Springback Simulation Research Articles

Prediction of the Interface Behavior of a Steel/CFRP Hybrid Part Manufactured by Stamping.

Carbon fiber-reinforced plastic (CFRP) is a lightweight material. The automotive industry has focused on producing a steel/CFRP hybrid part to reduce overall weight. After manufacturing, delamination can occur at the interface between the CFRP and steel owing to the hybrid part constituting dissimilar materials. However, most studies have focused only on designing the manufacturing processes for the hybrid part or evaluating the adhesive used at the interface. Therefore, it is necessary to predict the behavior of the interface after demolding the hybrid part. This study aimed to predict the interface behavior of a steel/CFRP hybrid part by considering its forming and cohesive properties. First, double cantilever beam (DCB) and end-notched flexure (ENF) tests were performed to obtain cohesive parameters, such as energy release rate of modes I and II (GI, GII). The experimentally obtained properties were applied to the bonding area of the hybrid part. Subsequently, a forming simulation was performed to obtain the stress of the steel blank in the hybrid part. The stress distribution after forming was utilized as the initial condition for spring-back simulation. Finally, the interface behavior of the hybrid part was predicted by a spring-back simulation. The simulation was conducted using the residual stress of steel outer and the cohesive properties on the interface, without the application of any external forces. The cases of spring-back simulation were divided as delamination occurrence and attached state. The simulation results for prediction of delamination occurrence and bonding showed good agreement in both cases with experimental ones. The proposed method would contribute to expanding the manufacturing of the hybrid part by stamping and reducing the manufacturing cost by prediction of delamination occurrence.

Towards high-accuracy axial springback: Mesh-based simulation of metal tube bending via geometry/process-integrated graph neural networks

Springback has always been a stubborn defect that affects the axial accuracy of metal bending. The finite element simulation of springback enables effective control and precise compensation to improve the forming quality. Affected by the material, size, and forming process, the generation pattern of the springback defect remains further exploration. Graph-based deep learning techniques support differentiable high-dimensional physics simulations with significantly lower computational resources and comparable accuracy. In this paper, a framework based on geometry/process-integrated Graph Neural Networks (GNN) is presented for simulating axial springback of mesh-based metal bending, with a specific focus on the tube bending. The framework adopts an encode-process-decode structure, equipped with parallel graph network blocks and data augmentation strategy, to capture the axial springback information with high fidelity in a form of mesh. Comparative experiments reveal that our framework achieves an accuracy comparable to that of finite elements method, yielding an average nodal error below 1 mm and outperforming three representative GNN baselines. The framework remarkably enhances the simulation efficiency, exhibiting a four-order-of-magnitude improvement on CPU and a six-order-of-magnitude improvement on GPU compared to finite elements method. Furthermore, we successfully apply the proposed framework to simulate the springback of plate V-bending, showcasing its robust generalization ability. These results illustrate the capability of our GNN framework to achieve the accurate and real-time springback simulation, with significant implications for digital twin development and bent tube quality optimization.

Appropriateness of hydrostatic pressure-based modeling for strength differential effect in advanced high strength steel

Although numerous models have been proposed to describe the strength differential (SD) effect, their appropriateness and efficiency in the case of advanced high strength steel (AHSSs) have not been investigated. To this end, this study investigates the SD effect in AHSS using a hydrostatic-pressure-dependent plasticity theory. Although pressure model can effectively predict the SD effect in AHSSs with only one coefficient, the original formulation is experimentally inconsistent in the first quadrant of a yield surface. Hence, this study developed a new formulation to remove the inconsistency in a simple manner and validated the pressure model using new experimental data reported for two recently developed AHSSs: DP980 and MART1500Y. The SD effect is characterized based on monotonic compression and tension tests in three different directions with respect to the rolling direction to obtain the stress–strain curves and r-values. Next, the pressure model is used to predict the plastic behavior of both steel sheets. The parallel transition of flow stress and similarity in r-values between the tension and compression states supports the appropriateness of the proposed pressure-based modeling. Furthermore, these insights substantiate the fact that deformation mechanisms cannot explain the SD effect in both steel sheets. Therefore, complex yield functions that describe the SD effect in general materials are not necessary in the case of AHSS. Additionally, the pressure model is incorporated into a distortional plasticity model for applying it to springback in the bending process. The distortional plasticity model with and without the pressure model is calibrated using tension–compression curves, thereby revealing that the SD significantly affects the calibration. Finally, a U-draw bending experiment and the corresponding finite element simulation are conducted to compare the springback; the results show that considering the SD effect improves the springback simulation accuracy.

