Isotropic-kinematic Hardening Model Research Articles

Multiaxial ratcheting-fatigue evaluation of pressurized elbow pipe under strong cyclic loading using damage-coupled cyclic plasticity model

Continuous damage mechanics (CDM) is based on the theories of continuous medium mechanics and continuous medium thermodynamics, which considers damage is an irreversible dissipative process within the materials, and employs the field-theoretic approach of image-only science to study the internal macroscopic damage evolution law of the materials and its influence on the deterioration of the macroscopic mechanical properties of the materials. Hence, within the framework of CDM, a damage-coupled cyclic plasticity constitutive model is proposed based on combined isotropic and Chen-Jiao-Kim (CJK) kinematic hardening rule for evaluating the ratcheting-fatigue behavior of 90° elbow pipes under strong cyclic loading in this paper. Stress return mapping and numerical solution procedures of the proposed model are formulated based on the backward finite difference method. Formulation of the consistent tangent operator is presented for the Finite Element implementation of the plasticity model in ABAQUS UMAT. The FE analysis of non-pressurized and pressurized elbow pipes under cyclic displacement-controlled loading is respectively performed using the implemented constitutive model. The results reveal that the predicted results of the damage-coupled cyclic plasticity constitutive model are better than combined isotropic-kinematic hardening model, and well consistent with the experimental data.

Effects of kinematic hardening of mucus polymers in an airway closure model

The formation of a liquid plug inside a human airway, known as airway closure, is computationally studied by considering the elastoviscoplastic (EVP) properties of the pulmonary mucus covering the airway walls for a range of liquid film thicknesses and Laplace numbers. The airway is modeled as a rigid tube lined with a single layer of an EVP liquid. The Saramito–Herschel–Bulkley (Saramito-HB) model is coupled with an Isotropic Kinematic Hardening model (Saramito-HB-IKH) to allow energy dissipation at low strain rates. The rheological model is fitted to the experimental data under healthy and cystic fibrosis (CF) conditions. Yielded/unyielded regions and stresses on the airway wall are examined throughout the closure process. Yielding is found to begin near the closure in the Saramito-HB model, whereas it occurs noticeably earlier in the Saramito-HB-IKH model. The kinematic hardening is seen to have a notable effect on the closure time, especially for the CF case, with the effect being more pronounced at low Laplace numbers and initial film thicknesses. Finally, standalone effects of rheological properties on wall stresses are examined considering their physiological values as baseline.

A Constitutive Model for Asymmetric Cyclic Hysteresis of Wrought Magnesium Alloys under Variable Amplitude Loading

A cyclic plasticity constitutive model was developed for materials with asymmetric cyclic behavior to explain the stabilized stress–strain response under variable amplitude loading. The proposed constitutive model incorporated the von Mises yield function with an adjustment to accommodate asymmetric yielding under tension and compression. A combined isotropic–kinematic hardening model was proposed to describe the evolution of the yield surface in the reference uniaxial frame and the actual frame. The history of plastic deformation is memorized by introducing internal variables, accumulated slip, and residual twins, which govern the cyclic flow behavior in the subsequent reversal. The additional conditions required to predict the stabilized hysteresis response of a material under variable amplitude loading were set out and incorporated into the constitutive model. The model was numerically implemented and programmed into a user material (UMAT) subroutine to run with the commercial finite element program, Abaqus/Standard 2019. The model was calibrated using the stabilized hysteresis response of ZEK100 and AZ31B sheets under constant amplitude strain-controlled cyclic loading for different strain amplitudes. To verify the model, constant amplitude and four different variable amplitude load spectra tests were performed and the stabilized stress–strain hysteresis response predicted by the model was compared with test results. It was demonstrated that the results are in very good agreement.

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.

Monotonic and Cyclic Modelling of Structural Steel for Finite Element Analysis

Nowadays, as a response to the promoted concept of performance-based seismic design, the finite element method (FEM) has become an omnipresent practice that supports the simulation of structural elements. This approach requires constitutive numerical models, which could reproduce both elastic and plastic behaviour of steel. Looking forward to a reliable FEM simulation, the modelling and calibration of steel undergoing monotonic and cyclic loading tests is investigated in this paper. With respect to monotonic tensile test, a sensitivity analysis regarding mesh refinement and finite element type is developed. Another inspected issue, such as high-strength steel modelling, taking into consideration low ductility and absence of yield plateau, is also presented. And finally, a model for structural steel, using the combined isotropic-kinematic hardening model, is introduced to simulate metal non-linear behaviour under ultra-low-cycle fatigue regime. All these numerical simulations are processed via Abaqus software package, and are validated by a set of experimental tests.

