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.     

Analytical and numerical approach to prediction of forming limit in tube hydroforming

Analytical and numerical analyses of forming limit in tube hydroforming under combined internal pressure and independent axial feeding are discussed in this paper. To predict the initiation of necking, Swift's criterion for diffuse plastic instability is adopted based on Hill's general theory for the uniqueness to the boundary value problem. In addition, in order to predict fracture initiation, Oyane's ductile fracture criterion is introduced and evaluated from the histories of stress and strain calculated by means of finite element analysis. From the comparison with a series of tube bulge tests, the prediction of the bursting failure based on the plastic instability and the ductile fracture criterion demonstrates to be reasonable so that these approaches can be extended to a wide range of practical tube hydroforming processes.     

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.     

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.     

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.     

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.     

弯曲轴线薄壁焊管内高压成形壁厚与变形规律的研究*

为了揭示焊缝对弯曲轴线类管件内高压成形的影响及缺陷产生的机制,采用试验和数值模拟的方法研究弯曲轴线焊管内高压成形的主要缺陷及壁厚分布规律,并分析焊缝在不同工序间的综合影响。结果表明,即使焊缝远离圆角区域,焊缝仍然是缺陷易发部位,弯曲使焊缝塑性下降,并导致在后续的工序中发生起皱甚至开裂。对于弯曲轴线薄壁焊管内高压成形,壁厚主要受弯曲和高压整形工序的影响,预成形工序对壁厚影响不大,而且焊缝的壁厚变化量始终小于其他区域。由此可知,焊缝是导致弯曲轴线薄壁焊管内高压成形缺陷产生的重要影响因素,将焊缝置于轻微压缩变形部位,是克服焊接接头性能下降导致的成形能力不足和避免缺陷产生的有效手段。     

Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram

Based on the mathematical formulations for predicting forming limits induced by buckling, wrinkling and bursting of free-expansion tube hydroforming, a theoretical “Process Window Diagram” (PWD) is proposed and established in this paper. The theory developed in the first part of the present work was formulated within the context of free-expansion tube hydroforming with both combined internal pressure and end feeding. The PWD is designed to provide a quick assessment of part producibility for tube hydroforming. The predicted PWD is validated against experimental results conducted for 6260-T4 60×2×320 (mm) aluminum tubes. An optimal loading path is also proposed in the PWD with an attempt to define the ideal forming process for aluminum tube hydroforming. Parametric studies show that the PWD has a strong dependency on tube geometry, material property and process parameters. To the authors’ knowledge, this is the first attempt that a PWD is being formulated theoretically. Such a concept can be advantageous in deriving design solutions and determining optimal process parameters for tube hydroforming processes.     

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.     

Effect of ductile fracture criteria on chevron crack formation and evolution in drawing

The purpose of this study is to clarify the mechanics of ductile fracture in bulk metal forming processes by finite-element analysis and experiments. The author has developed a computer program, based on a conventional computer program involving the finite-element method, by which the behavior of crack propagation after ductile fracture can be analyzed. The phenomenon in which a ‘chevron crack’ appears periodically in the axial direction during drawing has been simulated using the developed computer program. Special attention is focused on the effect of various kinds of ductile fracture criteria on chevron crack formation and evolution during drawing. Results obtained are summarized as follows. First, the analytical results obtained using Gurson's fracture criterion and using Oyane's fracture criterion agree well with the experimental result. Second, the analytical results using Cockcroft and Latham's fracture criterion and using Brozzo et al.'s fracture criterion agree somewhat with the experimental result. Finally, the analytical result obtained using Freudenthal's fracture criterion does not agree with the experimental result.     

Hydroforming of aluminum extrusion tubes for automotive applications. Part I: buckling, wrinkling and bursting analyses of aluminum tubes

Three possible failure modes have been identified in tube hydroforming: buckling, wrinkling and bursting. A general theoretical framework is proposed for analyzing these failure modes as an elastoplastic bifurcation problem. This framework enables advanced yield criteria and various strain-hardening laws to be readily incorporated into the analysis. The effect of plastic deformation on the geometric instability in tube hydroforming, such as global buckling, axisymmetric wrinkling and asymmetric wrinkling, is precisely treated by using the exact plane stress moduli tensor. A mathematical formulation for predicting the localized condition for bursting failure is established herein. Furthermore, the critical conditions governing the onset of buckling, axisymmetric wrinkling and asymmetric wrinkling are derived in closed-form expressions for the critical axial compressive stresses. Closed-form solutions for the critical stress are developed based on Neale–Hutchinson's constitutive equation and an assumed deformation theory of plasticity. It is demonstrated that the onset of asymmetric wrinkling always requires a higher critical axial compressive stress than the axisymmetric one under the context of tube hydroforming with applied internal pressure and hence the asymmetric wrinkling mode can be excluded in the analysis of tube hydroforming. Parametric studies show that buckling and axisymmetric wrinkling are strongly dependent on geometric parameters such as t₀/r₀ and r₀/ℓ₀, and that axisymmetric wrinkling is the predominant mode for short tubes while global buckling occurs for long slender tubes.     

Die shape design for T-shape tube hydroforming

In this paper, two design methods for T-shape tube hydroforming dies are proposed, namely, the extrusion-cutting-fillet method (ECFM) and the intersection-fillet method (IFM). Simulations on hydraulic expansion and axial feeding of T-shape tube hydroforming with two dies using the program DEFORM-3D were performed. The influence of the two dies on workpiece formability of T-shape tube hydroforming was examined. Experiments were carried out with SUS304 stainless steel tube at room temperature. A qualified product of T-shape tube, without wrinkling or bursting, was obtained using the die designed by the IFM method.     

