Springback Simulation Research Articles

Pressure and sliding velocity dependent surface asperity based friction model: Application to springback simulation

For accurate predictions of the formability and springback in the finite element sheet forming simulations, significant advances have been achieved in constitutive modeling that captures complex deformations occurring in the sheet forming process. However, friction behavior has been still modeled and implemented as a simple way though it is one of critical factors for accurate numerical simulations. For instance, sheet metal forming simulations often employ the Coulomb friction law with a constant friction coefficient, but it is known to be a function of other factors such as contact pressure, sliding rate and other surface quality. In this study, the microscopic surface asperity based friction model originally proposed by Westeneng [1], as one of microscale level friction models, was revisited by using additional contact assumptions. In particular, the model added the strain rate effect to the existing contact pressure dependent model in order to include the effect of both contact pressure and sliding velocity during sheet forming process. The calculated contact friction coefficient was compared to that by the measured for dual-phase 780 steel sheet under different pressure and sliding velocity. Moreover, the predicted friction model was employed in the simulation of U-draw bending springback by using a user friction subroutine, which was evaluated by the comparison of experimentally measured springback profile

Springback simulation analysis of angle shape forming of springs based on orthogonal experiment method

The springback phenomenon in the angle shape forming process of spring affects the efficiency and accuracy of spring machine adjustment. In this paper, the angle shape forming process and springback process of SWOSC-V material are simulated by finite element analysis software ABAQUS, and orthogonal experiments are designed. According to the simulation results, the importance order and changing trend of each parameter are determined, and the parameters of minimum springback angle and springback law are obtained. It provides a reference for practical application. It is proved that the combination of finite element method and orthogonal experiment can improve the efficiency of finding the springback law.

Determining the coefficients of a homogeneous anisotropic hardening model for ultrathin steel sheets

In the present work, the constitutive description of a 0.1-mm-thick ferritic stainless steel sheet was optimized for application to springback simulations after bending. Springback simulations require Bauschinger effects to be characterized carefully, which is a challenging task with an ultrathin sheet. The coefficients of the homogeneous anisotropic hardening (HAH) distortional plasticity model were calibrated with Zang's novel approach based on three-point bending conducted on pre-strained sheets (Zang et al., 2014). The Hockett–Sherby isotropic hardening law and the Yld2000-2d non-quadratic yield function were considered in this work to complete the HAH approach. Moreover, the degradation of elastic modulus was also accounted for in the finite-element simulations. The coefficients of the HAH model were calibrated using an inverse method by minimizing the difference between experimental and predicted specimen profiles after three-point bending and springback of pre-strained sheets. To validate the coefficients determined with this three-point bending test, U-draw bending tests were conducted and finite-element simulations were carried out. The springback predictions were found to agree well with the experimental results for all three pre-strains investigated, namely, 0% (as-received material) and 7.5% and 12.5% pre-strained ferritic stainless steel sheets.

Pulsed Electric Current V-Bending Springback of AZ31B Magnesium Alloy Sheets

The springback of AZ31B magnesium alloy sheets subjected to pulsed electric current-assisted V-bending tests was investigated. To study the effect of pulsed electric current on the bending-dominated deformation behavior of magnesium alloy sheets, the stress–strain responses from the electric current-assisted uniaxial tension and compression tests were experimentally measured. The stress–strain curves under pulsed electric current showed an instantaneous stress drop under the application of the electric pulse. The ductility was enhanced owing to the application of electric current. The electrically assisted V-bending tests helped reduce the springback compared with conventional room-temperature V-bending tests, and the magnitude of the springback reduction increased with the increase in the electric current density. A thermo-mechanical-electrical finite element model for the electrically assisted V-bending test was developed. To consider the Joule heating effect, temperature-dependent hardening and a yield function with strength differential were implemented for simulating the AZ31B sheet. The simulations could reproduce the experimental flow stress curves of the uniaxial tension/compression tests under pulsed electric current, characterized by an instantaneous stress drop and subsequent transient hardening behavior. The simulated springback profiles were in good agreement with the measured V-bending test data, thus validating the proposed finite element modeling procedure.

Application of Tailor Rolled Blank in A-pillar stiffener of a certain automotive body

Tailor Rolled Blank(TRB) can be used for manufacturing A-pillar stiffener in an automotive body in order to achieve the goal of automotive lightweight on the premise of meeting requirements of strength and rigidity. In this paper, forming and springback simulations of A-pillar stiffener made of TRB were carried out. Aiming at springback and thickness transition zone(TTZ) movement defects, annealing and rib were adopted in order to lower springback and TTZ movement. Research findings show that after annealing is adopted, TTZ movement increases slightly, and meanwhile rib can diminish TTZ movement. Rib and annealing can lower springback of TRB A-pillar stiffener, especially springback on the thinner side, and springback of the whole TRB part becomes uniform.

