Kinematic Hardening Model Research Articles

Verification of the Tanaka non-proportional isotropic cyclic hardening model under asynchronous loading

Non-proportional cyclic loading path induces intrinsic strain hardening to the low stacking fault energy materials. The hardening is manifested in increased stress response which underestimation leads to non-conservative life prediction. This study aims to verify the Tanaka non-proportional isotropic cyclic hardening model under a wide spectrum of multiaxial asynchronous loadings. The Tanaka model is coupled with the Chaboche kinematic hardening model for stress path estimation. Modeling results are compared with fatigue experiments for two non-alloyed steel grades, E235 and E355. The Tanaka model improves the performance of the Chaboche model and exhibits its applicability to asynchronous loading.

Influence of strain-hardening models and slopes on the predicted residual stresses in structural steel S235 weldments

The objective of this research is to systematically understand how strain-hardening models and phase- and temperature-dependent strain-hardening slopes affect the computed residual stresses in single-pass welded joints made of the widely used structural steel S235. Both experimental methods and numerical simulation have been utilized for investigation. The results reveal that the material plasticity model has a massive effect on the predicted welding residual stresses (WRS). The calculated magnitude of WRS in the base metal (BM) adjacent to the weld zone inside the plate is largest when the isotropic hardening model is used, while it is smallest applying the kinematic hardening model. The comparison of predictions with measurements shows that the isotropic hardening model can predict WRS more accurately for S235 steel. The change in the temperature-dependent strain-hardening slopes of the generated phases (austenite and bainite in this case) have practically no impact on the predicted WRS. The calculated longitudinal residual stress (LRS) amount in BM nearby the weld zone is highly sensitive to the applied strain-hardening slopes of the initial microstructure (ferrite here), while that of transverse residual stress (TRS) is not. In contrast to the strain-hardening slopes of the initial microstructure at elevated temperatures, that at room temperature plays a crucial role in the simulated LRS. In this study, guidance is provided on how the phase- and temperature-dependent strain-hardening slopes of a specific steel can be determined economically and reliably in numerical welding simulation.

Mechanical responses of in-situ TiB2/7050 composite subjected to monotonic and cyclic loadings: A comparative study with 7050-Al

The monotonic and cyclic behavior of in-situ TiB2/7050 composite and 7050-Al was investigated. The composite has higher modulus, strength but lower fracture strain than 7050-Al. Both materials showed slight cyclic softening and quick saturation. For strain cycling, they showed an instant drop of the stress amplitudes followed by gradual increase with variation of mean strain. For asymmetric stress cycling, ratcheting occurred and increased with the rising of mean stress or stress amplitude. The cyclic plasticity behavior of them is characterized by a combined model of kinematic and isotropic hardening.

Evaluating the effectiveness of combined hardening models to determine the behavior of a plate with a hole under combined loadings

Geometrical discontinuities in a material such as holes and notches on machine elements are called as critical regions due to the stress concentrations. They are the potential failure initiation locations Therefore, researchers put significant effort on the prediction of the material response in these discontinuities under repetitive loadings. 
 Cyclic plasticity is concerned with the nonlinear material response under cyclic loadings. In this study, numerical cyclic stress – strain response of a plate with a hole was evaluated under the combined loadings which are cyclic bending and tensile loadings. Oxygen Free High Thermal Conductivity (OFHC) Copper alloy was considered as material, and finite element simulations were performed in Marc software. A user defined material subroutine known as Hypela2 was utilized in order to define the material response. The plasticity model used in the present study comprises J2 plasticity along with combined isotropic – kinematic hardening model. Evolution of the backstress was introduced by Armstrong – Frederic type kinematic hardening model. The results were compared with the literature study, and it was seen that presented hardening model provides accurate results in small cyclic strain range.