Development of combined hardening model for spring-back simulation of DP600 in multi-stage sheet metal forming

High strength steel DP600 is widely used in automobile industry due to its excellent mechanical property compared to conventional steel, but spring-back issue is considered to be the major challenge of DP600 in forming process, as the spring-back is triggered by the release of complicated internal stress. In multi-stage sheet metal forming, the sheet may be subject to several cycles of loading and reverse loading, Bauschinger effect greatly influence the strain stress behaviour. A well designed material model can be used to accurately predict and compensate spring-back in forming process. A combined hardening model especially designed for multi-stage forming is proposed in this paper, and the iterated compensation method could be applied by using LS-DYNA to get an optimized result. An experimental testing facility was developed for calibration of this model with cyclic tension and compression strain stress curve. The compensation method is applied in the numerical simulation of a multi-stage manufacturing process of an A-pillar, the result demonstrates the feasibility of the combined hardening model.

Numerical simulation of springback and twisting of stamped thin U-shaped copper alloy sheets with a change of the blank alignment

An experimental database of springback and twisting of U-shaped elongated structures is available from a previous study. The materials are copper alloys: pure Cu, CuBe2, and CuFe2P, provided in thin sheets of thickness around 0.1 mm. After deep-drawing of rectangular blanks, which can be aligned with the tools or slightly misaligned, and tool withdrawal, the U-shaped structure exhibits an opening of the section (2D springback) and twisting (3D springback). Characteristic features of the deformed geometry are significantly different for the three alloys. This study is directed to understand the origin of that difference with a numerical simulation of the process. The mechanical behaviour of the materials was investigated in tension and hydraulic bulge test, out of comparison’s sake and to derive the hardening law over a strain range representative of the process. Finite element simulations are performed using the von Mises criterion coupled with isotropic hardening, to compare the predicted forming load and springback parameters with experimental values.

Investigation on the effect of friction and material behavior models on the springback simulation precision: application to automotive part B-Pillar and material TRIP800 steel

Investigation on the effect of friction and material behavior models on the springback simulation precision: application to automotive part B-Pillar and material TRIP800 steel

Characterizing springback stress behavior in VPB by experimental-numerical hybrid method

Springback is a stress-driven phenomenon during unloading, so the stress behavior during unloading is of great significance for exploring and understanding springback. However, the accuracy of stress field after loading procedure in FEM, as the basis of springback simulation, is greatly affected by the assumptions of material model and boundary condition. Moreover, the selection of constraints in springback simulation is crucial and highly subjective, thus affecting the authenticity of results. In this paper, the characteristic of springback stress is studied in viscous pressure bulging (VPB) using an experimental-numerical hybrid method, combining the DIC method and numerical calculation. The springback results under different viscous mediums are obtained and their laws are discussed. The measured springback data containing the information of material properties and boundary conditions are used to calculate springback stress by the presented numerical calculation program. The springback stresses of sections along rolling direction and transverse direction are obtained. The variation law of the magnitude and direction of springback stress vector with springback is revealed. Then the mechanism of springback stress variation and the springback reduction are analyzed. Results show that the springback stress conforming to objective and practical conditions can be obtained, and it changes regularly with springback. The viscous medium affects the shape and stress of sheet, causing the change of springback stress. Furthermore, the change of springback stress reduces the reverse bending moment to restrain the resulting springback.

Finite element implementation of hydrostatic pressure-sensitive plasticity and its application to distortional hardening model and sheet metal forming simulations

• The strength-differential (SD) effect of AHSS with ultimate tensile strength exceeding 1 GPa is modeled by a hydrostatic pressure-dependent distortional plasticity theory. • The finite element implementation of the pressure-dependent plasticity theory is proposed in the manuscript. The implemented theory is validated with the comparison study with the associated stand-alone code and experimental measurements. • Both the SD- and strain patch change effects of TIRP1180 are reproduced in finite element simulation by embedding the distortional plasticity model, HAH 20 , in the pressure-dependent yield condition. The effectiveness and applicability of the FE-implemented pressure-dependent distortional plasticity model in sheet metal forming simulations is validated through the springback prediction studies. In this work, the hydrostatic pressure-dependency of the distortional plasticity model HAH 20 was implemented using a finite element (FE) code to account for the strength-differential (SD) effect that has been observed in advanced high-strength steel sheets. To this end, a fully-implicit stress update algorithm formulation was introduced for the pressure-dependent plasticity theory. The implementation was validated by comparing the FE prediction of the material behavior during a number of tests with those of a stand-alone code of the constitutive description as well as with experimental data. In order to investigate the SD effect on the springback simulation results, the U-draw bending test was analyzed within this FE framework. Furthermore, in order to assess the effectiveness and stability of the formulation for a large-scale example, forming simulations of an automotive structural part were conducted. In addition to the SD effect, strain path changes and geometrical aspects were also investigated in this example. It was shown that the distortional plasticity-based pressure-dependent yield criterion well describes the asymmetric SD behavior in sheet metal forming simulations.

