristics and cyclic constitutive model of austenitic stainless steel under cyclic loading using a combination of experiments and numerical studies. The primary goal is to enhance the precision of numerical simulations predicting the seismic performance of stainless steel and to minimize the costs associated with calibrating the parameters of the cyclic constitutive model. By conducting cyclic loading experiments on stainless steel with different plate thicknesses, the hysteresis curves under different loading protocols were obtained. The loading protocol significantly influences the cyclic hardening behaviour of stainless steel. To calibrate material parameters in the Chaboche model more effectively, a new parameter calibration method based on genetic algorithm optimization is proposed. Additionally, a method is proposed to calibrate the material parameters of the Hu model by utilizing the monotonic tensile stress-strain curve of austenitic stainless steel, which provides a new material model option for the numerical simulation of stainless steel seismic performance. The applicability of the Chaboche model and the Hu model in numerical simulations of stainless steel members is then verified and compared using existing seismic performance test results. The findings indicate that the Hu model offers more accurate numerical simulations of cyclic loading on austenitic stainless steel members compared to the Chaboche model.

Hysteretic behavior of the segmented buckling‐resistant braces with LYP160

AbstractThe goal was to evaluate the hysteretic performance of buckling‐resistant braces with low yield point steel LYP160, the monotonic tensile and cyclic loading tests of LYP160 test specimens were conducted and the cyclic constitutive relationship was obtained. According to the load–displacement curves of the specimens, the low‐yield point steel was characterized by good ductility and energy absorption ability. With consideration of the Chaboche model for the materials, the cyclic hardening parameters of low‐yield point steel were obtained. On this basis, the hysteretic properties of buckling‐resistant braces under cyclic loads were simulated and analyzed. After the analysis and comparison of buckling‐resistant braces specimens with isotropic core plate and segmented variable section core plate, it can be found that: when the conventional buckling‐resistant braces with an isotropic core plate were loaded to L/100, the lateral deformation of the buckling‐resistant brace (BRB) would reach 17 mm. Additionally, serious squeezing could be observed on the lateral restraining members. The conventional BRB would become ineffective due to the accumulation of deformation at both ends of the BRB. When the segmented buckling‐resistant brace was applied, the core plate with variable section would buckle first in the middle area, other parts could continue to consume energy thanks to the action of the limit plate. It would avoid the situation that other areas would be unable to consume energy after the core plate yields at one area first. Under the action of cyclic loads, no stiffness degradation was noted in the segmented buckling‐resistant brace. Segmented buckling‐resistant braces demonstrated superior ductility and energy dissipation capacity.

Plastic behavior and shakedown limit of defected pressurized pipe under cyclic bending moment

Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness.

Mechanistic model for hydrogen accelerated fatigue crack growth in a low carbon steel

Fracture by hydrogen accelerated fatigue crack growth is a severe type of environmental failure. Although fatigue crack growth has been the subject of intense investigation over several decades, a complete mechanistic and predictive model is still lacking. Such a crack growth model is even more rare in the case of hydrogen in view of the lack also of constitutive models for material deformation under cycling loading that account for the hydrogen effect. In this study, we present a model for fatigue crack propagation induced by alternating crack tip plastic blunting and re-sharpening, which in the presence of hydrogen can be accelerated by hydrogen enhanced dislocation motion and generation. The Chaboche constitutive model, which is a nonlinear kinematic hardening model capable of capturing many features of material behavior under cyclic loading, is used for the calculation of the stress and strain fields at the propagating crack tip. The Chaboche model is calibrated using a sequence of experimental data from uniaxial strain-controlled cyclic loading tests and uniaxial stress-controlled ratcheting tests with a low carbon steel, JIS SM490YB, in the absence and presence of hydrogen. The numerical simulation results indicate that the proposed crack propagation model can predict Paris law behavior and can successfully demonstrate acceleration of fatigue crack growth in the presence of hydrogen. Significantly, the profiles of the steady-state opening stress and strain ahead of the fatigue crack tip in a compact tension (C(T)) specimen were found to have sections over which they vary as ln(1/r) with distance r from the crack tip, consistent with the crack-tip strain field for a non-stationary crack.

