Study on experimental approaches of forming limit curve for tube hydroforming

This paper proposes a set of experimental approaches to establish the forming limit curve (FLC) in different forming modes for tube hydroforming. In tension–compression strain state, analytical models are constructed to determine the linear strain paths at the pole of the hydroformed tube, and a self-designed free hydroforming apparatus with axial feeding and internal pressure are used to carry out the bulge tests. In plane strain state, the difference is that both ends of the tube are fixed with different punches. In tension–tension strain state, a novel hydroforming apparatus are designed. The novel device requires the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. The linear strain paths for the right hand side of FLC by finite element method simulation are calculated. The linear strain paths in different strain states are verified and the FLC of roll-formed QSTE340 seamed tube is constructed through the proposed experimental approaches. Comparison between simulation and experimental results for hydroforming process of front crossmember shows that the experimental FLC is accurate and valid for tube hydroforming.     

Feasibility study on optimized process conditions in warm tube hydroforming

Feasibility study has been performed to estimate the optimized process conditions in warm tube hydroforming based on the simulated annealing optimization method. Precise prediction and control of process parameters play an important role in forming at warm conditions. Optimal pressure and feed loading paths are obtained for aluminium AA6061 tubes through the simulated annealing algorithm in conjunction with finite element simulations. Numerous axisymmetric geometries are investigated and the effects of expansion ratio, corner fillet to thickness ratio, and initial diameter to thickness ratio are studied. For the feasibility estimation, warm hydroforming experiments have been conducted on aluminum AA6061 under optimal designed conditions. The results show that the optimization procedure used in this research is a reliable and feasible tool in determination of optimal process conditions for the sound warm hydroforming process.     

基于DASYLab的管材轴压胀形的加载控制

内压与轴向压力的合理匹配是管材轴压胀形成败的关键因素。本文利用数据采集与处理软件 DASYL ab实现了轴向压力基于内压的线性加载控制 ,为进一步研究更为复杂的管材轴压胀形的加载控制关系奠定了实验基础     

加载路径对液压胀形管材成形性能的影响

在管材液压胀形过程中,加载路径对管材成形性能有着重要的影响,一直是研究热点。本文介绍了目前管材液压胀形中的各种加载路径如线性加载、折线加载、脉动加载和由模糊逻辑控制加载路径方式,阐述了各种加载路径的特点、原理及其对管材成形性能的影响,指出了深入研究加载路径要解决的几个关键问题。     

Optimization of loading path in hydroforming T-shape using fuzzy control algorithm

The loading path is crucial to the quality of forming parts in the process of tube hydroforming, and thus the design and optimization of loading path is an important issue for tube hydroforming. Wrinkling is a catastrophic defect for thin-walled tube hydroforming. In order to avoid wrinkling, an adaptive simulation approach integrated with a fuzzy control algorithm is used to optimize the loading path of hydroforming a T-shaped tube. The tubular material used is stainless steel and has an outer diameter of 103 mm and the wall thickness of 1.5 mm. The controlled variables are the axial feeding, the counterpunch displacement, and the internal pressure. A code is developed to make the optimization automatically, which works together with LS-DYNA. Six evaluation functions are adopted for identifying geometrical shape and quality of T-shape. Failure indicators obtained from the simulation results are used as the input of the fuzzy control, and then process parameters are adjusted according to the expert experiences in the fuzzy controller. In this way, a reasonable loading path for producing a sound T-shape is obtained, and also a T-shaped product is successfully hydroformed by experiment. The result shows that the fuzzy control algorithm can provide an adequately reliable loading path for hydroforming T-shaped tubes.     

Analysis and finite element simulation of the tube bulge hydroforming process

To investigate the effect of the loading path on the forming result and get the reasonable range of the loading path in tube bulge hydroforming process, a mathematical model considering the forming tube as an ellipsoidal surface is proposed to examine the plastic deformation behavior of a thin-walled tube during the tube bulge hydroforming process in an open die, and thus different loading paths are gained based on this model. The finite element code Ls-Dyna is also used for simulating the tube bulge hydroforming process. The effect of the loading paths on the bulged shape and the wall thickness distribution of the tube are discussed, and then the reasonable range of the loading path for the tube bulge hydroforming process is determined.     

