An analysis of localized necking in aluminium alloy tubes during hydroforming using a continuum damage model

In this work, localized necking in aluminium alloy tubes subjected to free hydroforming is analyzed. The main objective is to study the influence of loading conditions, such as prescribed fluid pressure or volume flow rate in conjunction with axial end feed, on the nature of the forming limit curve (FLC). To this end, the strain histories experienced at the tube mid-length, which were computed in an earlier investigation [14] [Varma NSP, Narasimhan R. A numerical study of the effect of loading conditions on tubular hydroforming, Journal of Materials Processing Technology 2005; [Submitted for publication]], are analyzed using the Marciniak–Kuczynski (M–K) method along with an anisotropic version of the Gurson model. The Gurson constitutive parameters are determined following an inverse approach using the sheet FLC for the chosen alloy. The predicted FLC for combined pressure and axial contraction corroborates well with the experimental data obtained in [12] [Kulkarni A, Biswas P, Narasimhan R, Luo A, Stoughton T, Mishra R, Sachdev AK. An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming. International Journal of Mechanical Sciences 46:2004;1727–46] and is almost flat, whereas it is akin to the sheet FLC and increases with negative minor strain when fluid volume is specified. The forming limit strains for loading with specified fluid volume are in general higher when compared to those with prescribed fluid pressure. Finally, it is demonstrated that a transition from axial to circumferential necking occurs when high ratios of axial extension to volume flow rate are applied to the tube.     

内补液增压式THF性能测试装置开发及试验研究

材料性能对液压胀形工艺(THF)及产品质量有重大影响,传统单向拉伸试验所得材料性能不能很好反映管材液压胀形性能。开发了一种简单实用可在单动压力机上使用的试验装置,可用于不同材料及尺寸管材的液压胀形试验,以确定管材胀形性能。该装置不需要复杂的外部供液系统,而是利用其内部的补液腔自动、同步地建立起胀形所需液压力及轴向载荷,两载荷比值可通过合理设计补液腔直径得到。可以实现管材自然胀形、轴向压缩胀形、两端不同约束下的胀形和一定程度的比例加载胀形。一系列胀形对比试验表明：管端约束方式对自然胀形有较大影响,而对轴向压缩胀形影响较小;液压力、轴向载荷及其比值对轴向压缩胀形有较大影响。     

Investigation of deformation and collapse mechanism for magnesium tube in axial crushing test

This paper demonstrates the quasi-static axial compression and high-speed axial compression tests of extruded magnesium alloy circular tubes for evaluating the crash and fracture behavior of mg parts. To capture the buckling and fracture behavior of Mg tube during the axial compression tests, FE simulation adopts different types of flow curves depending on the deformation mode such as tension and compression with LS-DYNA software. The Mg tube undergoes compressive plastic strain prior to buckling while according to the model based on Hill yield criterion only bulging along the radial direction is predicted. Due to the tension-compression asymmetry of Mg alloys, diameter of Mg tube expands largely at the initial plastic strain before having bulging or folding while only a bulging mode typical for materials with cubic crystal structure can be predicted. Simulation results such as punch load and deformation mode are compared with experimental results in the axial crushing test with AZ61 alloy.     

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.     

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

This article studies tubular hydroforming of high strength low alloy (HSLA) and dual phase (DP600) straight tubes under the action of end feeding loads. Experiments demonstrate that higher end feed loads enhance the formability of the tubes and increase the internal fluid pressure for onset of necking and bursting. Because of the action of the internal pressure and the axial compressive load, the onset of localization (necking) is due to a complex three-dimensional state of stress. Using free expansion experiments, approximate upper and lower bound strain-based forming limit curves are determined for the tube materials. These limit curves, in turn, are used to derive upper and lower bound extended stress-based forming limit curves [Simha et al., Prediction of necking in tubular hydroforming using an extended stress-based FLC. Transactions of the ASME Journal of Engineering Materials and Technology 2007;129(1): 36-47]. In conjunction with finite element computations that use solid elements to model the tube, these stress-based limit curves are used to predict upper and lower bound necking pressures under the action of end feed loading. These predictions of necking pressures, when an appropriate coefficient of tube-die friction is used, are found to bracket the experimentally measured necking pressures. Computations using plane stress shell elements to model the tubes are shown to give erroneous results, since the plane stress approximation is not valid when tubes are hydroformed in a die.     

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.     