Experimental Study and Creep-Fatigue Life Prediction of Turbine Blade Material DZ125 Considering the Nonholding Effect and Coupling Effect of Stress and High Temperature

Abstract In response to the problem of creep-fatigue interaction damage failure of aero-engine turbine blade material, based on the modified damage evolution model of Kachanov-Rabotnov and Chaboche, a creep-fatigue life prediction model for nickel-based superalloy DZ125 is constructed considering the nonholding effect and coupling effect of stress and high temperature with the nonlinear interaction and superposition of creep damage and fatigue damage according to the continuum damage mechanics theory. Simultaneously, the microfracture morphology of DZ125 was analyzed using a scanning electron microscope, revealing the micromechanism of creep-fatigue interaction. The research results manifest that the creep-fatigue life prediction model has a high life prediction ability within ±2.0 times the dispersion band of the prediction results. Concurrently, a large number of intertwined tearing edges, microcracks, and microvoids appear in the fracture morphology, and creep and fatigue interact with each other in the form of effective stress. The above research can provide theoretical support for predicting the lifespan of mechanical structures in a high-temperature environment.

Hysteretic behavior and cyclic constitutive model of corroded low-alloy steel in a corrosive environment

To quantitatively analyze the mechanical properties of corroded low-alloy steel under monotonic and cyclic loading, a cyclic constitutive model was established. Accelerated corrosion, monotonic tensile testing, and cyclic loading testing of 28 groups of Q345B steel specimens were conducted to examine how corrosion affected the monotonic tensile and hysteresis characteristics of the specimens, and the combined hardening parameters based on the Chaboche model were calibrated and confirmed based on the test findings. The results showed that corrosion clearly affected the monotonic stress-strain curve of steel and that most mechanical indices deteriorated linearly with respect to the corrosion rate. The combination of corrosion and cyclic cumulative damage exacerbated the degradation of the deformation capacity of the steel and affected its energy consumption capacity and cyclic hardening. The constitutive model of corroded steel calibrated on the basis of cyclic loading test data could effectively simulate the hysteresis performance of corroded Q345B steel under cyclic loading.

Consistent memory surface model for plateau and hardening regions

Mild steels are frequently used in building structures because of their high strength, productivity, processability, and weldability. One key feature of mild steels is their yield plateau, which is followed by a hardening region in the stress–strain relationship. During large earthquakes, building members can experience a large plastic strain whose amplitude is difficult to predict beforehand. Constitutive equations applicable to the full-range strain field are necessary for accurate structural safety evaluation. This study provides novel constitutive equations for the plateau region, capable of reproducing a yield plateau. A set of hardening constants was proposed to satisfy the consistency condition of the plastic multiplier under any loading pattern. The closed form of the stress–strain relationship was derived to calibrate the material constants. The material constants were calibrated using two types of material test results. The results of the proposed model were consistent with the material test results under cyclic loading at various strain amplitudes. This was validated by comparing the shear buckling and lateral torsional buckling test results of an H-shaped beam with the finite element analysis (FEA) results. The numerical demonstration also highlighted the significance of not only material constitutive laws but also the introduction of residual stress and initial imperfections in reproducing the pre- and post-buckling behaviors. The convergence of the residual force for the proposed model was equivalent to those of the authors’ previous model and the Chaboche model. These results indicate that the proposed model can predict hardening phenomena at the material and structural levels in the plateau and hardening regions.

A novel constitutive model for S30408 stainless steel considering strain memory effect: Formulation and implementation

To predict seismic behavior of steel structures and conduct performance-based seismic design, a precise constitutive model to accurately reflect the elastic-plastic response of structural steel under various loading protocols is always needed, so that the strength, deformation capacity, and energy dissipation capacity of a steel component or system in case of a severe earthquake can be reasonably evaluated. On the other hand, the constitutive model should be convenient for practical engineering implementation and application. Previous studies show that certain type steel like stainless steel S30408 shows complex features under various strain ranges such as pronounced strain memory effect, unsaturated cyclic softening/hardening under small/large strain amplitudes, which differ from mild steel and low yield point steel. Therefore, the stainless steel S30408 is taken as the research object in this study to develop a new constitutive model to describe structural steels with such complex mechanical properties. First, a new nonlinear isotropic and kinematic hardening rule is extended based on the classical Chaboche model and a functional relationship between the hardening rate (defined as the variation value of peak stress in every adjacent cycle during cyclic loading) and the applied strain amplitude is established through a logistics function to describe the coupling effects. Second, the numerical implementation technique for three-dimensional is elaborated in detail. Third, the numerical implementation technique is extended to plane stress cases by the improved P projection method. Using the numerical integration algorithm, the proposed constitutive model can be successfully incorporated into ABAQUS/Standard through the UMAT subroutine interface which is suitable for both solid and shell elements.

