Theoretical And Numerical Study On Springback Prediction In Sheet Metal Forming

Springback is a key defect existing in sheet metal forming, which greatly affects the product geometrical accuracy. Springback is strongly influenced by the die profile, material properties, sheet initial geometry and processing parameters, thus it is an accumulated effect of the whole processing history. Specially, if the material undergoes inverse loading, the Bauschinger's effect and hardening model will severely affect the precision of predicted springback. If these influencing factors coexist, the prediction precision of springback can not currently meet the requirement of production and remains an important problem both in manufacturing industry and academe. By developing new theoretical model and finite element approach, the present work aims to explore the main factors that influence the sheet springback, control methods and the way to increase the precision in springback prediction. Meanwhile, these methods are applied to assess the springback ability of high strength steel, by which to provide theoretical basis for enterprises to develop corresponding assess regulation. The main work in this paper is as follows.1) Based on the assumption of plane strain and Hill'48 criterion for anisotropic yielding, the analytical models are established for analyzing V-bending, stretching bending, U-bending of sheet under different material hardening modes. By applying these models, the contribution of the hardening and processing parameters are analyzed. In addition to that, for stretching bending and U-bending problem, the critical forming condition that accounting for the blank holding force and stretch force are also established. Calculation results demonstrate a good correspondence to the experimental data. An outstanding advantage of the analytical model is its high precision and efficiency over numerical methods such as finite element, and it is more helpful to explore the mechanism of sheet springback.2) A non-linear combined hardening rule has been proposed to solve the springback problem of reverse bending. The stress-strain constitutive equations of different yielding criterion non-linear combined hardening have been deduced, and their stress-strain updating algorithms have been determined. The effects of different yielding criterion and hardening rule have been investigated. The simulation results show that for sheet forming and springback with reverse loading, the non-linear combined hardening rule based on Hill'48 or Barlat'89 yielding criterion predicts springback much closer to experiment data.3) Based on the theory of Mindlin shell and continuum element, the continuum-shell element theory and its strain and stress fields have been deduced. The selective reductive integration has been analyzed to solve the problems of volumetric and transverse shear locking in the non-linear analysis. The benchmarks of NUMISHEET'93 2-D draw bending, NUMISHEET'2002 unconstrained cylinder bending and box drawing, trimming and springback have been simulated by continuum-shell element. The comparison with experiment data shows that the continuum-shell element can improve the springback prediction accuracy effectively.4) The effects of FEM simulation parameters on sheet springback have been analyzed. The relation between the virtual kinetic energy and springback prediction accuracy has been deduced in theory. The study results indicate that the springback prediction by explicit algorithm is not accurate because of the application of virtual kinetic energy, and the implicit algorithm can improve the springback prediction accuracy. Under the condition of assuring simulation accuracy, the larger element dimension should be applied. The continuum-shell element predicts the springback best since it has the virtues of continuum element and Mindlin shell element. The number of integral points in sheet thickness direction should be seven for Mindlin or continuum shell element, and larger than seven integral points has no significant effect on springback prediction accuracy.5) The sensitivity of material property parameters variation on sheet springback has been analysis based on orthogonal experimental design and FEM numerical simulation. The study shows that the effect of Young's modulus is largest, then hardening coefficient, initial yielding stress, hardening exponent and anisotropy r0 . While the effects of anisotropies r4 5 and r9 0 variation can be ignored. The influence rules of material parameters on sheet springback by simulation consist well with those by theory analysis.6) The effects of technology parameters on sheet springback of DP or TRIP have been studied based on experiments and implicit simulations. The results show that for same type sheet, the springback increases with its strength. The springback increases with die clearance, punch round radius, stretching depth, the friction between punch and sheet, but decreases with die round radius and sheet thickness. Increasing blank holding force or friction between sheet and die to some extent can control springback. But they can't increase without control, and should be within a limit at which the resulted stretching force should not make the sheet rupture. The effects of technology parameters on springback based on simulations and experiments consist well with the theory analysis in this paper.