Effect of the yield surface evolution on the earing defect prediction

Although the prediction of earing in the cup drawing process is considerably related to the yield surface shape, the yield surface evolution is also essential for the final ear form. The bending-unbending issue is a fundamental subject occurring on the die and punch shoulders. Since the yield stress is loading path dependent in reversal loadings, the conventional hardening models used in the monotonic loading conditions bring about inaccurate outcomes for predicting the ultimate earing profile, and a kinematic hardening model should be incorporated into the constitutive equations. This study elucidates the yield surface evolution effect involving expansion and translation simultaneously on the ear formation. A sixth-order polynomial yield function was employed to precisely characterize the yield surface shape, while a combined isotropic-kinematic hardening model was implemented to represent the evolution of the yield surface. The translation of the yield surface position was defined by the Armstrong-Frederic hardening model. Punch force-stroke responses and the ear form profiles were predicted by the implemented plasticity model in Marc using the Hypela2 user subroutine and compared with the experimental results. The combined hardening assumption yielded an increase in the mean cup height when compared to the isotropic hardening assumption. Moreover, The HomPol6 coupled with the combined hardening showed a better agreement with the experimental results.

Failure of high-speed bearing at cyclic impact-sliding contacts: Numerical and experimental analysis

The thermal-induced failure mechanism of the bearing outer-ring guiding-surface is investigated within this work when subjected to cyclic impact and sliding actions. The paper combines numerical simulations and experimental analysis. A high-speed bearing oil interruption experiment is carried out for testing the severe damage of the bearing steel at high-speed impact-sliding contacts. A coupled thermo-elasto-plastic phase-field model is established and validated by experimental results. It then allows, by simulating the multi-physics problem, the predictions of damage propagation and failure for ductile materials at cyclic impact-sliding contacts. To this end, a temperature-dependent isotropic-kinematic hardening model combined with thermal softening, cyclic strain hardening, and damage degradation is employed. The results show that under high-speed cyclic impact-sliding conditions, the damage initiated and accumulated at the contact near-surface is accompanied by instantaneous high temperature and plastic deformation. The failure of bearing is induced by a strong thermal softening effect at high-speed sliding and rapidly propagated under cyclic impact loading. In addition, the impact velocity, impact frequency, and friction coefficient have significant effects on damage initiation and accumulation.

Analyses of the model parameters of kinematic-isotropic hardening rule using genetic algorithm approach for predicting cyclic-plasticity of metallic structural materials

Modeling of engineering components under cyclic loading is complex because cyclic-plastic phenomena like the Bauschinger effect, ratcheting, shakedown, and mean stress relaxation are to be considered in the constitutive modeling. This has led to several investigations on modeling the cyclic-plastic behaviour of materials under stress-controlled and strain-controlled testing; but amongst these, Chaboche's isotropic-kinematic hardening (CIKH) model is quite popular and a frequently used one. A new methodology has been recently proposed by some of the present authors to use genetic algorithm towards optimization of the parameters of CIKH modeling with a demonstration of its applicability for a few materials. This investigation aims to elucidate that this approach is applicable to both cyclically stable materials as well as cyclic softening or hardening materials using several examples on structural materials. The considered metallic materials include several aluminum (like AA7075-T6 alloy), iron (like CS-1026and Sa333 C-Mn steel), titanium (like TA16 alloy), zirconium (like Zr-4 alloy)-base alloys or superalloys (like INCONEL718). The merit of the analysis of cyclic plastic deformation behaviour of materials with the current approach is inherent in its achieving higher accuracy of fitting to the experimental data with a single set of material parameters under both strain- and stress-controlled cycling. This has been established with a comparative analysis of the accuracy of fitting by the present approach with the ones available from the existing reports. The parameters obtained using the approach for the different materials are compared to get insights into the mechanism of plastic deformation.