A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading

A novel continuum damage coupled unified viscoplastic model is used for simulating the stress–strain responses of SiMo 4.06 cast iron under Low-Cycle Fatigue (LCF), fatigue-creep and creep loading for temperatures up to 650 °C. The advanced constitutive model that is developed within the framework of the Chaboche model allows the simulation of various effects including strain rate sensitivity, cyclic hardening and softening, static recovery and strain range dependency. The hyperbolic sine flow rule and the static recovery of kinematic hardening rule are proposed in order to effectively simulate both stress relaxation and creep strains. The isotropic damage variable is introduced into the constitutive equations to represent the effects of material degradation. Three main damage mechanisms are considered: fatigue, creep and ductile damage. In addition, the model is further modified to take into account the progressive microdefects closure effect. Finally, the prediction capability of the proposed model is illustrated for the experimental data obtained from the various uniaxial material tests. A good correlation was achieved between the simulated and the experimental results.

Low-cycle fatigue mechanical behavior of 30CrMo steel under hydrogen environment and numerical verification of chaboche model

In order to investigate the fatigue behavior of the hydrogen storage material, 30CrMo steel, in a hydrogen environment, an electrochemical hydrogen charging method was employed. Low-cycle fatigue experiments were conducted on the material to obtain half-life stress–strain hysteresis curves, cyclic response characteristics, and strain-life relationships under different hydrogen charging durations. The results indicate that the material exhibited an overall cyclic softening behavior, transitioning from ductile fracture to brittle fracture after hydrogen charging, resulting in a significant reduction in fatigue life. The Manson-Coffin formula was fitted based on material cyclic response characteristics and strain-life relationship curves. Additionally, fatigue toughness and Chaboche kinematic hardening models were fitted based on low-cycle fatigue test data. Finite element analysis was used to validate the accuracy and reliability of the Chaboche kinematic hardening model. The Chaboche kinematic hardening model showed minimal error compared to experimental data and accurately described the influence of hydrogen on the low-cycle fatigue mechanical behavior of 30CrMo steel.

Effect of maximum applied cyclic stress on fretting fatigue stress distribution of flat-on-flat modified 9Cr-1Mo steel contact: Finite element analysis

Fretting fatigue experiments were conducted on a modified 9Cr-1Mo (P91) steel under flat-on-flat contact with maximum applied cyclic stress (σmax) levels of 450 MPa, 500 MPa and 550 MPa at a stress ratio of 0.3 and a contact pressure of 100 MPa. A decrease in the cyclic life was observed with an increase in σmax. Chaboche model with isotropic and kinematic hardening was employed in finite element analysis to evaluate the stress distribution near the contact pad and along the contact surface under fretting fatigue conditions. In addition, the contact-related parameters such as contact pressure, contact shear stress and relative tangential motion were also assessed. The relative tangential motion was found to increase with increasing σmax. Besides, the peak values of normal stress (parallel to the applied loading direction) and maximum principal stress were observed around the leading and trailing edges of the contact pad at the σmax. The amplitude of relative tangential motion and slip zone increases with σmax. The orientations of the principal plane and shear plane to the applied cyclic loading direction are −89.5° and −134.5°, irrespective of the σmax. The fracture surface of the failed specimen revealed that the direction of the crack was nearly perpendicular to the applied stress. Smith-Watson-Topper parameter was used for estimating the crack initiation life with σmax. It has been noticed that the fraction and dominance of crack initiation or propagation phase depend on the imposed cyclic condition for the steel.