Effect of constitutive model on springback prediction of MP980 and AA6022-T4

Springback simulation of stamped sheet metal components using finite element method depends on the accuracy of appropriate material models and consideration of appropriate experimental strategies. In this work, tension-compression tests with different strategies, e.g. tension-compression, compression-tension up to various strain levels and multicycle compression-tension tests were conducted to determine parameters of the Yoshida-Uemori (Y-U) nonlinear dynamic hardening model using optimization analysis software LS-OPT. Finite element simulations with LS-DYNA were performed to predict springback behavior of both the advanced high strength steel MP980 (a 980 MPa grade multiphase steel) and aluminum alloy 6022-T4, which was then compared to measurements of stamped U-channel specimens. Results suggest that although the various tension-compression testing strategies can significantly affect the determined values of Yoshida-Uemori model parameters, springback prediction accuracy with this model does not depend on the associated variation of model parameters, at least for the two-dimensional sidewall curl of a U-channel shape. For materials (e.g. MP980) exhibiting a clear Bauschinger effect but insignificant texture anisotropy, the selection of suitable yield criteria (e.g. Hill48), the consideration of elastic modulus degradation combined with the Y-U model can obviously increase the accuracy of springback prediction. In contrast, materials (e.g. AA6022-T4) that exhibit little Bauschinger effect but have significant texture anisotropy, the use of a yield criterion that accounts for anisotropy (e.g. YLD2000-2D) is more important for improving the accuracy of springback prediction.

Advanced Techniques used in Numerical Simulation for Deep-drawing Process

The present paper analyse the main characteristics of the numerical simulation by finite element method of the deep-drawing processes. Also the authors’ highlights the mathematical apparatus and the calculus method used for numerical simulations of metal forming processes in many of the current simulation software. The authors present the capabilities of the inverse analysis, direct analysis, implicit analysis (for springback simulation) and the optimisation analysis applied to explicit formulations.

Springback Prediction Using Finite Element Simulation Incorporated With Hardening Data Acquired From Cyclic Loading Tool

The aims of this article are to present the accuracy of springback prediction in U-bending sheet metal forming processes using finite element (FE) simulation incorporated with kinematics or mixed hardening parameters that are derived from cyclic data provided by the developed cyclic loading tool. The FE simulation results in the form of springback angles are compared with the experimental results for validation. It was found that the mixed hardening model provides better simulation results in predicting springback. This is due to the capability of the isotropic hardening part of this model to describe cyclic transient and the kinematic hardening part to improve description of the Bauschinger effect. Kinematic hardening however, on its own is capable of providing relatively good springback simulation illustrated by errors of less than 8 percent. Overall, the data provided by cyclic loading from the newly developed bending-unbending tool is considered valuable for simulating springback prediction.

Selection of optimal parameters in V-bending of Ti-Grade 2 sheet to minimize springback

Springback is a geometrical defect that occurs due to the removal of the bending force acting on the component the end of the forming process. In the present study, springback behavior of Ti-Grade 2 sheets is studied by finite element method and experimentation. The process parameters considered are punch radius, die opening and sheet thickness. Based on Taguchi (L9) Orthogonal array, the simulation and experiments were conducted. Simulated springback values were found to be in good agreement with experimental values. Signal-to-noise (S/N) ratio is used to determine the optimal combination of parameters that minimizes springback. Analysis of variance is employed to study the influence of process parameter on springback.

Effect of deformation induced nonlinear and anisotropic elasto-plasticity on sheet forming simulations

Anisotropy in initial yield and subsequent hardening in flow stress has been modeled in the finite element simulations to enhance the accuracy of formability and springback in sheet metal products. As continued efforts in the field of constitutive modeling, the evolution of anisotropy during the plastic deformation and its dependency on deformation path were also studied by many researchers. In addition to the plastic behavior, the elastic nonlinearity in pre-deformed sheet metals has been also regarded as a key factor which influences the accuracy of the sheet metal forming simulation, particularly in the springback simulation. In this study, recent reviews on the constitutive modeling for the deformation induced nonlinear and evolution of anisotropy are provided mainly using the published data [1,2]. To model the initial anisotropy the Hill 1948 yield function with non-associated flow rule and Yld2000-2d non-quadratic yield function were considered. Also, these yield surfaces evolve as a function of equivalent plastic strain. For better modeling the nonlinearity of elastic behavior during the deformation, recently developed multi-surface elasticity model was implemented in the simulation. To investigate the effect of the considered anisotropic plasticity and nonlinear elasticity on forming simulation, cylindrical circular cup drawing was experimentally conducted and its earing profile and springback after splitting of the formed cup in the circumferential direction were compared with the simulated results. The results showed that the finite element simulations could predict the deformed shapes after forming and springback with enhanced accuracy when the constitutive model could represent the complexity in the anisotropy and nonlinearity during plastic deformation.