A computationally fast and accurate procedure for the identification of the Chaboche isotropic-kinematic hardening model parameters based on strain-controlled cycles and asymptotic ratcheting rate

The Chaboche isotropic-kinematic hardening (CIKH) model provides a versatile and realistic description of the material stress–strain behavior under generic multiaxial cyclic loadings. However, identifying the backstress parameters is challenging, and can be formulated as an optimization problem using different approaches. Instead of a computationally expensive pointwise search, in this paper the global properties of the cyclic curves are fitted to the experimental data. The conditions introduced are the hysteresis areas, peak stress values and tangent moduli at the extreme points, however the framework can be easily adapted to other target quantities. One linear and two non-linear backstress components of the kinematic hardening model are introduced, although the analytical equations developed can be used to refine the model further, with more components. Two stabilized cycles are required to identify the main kinematic parameters. New analytical expressions for asymptotic ratcheting rates in uniaxial tests are developed and then used to tune the dynamics of the slightly non-linear (hence, slowest) backstress component. After obtaining the kinematic parameters, isotropic hardening laws can also be identified, by considering the evolution of the extreme points of the strain-controlled cycles before stabilization. Practical demonstrations of the procedure are provided by experimental tests carried out on a 7075-T6 aluminum alloy, 42CrMo4+QT steel, and a high-silicon ferritic ductile cast iron. An accurate reproduction of the material behavior is achieved, at a negligible computational cost.

Parameter Identification and Modeling of Hardening to Preserve Identical Predictions under Monotonic Loading

Advanced hardening models accurately describe the transient plastic behavior (reyielding, stagnation, resumption...) after various strain-path changes (reverse, orthogonal...). However, a common drawback of these models is that they usually predict monotonic loading with lower accuracy than the regular isotropic hardening models. Consequently, the finite element predictions using these models may sometimes lose in accuracy, in spite of their tremendous theoretical superiority. This drawback has been eliminated in the literature for the Chaboche isotropic-kinematic hardening model. In this work, a generic approach is proposed for advanced hardening models. Arbitrary models could be successfully compensated to preserve rigorously identical predictions under monotonic loading. A physically-based model involving a 4th order tensor and two 2nd order tensors was used for the demonstration. The parameter identification procedure was greatly simplified by rigorously decoupling the identification of isotropic hardening parameters from the other parameters.

A Microstructure Based Elasto-Plastic Polygonal FEM and CDM Approach to Evaluate LCF Life in Titanium Alloys

This work presents the influence of microstructure on the LCF life of two-phase titanium alloys. An elasto-plastic polygonal FEM and continuum damage mechanics approach has been used in this work. Damage coupled Chaboche-Lemaitre combined isotropic-kinematic hardening model is implemented to accurately capture the effects of deformation inhomogeneity and material plasticity. A new strain-based damage evolution law is proposed to predict the effect of mean grain size on the LCF life. The effect of different microstructural parameters i.e., topological variation, elastic anisotropy, mean grain size and shape, volume fraction of phases and initial voids is statistically analyzed on the LCF life.

Evaluation of material behavior of wire strips under cyclic bending load and preparation of an experimental test method

Steel fibers as concrete reinforcement improve the building material’s mechanical properties and enlarges its field of application. The production of steel fibers by the process chain notch rolling and cyclic bending promises energetic improvement compared to the conventional manufacturing process wire drawing. The innovative procedure is not yet researched extensively and modelling of the material behavior brings with it many challenges. Different stress states of both process steps require various material models and material failure must be considered. The study brings an appropriate modelling of the test sheet metal DP600 with a thickness of t0=0.8 mm for the second process step into focus. The wire strip’s notches are exposed to a cyclic tension-compression load for which high strength steel exhibits early yielding and a distinct transient region of the stress-strain curve after load reversal. For this reason, the isotropic-kinematic hardening model by Chaboche and Rousselier determined in tension-compression tests is validated by cyclic bending tests. For considering crack initiation, an appropriate ductile damage model for depicting material fatigue is identified. To allow practical realization of the process and validation of the material model, an experimental test method for manufacturing wire strip samples by notch stamping is introduced.

On the performance of monopile weldments under service loading conditions and fatigue damage prediction

AbstractThick weldments used in offshore structures frequently act as fatigue crack initiation sites due to stress concentration at weld toe as well as weld residual stress fields. This paper investigates the cyclic deformation behavior of S355 G10+M steel, which is predominantly used in offshore wind applications. Owing to the vast size difference of monopile structure and weld cross‐section, a global–local finite element (FE) method was used, and the weld geometry was adopted from circumferential weld joints used in offshore wind turbine monopile foundations. Realistic service loads collected using supervisory control and data acquisition (SCADA) and wave buoy techniques were used in the FE model. A nonlinear isotropic–kinematic hardening model was calibrated using the strain controlled cyclic deformation results obtained from base metal (BM) as well as cross‐weld specimen tests. The tests revealed that the S355 G10+M BM and weld metal (WM) undergo continuous cyclic stress relaxation. Fatigue damage over a period of 20 years of operation was predicted using the local stress at the root of the weldments as the life limiting criterion. This study helps in quantifying the level of conservatism in the current monopile design approaches and has implications towards making wind energy more economic.