Explicit and Implicit Integration of Constitutive Equations of Chaboche Isotropic-Kinematic Hardening Material Model

The proper selection of the material model and its parameters in numerical simulations of the material response under loading is a very important task. In the cyclic load one should assume different phenomena, e.g. ratchetting effect, the mean stress relaxation, creep, etc. The Chaboche kinematic hardening model is mainly applied in order to capture the Bauschinger effect due to its good description of the material behaviour under the cyclic loading. The modified Chaboche isotropic-kinematic hardening model is considered in this paper in order to simulate the strain-controlled and stress-controlled uniaxial cyclic tension-compression test. The implicit and explicit integration procedures are tested here, showing advantages and disadvantages of both methods. It is shown that both approaches provide similar results. The implicit integration method of constitutive equations is unconditionally stable and thus less calculation steps are required in comparison to the explicit procedure. The implicit and explicit integration of the Chaboche model including isotropic and kinematic hardening are then implemented for the 3D case in commercial ABAQUS program in the form of the user material procedure. The correctness of results obtained for the user material model is verified by comparison to results for commercially implemented Chaboche model.

Continuum damage mechanics of cyclic viscoplasticity using asymptotic numerical method

Conscious efforts on reduction of greenhouse gas emissions have led to an energy transition to renewable energy, however uncertainties of renewable energy production have resulted in higher thermal cycling demands from conventional power plants. Thermal load cycling at high temperature regions of steam turbine components leads to enhanced creep-fatigue damage accumulation. It is well established that such damage mechanism is numerically best predicted by unified constitutive modeling including damage as a variable as per the formalism of continuum damage mechanics at an expense of considerable computational efforts using finite element analysis. In this paper, the non-iterative Asymptotic Numerical Method (ANM), currently limited to partial cycle analysis with linear hardening plasticity model, is proposed for the first time to address cyclic viscoplasticity problems including damage capable of handling multiple cycles and most generalized loading conditions. Regularization techniques additionally necessary to implement loading-unloading-reloading criteria and advanced constitutive models etc. are presented. The constitutive model chosen for the formulation includes the non-linear multiple back stress variable modified Chaboche model to include damage combined with modified Chaboche-Rousselier isotropic hardening model to include damage, power law for viscoplasticity, Lemaitre’s damage potential and Kachanov-Rabotnov’s creep damage law. The method is verified with defined error measures and then applied to two high pressure steam turbine rotors, one with and another without thermal stress relief groove (TSRG) at the inlet under service type loading conditions to study the beneficial effect of the TSRG on creep-fatigue damage evolution. The accumulated errors of the proposed ANM and computational time are compared to a conventional Newton-Raphson solution.

A ELASTO-PLASTIC CONSTITUTIVE MODEL BASED ON CHABOCHE KINEMATIC HARDENING OF ALUMINUM ALLOY 7050-T7451

The elasto-plastic behavior of the aluminum alloy 7050-T7451 subjected to cyclic loading was investigated and modeled. The objective of this work is to improve the constitutive model of Chaboche with a special emphasis in the compression. In the proposed model, the part under tension of the stress-strain curve in the stable hysteresis cycle is modeled separately from the compressed one, where it is considered that they have different Modulus of Elasticity. The work includes both simulation and experimental data, and they are compared to each other. The values were collected experimentally by the application of symmetric cyclic strain-driven loading in the strain range between 0.75% and 2.25%. The experimental results were used to calculate the parameters of the constitutive model in a MATLAB® software. The responses obtained with the proposed model have greater adherence to the experimental results than those obtained with the Chaboche model.

Machine learning informed visco-plastic model for the cyclic relaxation of 316H stainless steel at 550 °C

Among the structural alloys for this fast reactor, 316H stainless steel has emerged as a promising candidate. Because the operating temperature of Sodium-cooled reactor is specifically designed to be 550 °C, this operating temperature triggers material inelastic behavior depends more on the coupling of fatigue and creep, which complicates the constitutive model. By introducing static recovery terms, previous studies could capture some experimental features, but failed to describe the interaction by fatigue and creep. In this work, in order to describe the fatigue and creep during cyclic relaxation of 316H stainless steel at 550 °C, we propose a modified visco-plastic constitutive model within the framework of unified Chaboche model. In the proposed model, the parameters related to the static recovery items are coupled, and thus cannot be identified from experiments using the traditional trial and error. To address this issue, we employed the Bayesian approach to identify these parameters. The parameter identification involves two steps: (i) constructing a Gaussian Process surrogate model using data generated from the finite element method, and (ii) obtaining the value of parameters through Markov Chain Monte Carlo sampling under the Bayesian framework. The proposed procedure, is demonstrated by the using experimental results of 316H stainless steel at 550 °C. Under the coupling of fatigue-creep, the material exhibits a cyclic-dependent accelerated stress relaxation before reaching the saturated stage and a steady state of relaxed stress after a long holding time. These mechanical responses are well predicted by the proposed model. Further, we conducted two kinds of multi-axial cyclic test, tensile test of notched bar and coupled tensile-torsion test, to validate the proposed constitutive model for the cyclic behavior under the multi-axial stress state.

