A prediction of bursting failure in tube hydroforming processes based on ductile fracture criterion

Bursting is an irrecoverable failure mode in tube hydroforming, in contrast with buckling and wrinkling. To predict bursting failure in the hydroforming processes, Oyane's ductile fracture criterion is introduced and evaluated from the results of stress and strain productions obtained from finite element analysis. The region of fracture initiation and the bursting pressures are predicted and compared with a series of experimental results. It is shown that the material parameters used in the criterion can be obtained from the forming limit diagram. From the simulation results of tube bulging, the prediction of the bursting failure based on the ductile fracture criterion was demonstrated to be reasonable. 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.     

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。     

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.     

Fracture predicting in bulk metal forming

An important concern in forming is whether the desired deformation can be accomplished without failure of the work material. This paper describes the utilization of ductile fracture criteria in conjunction with the finite element method for predicting failures in cold bulk metal forming. Four previously published ductile fracture criteria are selected, and their relative accuracy for predicting and quantifying fracture initiation sites is investigated. Experiments with ring, cylindrical, tapered and flanged upset samples are performed to investigate the validity of the workability criteria under conditions of stress and strain similar to those usually found in bulk metal forming processes. The implementation of ductile fracture criteria into a rigid—plastic finite element computer program is presented. Local stress and strain distributions throughout the deformation are computed and compared with experimental measurements. A general good agreement is found. However, only two of these workability criteria have successfully predicted the location at which fracture initiates for all the upset tests performed in this work. The paper concludes with a discussion of the importance of the critical damage at fracture to remain independent from the technological 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.     

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.     

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.     

Plastic instability in dual-pressure tube-hydroforming process

The tube-hydroforming process has become an indispensable manufacturing technique in recent years. Successful tube hydroforming requires bulging to take place without causing any type of instability such as bursting, wrinkling or buckling. The dual-pressure tube-hydroforming process was introduced to achieve a favorable tri-axial stress state in the deformation process. In this paper, the effect of applying counter pressure on plastic instability of thin-walled tubes is analyzed. It is concluded that in dual-pressure tube hydroforming, the onset of plastic instability is delayed and the ductility of the metal is increased.     

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.     

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。     

直缝焊管液压成形极限理论预测模型

直缝焊管广泛应用于汽车车身管状零件液压成形中,焊接区影响着焊管塑性变形规律,准确评价焊管缩颈或破裂现象是工程上倍受关注的问题。基于金相分析法和显微硬度测量法分析高频感应焊管的结构特征,并根据液压成形条件下高频感应焊管的变形特点,提出一种用于计算直缝焊管液压成形极限的理论方法。基于该方法,选用Swift硬化方程和Hill屈服准则推导出直缝焊管液压成形极限理论预测模型,在已知焊管(包含焊接区和基体区)材料性能参数条件下可获得直缝焊管液压成形极限图。运用此理论预测模型,计算出QSTE340高频感应焊管的液压成形极限图。成形极限的计算结果与试验对比表明,二者吻合较好,这证明所建立的直缝焊管液压成形极限的理论预测模型是正确的。     

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。     

基于成形应力极限的管材液压成形缺陷预测

基于塑性应力应变关系及Hill79屈服准则,推导出极限应力与极限应变间转化关系,进而建立2008T4铝合金的成形应力极限图(Forming limit stress diagram,FLSD)。采用LS-DYNA软件对三通管液压胀形过程进行模拟,应用FLSD预测胀形过程中破裂的发生及成形压力极限,并与传统成形极限图(Forming limit diagram,FLD)结果进行了对比。研究表明,FLD与FLSD预测结果中破裂缺陷位置相同,但极限内压力值存在很大差别,而FLSD预测结果与物理试验结果较吻合。考虑到FLD受应变路径影响显著的因素,将FLSD作为管材液压成形等复杂应变路径下的成形极限的判据更加方便可靠。     

Numerical analysis and design for tubular hydroforming

To get an optimum deformation path for tubular hydroforming, the hydroforming limit of isotropic and anisotropic tubes subjected to internal hydraulic pressure, independent axial load or torque is firstly proposed based on the Hill's general theory for the uniqueness to the boundary value problem and compared with those of the conventional sheet forming. The influences of the deformation path, the material properties and the active length–diameter ratio on the nucleation and the development of wrinkling during the free tubular hydroforming are also investigated. The above theory is used as a criterion and implemented with some new functions in our ITAS3D, an in-house finite element code for simulating the sheet forming, to control the materials flow and to prevent the final failure modes from occurring. Finally, the tubular hydroforming of an automobile differential gear box is taken as an example to show the efficiency and usefulness of the algorithm.     

Application of the hydroforming strain- and stress-limit diagrams to predict necking in metal bellows forming process

In order to predict the initiation of necking in metal bellows forming process, a methodology for determination of the forming limit diagram and the forming limit stress diagram is represented in this paper. The methodology is based on the Marciniak and Kuczynski (M–K) model. Comparison between the experimental and theoretical results for hydroforming stress and strain-limit diagrams as predicted by different methods indicates that the present approach is suitable for prediction of necking in tube hydroforming processes. Afterwards, the implementation of the hydroforming strain- and stress-limit diagrams into finite element numerical simulations for the forming of the metal bellows is established. A satisfactory agreement between the finite element method (FEM) and test results is achieved.     

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.