Analysis and finite element simulation of the tube bulge hydroforming process

To investigate the effect of the loading path on the forming result and get the reasonable range of the loading path in tube bulge hydroforming process, a mathematical model considering the forming tube as an ellipsoidal surface is proposed to examine the plastic deformation behavior of a thin-walled tube during the tube bulge hydroforming process in an open die, and thus different loading paths are gained based on this model. The finite element code Ls-Dyna is also used for simulating the tube bulge hydroforming process. The effect of the loading paths on the bulged shape and the wall thickness distribution of the tube are discussed, and then the reasonable range of the loading path for the tube bulge hydroforming process is determined.     

Experimental study and finite element analysis of simple X- and T-branch tube hydroforming processes

The tube hydroforming process is a relatively complex manufacturing process; the performance of this process depends on various factors and requires proper combination of part design, material selection and boundary conditions. Due to the complex nature of the process, the best method to study the behaviour of the process is by using numerical techniques and advanced explicit finite element (FE) codes. In this work, X- and T-branch components were formed using a tube hydroforming machine and experimental load paths (forming pressure and axial feed) were obtained for the processes via a data acquisition system integrated with the machine. Subsequently, the processes were simulated using LS-DYNA3D explicit FE code using the same experimental boundary, loading conditions and the simulation results were compared with the experimental results. It was found that the developed branch height and the wall thickness distribution along different planes were in good agreement with the experimental results.     

Analytical approach to bursting in tube hydroforming using diffuse plastic instability

Analytical studies on onset of bursting failure in tube hydroforming under combined internal pressure and independent axial feeding are carried out. Bursting is irrecoverable phenomenon due to local instability under excessive tensile stress. In this paper, in order to predict the bursting failure diffuse plastic instability based on the Hill's quadratic plastic potential is introduced. The incremental theory of plasticity for anisotropic material is adopted and then the hydroforming limit and bursting failure diagram with respect to axial feeding and hydraulic pressure are presented. The influences of the plastic anisotropy on plastic instability, the limit stress and the bursting pressure are also investigated. Finally, the stress-based hydroforming limit diagram obtained from the above approach is verified with experimental results.     

An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming

In this paper, a combined experimental and numerical investigation of free hydroforming of aluminium alloy tubes is conducted. The tubes are subjected to different loading histories involving axial compression and internal pressure. The circumferential and axial strains experienced by the tubes are continuously recorded along with the pressure and axial load. The numerical simulations are carried out using both 2D axisymmetric and 3D finite-element formulations by applying the experimentally recorded axial load and internal pressure. In the latter, a geometric imperfection is introduced in the form of wall thickness reduction at the tube mid-length in order to trigger necking which happens after significant bulging and beyond the stage of peak pressure. The strain histories and peak pressures obtained from the simulations agree well with those determined from the experiments. Further, the forming limit curve predicted by the simulations as well as from a M–K analysis incorporating the computed strain paths corroborate well with the experimental data. The role of nonproportional straining on the mechanics of failure of the tubes due to bulging and necking is studied in detail.     

Bursting failure prediction in tube hydroforming using FLSD

In tube hydroforming, circular components are hydrobulged or hydroformed from tubular blanks with internal pressure and simultaneous axial loading. Thus the tube can be fed into the deformation zone during the bulge operation allowing more expansion and less thinning without any defects such as wrinkling, buckling, and bursting. By contrast with the buckling and the wrinkling, the bursting is generally classified as an irrecoverable failure mode. Hence in order to obtain the sound hydroformed products, it is necessary to predict the bursting behavior and to analyze the effects of process parameters on this failure condition in hydroforming processes. In this study, a forming limit stress diagram (FLSD) is constructed by plotting the calculated principal stresses based on the local necking criterion. Using the theoretical FLSD, we carry out the numerical prediction of bursting failure in a hydroforming process, which usually has non-linear strain path. Finite element analyses are carried out to find out the state of stresses during simple hydroforming operation, in which the FLSD is utilized as the forming limit criterion for assessment of the initiation of necking, and influences of the material parameters on the formability are investigated. In addition, the numerical results obtained from the FEM combined with the FLSD are confirmed with a series of bulge tests in view of bursting pressure and show a good agreement. Consequently, it is shown that the theoretical and numerical approach to bursting failure prediction proposed in this paper will provide a feasible method to satisfy the increasing practical demands for assessment of the forming severity in hydroforming processes.     