High accuracy springback simulation by using material model considering the SD effect

In order to enhance the accuracy of springback simulation, the strength differential (SD) effect, i.e., the difference in flow stress between tension and compression, of a high strength cold-rolled steel sheet with a tensile strength of 980 MPa is measured by means of in-plane tension-compression test apparatus. Bi-axial stress tests are also performed to measure the contour of plastic work of the test material. From those experimental results, the material model which can consider the SD effect is determined. Furthermore, this material model is implemented into commercial FEM code by using user-subroutine function. To check the validity of this model and established FEM analysis system, curvature-hat crush forming experiment is performed. By comparing the experimental result and forming simulation result, the accuracy of the material model which can consider the SD effect is validated. Consequently it is concluded that the use of material model which is capable of reproducing the SD effect is a must to enhance the accuracy of springback simulation.

Spring-back prediction based on a rate-dependent isotropic–kinematic hardening model and its experimental verification

This paper deals with spring-back prediction with a rate-dependent isotropic-kinematic hardening model with tension/compression in high speed U-draw-bending tests. In order to verify the validity of the present model, spring-back simulation is carried out and its results are compared with experimental results. A rate-dependent isotropic-kinematic hardening model has been proposed by combining the rate-dependent function of material parameters and the Chaboche type model for the TWIP980 steel sheet under tension and compression. The proposed model can accommodate the strain rate effect on the material properties by providing rate-dependent hardening curves under loading and reverse loading condition. This change of the rate-dependent material properties is important to predict spring-back under high speed deformation in practical sheet metal forming undergoing tension and compression during the deep-drawing forming. High speed U-draw-bending tests have been performed to investigate the strain rate effect on spring-back of the TWIP980 steel sheet after draw-bending at intermediate strain rates of up to a hundred per second. The experimental results have been compared with simulation results of high speed U-draw-bending and spring-back analysis with four hardening cases: isotropic; isotropic-kinematic; rate-dependent isotropic; rate-dependent isotropic-kinematic hardening models. It is demonstrated with the comparison that the rate-dependent isotropic-kinematic hardening model proposed provides the best prediction of spring-back after U-draw-bending at intermediate strain rates among the four hardening cases.

Crystal-plasticity finite-element simulation of time-dependent springback in a commercially-pure titanium sheet

A crystal-plasticity finite-element method was used to examine the deformation mechanism of time-dependent springback in a commercially-pure titanium sheet. To reproduce the viscoplastic behavior of the sheet, the material parameters were calibrated to reproduce the strain-rate dependency of the stress-strain curve under uniaxial tension. A two-dimensional draw bending process was simulated and the change in the sidewall curvature was evaluated. The simulation results showed that the curvature increased with the elapsed time after unloading, consistent with experimental results reported elsewhere. The deformation mechanism during the process was discussed in terms of evolution of stress and relative activities of slip and twinning systems.

Kinematic hardening performance of 5052 aluminium alloy subjected to cyclic compression-tension

In order to study the kinematic hardening performance of 5052 aluminium alloy, experiments of cyclic compression-tension were conducted in this work. The kinematic hardening performance including the Bauschinger effect, transient hardening and permanent softening shown by the forward-reverse stress-strain curves was discussed. The famous Yoshida-Uemori hardening model was adopted to characterize the kinematic hardening behaviour of AA5052. The parameters in Yoshida-Uemori hardening model were identified with an inverse method composed by experiments, finite element simulation and optimization. Experiments of cyclic loading-unloading uniaxial tension were also performed to identify the degradation of the elastic modulus of AA5052 with the plastic strain. U-bending springback simulation using the Yoshida-Uemori hardening model was conducted. The results showed that the investigated AA5052 has strong Bauschinger effect, transient hardening and permanent softening. The percentage of elastic modulus degradation could reach 16.7% at 8.8% plastic strain. The Yoshida-Uemori hardening model can capture the kinematic hardening behaviour of AA5052 very well.

A constitutive law based on the self-consistent homogenization theory for improved springback simulation of a dual-phase steel

It has been widely observed that below the flow stress of a plastically deformed material the stress–strain response of the material does not obey the linear relation assumed in classical elasto-plastic models. As a matter of fact, a closer observation indicates that the stress–strain response of the material is nonlinear upon unloading. This results in a larger strain recovery than predicted by the linear elastic law which consequently results in an error in springback prediction. Furthermore, when the material undergoes compression after tension, it exhibits Bauschinger effect, transient behavior and permanent softening. The accuracy of the springback prediction is dependent on the capability of the model in capturing the above mentioned phenomena. In this work a constitutive law based on the self-consistent homogenization method is developed. In this model the stress inhomogeneity in the material is realized through considering a distribution in yielding of individual material fractions. The model was calibrated using stress–strain curves obtained from tension–compression experiments. The model has shown to be capable of predicting the nonlinear unloading behavior and the Bauschinger effect while maintaining computational efficiency for FEM simulations.