Characterization and modeling of the hardening and softening behaviors for 7XXX aluminum alloy subjected to welding thermal cycle

The evolution of thermo-elasto-plastic stress-strain during welding process plays a key role in determining the welding residual stresses and mechanical properties of welded joints for age-hardening 7XXX aluminum alloy, which is influenced by the softening and hardening behaviors. In this study, a Gleeble 3800 thermo-mechanical testing machine was employed to simulate the welding thermal cycle process of 7XXX aluminum alloy, and dynamic yield strengths under different temperatures were measured to elucidate the softening behavior. An isothermal multi-level cyclic loading tests at various temperatures were conducted to characterize the cyclic hardening feature. The calculation formulas for the proportion of kinematic and isotropic hardening model were deduced, and the cyclic hardening behavior was quantitatively described. A softening model and a nonlinear mixed hardening model were explored to simulate the evolution of dynamic yield strength and the cyclic hardening behavior, and excellent agreements were obtained between predicted and measured dynamic yield strengths and cyclic stress-strain curves.

Characterization of kinematic and distortional hardening by cyclic twin-bridge shear tests for sheet metal with inverse engineering approach

This study characterizes the plastic behavior under cyclic loading for an aluminum alloy of 5182-O and advanced high strength steel of QP1180. Twin-bridge shear specimens were loaded cyclically to evaluate the reverse shear loading behavior of the tested materials with different pre-strain from small (0.05 major strain) to large (0.15). The plastic behavior under cyclic loading is modelled by kinematic and distortional hardening models under the non-associated flow rule (NAFR) by anisotropic Drucker (Aniso-Drucker) yield function. An additional shear constraint proposed by (Abedini et al., 2018) is imposed on the plastic potential of NAFR. The Zang and HAH20 models are selected as kinematic and distortional hardening models respectively. They are calibrated inversely by the reverse torque-torsion angle curves from experiments. Finally, V-bending tests with the pre-strained strips were carried out and simulated by the calibrated hardening model to evaluate its predicting accuracy. The results show that twin-bridge shear test combined with the recommended inverse engineering approach is implementable to overcome the drawback of the simple shear test due to inhomogeneous deformation in large strain. The constitutive models are critical for the inverse calibration. It is found that the calibration accuracy under NAFR is higher than the associated flow rule (AFR) especially for large strain conditions. Also, the additional shear constraint imposed on the plastic potential of NAFR is found to be an effective approach to enforce the simulated shear stress at zero hydrostatic pressure. As for hardening model, the HAH model has more flexibility compared to the kinematic hardening model benefiting from its distortional hardening form. Also, parameters related to permanent softening in the new HAH20 model need to be evaluated carefully at the large deformations.

Kinematic Hardening Model Comparison of Square Hollow Section Under Cyclic Bending

This study compares the different linearity of the kinematic hardening model of the Square Hollow Section (SHS) under cyclic bending loading. Four specimens of a simple support beam cyclically tested in previous research are listed as hot-rolled, hot-finished, and two cold-formed. Using the bilinear, multilinear, and Chaboche models, each specimen is modeled in kinematic hardening. The variables or node sets for each linearity model are estimated using tensile test data, and Chaboche variables are obtained using the least-square fitting method. Each linearity model for each specimen is built-in FEA using a shell model. The numerical model applied the same cyclic loading history as the previous test. The numerical analysis comparison concluded that Chaboche and the multilinear kinematic model generate the expected result fitted to test hysteresis of cold-formed one and cold-formed 2 SHS, but the bilinear models are not fitted. Moreover, all kinematic models are not fit for the hot-rolled and hot-finished SHS compared to the test hysteresis. So, for hot-rolled and hot-finished SHS, the combined hardening is suggested; there is a possibility it is because of the lower yield ratio that both sections have. Overall, during a cyclic bending analysis of cold-formed SHS, multilinear or Chaboche models are preferable if the data is limited.

Shakedown analysis of bounded kinematic hardening engineering structures under complex cyclic loads: Theoretical aspects and a direct approach

There exist two basic formulations of static shakedown theorem for bounded kinematic hardening (KH) model in literature. Whether the two formulations are equivalent, whether the conditions of loading-path-independence are satisfied, and how to employ the shakedown theorem to obtain the safety margin of realistic engineering structures under cyclic loading are some key issues to be solved and addressed. This paper presents theoretical aspects of the static shakedown theorem of KH and proposes a direct approach for shakedown analysis of KH structures. The presented direct approach allows for both the two shakedown formulations and considers the simultaneous influences of multiple load vertices. The two formulations are suitable for plastic models with different hardening laws and determine different shakedown load boundaries in the region of incremental collapse. Instead of dealing with a complicated problem of mathematical programming, the presented approach performs several linear elastic finite element iterative calculations, which ensures its high computational efficiency. Furthermore, the direct approach is implemented into Abaqus software platform so that it becomes a general tool to handle large-scale shakedown problems of engineering structures with complex geometry and loading conditions. An illustrative sample with analytical solution and three numerical examples from power plant engineering are adopted to validate these theoretical aspects and to present the potential of the direct approach.