Reduction of Young’s modulus for a wide range of steel sheet materials and its effect during springback simulation

Springback is among the key issues to be addressed in order to facilitate the application of AHSS in the automotive body. Since numerical simulations have become a standard tool during process design in automotive panel production, advanced material models considering springback-related material properties are increasingly getting into the focus. Next to the Bauschinger-Effect, describing early re-yielding during load reversal, also a reduction of Young’s modulus with increasing plastic strain is depicted in several material models implemented in different FEM codes. Herein, we focus on this Young’s modulus reduction. The initial Young’s modulus as well as its reduction are measured from uniaxial tensile tests with multiple unloading-reloading cycles without load reversal. Results are shown for steel sheet materials ranging from mild steels to AHSS containing retained austenite. Differences of the Young’s modulus decrease among the different steel grades are discussed with respect to their respective microstructure. Material models, depicting the Young’s modulus reduction, are fitted to the obtained data. The consequence of considering this effect during forming simulation is shown for bending-under-tension tests of DP600, representing the largest reduction.

Numerical and experimental investigation of the transmission moment of clinching points

In clinching, the combinations of requirements, materials, component dimensions and tools influence the resulting joint geometry and the resulting bonding mechanisms. These in turn affect the property profile of the joint. For example, it is possible to use different tools to flexibly adapt clinching points to the respective required load regime. Clinching points dimensioned in this way can be geometrically similar, but have different mechanical stress states, which leads to different properties in terms of load-bearing behavior. Within the scope of this work, the clinching process with different tools in optimal and compromise design and its effect on the force and form-closure component, is investigated in a torsion test of the clinched connection. Clinched steel sheets with two thicknesses and joining directions are analyzed. Virtual experiments are carried out using finite element analyses (FEA) of the joining process and are followed by a springback simulation. Subsequently, the surface pressure between the two joining partners in the clinching points is calculated on the basis of the results from the FEA and the transmittable moment of the connection, as an indicator for the force-closure component, is determined. Finally, the experimental and simulated data are compared and discussed.

Predicting springback variation and process-reliable tolerance limits of outer car-body panels by stochastic sheet metal forming simulation

Modern car-body design entails increasing requirements for the dimensional accuracy of outer car-body panels. However, tolerance limits to be met in this regard are based on specifications from component engineering aimed at ensuring dimensional accuracy of the product, less on real structural springback behaviour of outer car-body panels. Process-reliable tolerance limits for outer car-body panels can be characterized by a bandwidth in springback variation caused by fluctuations in material characteristics and process parameters during production. Differences between assumptions from component engineering and real structural springback behaviour of outer car-body panels thus leads to avoidable iterative corrections in die manufacturing and following processes. Therefore, the goal of this research work presented in this paper is to predict springback variation potentially occurring during production already in the virtual design stage of a car-body and hence set process-reliable tolerance limits. Stochastic sheet metal forming simulation is used for prediction of springback variation. Here, deterministic multi-stage springback simulation of a sidewall panel is extended by stochastic variation of material properties and process parameters. Simulation results are validated by measurement reports from series production. Results presented show strong fit in characteristics of springback variation between stochastic simulation and series measurement reports. In future, stochastic simulation results can be fed back into component engineering, making die manufacturing and following joining and assembly processes more effective.

Dimensionally accurate parts made of high-strength steels - compressive stress superposition instead of tool compensation

As a result of the increasing use of high-strength and ultra-high-strength steels as part of the automobile lightweight construction strategies, the issue of dimensional accuracy of component structures is increasingly becoming the focus of toolmakers, pressed part suppliers and automobile manufacturers. In particular, the modern dual-phase steels with strengths of over 800 MPa possess-depending on the respective component geometry and the forming process employed-a pronounced springback behaviour. The compensation measures commonly used so far are more and more reaching their limits, which in turn impairs the process ability of these grades in the cold forming process. The smartform® process developed by thyssenkrupp Steel Europe AG allows the cold forming of high-strength steels with high repeatable accuracy, which significantly expands their areas of application. In this process, the tensile stresses from the forming operation causing the springback of the part are eliminated by compressive stress-superposition, which leads to high dimensional stability. There is almost no need to adapt the tool surfaces to achieve a dimensionally accurate part. How close the formed component comes to the dimensional tolerances specified by the end user is usually determined within the framework of numerical method development. In this context, the result of a springback simulation depends on various parameters. The description of the material behaviour is of major importance. Moreover, the use of extended material models can have an influence on the predictive accuracy and reduce the deviations between simulation and real material behaviour. It remains to be identified to what extent the increase in accuracy is proportional to the modelling effort.