Deformation behaviour of elastic-plastic tubes under external pressure and axial load

A constitutive equation taking into account corner formation on the yield surface and the Bauschinger effect is developed. The behaviour of circular long tubes subjected to external pressure and axial load under plane strain and generalized plane-strain conditions are analyzed in conjunction with the proposed constitutive equation. The influence of axial load, the Bauschinger effect and corner formation, including the corner angle, and the mobility of the corner axis to the direction of stress history upon such global deformation behaviour as maximum pressure, pressure vs displacement relation and axial strain, are clarified. With regard to local deformation, these effects on the strain rate and strain localization, surface unevenness and shear band formation from the highly strained internal surface are investigated.     

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.     

Determination of forming limit diagrams of sheet materials with a hybrid experimental-numerical approach

A new methodology is proposed to obtain the forming limit diagram (FLD) of sheet materials by utilizing routinely obtained experimental punch load versus displacement traces from hemispherical punch stretching experiments and by analyzing strain history of the test samples from finite element simulations of the experiments. The simulations based characteristic points of diffuse and localized necking are utilized to obtain the limit strains. The proposed method for FLD determination considers out-of-plane displacement, punch-sheet contact and friction, and avoids using experimental strain measurement in the vicinity of the neck on the dome specimens and the rather arbitrary inhomogeneity factor to trigger localization such as in the commonly used Marciniak-Kuczynski method. A criterion of maximum in the ‘pseudo’ major strain acceleration for the onset of localized necking, proposed earlier by the present authors, is utilized to determine the limit strain in FE simulations as well as in FLD verification experiments. The proposed overall approach for obtaining FLD is rapid and accurate and could be implemented for routine FLD generation in a laboratory setting with significant reduction in cost, effort and subjectivity.     

Axisymmetric deformation of circular elastic-plastic tubes under axial tension and internal pressure

The axisymmetric bifurcation and post-bifurcation behaviour of circular tubes subjected to the combined action of axial tension and internal pressure are investigated numerically using the finite element method. It is assumed that the tubes are made of elastic-plastic strain hardening material with a smooth yield surface and that they deform without shear stress at both ends under the proportional stress path based on the stress values averaged over the cross-section.The bifurcation point and associated mode shape are obtained for each stress path. The initial to medium nonuniform deformation was studied for several specific stress paths and the growth of necking of the tube wall and swelling of the middle plane due to bifurcation are clarified.     

Modelling grain growth evolution and necking in superplastic blow-forming

A stability analysis is carried out to investigate necking in superplastic materials characterised by the sinh-law constitutive equation . The effects of load and the strain rate sensitivity parameter β on necking are quantitatively studied and a necking map is obtained for conditions of uniaxial loading. Finite element simulations of a superplastic blow-forming process are carried out in order to investigate both non-uniform thinning and grain size distribution which result from the use of the sinh-law constitutive equation. The pressure cycle required to ensure a target maximum strain rate is not exceeded in the material is obtained. The effects of strain rate and the magnitude of the parameter β on the grain size and through-thickness strain distributions for the formed part are investigated.     

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。     

Finite deformations of an initially stressed cylindrical shell under internal pressure

This paper investigates the large deformations of an extended thick cylindrical tube under internal pressure, with emphasis on the static nonlinear behavior and instabilities of the shell. Thick elastic tubes that undergo large elastic deformations under internal pressure can exhibit novel instabilities. After some deformation, part of the tube becomes highly deformed taking the form of a bulge, while the remainder appears almost unchanged. This local instability phenomenon corresponds to a limit point along the nonlinear equilibrium path. After the onset of these highly nonuniform deformations, the local bulge initially grows with a marked decrease in internal pressure while the rest of the tube unloads. First, a detailed experimental analysis is carried out involving different geometries and initial axial forces and the influence of the axial force and of the internal pressure on the critical pressure is investigated. The shell used in the experiments is composed of an isotropic, homogeneous and hyperelastic rubber, which is modeled as a Mooney–Rivlin incompressible material, described by two elastic constants. These constants are obtained by comparing the experimental and numerical solutions for the shell under axial tension. The governing shell equations are solved numerically using the finite-element method, using the program ABAQUS. The experimental results are, as shown in the paper, in satisfactory agreement with the numerical analysis.     

