Cross-section distortion and springback characteristics of double-cavity aluminum profile in force controlled stretch-bending

3D elastic-plastic FE model for simulating the force controlled stretch-bending process of double-cavity aluminum profile was established using hybrid explicit−implicit solvent method.Considering the computational accuracy and efficiency,the optimal choices of numerical parameters and algorithms in FE modelling were determined.The formation mechanisms of cross-section distortion and springback were revealed.The effects of pre-stretching,post-stretching,friction,and the addition of internal fillers on forming quality were investigated.The results show that the stress state of profile in stretch-bending is uniaxial with only a circumferential stress.The stress distribution along the length direction of profile is non-uniform and the maximum tensile stress is located at a certain distance away from the center of profile.As aluminum profile is gradually attached to bending die,the distribution characteristic of cross-section distortion along the length direction of profile changes from V-shape to W-shape.After unloading the forming tools,cross-section distortion decreases obviously due to the stress relaxation,with a maximum distortion difference of 13%before and after unloading.As pre-stretching and post-stretching forces increase,cross-section distortion increases gradually,while springback first decreases and then remains unchanged.With increasing friction between bending die and profile,cross-section distortion slightly decreases,while springback increases.Cross-section distortion decreases by 83%with adding PVC fillers into the cavities of profile,while springback increases by 192.2%.

Sensitivity of springback and section deformation to process parameters in rotary draw bending of thin-walled rectangular H96 brass tube

In order to study the effects of the process parameters on springback and section deformation, a sensitivity analysis model was established based on the combination use of the multi-parameter sensitivity analysis method and the springback/section deformation prediction finite element model, and by using this model the sensitivities of the springback and the section deformation to process parameters were analyzed and compared. The results show that the most sensitive process conditions for springback angle are the boost speed and the pressure of pressure die, and the most sensitive process condition for section deformation is the number of cores. When the clamp force, the boost speed and the pressure of pressure die are utilized to control section deformation, the effect of these process parameters on springback should be considered. When the process parameters are mainly used to control springback, the effect of these process parameters on the section deformation should be always considered.

Springback prediction for incremental sheet forming based on FEM-PSONN technology

In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.

Theoretical analysis on springback of L-section extrusion in rotary stretch bending process

The theoretical analysis of springback in rotary stretch bending process of L-section extrusion was studied. The models for characterizing the springback angle after unloading were established based on the stress and strain distributions in the cross-section of the part. With the proposed model, analysis of the effect of pre-stretch force and post-stretch force on springback angle shows that springback decreases as the pre-stretch force or post-stretch force increases. Comparative study with experiments clearly demonstrates that the prediction of springback can resort to the current model without the loss of accuracy.

Springback and tensile strength of 2A97 aluminum alloy during age forming

The analysis of variance(ANOVA), multiple quadratic regression and radial basis function artificial neural network(RBFANN) methods were used to study the springback and tensile strength in age forming of 2A97 aluminum alloy based on orthogonal array. The ANOVA analysis indicates that the springback reaches the minimum value when age forming is performed at 210 °C for 20 h using a single-curvature die with a radius of 400 mm, and the tensile strength reaches the maximum value when age forming is performed at 180 °C for 15 h using a single-curvature die with a radius of 1000 mm. The orders of the importance for the three factors of pre-deformation radius, aging temperature and aging time on the springback and tensile strength were determined. By analyzing the predicted results of the multiple quadratic regression and RBFANN methods, the prediction accuracy of the RBFANN model is higher than that of the regression model.

