Work-hardening Stagnation Research Articles

Size effect on the cyclic deformation behavior of superalloy ultrathin sheet: Characterization and multiscale modelling

Superalloy ultrathin sheets have high strength, outstanding oxidation resistance, corrosion resistance and fatigue performance, and its thin-walled components occupy a considerable proportion in aeroengines. In the microforming process of aeroengine thin-walled components, the superalloy ultrathin sheet is often deformed under complex loading states and shows obvious springback. However, the forming and springback laws of superalloy ultrathin sheet in the microforming process are not clear and often affected by size effect. In addition, the existing nonlinear kinematic hardening models cannot accurately forecast the deformation and springback of superalloy ultrathin sheets. To address this issue, the cyclic shearing tests were performed to systemically explore the size effect on Bauschinger effect, permanent softening, transient hardening and work hardening stagnation of superalloy ultrathin sheets under cyclic loading states. The mechanism of size effect on cyclic mechanical response was systematically revealed through microstructure evolution combined with surface layer effect. In addition, a new multiscale cyclic hardening model was proposed based on the Y-U model and size effect on cyclic deformation behavior of superalloy ultrathin sheets. The new multiscale cyclic hardening model coupling surface layer effect and grain boundary strengthening effect was constructed by modeling the relationship between the cyclic mechanical response and size effect. Comparisons between the original Y-U model and the new proposed model on the characterization effect of shear stress-strain curves demonstrated that the proposed cyclic hardening model can accurately present the cyclic deformation behavior. To further verify the prediction capability of the proposed cyclic hardening model, the springback behavior of superalloy ultrathin sheet in U-bending test and hydroforming of seal ring was predicted via the proposed model combined with the decrease of elastic modulus and Yld2000–2d yield criterion, and the predicted results were compared with experimental ones. Comparative research revealed that the proposed cyclic hardening model can accurately describe the cyclic deformation behavior and springback of superalloy ultrathin sheets affected by size effect.

Size effect on nonlinear unloading behavior and Bauschinger effect of Ni-based superalloy ultrathin sheet

• Cyclic deformation behavior of superalloy foil is represented by cyclic shear test. • Nonlinear unloading behavior at microscale becomes evident. • Bauschinger effect are affected by both geometric and grain size effect. • Size effect on instantaneous and permanent softening is revealed. • Work hardening stagnation is related to dislocation evolution and size effect. Superalloy ultrathin sheet is widely utilized in thin-walled components of aero-engine because of its excellent comprehensive performance. Nevertheless, it is hard to precisely predict the springback phenomenon during the plastic deformation of superalloy ultrathin sheet due to the size effect. To explore size effect on nonlinear unloading behavior and Bauschinger effect of Ni-based superalloy sheets, the uniaxial tensile, cyclic loading and unloading, and cyclic shearing tests were conducted on superalloy ultrathin sheets with diverse grain sizes and thicknesses of 0.2 and 0.25 mm. The experimental results demonstrated that the increasing grain size is accompanied with the decrease of flow stress of superalloy ultrathin sheet and the change of density of forest dislocation and moving dislocation. The dislocation annihilation rate of superalloy ultrathin sheet increases with decreasing t / d ratio, and the nonlinear unloading behavior becomes more obvious. Meanwhile, the degradation of elastic modulus becomes more evident with the increasing grain size. Driven by back stress, Bauschinger effect of superalloy ultrathin sheet becomes more apparent with larger t / d ratio. In addition, the fine-grained superalloy ultrathin sheet shows obvious earlier re-yielding and large instantaneous softening rates and the variation of t / d ratio also affect the permanent softening and work-hardening stagnation of superalloy ultrathin sheet.

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.

Consequences of large strain anisotropic work-hardening in cold forging

The influence of anisotropic work-hardening on the component properties and process forces in cold forging is investigated. The focus is on the material behaviour exhibited after strain path reversals. The work-hardening of three steels is characterized for large monotonic strains (equivalent strains up to 1.7) and subsequent strain path reversals (accumulated strains up to 2.5). Tensile tests on specimens extracted from rods forward extruded at room temperature reveal an almost linear work-hardening for all investigated steels. The application of compressive tests on extruded material gives insights into the non-monotonic work-hardening behaviour. All previously reported anisotropic work-hardening phenomena such as the Bauschinger effect, work-hardening stagnation and permanent softening are present for all investigated steels and intensify with the pre-strain. Experimental results of 16MnCrS5 were utilized to select constitutive models of increasing complexity regarding their capability to capture anisotropic work-hardening. The best fit between experimental and numerical data was obtained by implementation of a modified Yoshida-Uemori model, which is able to capture all observed anisotropic work-hardening phenomena. The constitutive models were applied in simulations of single- and multi-stage cold forming processes, revealing the significant effect of anisotropic hardening on the predicted component properties and process forces, originating in the process-intrinsic strain path reversals as well as in strain path reversals between subsequent forming stages. Selected results were validated experimentally.