Simulation analysis of deformation spring-back of free-form surface composite with cellular foam filling

Due to the complex thermo-chemical-mechanical coupling during the curing and forming process of composite materials, spring-back is commonly observed after forming, which makes the shape of parts after curing and forming deviate from the design shape, resulting in difficult or even impossible assembly. In order to reduce the influence of the spring-back deformation on the forming, the finite element analysis software was used to analyze the curing deformation of the free-form composite part with foam filling, and the numerical simulation and analysis of the curing deformation of the complex curved parts were realized. The simulation analysis involves warping deformation under different angles and radii, which breaks through the unitary shape of previous research objects. In addition, the effect of foam on skin is also considered in the simulation process, and it is found that the shrinkage of the foam will affect the spring-back deformation of parts. Through finite element software, the spring-back simulation of multi-surface composite material after curing was carried out, and the results were compared with those obtained by digital measurement, the comparative analysis shows the effectiveness of the curing deformation prediction model in this paper.

Prediction of bending springback of the medium-Mn steel considering elastic modulus attenuation

The improvement of lightweight and safety is the development requirement of automobile parts. Therefore, the demand of thin-walled parts with ultra-high strength is more urgent. However, with the increase of strength, the springback phenomenon of parts is particularly serious, which greatly affects the forming quality of parts. Generally, the springback of automobile parts should be controlled within 5%. Thus, the accurate simulation and prediction of springback can provide important support for the manufacture of ultra-high strength automobile thin-walled parts. In this paper, the bending springback of the medium-Mn steel, as one of the third-generation automobile steels, was studied based on experiment and simulation under different conditions. Tensile tests were carried out to evaluate comprehensive mechanical properties with high strength and high plasticity. Cyclic loading-unloading tests were conducted to analyze the changing rules of unloading elastic modulus and inelastic recovery with strain. The correlation model between unloading elastic modulus and true plastic strain was further established and the model parameters were obtained. Furthermore, V-shaped bending tests were carried out under different conditions to analyze the effects of rolling direction, bending angle, and punch fillet radius on springback. The effect of rolling direction on springback angle is negligible. The bending angle has a positive effect on springback angle, while the punch fillet radius has a negative effect. Finally, the material model with constant and variable elastic moduli were developed by using user-defined material subroutines for the medium-Mn steel. V-shaped bending tests under constant and variable elastic moduli were simulated and compared with the experimental result. The simulated result with variable elastic modulus was closer to the experimental one, which proves the importance of considering the change of unloading elastic modulus in the numerical simulation of medium-Mn steel. The research result of this paper is helpful to enhance the simulation accuracy of springback of medium-Mn steel part and promote its industrial application.

Simulation of springback in cyclic wipe-bending

This paper proposes a bending method to measure the robustness of advanced material constitutive models, which are developed aiming to precisely express material responses including the Bauschinger effect, permanent softening, etc. Such constitutive models, in general, require multiple sophisticated material tests, e.g. cyclic uniaxial tension-compression, followed by appropriate numerical optimizations to identify corresponding material model parameters. These tests, for example, intrinsically require anti-buckling measures for specimens that can lead to redundant frictional forces and biaxial effects. Besides, the strategy for the optimization of material parameters or the selection of elastic modulus model is also an important point to influence the final performances. In an effort to provide more robust reliability for springback simulation results, a wipe-bending tool enabling cyclic load reversals has been developed as an intermediate validator positioned between the role of the cyclic uniaxial tension-compression and that of the U-drawbending. Predicted springback results employing the Yoshida-Uemori model have shown that this approach can be considered as an effective way to confirm both the reliability of material model parameters and the capability of a selected constitutive model in a part development or tooling stage.

Inelastic strain recovery of magnesium alloys and a new elastic modulus model

Cyclic loading-unloading uniaxial tension experiments were performed for AZ31B magnesium sheets. The inelastic strain recovery behavior of the AZ31B sheets unloaded under different plastic strain was investigated. An interesting phenomenon on the elastic modulus change was presented. A new elastic modulus model was presented to characterize the inelastic strain recovery of the AZ31B sheets. Unlike the available models, this elastic modulus model takes both the instant stress and the plastic strain as the variables. The new elastic modulus model was incorporated into the ABAQUS software using the user subroutines. Validation of the subroutines and springback simulations were conducted with the presented elastic modulus models. The results showed that the inelastic strain recovery of the AZ31B sheets can reach 24% of the total strain recovery. The instant elastic modulus model can predict a perfect unloading path. The new elastic modulus model works better than the constant elastic modulus.