Constitutive modeling and springback simulation for 2524 aluminum alloy in creep age forming

The constitutive modeling and springback simulation for AA2524 sheet in creep age forming（CAF） process were presented.A series of creep aging tests were performed on AA2524 at the temperature of 180-200 °C and under the stress of 140-210 MPa for 16 h.Based on these experimental data,material constitutive equations which can well characterize creep aging behaviors of the tested alloy were developed.The effect of interior stress distributed along the sheet thickness on springback was simulated using FE software MSC.MARC by compiling the established constitutive models into the user subroutine.The simulation results showed that the amount of sheet springback was 61.12% when merely considering tensile stress existing along the sheet thickness;while sheet springback was up to 65.93% when taking both tensile and compressive stresses into account.In addition,an AA2524 rectangular sheet was subjected to CAF experiment in resistance furnace.The springback value of the formed rectangular sheet was 68.2%,which was much closer to 65.93%.This confirms that both tensile and compressive stresses across the sheet thickness should be considered in accurately predicting springback of the sheet after forming,which can be more consistent with experimental results.

An analytical model for predicting sheet springback after V-bending

Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simu-lating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.

Springback analysis of 6016 aluminum alloy sheet in hot V-shape stamping

Springback behavior of 6016 aluminum alloy in hot stamping was investigated by a series of experiments under different conditions using V-shape dies and a finite element model which was validated reliable was used to further elucidate the springback mechanism. The effects of initial blank temperature, blank-holding force, die closing pressure and die corner radius were studied. It is found that springback decreases remarkably as the initial blank temperature rises up to 500 °C. The springback also reduces with the increase of die holding pressure and the decrease of die corner radius. Under different initial temperatures, the influence of blank-holding force is distinct. In addition, the bending and straightening of the side wall during the stamping process is found to interpret the negative springback phenomenon.

Semi analytical modeling of springback in arc bending and effect of forming load

The analytical model for springback in arc bending of sheet metal can serve as an excellent design support.The amount of springback is considerably influenced by the geometrical and the material parameters associated with the sheet metal.In addition,the applied load during the bending also has a significant influence.Although a number of numerical techniques have been used for this purpose,only few analytical models that can provide insight into the phenomenon are available.A phenomenological model for predicting the springback in arc bending was proposed based on strain as well as deformation energy based approaches.The results of the analytical model were compared with the published experimental as well as FE results of the authors,and the agreement was found to be satisfactory.

Optimization on springback reduction in cold stretch forming of titanium-alloy aircraft skin

An optimization method was presented for cold stretch forming of titanium-alloy aircraft skin to determine process parameters and to reduce springback.In the optimization model,a mathematical formulation of stress difference was developed as an indicator of the degree of springback instead of implicit springback analysis.Explicit finite element method(FEM)was used to analyze the forming process and to provide the stress distribution for calculating the amount of the stress indicator.In addition,multi-island genetic algorithm(MGA)was employed to seek the optimal loading condition.A case study was performed to demonstrate the potential of the suggested method.The results show that the optimization design of process parameters effectively reduces the amount of springback and improves the part shape accuracy.It provides a guideline for controlling springback in stretch forming of aircraft skin.

Springback analysis and strategy for multi-stage thin-walled parts with complex geometries

Springback of a SUS321 complex geometry part formed by the multi-stage rigid-flexible compound process was studied through numerical simulations and laboratory experiments in this work.The sensitivity analysis was provided to have an insight in the effect of the evaluated process parameters.Furthermore,in order to minimize the springback problem,an accurate springback simulation model of the part was established and validated.The effects of the element size and timesteps on springback model were further investigated.Results indicate that the custom mesh size is beneficial for the springback simulation,and the four timesteps are found suited for the springback analysis for the complex geometry part.Finally,a strategy for reducing the springback by changing the geometry of the blank is proposed.The optimal blank geometry is obtained and used for manufacturing the part.

