Combined 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.

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.

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.

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.

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).

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.

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.

Numerical analysis of optimum treatment parameters by high frequency mechanical impact

In the study, finite element analyses were carried out systematically to investigate the optimum treatment parameters of high frequency mechanical impact (HFMI) on the basis of notch effect reduction and residual stress, which are generally considered to be the dominating factors of fatigue strength improvement of welded joints by HFMI treatment. Taking strain rate into account, the combined isotropic-kinematic hardening model was used to describe the elastic-plastic behavior of the HFMI-treated welded joint of S355 steel. The notch stress concentration factors (SCFs) and residual stresses under different impact depths and diameters of indenter were determined, respectively. Moreover, their synthetic effects on stress distributions of HFMI-treated joints under static load were investigated. It is found that the stress distributions of HFMI-treated joints under static load are affected significantly by impacted groove depth, independent of indenter diameter. The HFMI treatment can achieve the optimal status when the original weld toe is just removed with a groove depth ranging from 0.1 to 0.2 mm. At final, the optimized diameters of 3 to 4 mm are recommended for the indenter in terms of stress concentration and avoidance of crack.

리스트라이킹이 고강도강 스탬핑에서의 형상정밀도에 미치는 영향에 관한 연구

Recently the application of high strength steel sheets, such as DP, TRIP, and TWIP, is rapidly increasing in the automotive industry. Despite this trend, springback is still one of major obstacles that has yet to be overcome. In this study, we conducted U-draw bending experiments and analyzed the process with FEM, focusing on the springback. In the FE analysis, the effects of the hardening model ware studied by comparing the results among an isotropic hardening model, a combined isotropic-kinematic hardening model and the experiment. The effects of the restriking process on shape correction was also =studied by comparing the results of the springback analysis and the experiment.

Anisotropic Hardening Behaviour and Springback of Advanced High-Strength Steels

Advanced high-strength steels (AHSSs) exhibit large, and sometimes anisotropic, springback recovery after forming. Accurate description of the anisotropic elasto-plastic behaviour of sheet metals is critical for predicting their anisotropic springback behaviour. For some materials, the initial anisotropy is maintained while hardening progresses. However, for other materials, anisotropy changes with hardening. In this work, to account for the evolution of anisotropy of a dual-phase steel, an elastoplastic material constitutive model is developed. In particular, the combined isotropic–kinematic hardening model was modified. Tensile loading–unloading, uniaxial and biaxial tension, and tension–compression tests were conducted along the rolling, diagonal, and transverse directions to measure the anisotropic properties, and the parameters of the proposed constitutive model were determined. For validation, the proposed model was applied to a U-bending process, and the measured springback angles were compared to the predicted ones.

Evaluation of Combined Hardening Parameters for Type 304LN Stainless Steel Under Strain-Controlled Cyclic Loading

Low cycle fatigue (LCF) is the primary degradation mechanism affecting coolant piping of pressurized water reactor caused by combination of pressure and transient mechanical or thermal loads. In the case of LCF, stresses are high enough for plastic deformation to occur and the fatigue life is correlated with the cyclic plastic strain. Modelling cyclic plastic deformation of a material requires hardening parameters, which have to be obtained from LCF test results. It is customary in low cycle fatigue tests that the strain ranges are kept constant and the stresses are allowed to vary which typically leads to a hysteresis loop that consists of linear and nonlinear parts. In this paper, numerical studies on mechanical behaviour of Type 304LN stainless steel under fully reversed strain-controlled cyclic loading have been carried out. A linear combination of the two hardening types, isotropic and kinematic, governed by a scalar parameter, β (0 ≤ β ≤ 1) is used. A value of β = 1 indicates a pure isotropic hardening while a value of β = 0 indicates pure kinematic hardening. The details of the combined isotropic-kinematic hardening model are also presented. Constitutive relations for the classical von Mises theory along with a bilinear hardening theory have been used. The model is implemented in finite element software ABAQUS using a user subroutine written in FORTRAN, UMAT. An iterative method is adopted to arrive at the model’s hardening parameters and the value of β.

Cyclic hardening and softening behavior of the low yield point steel BLY160: Experimental response and constitutive modeling

The ability to model the cyclic behavior of low yield point steel accurately is essential for its application to seismic design. In this study, uniaxial tests of monotonic and strain controlled cyclic loading are conducted to investigate the mechanical properties of the low yield point steel BLY160. As observed in the test, work-hardening is an important hysteretic characteristic, which significantly influences the energy dissipation capacity of the steel. However, the cyclic softening in both stiffness and stress evolve as the plastic strain accumulates, which is manifested in the decrease of both the stress amplitude and the elastic domain of the stress–strain hysteresis loops. This change in the shape of the cyclic loops is called the “flattening effect” in this paper. To describe the cyclic hardening and softening effect by using one unified set of material parameters, a more sophisticated model based on the concept of internal variables is proposed as an extension of the combined isotropic-kinematic hardening model. The novel idea of a “transformation zone” with the introduction of an additional internal variable is proposed to synchronize the updates of isotropic and kinematic hardening such that the simultaneous change in the stress amplitude and the elastic region can be reproduced. Note that the cyclic softening develops in three stages: incubation, growth and the stabilization period. The logistic function, which presents a curve with an “S” shape, is first used to trace the evolution of the softening. Finally, the model parameters are identified by the test data, and the accuracy of the proposed model is verified by comparing the simulated performance and the experimental response under different loading histories. The results demonstrate that the extended model can elaborately describe the evolutional processes of cyclic hardening and softening by incorporating characteristics, such as the nonlinear transient behavior from elastic to plastic status, early yield under reversed loading and strain history dependence.