An investigation of the optimal load paths for the hydroforming of T-shaped tubes

This paper proposes a new method to design the optimal load curves for hydroforming T-shaped tubular parts. In order to assess the mathematical models, a combination of design of experiment and finite element simulation was used. The optimum set of loading variables was obtained by embedding the mathematical models for tube formability indicators into a simulated annealing algorithm. The adequacy of the optimum results was evaluated by genetic algorithm. Using this method, the effect of all loading paths was considered in hydroforming of T-shaped tubes. Eliminating of variables with lower effect could simplify the problem and help designers to study the effect of other parameters such as geometrical conditions and loading parameters. Applying the optimal load paths obtained with the proposed method caused an improvement in the thickness distribution in the part as well as a decrease in maximum pressure.     

Prediction of failure in tube hydroforming process using a damage model

In tube hydroforming process (THP), two types of loading, internal pressure and axial feeding and in particular the combination of them, are needed to feed the material into the cavities of the die to form the workpiece into the desired shape. If the variation of pressure versus axial feeding is not determined properly, the workpiece may be buckled, wrinkled or burst during THP. The appropriate variation is normally determined by experiment which is expensive and time-consuming. In this work, numerical simulation using Johnson-Cook models for predicting the elasto-plastic response and the failure of the material are employed to obtain the best combination of internal pressure and axial feeding. The numerical simulations are examined by a number of experiments conducted in the present investigation. The results show very close agreement between the numerical simulations and the experiments, suggesting that the numerical simulations using Johnson-Cook material and failure models provide a valuable tool to examine the different parameters involved in THP.     

A prediction of bursting failure in tube hydroforming process based on plastic instability

Based on plastic instability, an analytical prediction of bursting failure on tube hydroforming processes under combined internal pressure and independent axial feeding is carried out. Bursting is an irrecoverable phenomenon due to local instability under excessive tensile stresses. In order to predict the bursting failure, three different classical necking criteria – diffuse necking criteria for a sheet, and a tube, and a local necking criterion for a sheet – are introduced. The incremental theory of plasticity for an anisotropic material is adopted and the hydroforming limit, as well as a diagram of bursting failure with respect to axial feeding and hydraulic pressure are presented. In addition, the influences of material properties such as anisotropy parameter, strain hardening exponent and strength coefficient on plastic instability and bursting pressure are investigated. As a result of the above approach, the hydroforming limit with respect to bursting failure is verified with experimental results.     

小型桥壳液压胀形初始变形条件分析及成形试验

介绍了小型汽车桥壳的液压胀形工艺,提出了初始胀形内压的表达式,预测了初始胀形内压与轴向推力的匹配关系（即经向应力比的大小）对预胀形时各部分变形顺序的影响。在普通液压机上进行了两种加载路径下的液压胀形试验,在初始经向应力比小于零并保持恒内压的条件下,预胀形管坯先变形成两侧高、中部低的双鼓形,经增压后将中部胀起;在初始经向应力比大于零且内压恒定的条件下,预胀形管坯中部沿轴向胀裂;两种加载路径下,管坯扁锥体凸起与胀形区之间均产生了明显内凹缺陷。理论分析与试验结果均表明,初始变形条件对小型桥壳的预胀形有重要影响。     

A gradient-based decomposition approach to optimize pressure path and counterpunch action in Y-shaped tube hydroforming operations

In tube hydroforming, the concurrent actions of pressurized fluid and mechanical feeding allows obtaining tube shapes characterized by complex geometries such as different diameters sections and/or bulged zones. Main process parameters are material feeding history (i.e., the punches velocity history), internal pressure path during the process, and (in T- or Y-shaped tube hydroforming) counterpunch action. What is crucial, in such processes, is the proper design of operative parameters aimed to avoid defects (for instance underfilling or ductile fractures). Actually, the design of tube hydroforming operations is mainly aimed to prevent bursting or buckling occurrence and such issues can be pursued only if a proper control of process parameters is performed. In this paper, a design procedure for Y-shaped tube hydroforming operations was developed. The aim of the presented approach is to calibrate both internal pressure history during the process and counterpunch action in order to reach a sound final component. The approach utilized to optimize the aforementioned parameters is founded on gradient-based techniques and the optimization problem here addressed depends on a considerable number of design variables. In order to reduce the total number of numerical simulations/experiments necessary to reach the optimal values of the design variables, the basic idea of this paper is to develop a sort of decomposition approach aimed to take into account subsets of design variables in the most effective way. The proposed decomposition approach allows avoiding about 50% of the numerical simulations necessary to solve the same problem by traditional gradient technique.     