The Current Status and Development of Practical Sheet Metal Forming Simulation

Sheet metal forming simulation is widely used for predicting formability and springback behavior of stamping parts. The increasing usage of low formability material such as high-strength steel and aluminum alloy has grown the importance of CAE technologies. JSOL responds to the expanding demand for CAE by developing and providing software JSTAMP (LS-DYNA). This presentation reports the current and development statuses of the practical use of CAE technologies. The current status is described by taking the springback simulation results as the example. The accuracy and the simulation time of springback prediction and springback compensation of the tool is presented. For the development effort, this presentation mentions the result obtained from different yield function to accomplish more accurate simulation, and the approach to optimizing CAE for hot forming. The technical development addressing the application of CAE for CFRP which are expected to become more common material for automobile part is also introduced.

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.

Effect of the hardening rules on the creep age forming prediction of 7050 aluminum alloy with experimental verification

The creep age forming (CAF) has been used in the aerospace sector due to its attractive characteristics that allows producing a component with low residual stress. The process has been studied from the finite-element simulations which are used mainly to predict the springback. However, to accomplish the simulation, it is necessary to set the CAF constitutive equations in the finite-element software. In addition, it is also necessary to define the hardening rule which is applied to determine the creep strain. This work aims to investigate CAF applying the finite-element analysis with the time-hardening rule and strain-hardening rule and thus predicting creep strain, stress relaxation, and springback. The finite-element simulations were accomplished in dies with single and double curvatures and the blank’s material was the alloy AA7050. Furthermore, the Marin–Pao model was implemented in the MSC.Marc software through a user subroutine. This model was fitted to the creep experimental curves and it generated good agreement with the experimental data. The results of the simulations that used the time-hardening rule were similar to the strain-hardening rule, and therefore, if it had been chosen a hardening rule, it would not have generated a significant impact in the CAF simulation results. At the end, the simulated springback was compared to the experimental springback from the literature and the percentage error ranged from 0.46% to 15.33% that indicate the proximity with the literature data. Moreover, other experimental validation was performed, and when compared to the results of this methodology, the calculated error in springback was 6.3%.

Split-Ring Springback Simulations with the Non-associated Flow Rule and Evolutionary Elastic-Plasticity Models

Finite element simulations and experiments for the split-ring test were conducted to investigate the effect of anisotropic constitutive models on the predictive capability of sheet springback. As an alternative to the commonly employed associated flow rule, a non-associated flow rule for Hill1948 yield function was implemented in the simulations. Moreover, the evolution of anisotropy with plastic deformation was efficiently modeled by identifying equivalent plastic strain-dependent anisotropic coefficients. Comparative study with different yield surfaces and elasticity models showed that the split-ring springback could be best predicted when the anisotropy in both the R value and yield stress, their evolution and variable apparent elastic modulus were taken into account in the simulations. Detailed analyses based on deformation paths superimposed on the anisotropic yield functions predicted by different constitutive models were provided to understand the complex springback response in the split-ring test.

Numerical study on springback prediction of aged steel based on quasi-static strain-hardening material model

Material model of aged steel, the material’s stress and strain behavior in the region of yielding, plays a critical role in springback prediction of FEA simulation. In most of the FEA simulations, the material is modeled as a linear elastic and then after yielding, a linear strain-hardening model or a power-law strain-hardening model. In the prediction of springback by FEA simulation, there is always a problem that the prediction is far away to the true springback of the products or samples. This paper employs a quasi-static strain-hardening material model which gives a more accurate description of the material properties of aged steel for FEA simulation of the forming. A typical V-bending for aged steel is simulated with finite element software, ABAQUS, to predict the springback. A 2D model which consists of multiple rigid bodies and a deformable body is performed in this study adopting four-node linear plane-strain elements. Meanwhile, a 2D model that applies a power-law strain-hardening material model is implemented as a contrast. By comparing the results from the simulations based on different material models with those from experiments, a better correlation between the simulations using a quasi-static strain-hardening material model and the experiments is achieved. Besides, the bending process for aged steel is also analyzed utilizing quasi-static strain-hardening material model with variable ageing coefficients. It is drawn that the greater the ageing coefficient within certain range, the greater the springback simulation accuracy by comparison between simulation and experiment results. In addition, as the upper yield stress is not easy to be measured directly, a method for reverse calculation of upper yield stress through springback ratio and quasi-static flow stress is proposed.