Springback Prediction and Optimization of Variable Stretch Force Trajectory in Three-dimensional Stretch Bending Process

Most of the existing studies use constant force to reduce springback while researching stretch force. However, variable stretch force can reduce springback more efficiently. The current research on springback prediction in stretch bending forming mainly focuses on artificial neural networks combined with the finite element simulation. There is a lack of springback prediction by support vector regression（SVR）. In this paper, SVR is applied to predict springback in the three-dimensional stretch bending forming process, and variable stretch force trajectory is optimized. Six parameters of variable stretch force trajectory are chosen as the input parameters of the SVR model. Sixty experiments generated by design of experiments（DOE） are carried out to train and test the SVR model. The experimental results confirm that the accuracy of the SVR model is higher than that of artificial neural networks. Based on this model, an optimization algorithm of variable stretch force trajectory using particle swarm optimization（PSO） is proposed. The springback amount is used as the objective function. Changes of local thickness are applied as the criterion of forming constraints. The objection and constraints are formulated by response surface models. The precision of response surface models is examined. Six different stretch force trajectories are employed to certify springback reduction in the optimum stretch force trajectory, which can efficiently reduce springback. This research proposes a new method of springback prediction using SVR and optimizes variable stretch force trajectory to reduce springback.

Springback prediction of TC4 titanium alloy V-bending under hot stamping condition

In this paper,the springback of TC4 titanium alloy under hot stamping condition was studied by means of experiment and numerical analysis.Firstly,an analytical model was established to predict the V-shaped springback angleΔαunder the stretch-bending conditions.The model took into account of blank holder force,friction,property of the material,thickness of the sheet and the neutral layer shift.Then,the influence of several process parameters on springback was studied by experiment and finite element simulation using a V-shaped stamping tool.In the hot stamping tests,the titanium alloy sheet fractured seriously at room temperature.The titanium alloy has good formability when the initial temperature of the sheet is 750–900°C.However,the springback angle of formed parts is large and decreases with increasing temperature.The springback angleΔαdecreased by 50%from 0.5°to 0.25°,and the angleΔβdecreased by 46.7%from 1.5°to 0.8°when the initial temperature of sheet increased from 750°C to 900°C.The springback angle of titanium alloy sheet increases gradually with the increase of the punch radius,because of the increase of elastic recovery,the complex distribution of stress,the length of forming region and the decreasing degree of stress.Compared with the simulation results,the analytical model can better predict the springback angleΔα.

Springback Mechanism Analysis and Experiments on Robotic Bending of Rectangular Orthodontic Archwire

Fixed-appliance technology is the most common and effective malocclusion orthodontic treatment method, and its key step is the bending of orthodontic archwire. The springback of archwire did not consider the movement of the stress-strain-neutral layer. To solve this problem, a spring- back calculation model for rectangular orthodontic archwire is proposed. A bending springback experiment is conducted using an orthodontic archwire bending springback mea- surement device. The springback experimental results show that the theoretical calculation results using the proposed model coincide better with the experimental testing results than when movement of the stress-strain-neutral layer was not considered. A bending experiment with rectangular orthodontic archwire is conducted using a robotic orthodontic archwire bending system. The patient expriment result show that the maximum and minimum error ratios of formed orthodontic archwire parameters are 22.46% and 10.23% without considering springback and are decreased to 11.35% and 6.13% using the proposed model. The proposed springback calculation model, which considers the move- ment of the stress-strain-neutral layer, greatly improves the orthodontic archwire bending precision.

A Numerical-analytic Method for Quickly Predicting Springback of Numerical Control Bending of Thin-walled Tube

Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process was put forward. The method is based on springback angle model derived using analytic method and simulation results from three-dimensional （3D） rigid-plastic finite element method （FEM）. The method is validated through comparison with experimental results. The features of the method are as follows： （1） The method is high in efficiency because it combines advantages of rigid-plastic FEM and analytic method. （2） The method is satisfactory in accuracy, since the field variables used in the model is resulting from 3D rigid-plastic FEM solution, and the effects both of axial force and strain neutral axis shift have been included. （3） Research on multi-factor effects can be carried out using the method due to its advantage inheriting from rigid-plastic FEM. The method described here is also of general significance to other bending processes.