A novel analytical model to predict springback of DP780 steel based on modified Yoshida-Uemori two-surface hardening model

Advanced high strength steels are widely used in the automotive industry due to their appropriate strength to weight ratio. This alloy has unique hardening behavior. In this paper, a novel analytical model is introduced to predict springback in U-shaped bending process of as-received and pre-strained DP780 dual phase steel specimens. This model is based on the Hill48 yield criterion and plane -strain condition. The effect of sheet thinning and the motion of the neutral surface is taken into account on the springback. The modified Yoshida-Uemori two surface hardening model is applied to investigate the effect of work hardening stagnation. This novel model is examined on the Numisheet 2011 benchmark 4. The effects of the blank holder force and work hardening stagnation are studied on the sheet springback phenomenon. By comparison of the present model with previous alternate models, obtaining the more accuracy is tangible. Also, it is demonstrated that the springback parameters have more changes with increasing the blank holder force. Also, the parameter of the work hardening stagnation has more effect on the pre-strained specimen as compared to the as-received sample.

Numerical Prediction of Forming Car Body Parts with Emphasis on Springback

Numerical simulation is an important tool which can be used for designing parts and production processes. Springback prediction, with the use of numerical simulation, is essential for the reduction of tool try-outs through the design of the forming tools with die compensation, therefore, increasing the dimensional accuracy of stamped parts and reducing manufacturing costs. In this work, numerical simulation was used for performing the springback analysis of car body stamping made of aluminium alloy AA6451-T4. The finite element analysis (FEM) based software PAM-STAMP 2G was used for performing the forming and springback simulations. These predictions were conducted with various combinations of material models to achieve accurate springback prediction results. Six types of yield functions (Barlat89, Barlat2000, Vegter-Lite, Hill90, Hill48 isotropic, and Hill48 orthotropic) were used in combination with the Voce hardening model. Springback analysis was conducted in three sections of the formed part; the numerical results were compared with the experimental values. It was found that the combinations of Barlat’s yield functions and the Voce hardening law were most accurate in terms of springback prediction. Additionally, it was found that the phenomena that were investigated, which are required for the determination of the kinematic hardening model, such as the change of Young’s modulus E, the transient behaviour, work-hardening stagnation, and permanent softening, were not observed in the aluminium alloy studied.

On the non-linear unloading behavior of a biaxially loaded dual-phase steel sheet

The response of the dual-phase steel DP 590 under continuous loading and unloading from a biaxial stress state is examined using a combination of experiments and analysis. The experiments utilize cruciform specimens of a custom geometry that develop quite uniform strain fields in the test-section and allow the development of large strains (>12%, depending on the loading path). Experiments along 9 radial stress paths in the first quadrant of the plane-stress space were performed. The first part of each unloading and reloading follows the prediction of orthotropic elasticity using the initial elastic properties. A second linear slope is observed, before the responses become fully non-linear. The non-linear strain recovery is measured to be about 1/5 of the linearly elastic strain for this material. Furthermore, the chord modulus reduces exponentially to a value of ∼90% of the initial. The biaxial cruciform experiments are also used to determine contours of constant plastic work and to calibrate the Yld2000-2D anisotropic yield function. A combined isotropic/kinematic hardening model with a simple exponential-decay shrinkage of the yield surface is adopted. The non-linear unloading response is represented by a 4-term Chaboche non-linear kinematic hardening model using the Ziegler back-stress evolution rule. Plasticity during unloading is assumed to occur as soon as deviation from proportionality is detected. The 4 terms are necessary for capturing both the second linear slope after (re-) yielding and the work-hardening stagnation observed in the experiments. The agreement between experiments and predictions for the induced strain paths is very good. The predictions of the non-linear strain recovery are good overall, and are independent of the yield surface adopted. In summary, it is proposed to capture the biaxial unloading behavior using a constitutive model that includes an anisotropic yield function suitable for predicting the induced strain paths, and a non-linear kinematic hardening rule suitable for predicting the tension–compression behavior of the material at hand.