Experimental and Numerical Study of the Effects of the Reversal Hot Rolling Conditions on the Recrystallization Behavior of Austenite Model Alloys

The experimental and numerical study of the effects of the recrystallization behavior of austenite model alloys during hot plate rolling on reverse rolling is the main goal of the paper. The computer models that are currently applied for simulation of reverse rolling are not strain-path-sensitive, thus leading to overestimation of the processing parameters outside the accepted process window (e.g., deformation in the partial austenite recrystallization region). Therefore, in this work, a particular focus is put on the investigation of strain path effects that occur during hot rolling and their influence on the microstructure evolution and mechanical properties of microalloyed austenite. Both experimental and numerical techniques are employed in this study, taking advantage of the integrated computational material engineering concept. The combined isotropic–kinematic hardening model is used for the macroscale predictions to take into account softening effects due to strain reversal. The macroscale model is additionally enriched with the full-field microstructure evolution model within the cellular automata framework. Examples of obtained results, highlighting the role of the strain reversal on the microstructural response, are presented within the paper. The combination of the physical simulation of austenitic model alloys and computer modeling provided new insights into optimization of the processing routes of advanced high-strength steels (AHSS).

An isotropic-kinematic hardening model for cyclic shakedown and ratcheting of sand

Modeling the cyclic shakedown and ratcheting of sand remains a great challenge. An isotropic-kinematic hardening model is presented within the bounding-surface framework. By incorporating new features, a combined isotropic-kinematic hardening rule is extended to the deviatoric stress-ratio space. The hardening rule treats cyclic loading as a sequence of monotonic loading events. The kinematic mechanism of this hardening rule assumes that the bounding surface instantaneously translates from the image point to the stress reversal point when the loading path reverses. Then each stress reversal is regarded as an initiation of a new loading event. In each loading event, the isotropic model, which consists of an open wedge-type surface with a circular deviatoric section, may expand or shrink around a generalized homological center to track the variation in the soil fabric. This isotropic mechanism enables the model to capture the gradual evolution of soil stiffness under numerous loading cycles. By introducing a maximum prestress surface, an additional mechanism is deployed to avoid the overshooting problem and to promote the simulation of the post-cyclic behavior. A unified hardening function is defined in the model for all loading events. After calibrating the basic parameters by monotonic tests, only three extra cyclic parameters are required to describe the cyclic behavior of sand. The model behaviors are validated against serval cyclic triaxial tests. The comparison between experimental and predicted results demonstrates the model capabilities in describing the cyclic shakedown and ratcheting responses of sand.

Analysis of UOE forming process accounting for Bauschinger effect and welding

ABSTRACT UOE forming is commonly used to manufacture offshore and onshore line pipes. The process involves multi-step plastic deformation of High Strength Low Alloy (HSLA) steel plates combined with welding along the seam. The strain path continuously changes during the manufacturing process leading to yield strength variation due to Bauschinger effect. In the present work, the Bauschinger effect in line pipe is analyzed using finite element (FE) method assuming the material to follow Chaboche combined isotropic-kinematic hardening model. The material parameters for the model were obtained from a single cycle compression-tension experiment performed using X-80 steel grade. The evolution of yield strength at select locations is estimated by extracting the strain path evolution from FE results. In general, the welding process is ignored in such studies as the changes induced are local. In the present study, the welding process is simulated to quantify its contribution. The effect of welding was found to be negligible in the overall stress distribution. However, the welding affects the ovality of the pipe, which in turn has a significant influence on the service load including buckling and collapse under external pressure.