Rapid Springback Compensation for Age Forming Based on Quasi Newton Method

Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment （DA） method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method （0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively）. In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel＇s design contour is less than 1 mm. Finally, the iterations with different mesh sizes （40 mm, 35 mm, 30 mm, 25 mm, 20 mm） in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.

An Iterative Compensation Algorithm for Springback Control in Plane Deformation and Its Application

In order to solve the springback problem in sheet metal forming, the trial and error method is a widely used method in the factory, which is time-consuming and costly for its non-direction and non-quantitative. Finite element simulation is an e ective method to predict the springback of complex shape parts, but its precision is sensitive to the simulation model, particularly material model and boundary conditions. In this paper, the simple iterative method is introduced to establish the iterative compensation algorithm, and the convergence criterion of iterative parameters is put forward. In addition, the new algorithm is applied to the V-free bending and stretch-bending processes, and the convergence of curvature and bending angle is proved theoretically and verified experimentally. At the same time,the iterative compensation experiments for plane bending show that, the new method can predict the next compensaantido tnh ev atlaureg ebta cseurdv oatnu trhe ew sitphri tnhgeb earcrko ro fo fe laecshs ttehsat,n s0 o. 5 th%a ta rteh eo btatraigneet db aefntedri n2 g-3 a nitgelrea tiwoitnhs.t Thhei se rrreosre aorf clhe sps rtohpaons e±s 0 a.1%new iterative compensation algorithm to predict springback in sheet metal forming process, where each compensation value depends only on the iteration parameter di erence before and after springback for the same forming process of same material.

Effect of bending temperatures on the microstructure and springback of a TRIP steel sheet

Transformation-induced plasticity(TRIP)steel possesses high strength and formability,enabling the use of a thinner gauge material and allowing for the fabrication of complex shapes.In this research,we measured the effect of bending temperatures on the microstructure and air-bending springback angle of TRIP steel at temperatures from 25 to 600
C.Real-time in situ X-ray diffraction and scanning electron microscopy were used for pre-and postbending analysis.As the prebending temperature increased from 25
C to 600
C,the retained austenite(RA)volume fraction decreased,and the RA transformed to bainite at temperatures above 400
C.The springback angle was positively correlated with the prebending RA volume fraction,with the smallest springback angle achieved at 400
C.Additionally,the springback angle was positively correlated with the bending angle,because the RA transformation ratio contributed to increased strain hardening.Further microstructure analysis revealed that the RA became elongated in the tension direction as the bending temperatures increased.

Grain size effect on cyclic deformation behavior and springback prediction of Ni-based superalloy foil

In order to clarify the influence of grain size on cyclic deformation response of superalloy sheets and springback behavior,cyclic loading-unloading and shearing tests were performed on the superalloy foils with 0.2 mm in thickness and diverse grain sizes.The results show that,the decline ratio of elastic modulus is weakened with increasing grain size,and the Bauschinger effect becomes evident with decreasing grain size.Meanwhile,U-bending test results determine that the springback is diminished with increasing grain size.The Chaboche,Anisotropic Nonlinear Kinematic(ANK)and Yoshida-Uemori(Y-U)models were utilized to fit the shear stress-strain curves of specimens.It is found that Y-U model is sufficient of predicting the springback.However,the prediction accuracy is degraded with increasing grain size.

Constitutive modeling and springback prediction of stress relaxation age forming of pre-deformed 2219 aluminum alloy

Stress relaxation ageing behavior of pre-deformed AA2219 is studied through stress relaxation age experiments and finite element(FE) simulation. The results show that the stress can promote the process of ageing precipitation, and shorten the time to reach the peak strength. Meanwhile,the residual stress and yield strength increase along with the increase in the initial stress. Based on microstructure evolution and ageing strengthening theory,a unified constitutive model is established and incorporated into the FE simulation model through a user subroutine. It is found that the relative error of the radius is 3.6% compared with the experimental result and the springback is 16.8%. This indicates that the proposed stress relaxation ageing constitutive model provides a good prediction on the springback of such stiffened panel during its ageing process.