Multi-objective optimization and sensitivity analysis of tube hydroforming

Tube hydroforming is a manufacturing process used to produce structural components in cars and trucks, and the success of this process largely depends on the careful control of parameters such as internal pressure and end-feed force. The objective of this work was to establish a methodology, and demonstrate its effectiveness, to determine the optimal process parameters for a tube hydroformed in a die with a square cross section. The Taguchi method was used to establish a design of virtual hydroforming experiments, and numerical simulations were carried out with the finite element code LS-DYNA®. A sensitivity analysis was also carried out with analysis of variance. Multi-objective functions that consider necking/fracture, wrinkling, and thinning were formulated, and the response surface methodology was used with the most sensitive factors to obtain a defect-free part. An objective function, based on the final corner radius in the part, was also included in the optimization model. The forming severity of virtual hydroformed parts was evaluated using the forming limit stress diagram and the forming limit (strain) diagram. Finally, the normal-boundary intersection method and the L ₂ norm were used to obtain the Pareto-optimal solution set and the optimal solution within this set, respectively. The hydroforming process for this part was also optimized using the commercial optimization software LS-OPT®, with two different single-objective algorithms. However, the optimum load path predicted with the proposed methodology was shown to achieve a smaller corner radius. The proposed optimization technique helped to define a process window that leads to a robust manufacturing process and improved part quality.     

A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming

The production of a tubular hydroformed part often requires a combination of internal pressure and axial force at the tube ends to fully form the tube to its specified geometry. A successful hydroforming process requires not only achieving a part that conforms to the design specifications, but also ensures that the part has a reasonably uniform thickness distribution and is free of defects, such as wrinkles, severe thinning, or fractures. The load path design (pressure vs. end feed history) largely determines the robustness of the process and the quality of the finished parts. In this paper, a hybrid constrained optimization method was proposed to solve this type of multi-objective problem by coupling a multi-objective genetic algorithm and a local search. The load path design procedure was developed by considering five objectives: four formability objectives (i.e., to minimize the risk of wrinkling, global and local thinning, and fracture) and a geometric objective (to minimize the corner radius). A Kriging predictor was used to accelerate the computation of genetic operations and generate new feasible solutions. Finite element simulations of the hydroforming process were also used after each generation to accurately evaluate the objectives of the offspring, and solutions with rank 1 were retained throughout all generations. Once the Pareto solutions were obtained by multi-objective genetic algorithm, a local search was carried out in the regions of interest with the assistance of visualization. This optimization method was applied to the hydroforming of a straight tube to create a part with an expanded region with a square cross section; the optimum load path produced a very safe part with a corner radius of only 9.115?mm and a maximum thinning of only 23.9%.     

Coupled buckling and plastic instability for tube hydroforming

In this paper, the hydroforming limit of isotropic tubes subjected to internal hydraulic pressure and independent axial load is discussed.Swift's criterion is often used in this case for the prediction of diffuse plastic instability. Here, we first highlight the existence of two different Swift's criteria (for sheets and for tubes).Then, we recall that these types of approaches do not take into account buckling induced by axial loading. In fact, buckling may obviously occur before plastic instability; consequently, Swift's criteria must not be used alone to predict instability in the case of tube hydroforming.Numerical simulation was used to confirm these points and to analyse both the buckling and striction phenomena together. The two types of instability must be treated together in a reasonable approach to the hydroforming process.In this paper, the material verifies a “J2-flow” constitutive rate constitutive law. Jaumann's derivative was chosen and the Prandtl–Reuss equations with von Mises’ yield criterion and the associated flow rule were used. Isotropic hardening was taken into account.