Springback prediction of multiple reciprocating bending based on different hardening models

The metal forming process often involves multiple reciprocating bending springback problems. The springback prediction of reciprocating bending is more difficult than that of single bending. Based on the isotropic hardening model, the kinematic hardening model, the mixed hardening model and the YU model, the effects of different hardening models, variable elastic modulus and bending times on the springback are studied. An experimental method for measuring the springback of multiple reciprocating bending is adopted. The multiple reciprocating pure bending is realized by arc-shaped punch and die. The results show that different hardening models have good predictions for the springback of the first bending. However, as the number of bending increases, compared with the increasing error value of other hardening models, only the YU model that considers the variable elastic modulus can realize the accurate prediction of springback, and the error of springback results is within 5% for each bending. The research work is a basic research on the springback problem of multiple reciprocating bending, which can improve the simulation accuracy of metal forming processes involved in this problem, especially for the roller straightening and setting round process with more reciprocating bending.

Anisotropic distortional hardening based on deviatoric stress invariants under non-associated flow rule

An anisotropic distortional hardening (ADH) model is developed under non-associated flow rule by evolving the analytical asymmetric Yoon2014 yield criterion (Hu and Yoon, 2021). The deviatoric stress invariants in the proposed hardening model are analytically expressed. Then, the evolving equations are imposed to describe Bauschinger effect and transient behavior. The anisotropic parameters in yield function can be directly expressed with the four hardening curves along 0°, 45°, 90° and equi-biaxial directions under the proportional loadings. Most importantly, nonlinear strain paths are incorporated in the model. Permanent softening & strengthen, work-hardening stagnation & overshooting behaviors during strain path changes have also been taken into account in the proposed model. The corresponding parameters for these characteristics are relatively independent, although optimization is required for the parameter identifications. The effectiveness and accuracy of the proposed ADH model have been compared with the kinematic hardening models for SPCC material. The constitutive description for 780R AHSS from the proposed model has also been compared with the YU model (Yoshida et al., 2015) under tension-compression along RD, DD and TD. The accuracy of the proposed model under complex strain paths has also been verified by comparing with the results predicted from the eHAH model (Barlat et al., 2013) for EDDQ and DP780. In addition, a plastic potential function is developed based on the form of the proposed model for non-associated flow rule. The accuracy has been verified by applying it to 780R AHSS, EDDQ and DP780.

Load step reduction for adjoint sensitivity analysis of finite strain elastoplasticity

In this paper, load step reduction techniques are investigated for adjoint sensitivity analysis of path-dependent nonlinear finite element systems. In particular, the focus is on finite strain elastoplasticity with typical hardening models. The aim is to reduce the computational cost in the adjoint sensitivity implementation. The adjoint sensitivity formulation is derived with the multiplicative decomposition of deformation gradient, which is applicable to finite strain elastoplasticity. Two properties of adjoint variables are investigated and theoretically proved under certain prerequisites. Based on these properties, load step reduction rules in the sensitivity analysis are discussed. The efficiency of the load step reduction and the applicability to isotropic hardening and kinematic hardening models are numerically demonstrated. Examples include a small-scale cantilever beam structure and a large-scale conrod structure under huge plastic deformations.