双台阶钻柱螺纹联接弹塑性接触特性数值仿真

建立了双台阶钻柱螺纹接头有限元模型，采用弹塑性接触有限元混合法开发了钻柱螺纹接触特性分析程序，并对双台阶钻柱联接螺纹进行了应力应变分析，求得联接状态下由预紧力以及轴向力、内外压力、弯矩和扭矩所引起的螺纹联接部位的位移场和应力场，为评价其承载性能及密封性能提供了一种数值方法。     

Blank optimization for free bulging of Inconel 718 to maximize bulged height at high temperatures

Thickness profiled blank is designed via the optimization technique to maximize the bulged height in free bulging for Inconel 718. The thickness of the blank is described by the Bezier curve by using four control points. The location of each control points is used for the design variables of optimization. The material parameters for the flow stress equation of Inconel 718 are obtained from the free bulging test at constant pressure condition by using a flat blank and verified via numerical analysis. The objective function and constraints for optimization are the maximization of the bulged height within a limited strain range. The equivalent static load method for non-linear static response structural optimization with a move limit scheme is used for optimization. The result of optimization shows 21.95% increased bulged height and uniformly distributed strain after bulging. The free bulging test using blank with optimized profile is conducted to verify the optimization process. The results of bulged height and deformed shape are compared with those from numerical analysis, and the comparison shows good agreement.     

An analysis of axisymmetric hydrostatic bulging by the upper-bound method

An upper-bound solution for the analysis of hydrostatic bulging is found by minimizing the plastic energy consumption rate divided by the fluid volume change rate. The corresponding upper-bound pressure is found through optimization with respect to some parameters given in the assumed velocity field. Computations are carried out for axisymmetric hydrostatic bulging of isotropic work-hardening sheet metal. The computed results are then compared with those by the finite-element method and by the finite-difference method as well as the reported experimental results. The comparison shows that the present method renders excellent predictions in pressure and strain distributions with much reduced computational time, which are still in close agreement with those obtained by the numerical methods.     

初始缺陷和比例加载路径对圆柱壳弹塑性稳定性的影响

应用非线性弹塑性稳定性理论研究圆柱壳在轴向力和内压联合作用下的弹塑性稳定性问题,得到了不同比例加载路径、初始缺陷和塑性变形发展程度对弹塑性失稳的影响规律曲线。结果表明,在内压的作用下,柱壳的临界轴向压应力在初始阶段有所提高,但从某一内压值开始将会有所下降。对于同一比例加载路径,随着缺陷因子的增加,临界屈曲轴向压应力随着相应地递减。而对于同样的缺陷因子,比例加载参数小于1.0时,临界屈曲轴向压应力随着比例加载参数的增大而增大;比例加载参数大于1.0时,临界屈曲轴向压应力随着比例加载参数的增大而减小;比例加载参数等于1.0为理想加载比例参数值。该研究丰富了内高压成形工艺的理论基础。     

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.     

The effect of axial loading and axial restraint on the thermal ratchetting of thin tubes

The finite element method has been used to investigate the thermal ratchetting behaviour of thin tubes subjected to steady, internal pressure and cyclic, linear, through-thickness temperature distributions. An elastic-perfectly plastic material behaviour model was used and uniaxial behaviour was related to multiaxial behaviour via the von Mises yield criterion and the Prandtl-Reuss flow rule. Results for a tube without axial stress, a tube with axial stress (corresponding to a tube with an end closure) and a tube constrained to have no axial strain, are presented. Correlations with a simplified analytical solution were attempted. Good correlations were obtained for the tubes without axial restraint. The correlation for the axially constrained tube was poor because the thermal loading is essentially different. In the case of the axially constrained tube, if the thermal load is high enough, yielding occurs through the whole of the wall thickness simultaneously in each half cycle. This is not possible in the other two cases considered.     

Energy absorption of pressurized thin-walled circular tubes under axial crushing

By pressurizing cellular materials, honeycombs, or thin-walled structures, their energy absorption can be greatly enhanced, and this enhancement can be controlled by the applied pressure. This concept shines light on the possibility of achieving adaptive energy absorption. To investigate the effect of internal pressure on energy absorption of thin-walled structures, this paper presents a study of axial crushing of pressurized thin-walled circular tubes. In the experiments, three groups of circular tubes with radius/thickness ratio R/t=120-200 were axially compressed under different pressurizing conditions. The results show that with an increase of internal pressure, the deformation mode switches from diamond mode with sharp corners to that with round corners, and eventually to ring mode. In diamond mode, the mean force of the tubes increases linearly with internal pressure. The enhancement comes from two mechanisms: direct effect of pressure and indirect effect due to interaction between pressure and tube wall. After the deformation switches to ring mode, the enhancement resulting from the second mechanism becomes weaker. Based on experimental observations, the deformation mode, energy dissipation mechanisms as well as interaction between internal pressure and tube wall are analyzed theoretically and the theoretical results are in good agreement with the experimental ones.