A new strategy to describe nonlinear elastic and asymmetric plastic behaviors with one yield surface

This paper proposes a new strategy to describe both nonlinear elastic and asymmetric plastic behaviors (early re-yielding, transient Bauschinger effect, permanent softening, and work-hardening stagnation) only with one yield surface. There have been the popular models, such as Yoshida-Uemori and Quasi-Plastic-Elastic (QPE) models, that have led to remarkable improvements in describing material's behavior and predicting springback. Although the Yoshida-Uemori model describes the asymmetric plastic behavior, it is challenging to follow the nonlinear elastic response. On the other hand, the QPE model does not capture the work-hardening stagnation though it follows the nonlinear elastic behavior. Besides, the above models have multiple surfaces leading to a complex mathematics and, then leading to increased computation time. In this study, a new one surface method incorporates state of strain change or state of energy change as well as the stress state in determining the deformation mode, so that it is possible to keep only one yield surface. In order to capture the work-hardening stagnation, the one surface method traces the equivalent plastic strain, then compares the change in the incremental equivalent plastic strain of the current path to the accumulated one up to the previous path when the loading direction reverses. This way makes the computation time much faster than an existing method which employs an additional surface to capture the work-hardening stagnation. The one surface method has been implemented into a user-defined material (UMAT) subroutine, and validated by comparing it with the experimental results and the results from Yoshida-Uemori and QPE models with cycling loading conditions and U-draw bending test. This work shows that the one surface method can describe both nonlinear elastic and asymmetric plastic behaviors with the reduction of complexity and computation time.

Evolutionary anisotropy and flow stress in advanced high strength steels under loading path changes

Chaboche kinematic hardening, Yoshida–Uemori, and homogenous anisotropic hardening (HAH) models were evaluated in terms of their prediction capability of flow stress and evolutionary r-value under loading path changes. The first two models are based on kinematic hardening, whereas the HAH model is based on distortional hardening. Continuous compression–tension (CT) tests with pre-strains for dual-phase 780 and transformation-induced plasticity (TRIP) 780 steel sheets were conducted. For the initial anisotropy described by the Yld2000-2d model, uniaxial tension tests for three material orientations and a biaxial test were performed. During the CT tests, both stress and r-value variations with plastic strain were measured. All the models were implemented into the finite element software ABAQUS using user material subroutines. Experimentally, both sheets exhibited typical anisotropic hardening features such as the Bauschinger effect, transient hardening, and long-range softening. The TRIP 780 exhibited small work-hardening stagnation. In addition, the evolutionary r-value during the second loading was significant. The three models could predict most of the features in the stress–strain curves during the second loading. However, only the HAH model could predict the experimentally observed r-value evolution. This evolutionary r-value predicted by the HAH model could be explained by distortion of the yield locus during the first loading and its rapid recovery toward the initial yield locus shape.

Experimental and Numerical Investigation of Sheet Metal Behavior under Cyclic Tension-Compression Loading

Measurement of hardening under reversed uniaxial loading is because of its simplicity very effective mechanical test to achieve several important features of material behavior. In this paper is described special fixture which serves as a prevention of the sheet buckling during the cyclic tension-compression test. Result of the cyclic tension-compression test can consider several important features of the material behavior, which are necessary to be defined in the numerical simulation process. Experimental part of this paper consists of comparison results of strain path obtained from numerical simulation and real experiment. While in numerical simulation process was used material model describing isotropic hardening, real material behaved differently. Difference between strain paths also causes differences between results of springback values obtained in numerical simulation. New material models which include Bauschinger effect whether workhardening stagnation can diminish differences between results of an experiment and a numerical simulation and thus may also improve accuracy of the numerical simulation.