Explicit dynamics finite element analyses of asymmetrical roll bending process

In this article, results obtained from a preliminary study that contains a set of explicit dynamics finite element analyses of a metal plate bending process are presented through 3D asymmetrical three roller models. ANSYS Ls-Dyna explicit dynamics finite element (ED-FEA) preprocessor and solver were used to carry out dynamic simulations. Explicit dynamics of a low-velocity process such as the roll-bending of a metal plate is a computationally expensive method. Since plastic deformation occurs on the plate in addition to elastic flexure to eventually possess a circular geometry, the plate material is considered a non-linear material. In this particular study, an aluminum plate was modeled with the Bilinear Kinematic Hardening model including plasticity parameters such as the tangent modulus. A very significant parameter called the mass scaling factor was taken into account to be able to define a specific time-step that was used to determine the computation time interval and the total temporal cost. However, exaggerated reduction of the computation time results in unphysical consequences. The results were presented before and after redesigning the lower and side rolls having a convex geometry and the peripheral velocity of upper roll rotation was decreased to minimize the distortion that occurred on the pre-bent side walls of the aluminum plate.

Analytical Prediction of Stretch-Bending Springback Based on the Proportional Kinematic Hardening Model

Pre-stretching and post-bending are the simplest loading methods for the profile stretch-bending technical process. The inner layers of the profile are stretched and then compressed during the loading process. Considering the Bauschinger effect of metal materials, a new material model called the proportional kinematic hardening model was proposed. The stretch-bending mechanical model was established under a pre-stretching and post-bending loading path. The stress and strain on the cross section of profiles were analyzed. The analytic expressions of curvature radius of the strain neutral layer and bending moment were derived after loading. The analytic method for determining the curvature radius of the geometric center layer after unloading and springback during stretch-bending was established. The rectangular section ST12 profile with symmetrical characteristics is adopted, the stretch-bending experimental results show that the new proportional kinematic hardening model is more accurate than the classical kinematic hardening model in predicting the stretch-bending springback.

Application of a semianalytical strain assessment and multiaxial fatigue analysis to compare rolling contact fatigue in twin‐disk and full‐scale wheel/rail contact conditions

AbstractA semianalytical model is introduced to assess rolling contact fatigue problems in railway applications. The constitutive law is based on the nonlinear kinematic and isotropic hardening model of Chaboche–Lemaitre, which allows the cyclic elastoplastic strain under the contact surface to be evaluated. The much higher computational effectiveness in comparison with finite element (FE) analyses is quantified. The Dang Van multiaxial fatigue criterion is implemented to evaluate the rolling contact fatigue in the subsurface elastic region where cracking is relatively rare but more dangerous than surface cracks. The influence of the presence of sulfides in the wheel matrix in decreasing fatigue strength is also assessed by means of Murakami's approach. The model is used to compare conditions under small‐scale twin‐disk experiments to full‐scale wheel/rail contact conditions. It is found that, for the same Hertzian pressure, the small‐scale contact is more conservative in that it causes a deeper plasticized layer as compared with the elliptical full‐scale contact. In the investigated cases, crack initiation is also not expected according to Dang Van criterion in neither of the studied contact conditions.

Transitions in the strain hardening behaviour of tempered martensite

Martensite is a key constituent in advanced high strength steels (AHSS). The mechanical response of martensite has received particular attention in recent years due to its very high strain hardening rate. Previous studies have shown that the strain hardening behaviour of as-quenched and low temperature tempered martensite can be described by considering martensite as a composite, with constituents showing a spectrum of yield strengths or residual transformation stresses, or more likely, a combination of both effects. However, the composite models are unable to explain the flow behaviour of martensite tempered above 400°C when the composite effect starts to diminish and a transition in the strain hardening behaviour is observed. In this contribution, we conduct a systematic study on the flow behaviour of high temperature tempered martensite with three AHSS compositions. The evolution of the strain hardening behaviour is studied using monotonic and tension-compression tests while the evolution in microstructures is monitored using thermal analysis, interrupted X-ray diffraction and microscopy. A continuous loss of strain hardening capacity is observed in all steels during tempering at lower temperatures due to the diminishing composite effects. When the tempering temperature is above 500°C, all samples show strain hardening rates below the E/50 limit for dislocation storage and a gradual increase in the strain hardening capacity is observed during tempering. To rationalise the tension-compression flow behaviour of martensite tempered at 600°C, a combined isotropic and kinematic hardening model considering dislocation storage and back stresses generated at cementite particles is proposed. The need to combine the composite models that work well for as-quenched and low temperature tempered martensite, with the dislocation-based models that work well for high temperature tempered martensite, is discussed in the context of self-consistently describing the transitions in strain hardening behaviour as a function of tempering temperature.