Measurements of Bauschinger effect and transient behavior of a quenched and partitioned advanced high strength steel

In recent decades, the needs for new advanced high strength steels (AHSS) with high ductility and strength have rapidly increased to achieve the targets of more fuel-efficient and safer vehicles in automotive industry. However, several undesirable phenomena are experimentally observed during the forming of such materials, particularly with complex loading and large plastic deformation. Springback is one of the most important problems that should be compensated in sheet metal forming process. In this paper, we investigated the hardening behavior of a Q&P (quench and partitioning) steel designated by QP980CR, which is a new third generation advance high strength steel, from the Baosteel Group Corp. in Shanghai, China. The uni-axial tensile and cyclic simple shear tests were conducted. The uni-axial tensile tests were performed on the specimens at 0°, 45° and 90° to rolling direction (RD). The flow stress and transverse strain evolution were obtained in view of the digital image correlation (DIC) measurement. The plastic anisotropy was optimized from the uni-axial tensile tests and thereafter incorporated into the simulations of cyclic simple shear tests. The cyclic simple shear tests were conducted with three prestrains to measure the Bauschinger effect, transient behavior and permanent softening, and to determine the material parameters of the combined isotropic-kinematic hardening model.

An extended homogenous yield function based anisotropic hardening model for description of anisotropic hardening behavior of materials

Except for the Bauschinger effect and permanent softening, work hardening stagnation and cross-effect are often observed deformation behaviors for sheet metals subjected to strain path changes. These complex deformation behaviors are assumed to have great effect on the sheet forming process and the following spring back. To constitutively, and more precisely model these plastic behaviors, extensive models have been successfully developed. Particularly, the combined isotropic-kinematic hardening model is powerful to capture the plastic behavior of sheet metals during forward and reverse loading. However, there is strong coupling between anisotropic yielding and anisotropic hardening with the kinematic hardening. Recently, Barlat et al. (2011) [61] proposed a homogenous yield function based anisotropic hardening model to describe the Bauschinger effect, which is not formulated with the kinematic hardening rule. In the present work, the original anisotropic hardening model is extended to capture the often observed cross-effect during multi-stage loading and work hardening stagnation during reverse loading. Although only four coefficients are newly introduced in the extended model, it can capture well the main trends of work hardening stagnation and cross-effect. The capability of this extended model is demonstrated with applications to two materials, namely, high strength steel and mild steel DC06.

Experimental evaluation and constitutive modeling of non-proportional deformation for asymmetric steels

Recently non-proportional deformation has received increased attention from researchers working in the area of experimental and computational modeling of metal deformation. However, most of them are numerical in nature with limited experimental data available, making it further difficult to model non-proportional deformation. In the present work, two-stage uniaxial tests, along with uniaxial cyclic and biaxial tests for different stress ratios, have been performed to evaluate deformation behavior of ultra-low carbon high strength automotive steel. Behaviors like cross-effect and hardening stagnation, which are attributed to the evolution of complex dislocation structures, were observed in this steel. It was also noticed that this steel exhibits tension–compression asymmetry. As for constitutive modeling, a modified asymmetric yield function is proposed to be used with a combined isotropic–kinematic hardening model. Also methods to account for the hardening stagnation during reverse loading and the cross-effect during two-stage deformation are proposed. The resulting constitutive model showed reasonably good agreement with experimental results.

A combined isotropic-kinematic hardening model for the simulation of warm forming and subsequent loading at room temperature

A coupled isotropic-kinematic hardening material model was developed based on phenomenological observations of performed two stage experiments on a medium carbon steel – SAE 1144, where the first deformation is performed at elevated temperatures and the second deformation at room temperature. Above all, deformations with orthogonal loading at various temperatures were investigated in order to determine the influence of the loading direction as well as of the temperature. Bergström’s theory of work hardening as well as the nonlinear kinematic hardening of an Armstrong–Frederick type were used as a basis for the model development. In the proposed model a relationship between material coefficients of the classical Bergström model and temperature was investigated. The aim of the new material model was to introduce the least possible amount of new parameters as well as to facilitate the mathematical determination of parameters during the fitting of the model with experimental data. The developed model was implemented in an in-house FE-Code in order to simulate the material behavior due to the dynamic strain aging and the hardening behavior after the dynamic strain aging process. Representative simulation results were compared with the experimental data in order to validate the efficiency and the application range of the model.

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

Abstract This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.