Research on the Fatigue Crack Growth Behavior of a Zr/Ti/Steel Composite Plate with a Crack Normal to the Interface.

The current work reveals the influence of loading parameters on the crack growth behavior of a Zr/Ti/steel composite plate with a crack normal to the interface by using an experiment and the finite element method. The Chaboche model was first used to study cyclic plastic evolution in composite materials. The results reveal that an increase in Fmax, Fm, and Fa can promote da/dN; meanwhile, an increase in R will reduce da/dN. The plastic strain accumulation results indicate that Fm mainly contributes to the tensile strain and compressive stress after the first cycle. Additionally, Fa increases the stress range and compression stress and greatly improves the plastic strain accumulation degree in subsequent loading cycles. The Fmax can significantly increase the stress amplitude and plastic strain accumulation level. When R increases, the plastic strain accumulation increases a little, but the stress amplitude and compression stress decrease greatly. Furthermore, it is also found that the elastic-plastic mismatch also affects the plastic evolution, that is, strengthening or weakening the effect of the loading parameters.

Cyclic Hardening and Fatigue Damage Features of 51CrV4 Steel for the Crossing Nose Design

A crossing nose is a component of railway infrastructure subject to very severe loading conditions. Depending on the severity of these loads, the occurrence of structural fatigue, severe plastic deformation, or rolling fatigue may occur. Under fatigue conditions with high plastic deformation, cyclic plasticity approaches, together with local plasticity models, become more viable for mechanical design. In this work, the fatigue behavior in strain-controlled conditions of 51CrV4 steel, applicable to the crossing nose component, was evaluated. In this investigation, both strain-life and energy-life approaches were considered for fatigue prediction analysis. The results were considered through obtaining a Ramberg-Osgood cyclic elasto-plastic curve. Since this component is subject to cyclic loading, even if spaced in time, the isotropic and kinematic cyclic hardening behavior of the Chaboche model was subsequently analyzed, considering a comparative approach between experimental data and the FEM. As a result, the material properties and finite element model parameters presented in this work can contribute to the enrichment of the literature on strain-life fatigue and cyclic plasticity, and they could be applied in mechanical designs with 51CrV4 steel components or used in other future analyses.

Impact of the plasticity modeling on fatigue life prediction for steels showing modest non-proportional hardening

This study evaluated the influence of Tanaka parameter-based cyclic plasticity modeling on fatigue life estimation under multiaxial loading. The life predictions based on the experimental stress–strain data, simulated by the Chaboche cyclic plasticity model and Chaboche model with the implemented Tanaka parameter, were compared for this purpose. The fatigue life was then calculated using three popular prediction models for the two steel grades exhibiting moderate non-proportional hardening. Eleven multiaxial loadings were investigated, including proportional, 90° out-of-phase, and asynchronous cases. Modeling the cyclic material response using the coupled Chaboche and Tanaka models revealed to have improved all fatigue life predictions.

Elastic–plastic analysis of high load ratio fatigue tests on a shot-peened quenched and tempered steel, combining the Chaboche model and the Theory of Critical Distances

This study aimed to predict the uniaxial fatigue strength of shot peened notched specimens made of 42CrMo4 quenched and tempered steel. The Chaboche kinematic hardening rule was employed to model the cyclic plastic behaviour of the tested samples and the evolution of the residual stresses, which were measured with X-ray diffraction and then reproduced through a finite element software with a novel proposed procedure. This latter introduced a distribution of eigenstrains to reproduce the initial residual stresses and a hardening of the material to replicate the residual stresses measured after the loading for a run-out specimen. The Theory of Critical Distances combined with the Smith-Watson and Topper multiaxial fatigue criterion were then employed to predict the fatigue strength resulting in a good level of accuracy.