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.     

Bursting failure prediction in tube hydroforming processes by using rigid–plastic FEM combined with ductile fracture criterion

The most common failure in tube hydroforming is the bursting failure due to excessive thinning of large deformation. To evaluate the forming limit of hydroforming processes, the Oyane's ductile fracture integral I was introduced and calculated from the histories of stress and strain according to every element by using the rigid–plastic finite element method. The region of fracture initiation and the forming limit for three hydroforming processes, such as a tee extrusion, an automobile rear axle housing, and a lower arm under different forming conditions are predicted in this study. Also it is shown that the material parameters used in the ductile failure can be obtained from the experimental forming limit diagram. From the results, the prediction of the bursting failure and the plastic deformation for the three hydroforming examples demonstrates to be reasonable so that this approach can be extended to a wide range of practical tube hydroforming processes.     

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.     

Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet

Forming limit curves at neck and at fracture have been experimentally determined, and surfaces of fractured dome specimens have been observed optically and in the SEM, for an automotive AA6111-T4 sheet material. Various continuum ductile fracture criteria from the literature along with the assumptions of power law hardening, Hill’s quadratic yield criterion, and proportionality of stress and strain paths have been utilized for prediction of forming limit curve at fracture and compared with the experimental curve to assess the applicability of the different fracture criteria. The maximum shear stress criterion by Tresca predicts reasonably well the fracture limits of AA6111-T4 sheet material for a range of strain ratios, and is consistent with the microstructural observations. The criterion can be used to predict fracture limit curves from uniaxial tensile data and plane strain limit at fracture. A methodology for incorporating such a ductile fracture criterion into FE simulations of sheet stampings for prediction of fracture is discussed.     

Analysis of forming limit in tube hydroforming

The automotive industry has shown increasing interest in tube hydroforming. Despite many automobile structural parts being produced from cylindrical tubes, failures frequently occur during tube hydroforming under improper forming conditions. These problems include wrinkling, buckling, folding back, and bursting.We perform analytical studies to determine forming limits in tube hydroforming and demonstrate how these forming limits are influenced by the loading path. Theoretical results for the forming limits of wrinkling and bursting are compared with experimental results for an aluminum tube.     

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.     

Numerical improvement of thin tubes hydroforming with respect to ductile damage

Fully coupled constitutive equations, formulated in the framework of the thermodynamics of irreversible processes with state variables, accounting for isotropic hardening as well as the isotropic ductile damage are used to simulate numerically, by the finite element analysis, 3D metal hydroforming processes with damage occurence. An implicit integration scheme for local time integration of the constitutive equations and a dynamic explicit resolution scheme to solve the associated dynamic equilibrium problem are used. The effects of friction coefficient, material ductility and hydro bulging condition, on the hydroformability of various thin tubes are discussed.     

Finite element analysis of limit strains in biaxial stretching of sheet metals allowing for ductile fracture

To predict limit strains in biaxial stretching of sheet metals, a criterion for ductile fracture is combined with the finite element simulation. The limit strains are determined by substituting the values of stress and strain obtained from the finite element simulation into the ductile fracture criterion. Material constants in the criterion are obtained from the fracture strains measured in the biaxial stretching tests. Calculations are carried out for various strain paths from balanced biaxial stretching to uniaxial tension of aluminium alloy sheets, and compared with the experimental results. The predicted limit strains are in good agreement with the measured ones not only just at the fracture site but also at outside of the fracture site. It is demonstrated that the forming limit diagrams are successfully predicted by the present approach.     

Analytical and numerical study on plastic instabilities for axisymmetric tube bulging

In this paper, plastic instabilities of elasto–plastic tubes subject to internal pressure are discussed. For diffuse necking prediction, the classical intrinsic criteria for diffuse necking are accurate for long cylindrical tubes. However, for short tubes, geometric changes are important, and the intrinsic criteria become insufficient. For this purpose, a new diffuse necking criteria is proposed including geometric effects in the prediction.On the other hand, for the local necking prediction, the Hill's criterion is not accurate for short tubes, due to the biaxial stretching. As an alternative, a local necking criterion based on a modified Hill's assumption for localized necking is proposed. The numerical calculations carried out for different tube dimensions, explains the geometrical effects on the localization of deformations for pressurized tubes, and improves the accuracy of the proposed criteria.     

Predicting of plastic instability and forming limit diagrams

An analytical method is presented for predicting forming limit diagrams achieved during sheet metal forming operations for sheets having planar isotropy. This method is based on the three-phase deformation idealization developed by Johns and Gillis. The Johns–Gillis and Pishbin–Gillis model were restricted to the Hill yield criterion which is not suitable for aluminum alloys (R<1). The present work used the Hosford criterion that is widely used for materials with R<1, in conjunction with the power-law, the Tian–Zhang and the Vocé hardening equations. Results from this analysis are compared with the experimental data for AA3105 and AA8011 aluminum alloys. The results indicate good prediction of limit strains for the two alloys when the Vocé and the Tian–Zhang equations are applied.     