Semi-Automated Procedure to Estimate Nonlinear Kinematic Hardening Model to Simulate the Nonlinear Dynamic Properties of Soil and Rock

The strain-dependent nonlinear properties of ground materials, such as shear modulus degradation (G/Gmax) and damping, are of significant importance in seismic-related analyses. However, the ABAQUS program lacks a comprehensive procedure to estimate parameters for a built-in model. In this study, a nonlinear kinematic hardening (NKH) model with three back-stress values was used, which allows better fitting to the backbone curves compared to the simplified nonlinear kinematic hardening (SNKH) model previously proposed. Instead of modeling in ABAQUS, a semi-automated procedure was implemented in MATLAB, which can predict shear stress–shear strain hysteretic loops, to find the fitting parameters to the target G/Gmax and/or damping curves. The procedure was applied for three soil and two rock samples, and the results indicate a good match between model and target backbone curves, which proves the application of the procedure and the NKH model in simulating the nonlinear properties of ground materials.

Fatigue analysis of closed-cell aluminium foam using different material models

The fatigue analyses of AlSi7 closed-cell aluminium foam were performed using a real porous model and three different homogenised material models: crushable foam model, isotropic hardening model and kinematic hardening model. The numerical analysis using all three homogenised material models is based on the available experimental results previously determined from fatigue tests under oscillating tensile loading with the stress ratio R=0.1. The obtained computational results have shown that both isotropic and kinematic hardening models are suitable to analyse the fatigue behaviour of closed-cell aluminium foam. Besides, the kinematic hardening material model has demonstrated significantly shorter simulation time if compared to the isotropic hardening material model. On the other hand, the crushable foam model is recognized as an inappropriate approach for the fatigue analyses under tension loading conditions.

P-Y curves for laterally loaded single piles: Numerical validation

Pile foundations are widely used in marine and coastal engineering structures. The correct analysis method must be used to ensure the safety of piled systems used in marine and coastal structures. Despite several methods available in the literature, the numerical method is increasingly applied for understanding the loading mechanism of pile-soil interaction under vertical, lateral, or seismic loadings. The present study focuses on the numerical validation of centrifugal test results of the single pile in dense sand under lateral loading. An extensive parametric study is carried out to validate numerical models due to the lack of experimental tests such as shear or triaxial tests. In the numerical model, the soil is represented by a kinematic hardening model, which is simple to calibrate in finite element analysis, whereas pile is modeled as an elastic material. The p-y family of the curve is back-calculated for a single pile and an algorithm is generated. Two interface models between soil and pile, namely full contact and frictional slip contact, are investigated to represent the behavior under horizontal loading. Then, the analyses are extended to vertical loading to assess the influence of interface models.

Prediction of anisotropic strengths of steel plate after prior bending-reverse bending deformation: Application of distortional hardening model

In this study, the strengths of a steel pipe in different material orientations are predicted using a distortional anisotropic hardening model, namely, the HAH model, implemented in a finite element simulation. The investigated hardening can capture the transient flow behavior under bending and reverse bending strain paths. In addition, the model reproduces the material behavior under orthogonally applied tension from the prior deformation path. To improve the predictive accuracy of the existing distortional hardening model, we additionally implement the multi-component evolution rule of the Bauschinger effect and transient hardening behavior. Two-step tension tests are used to identify the constitutive parameters related to the loading path changes in the bending and reverse bending (BRB) test, which mimics the common pipe manufacturing process in a practical manner. The predicted strengths along the circumferential and transverse directions to the major bending direction agree well with the experimentally measured strengths when the distortional hardening model is employed. By contrast, the classical isotropic hardening and kinematic hardening model over- and under-estimate the yield strength of the specimens after prior BRB loading. The improved accuracy of the strength prediction with the investigated HAH is attributed to the anisotropic identification of the flow behavior under both load reversal and cross-loading conditions, whereas the isotropic-kinematic hardening only considers the back stress evolution at load reversal. In addition to the strengths, the stagnated flow behavior after BRB loading can be well predicted with the HAH model with a properly calibrated yield point elongation using an inverse identification method.

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.