Material modeling and simulation of continuous-bending-under-tension of AA6022-T4

In earlier contributions, we discussed continuous-bending-under-tension (CBT) experiments on AA6022-T4. We found that CBT significantly enhanced the elongation-to-fracture and strength, over uniaxial tension. In the present paper, our understanding of CBT is expanded beyond these experimental observations, with the aid of material modeling and numerical simulations of the process. Cyclic tension-compression experiments were performed on this material, using strain histories that are expected to replicate the loading during CBT, i.e., different combinations of constant strain amplitude and linearly increasing mean value, to failure. During these experiments, a limited but not negligible amount of kinematic hardening was discovered. Some of these experiments are used for calibration of a combined isotropic-kinematic hardening model, while the rest are used for experimental validation of the model. The modeling framework is based on a rate-independent, associated flow rule with the von Mises yield criterion as the plastic potential. Isotropic hardening is introduced by a simple, exponential-decay model of the growth of the yield surface with plastic deformation. Non-linear kinematic hardening is introduced by a 4-term, Chaboche-type model. The large strain hardening curve is identified by extrapolation, an approach that is validated later in the work and contrasted with alternative options. This material modeling framework is introduced in finite element models of the CBT process. The model is meshed with linear, reduced-integration elements, with 7 elements through the thickness. It is found that the numerical model reproduces the experimental force-displacement curve, including the succession of spikes and plateaus typical of CBT, very closely. The model also replicates the development of strain on the surface during CBT, and compares well with post-test strain measurements. After these validations, the model is used to probe the mechanics of the CBT process, e.g., the development of stress and strain through the thickness and per cycle, the location and onset of failure, as well as the failure angle, which in CBT differs from the localized neck angle found in a typical uniaxial tension experiment.

Effect of Elastic Module Degradation Measurement in Different Sizes of the Nonlinear Isotropic–Kinematic Yield Surface on Springback Prediction

Commercial finite element software that uses default hardening model simulation is not able to predict the final shape of sheet metal that changes its dimensions after removing the punch due to residual stress (strain recovery or springback). We aimed to develop a constitutive hardening model to more accurately simulate this final shape. The strain recovery or balancing of residual stress can be determined using the isotropic hardening of the original elastic modulus and the hardening combined with varying degrees of elastic modulus degradation and the size of the yield surfaces. The Chord model was modified with one-yield surfaces. The model was combined with nonlinear isotropic–kinematic hardening models and implemented in Abaqus user-defined material subroutine for constitutive model (UMAT). The Numisheet 2011 benchmark for springback prediction for DP780 high-strength steel sheet was selected to verify the new model, the Chord model, the Quasi Plastic-Elastic (QPE) model, and the default hardening model using Abaqus software. The simulation of U-draw bending from the Numisheet 2011 benchmark was useful for comparing the proposed model with experimental measurements. The results from the simulation of the model showed that the new model more accurately predicts springback than the other models.

Accounting Bauschinger effect in the numerical simulation of constrained groove pressing process

Constrained groove pressing (CGP) is one of the severe plastic deformation techniques to achieve ultrafine grains in bulk sheet metals. The CGP process induces large plastic strain through incremental steps of shear and reverse shear using grooved and flat dies. The equivalent plastic strain distribution during CGP process can be correlated to the extent of grain refinement and the uniformity of ultrafine grains. The numerical analysis in the past have assumed isotropic hardening to model CGP process that does not consider the Bauschinger effect due to continuous change in deformation path between subsequent stages. In the present work, the effect of Bauschinger effect is considered using a combined isotropic-kinematic hardening model in simulation. The finite element model assuming isotropic hardening is validated with the results available in literature. Experiments on CGP were performed using three different materials and were modelled using both isotropic and combined hardening models. The maximum strain and the strain inhomogeneity predicted using combined hardening models were consistently greater than the isotropic hardening assumption.

A study on spring-back in U-draw bending of DP350 high-strength steel sheets based on combined isotropic and kinematic hardening laws

In this article, a numerical model for predicting spring-back in U-draw bending of DP350 high-strength steel sheet was presented. First, the hardening models were formulated based on combined isotropic–kinematic hardening laws, along with the traditional pure isotropic and kinematic hardening laws. A simplified method was proposed for determining the material parameters. Comparison of stress–strain curves of uniaxial tests at various pre-strains predicted by the numerical models and experiment showed that the combined isotropic–kinematic hardening model could accurately describe the Bauschinger effect and transient behavior subjected to cyclic loading conditions. Then, a finite element model was created to simulate the U-draw bending process using ABAQUS. Simulations were then conducted to predict the spring-back of DP350 high-strength steel in U-draw bending with geometry provided in the NUMISHEET’2011 benchmark problems. It was shown that the predictions of spring-back using the proposed model were in good agreement with the experimental results available in the literature. Finally, the effects of various tool and process parameters such as punch profile radius, die profile radius, blank holding force, and punch-to-die clearance on the spring-back were investigated. The simulation results suggested the significance of tool and process parameters on the final shape of the formed parts influenced by the spring-back.