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.     

内高压成形机理与关键技术

在中国国家杰出青年科学基金资助项目“镁合金热态液力成形技术”、中国国家自然科学基金资助项目“轻体件高内压液力成形机理的研究”、“管材热态内压成形新方法及其机理研究”和“激光拼焊管内高压成形机理”、以及中国教育部高等学校博士学科点专项科研基金资助项目“镁合金热态内高压成形机理研究”共同资助下,开展内高压成形机理及关键技术研究,在内高压成形塑性变形规律、起皱和破裂等失稳行为、提高成形极限和降低成形压力方法,以及液力胀接、热态内压成形和拼焊管内高压成形等方面取得重要进展,并在汽车和航天等领域实现内高压成形技术产业化应用,报告上述研究的理论和工程体系。 根据塑性变形特点,将内高压成形分为变径管内高压成形(IHPF of TPVD)、弯曲轴线管内高压成形(IHPF of TPCA)和多通管内高压成形(IHPF of TPB/BT)等3类,提出IHPF of TPVD由充填、成形、整形等步骤组成,IHPF of TPCA由弯曲、预成形、内高压成形等步骤组成,IHPF of TPB/BT由胀形、补料、整形等步骤组成。以此为出发点,通过实验和理论分析,研究IHPF塑性变形规律与失稳行为。     

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.     

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.     

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.     

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.     

Determination of flow stress of thin-walled tube based on digital speckle correlation method for hydroforming applications

The flow stress, used to describe the plastic deformation behavior of thin-walled tube, is one of the most important parameters to ensure reliable finite element simulation in the tube hydroforming process. In this study, a novel approach of on-line measurement based on digital speckle correlation method is put forward to determine flow stress of thin-walled tube. A simple experimental tooling is developed and free-bulged tests are performed for 304 stainless steel and H62 brass alloy tubes. An analytical approach is proposed according to the membrane theory and the force equilibrium equation. The developed method is validated by means of FE simulations. The results indicate that the present method is acceptable to define the flow stress in the tube hydroforming process.     

A contribution to determining the friction coefficient in hydroforming of tubes

Hydroforming is a relatively new technology, which enables complex shaped hollow parts to be produced efficiently. Compared to alternative methods, this technology is characterised by significant potential advantages, such as complex shape production, lightweight design, high accuracy, and process integration. The tribological aspects of hydroforming are very significant, as friction influences all the main process parameters practically in a direct or indirect way. However, there is a paucity of information relating to hydroforming tribology. In most reports on this subject only qualitative data regarding the friction coefficient are given. However, for finite‐element method simulation and optimal process and tool design, quantitative data are indispensable. This paper describes an attempt to determine the coefficient of friction in both the elastic and plastic states of a workpiece during tube hydroforming processes. Push‐through tests were carried out in order to determine the coefficient of friction in the elastic state, and tube upsetting tests were conducted for the plastic state. Various commercial lubricants were used in the experiments.     

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。     

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.     

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.     

一种估计管材硬化模型参数的方法

管材力学性能参数的准确性是影响管材塑性成形有限元数值模拟质量的关键因素之一。单向拉伸试验的试件取自滚弯和焊接等制管工序之前的平板坯料 ,所测应力—应变关系无法真实描述管材的塑性变形行为。单向拉伸试验也不能精确反映管材在实际塑性成形中所处的复杂应力状态。基于各向同性硬化假设 ,本文提出了一种轴压胀形、单向压缩试验和数据拟合技术相结合的估计管材硬化模型参数的方法。有限元数值模拟结果显示 ,由这种方法所估计出的管材硬化模型参数是相当准确的。     

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.     

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.     

Analysis and design of hydroformed thin-walled tubes using enhanced one-step method

This paper deals with the analysis and design of tube hydroforming parameters in order to reduce defects which may occur at the end of the forming process, such as necking and wrinkling. We propose a specific methodology based on the coupling between an enhanced one-step method for the rapid simulation of tube hydroforming process and a surrogate model based on a metamodeling technique. The basic formulation of the one-step method has been modified and adapted for the modeling of 3D tube hydroforming problems in which the initial geometry is a circular tube expanded by internal pressure and submitted to axial feeding. In the surrogate model, approximate responses are built using moving least squares method and constructed within a moving region of interest which moves across a predefined discrete grid of authorized experimental designs. Two applications of tube hydroforming of aluminum alloy 6061-T6 have been utilized to validate our methodology. The final design is validated using experiments together with the classical explicit dynamic incremental approach using ABAQUS? commercial code.     

管件液压成形技术在汽车制造中的应用研究

阐述了管律液压成形的基本概念及其优点，介绍了在汽车制造领域中的应用，综述了管件液压成形技术的研究成果，重点介绍材料、塑性失稳、加载路径优化、预成形等问题；讨论了应用研究中进一步的发展方向。     

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.     

超高压管材液压成形控制系统的研制

介绍了管材液压成形工艺,根据液压成形原理,自主研制出具备高压发生器、阀门管路等配件的超高压液压系统,同时通过可编程控制器实现对电磁元件的控制,有效地解决了管材在液压成形过程中的端口密封、进给补料等关键问题,为管材液压成形的实验研究奠定了基础。     

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.