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.     

A comparative study of implicit and explicit FEM for the wrinkling prediction in the hydroforming process

The recent application of tube hydroforming in the automotive industry demands finite element analysis, since it is rapidly being used as an effective tool for the evaluation and optimisation of the design of hydroforming dies and processes. In this paper, attention is paid to the comparison of an implicit and an explicit FEM widely used for the hydroforming process. The influences of time scaling and mass scaling, which have been commonly used in order to save computational time in the explicit method, are especially investigated. The comparisons focus on the predictability of wrinkling and stress with various scaling factors in the explicit method. Through verifications with experimental results, a useful guideline in determining the scaling factors is proposed.     

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.     

On the prediction of the effect of process parameters upon forming limit strains in sheet metals

Plasticity analysis of sheet metal forming requires a detailed knowledge of the influence of process parameters on the stress–strain relationships from yielding up to localized necking, for accurate prediction of forming limits. Achievable strain and stress–strain relationships are sensitive to modulations in process parameters, chiefly temperature and strain rate. However, the effects of changes in strain rate and temperature are often complex as they also depend on the levels of strain, strain rate and the temperature employed. Such variations could be either triggered by the process dynamics of the forming operation or imposed for optimal exploitation of the material ductility. In this study, the influence of such process parameter modulations upon formability has been theoretically modelled, following the Sing–Rao prediction approach. The limit strains thus predicted compare favourably with experimental results for a drawing steel, thus validating the present formalism. This approach can also be adopted to accommodate non-linear straining conditions. Thus, theoretical modelling of strain-path-dependent forming limits, which has not been explored adequately so far, now becomes feasible.     

An analytical approach for the prediction of forming limit curves subjected to combined strain paths

In the present work, an analytical approach for the prediction of forming limit curves is proposed to incorporate the effect of combined strain paths. The effect of combined strain paths (considering the directional dependency of pre-straining and further straining) is addressed by integrating the incremental equivalent strain expression in two stages i.e., pre-strain and subsequent loading. In each stage, the strain path is assumed to be linear and different combinations of pre-strain (uniaxial, plane-strain and equi-biaxial) are considered. Material anisotropy is taken into account in each stage. The predictions of the present model are compared with the experimental results on forming limit curves under combined strain paths for Al6111-T4 [24] and are found to be in good agreement with each other.     

Analytical model for planar tube hydroforming: Prediction of formed shape, corner fill, wall thinning, and forming pressure

An analytical model for planar tube hydroforming based on deformation theory has been developed. This analytical model can be used to predict hydroformed shape, corner fill, wall thinning, and forming pressure. As the model is based on a mechanistic approach with bending effects included, local strain and stress distribution across the wall thickness can be determined. This includes strain and stress distributions for the outer layer, inside layer, and middle layer. The model is validated using finite element analysis and tube hydroforming experiments on irregular triangular, irregular quadrilateral, and pentagonal hydroformed shapes.     

疲劳对金属塑性变形及延性断裂过程的影响

通过慢速拉伸曲线,研究金属的塑性变形过程和延性过程中细微的变化,以及疲劳对它们的影响。在对金属材料做静拉伸试验时,在一般速率拉伸和在慢速拉伸下,所得到的拉伸曲线的表现是不同的。比较了拉伸速率10mm/min和0.2mm/min的拉伸曲线,在弹性变形范围内,2种速率下的曲线基本上是一样的;在塑性变形阶段,慢速拉伸曲线将随着载荷的增加,曲线逐渐变粗,当通过最大载荷点1段后,曲线变到最粗,然后变成1条线;在断裂阶段,曲线出现间断卸载的叉枝,直到断裂。     

Optimum design of preform geometry and forming pressure in tube hydroforming using the equi-potential lines method

The quality of a tube-hydroformed component as well as the tooling cost and processing time involved in the process are notably affected by the component’s preform. Hence, it is necessary to produce a proper preform shape for the successful hydroforming from the initial tube to final shape. In this paper, the notion of equi-potential lines (EPLs) is used to find an appropriate preform shape in the tube hydroforming process for the first time. The EPLs generated between two conductors of different voltages show minimum work paths between the initial and final shapes. Based on this similarity, the EPLs method is utilized for preform shape design. Next, the forming pressure of the preform is determined using finite element analysis. Finally, the computationally expensive procedure introduced above is significantly facilitated by employing a multi-layer perceptron neural network which is trained using results from application of the procedure to a set of uniformly distributed random input vectors. Real-world examples are presented to demonstrate the applicability and efficiency of the proposed approach.     

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.