Effect of tension-compression testing strategy on kinematic model calibration and springback simulation of advanced high strength steels

Various studies show that application of kinematic hardening models significantly improves the accuracy of springback simulation in sheet metal forming. The springback simulation using kinematic hardening models, e.g., the Yoshida-Uemori (YU) model, is highly dependent on the testing strategy and the calibration of model parameters. In this study, the effect of tension-compression (T-C) testing strategy on calibration of YU model parameters and springback simulation of advanced high strength steels was investigated. A single-element model with T-C conditions was built in LS-OPT to determine YU model parameters on the basis of T-C tests. U-bending tests of two 980 MPa grade steels were performed to evaluate the springback prediction. Results indicate that T-C strategies, including tension-compression sequence and prestrain level show little effect on the calibrated YU model parameters as well as springback simulation of a dual phase steel DP980. However, for a TRIP-assisted high strength steel QP980, T-C strategy significantly affects both the YU model parameters and springback simulation, which is related to the complex loading-path-dependent retained austenite transformation in the QP980. A compromise strategy of T-C testing is proposed to calibrate the YU model parameters of the steel QP980, which are capable to accurately simulate its springback in U-bending.

Model for description of nonlinear unloading-reloading stress-strain response with special reference to plastic-strain dependent chord modulus

To describe the nonlinear stress-strain response in the unloading-reloading process, a model was proposed for the variation of the elastic modulus during the process. This model is directly associated with the widely used equation for the plastic-strain dependent chord modulus, and no additional material parameters are needed for modeling. In this model, nonlinearly changing elastic modulus is explicitly determined from the current stress state, instead of using an accumulated-strain measure. Therefore, it is robust against the numerical noise (e.g., stress oscillation) in computation. Based on the same elastic modulus model, two types of calculation models were constructed, namely, a micro-plasticity model and nonlinear-elasticity model. From the numerical simulations of the non-proportional unloading-reloading processes, it was found that the stress-strain responses calculated by the two models were very similar to each other. The model was validated by comparing the calculated stress-strain results with the corresponding experimental observations on a DP980 advanced high-strength steel sheet (AHSS). The influence of the nonlinear unloading behavior on the springback prediction was discussed by performing two cases of springback simulations (a uniform bending-unbending and a hat-shaped draw-bending) on two types of AHSSs (dual-phase DP980 and precipitation strengthen 780 R), by using several types of elastic modulus models. The best choice for springback simulation is to use the nonlinear elastic model to describe the realistic stress-strain responses in the yield surface, along with an appropriate kinematic hardening model of plasticity to express smooth elastic-plastic transition behavior. In comparison with the springback calculation by the nonlinear model, a certain amount of errors were found when using the plastic-strain dependent linear models, however, they were not very large. Thus the second best option in springback simulation would be to use the chord modulus model because of its simple modeling and high computation efficiency.

Enhancement of Accuracy of Springback Simulation Using the Material Model Considering the Strength Differential Effect

Enhancement of Accuracy of Springback Simulation Using the Material Model Considering the Strength Differential Effect

Mechanical properties, springback, and formability of W-temper and peak aged 7075 aluminum alloy sheets: Experiments and modeling

High strength aluminum alloys have drawn much attention as the requirement for lightweight vehicle design increases in the automotive industry. However, inferior formability due to higher strength poses a technical hurdle against successful application of high strength aluminum sheets in automotive components. In this study, the mechanical properties of 7075 aluminum alloy sheet after W-temper heat treatment, which consists of solution heat treatment and subsequent quenching, are investigated. Detailed experimental and numerical studies are conducted on the anisotropy, non-proportional deformation behavior, and corresponding constitutive modeling in comparison with the corresponding characteristics of peak aged T6 heat-treated as-received alloy sheets. Based on the experimentally characterized mechanical properties and associated constitutive laws, the formability and springback of the W-tempered sheet are analyzed using the Marciniak–Kuczyinski forming limit diagram and U-draw bending springback simulations, respectively, by employing the Yld2000-2d anisotropic yield function and distortional hardening-based homogeneous anisotropic hardening model. Additionally, the improved constitutive modeling of the W-tempered 7075 aluminum sheets due to the effect of serrated flow characteristics on the hardening and frictional behaviors is discussed.