Effect of nonlinear strain paths on forming limits under isotropic and anisotropic hardening

The path-dependence of the conventional Forming Limit Diagram (FLD) is an important issue for its applications in industry. Great efforts have been made to understand the nature of the path-dependence with both experimental and theoretical approaches, many of them attempting to find a path-independent way for the application of forming limits. In this paper, we focus on the nonlinear strain path effect on forming limit predictions using both isotropic and anisotropic hardening models. The Forming Limit Diagram (FLD), Forming Limit Stress Diagram (FLSD) and Forming Limit Effective Strain Diagram (epFLD) of sheet metals subject to linear and nonlinear strain paths are analyzed and compared using the Marciniak–Kuczynski approach. An anisotropic hardening model based on Yoshida and Uemori development is adopted in this study, and it is coupled with the traditional Hill’48 yield surface. This model is capable of describing the complex Bauschinger phenomenon after the material undergoes the reverse loading process such as the early re-yielding, work-hardening stagnation and permanent softening. Two different scenarios for the change of strain paths are also investigated. In the first scenario, the sheet material is initially loaded with a fixed strain increment ratio, unloaded to the free stress state, and then reloaded with a different strain increment ratio until the forming limit is reached. In the second scenario, the material does not undergo elastic unloading. Instead, the strain path is abruptly changed to a different strain increment ratio and the material undergoes continuous loading until the forming limit is reached. It is found that the work-hardening behavior after the pre-straining and the loading scenario plays an important role in the path dependent behavior of forming limits. Detailed analysis reveals that the M–K approach may have contributed to the significance of path-dependence observed in this study, especially at high pre-strain levels.

Yoshida–Uemori material models in cyclic tension–compression tests and shear tests

Demands for energy conservation and impact resistance have made high-strength steel a crucial material in sheet metal parts for the automotive industry. However, during metal stamping, the springback associated with high-strength steel plates is significantly greater than for mild steel. This makes numerical simulation and prediction in stamp forming extremely difficult. The Yoshida–Uemori material model comprehensively describes the Bauschinger effect and work hardening stagnation that occur in metal during cyclic large plastic deformation, making it an important model for the simulation of high-strength steel stamp forming. This study employed cyclic tension–compression tests and shear tests to explore the construction of a Yoshida–Uemori model and verify its accuracy using numerical simulation.

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.

Extension of quasi-plastic–elastic approach to incorporate complex plastic flow behavior – application to springback of advanced high-strength steels

Materials modeling and numerical formulations were conducted to describe the complex material behavior upon strain path change in order to enhance the prediction accuracy of springback in advanced high strength steels (AHSS). An approach without kinematic hardening rule, or the homogeneous anisotropic hardening (HAH) model, was incorporated to the newly conceived quasi-plastic–elastic strain (QPE) formulations. The HAH model is able to capture complex plastic flow behavior of sheet metals such as the Bauschinger effect, transient behavior, work-hardening stagnation and permanent softening. The QPE approach was developed to reproduce the nonlinear elastic behavior during unloading and reloading. The two models were independently validated for predicting springback, with better performance than conventional constitutive models. In this study, the two models are combined and extended to enhance the prediction capability of springback in AHSS. For this purpose, fully implicit numerical algorithms were re-formulated to link the two modeling approaches using general anisotropic yield function and hardening for shell element. The original model was only valid for continuum isotropic element with analytical stress integration procedure. Simulations of 2D draw bending test were performed to validate the developed approach for two AHSS, DP780 and TRIP780, sheets. The springback prediction was significantly improved if most of the complex material behavior relating to elasticity and plasticity were taken into account in the finite element simulations.

Dislocation-based model for the prediction of the behavior of b.c.c. materials – Grain size and strain path effects

Sheet metal forming processes involve multi-axial strain paths. For the numerical simulation of such processes, an appropriate constitutive model that properly describes material behavior at large strain is required. For accurate and time-effective simulations, it is crucial to use plasticity models based on physics, as material macroscopic behavior is closely related to the evolution of the associated microstructures. Accordingly, a large strain work-hardening phenomenological model that incorporates the intragranular microstructure evolution through a dislocation density approach is proposed. The model is defined by a yield criterion and hardening laws that are all grain-size dependent. The classical Hill criterion in which grain-size dependency was introduced is proposed. Hardening laws are given by a combination of kinematic and isotropic contributions that respectively take into account the evolution with strain of cell blocks formed by geometrically necessary boundaries (GNBs) and individual dislocation cells delineated by incidental dislocation boundaries within cell blocks (IDBs). On the one hand, IDBs evolution contribution is described by a modified Rauch et al. isotropic model, which is able to describe work-hardening stagnation and work-softening. On the other hand, GNBs evolution contribution is described by a grain-size dependent tensorial back-stress expression proposed by Aouafi et al. (2007) to describe the plastic anisotropy and Bauschinger effect. Moreover, the proposed model aims to accurately predict steel behavior through an innovative approach by only changing few “simply measurable” microstructure data (e.g. chemical composition, grain size, etc.). The predictive capabilities of the model are assessed for interstitial free (IF) and dual phase (DP) steels with grain sizes varying respectively in the 8–40μm and 1–10μm value range. Different loading paths are analyzed, namely the uniaxial tensile test, reversal simple shear and orthogonal tests.

Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension

The mechanical behavior of mild and dual phase steel sheets is investigated at room temperature in quasi-static conditions under different strain paths: uniaxial tension, simple shear and balanced biaxial tension. The aim is to characterize both the anisotropy and the hardening, in order to identify material parameters of constitutive equations able to reproduce the mechanical behavior. In particular, a good description of flow stress levels in tension and shear as well as plastic anisotropy coefficients is expected. Moreover, the Bauschinger effect is investigated with loading–reloading in the reverse direction shear tests and the balanced biaxial tension test gives insight of the mechanical behavior up to very high equivalent plastic strains. Yoshida–Uemori hardening model associated with Bron–Besson orthotropic yield criterion is used to represent the in-plane mechanical behavior of the two steels. The identification procedure is based on minimization of a cost function defined over the whole database. The presented results show a very good agreement between model predictions and experiments: flow stress during loading and reverse loading as well as plastic anisotropy coefficients are well reproduced; it is shown that the work-hardening stagnation after strain path reversal is well estimated in length but Yoshida–Uemori model underestimates the rate of work-hardening.

Material modelling for accurate springback prediction

The magnitude of the springback depends mainly on the residual stresses in the work piece after the forming stage. An accurate prediction of residual stresses puts, in turn, high demands on the material modelling during the forming simulation. Among the various ingredients that make up the material model, the hardening law is one of the most important ones for an accurate stress distribution prediction. The hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behaviour, permanent softening and work-hardening stagnation. Five different hardening models and four different steel grades have been evaluated in the present investigation. The unknown material parameters were identified by inverse modelling of a three point bending test. The model’s ability the reproduce experimental force-displacement relationships were evaluated. A simple springback experiment was performed for confirmation.

Modeling of reverse loading effects including workhardening stagnation and early re-plastification

This paper deals with the Bauschinger effect in sheet metal forming simulation. The concept of a new material model is presented able to accurately handle the phenomena of early re-plastification, transient softening and workhardening stagnation at load reversal. Besides the standard data used for simulations based on isotropic hardening, the model requires only four additional, physically comprehensible material parameters. The model is verified by means of tension-compression tests and springback simulations for hat profiles for three typical high-strength steel alloys.

Towards an accurate description of the anisotropic behaviour of sheet metals under large plastic deformations: Modelling, numerical analysis and identification

On the basis of the microstructural evolution after two-stage non proportional loading at finite strains, a so-called microstructural model was developed by Teodosiu and Hu (1995) that accurately describes the macroscopic anisotropic behaviour such as the Bauschinger effect, the work-hardening stagnation and the work-softening of polycrystalline metals. Many intragranular deformation mechanisms, corresponding to the formation and the evolution of persistent dislocation structures, have been taken into account in choosing the scalar and tensorial internal variables of the elastoplastic model and postulating their evolution equations. In the work discussed here, after a detailed description of Teodosiu–Hu model, several rheological tests and their numerical simulations on different polycrystalline materials are performed in order to evaluate the accuracy and the efficiency of the proposed model. To this aim, a sensitivity study of the material parameters is first carried out in order to show their different effects on the macroscopic behaviour. Therefore, a strategy for their identification is discussed. Regarding to the respective mechanical response of several materials, two simplifications of the proposed model are presented in order to take into account their specific behaviour. Finally, identification of the proposed models is performed and compared to more classical anisotropic work-hardening phenomenological models.

A model of large-strain cyclic plasticity and its application to springback simulation

This paper presents a framework of constitutive modeling of large-strain cyclic plasticity which describes both the deformation- and texture-induced anisotropies of materials. In this model, the transient Bauschinger effect is described accurately by a new equation of the backstress evolution, and the strain-range and mean-strain dependencies of cyclic strain hardening are expressed by a model of workhardening stagnation. For the description of texture-induced anisotropy, any of widely accepted yield criteria of orthotropic anisotropy is easily incorporated into this model. This paper demonstrates the advantage of the present model in the springback analysis over other classical models by comparing the FE simulations of draw bending with the corresponding experimental results.