不同应力状态下的高强钢板断裂机理及预测

板料成形过程的宏观断裂行为依赖于其微观断裂机理,因此成形过程模拟中的断裂准则的准确选择对于断裂预测具有重要意义。以高强钢TRIP780板料为研究对象,设计从剪切到拉伸应力状态的五种断裂试验,结合宏观拉伸试验和扫描电子显微镜（Scanning electron microscope,SEM）分析研究不同应力状态下TRIP780板料的断裂机理,得到不同应力状态下正应力和切应力与断裂机理的关联关系,引入正应力与切应力的影响构建MMC断裂准则,应用于板料压剪应力区间的断裂行为预测。结果表明,反映断裂机理的MMC准则能适用于板料压剪和拉剪变形应力状态下断裂失效的准确预测。     

断裂力学判据存在的一个问题及讨论

利用细观力学对材料断裂机理的认识，结合脆性材料常规破坏试验结果，提出了一个新的拉断破坏条件，该拉断强度条件与常用的几何脆断强度条件相比，能更好地解释材料在复杂应力状态下发生的脆断与小塑性韧断，并对常用的断裂力学判据存在的问题进行了讨论，通过分析影响裂尖空穴扩张的主要因素，给出能适应不同应力状态的新的断裂判据。     

Increasing the stability of T-shape tube hydroforming process under stochastic framework

Metal forming processes present several sources of uncertainties coming from material properties, geometric characteristics, and loading paths. During the manufacturing phase, such parameters may vary affecting the process stability and increasing the defect parts. Stochastic framework seems more pertinent than classical deterministic approaches to treat such problems since it is intended to include variabilities at the early design stage. In the present work, tube hydroforming process widely used in various industry applications is investigated. To ensure the process stability, loading paths should be optimized with taking into account randomness associated to the input parameters. To control the potential failure modes, the Forming Limit Stress Diagram is implemented in the finite element code to avoid necking while a simple geometrical criterion is defined for wrinkling. A global sensitivity analysis using the variance-based method is done which shows that the selected random parameters impact considerably the variance of failure indicators. Then, a numerical example of T-shape tube hydroforming process is proposed to show the efficiency of the stochastic framework. Statistical and probabilistic observations of the optimum solution show that the stochastic approach yields to an optimum less sensitive to such fluctuations which improves the process stability and minimizes considerably the percentage of defect parts in a mass production environment.     

Experimental research on ductile fracture criterion in metal forming

Ductile fracture criterion is key limitation parameter in material forming. Accuracy predicting surface and internal failure in plastic deformation process affects on the technology design of workpiece and die greatly. Tension, compression, torsion and shearing test on 45# steel are utilized for providing the experimental values of the critical values at fracture, and 11 widely used ductile fracture criterion are selected to simulate the physical experiments and their relative accuracy for predicting and quantifying fracture initiation sites are investigated. The comparing results show that metal forming process under high triaxiality can be estimated successively using both Normalized Cockcroft-latham and the Brozzo ductile fracture criteria, but the Ayada and general Rice-Tracey model work very well for the low triaxiality cases.     

Study on the crushing and hydroforming processes of tubes in a trapezoid-sectional die

A study on the bulging processes of tubes in a trapezoid-sectional die has been carried out through finite-element (FE) analysis. A FE model of the single-step hydroforming process and several FE models of crushing combined with subsequent hydroforming processes in a trapezoid-sectional die with different die closing seams are proposed. The simulations are performed using the FE code LS-DYNA. For the single-step hydroforming process, the effects of loading paths on the formability of the trapezoid-sectional part are investigated. In the case of the crushing combined with subsequent hydroforming processes, the effects of die closing seams, tube diameters, and preforming loading paths on the forming process and the final parts are analyzed. A comparison between the parts formed through single-step hydroforming process and through crushing combined with subsequent hydroforming processes is performed. Finally, an experiment of tube hydroforming in a trapezoid-sectional die is carried out on the hydroforming machine developed by Shanghai Jiaotong University. The simulation results show good agreement with the experimental results.     

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.     

脉动液压成形技术与设备

介绍脉动液压成形技术的成形原理、工艺特点及应用领域。从工艺和材料两方面对脉动液压成形提高材料成形能力的机理进行研究,试验证明脉动载荷一方面能够促进管材液压成形时的补料、降低摩擦力的阻碍作用并利用成形过程中小褶皱的出现与消失提高变形的均匀性;另一方面,对于奥氏体不锈钢,脉动载荷可以增强形变过程中的相变增塑效应,从而提高其成形性。自主设计并研制出能实现工业化生产需求的自动化程度高的脉动液压成形设备,为该项技术在汽车、航空及航天制造领域中的推广和应用提供重要的理论指导和实践探索。     

铝合金球壳液压胀形试验研究

研究了板厚1.5mm的3A21O铝合金板材和焊接接头的塑性成形能力,进行了铝合金球壳的整体液压胀形实验。实验结果表明:在保证焊接质量的前提下,铝合金球壳的胀形过程能够顺利进行。分析了壳体胀形过程中的变形和应力分布规律,从理论上给出了球壳的胀形屈服应力和开裂应力,最后采用动态显式有限元分析软件LS-DYNA给出了壳体的壁厚分布。