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.     

An analytical model for plate wrinkling under tri-axial loading and its application

The prediction and prevention of wrinkling have been challenging issues in sheet metal forming processes. In an effort to provide the design and process engineers a reliable and efficient tool in assessing the onset of flange wrinkling, an analytical model, based on the wrinkling criterion proposed by Cao and Boyce [1], is presented here. The critical buckling stress and wavelength as functions of normal pressure are calculated using a combination of energy conservation and plastic bending theory. The present results are in excellent agreement with those obtained from Cao and Boyce’s numerical approach which has demonstrated its excellent predictive capability by comparing the experimental study of a conical cup [1] and a square cup forming [2]. Additionally, the effects of the tension in the plane of sheet and material properties on the initiation of flange wrinkling are investigated.     

On the analysis of sheet metal wrinkling

An analysis for the prediction of wrinkling in curved sheets during metal forming is presented. Using a local approach, similar to that employed for conventional forming limit diagram representations, we construct “wrinkling limit curves” (WLCs) which represent the combinations of the critical principal stresses for wrinkling in curved sheet elements. Wrinkling limit curves are first determined using a bifurcation analysis for plastic buckling in short-wavelength shallow modes. A study of the effects of material properties and sheet geometry on the critical conditions for wrinkling is carried out. We then analyse the effects of geometric imperfections on wrinkling. This analysis is based on the implementation of a finite element scheme. The influence of nonproportional loading is also investigated. In our analysis the material is assumed to be isotropic, elastic-plastic with the plastic part modelled using both J₂ deformation theory and J₂ flow theory of plasticity.     

Plastic buckling of tubes under axial compression and internal pressure

The plastic buckling and collapse of long cylinders under combined internal pressure and axial compression was investigated through a combination of experiments and analysis. Stainless-steel cylinders with diameter-to-thickness values of 28.3 and 39.8 were compressed to failure at fixed values of internal pressure up to values 75% of the yield pressure. The first effect of internal pressure is a lowering of the axial stress–strain response. In addition, at some plastic strain level, the cylinder develops uniform axisymmetric wrinkling. Under continued compression, the wrinkles grow stably, gradually reducing the axial rigidity of the structure and eventually lead to a limit load instability. All pressurized cylinders remained axisymmetric until the end of the test past the limit load.The critical stress and wavelength were established using classical plastic bifurcation theory based on the deformation theory of plasticity. The evolution of wrinkling, and the resultant limit state, were established by modeling a periodic domain that is one half of the critical wavelength long. The domain was assigned an initial imperfection corresponding to the axisymmetric buckling mode calculated through the bifurcation check. The inelastic material behavior was modeled through the flow theory of plasticity with isotropic hardening. The variations of the axial response and of the limit strain with pressure observed in the experiments were reproduced well by the model. Inclusion of Hill-type anisotropic yielding in all constitutive models was required for good agreement between predictions and experiments.     

Effect of planar anisotropy on wrinkle formation tendencies in curved sheets

Wrinkle formation tendencies in the form of short-wavelength shallow buckling modes are investigated for sheet materials exhibiting planar anisotropy. The critical state for the onset of these short-wavelength shallow modes are determined from plastic bifurcation theory. A local analysis is performed by considering the current deformed state of a sheet element in a doubly-curved, biaxial plane stress state. The planar anisotropy is prescribed using recently proposed anisotropic yield criteria. Parametric studies are performed to assess the effects of the various material and geometric parameters on wrinkling.     

智能化拉深控制中的法兰起皱临界条件

建立了轴对称件拉深法兰起皱的数学模型。从能量平衡原理出发，推导了考虑几何参数、摩擦系数和材料性能参数及板材皱曲时约束条件的轴对称拉深成形过程中法兰起皱临界压边力的变化规律，给出了皱曲判据。理论分析与实验吻合较好，为拉深过程的智能化控制提供了理论依据。     

Theoretical and experimental study on the effects of explosive forming parameters on plastic wrinkling of annular plates

Wrinkling is increasingly becoming one of the most common and troublesome modes of unacceptable deformation in sheet metal-forming prediction that is very important on the design of die geometry and processing parameters. In an effort to provide a reliable and efficient tool to predict the critical blank holding force for prevention of wrinkling, an analytical model for flange wrinkling in high-velocity forming processes, such as explosive forming, is presented here. With consideration of constant blank holder force and using a combination of energy method and plastic bending theory, the critical radial displacement and number of wrinkling waves are obtained. For validation, some experimental tests have been performed that their results have adequate agreements with the analytical ones. Moreover, the effects of process parameters such as blank holding force, radii ratio, and material mechanical properties on wrinkling behavior has been discussed.     

大型复杂型面铝合金翻边件电磁成形塑性流动行为研究

大型复杂型面铝合金翻边件电磁成形是一个电磁场和结构场耦合作用下的复杂塑性成形过程。由于大型复杂型面的影响,使得铝合金翻边件在电磁成形过程中的塑性流动行为与传统带凸模翻边成形不同。基于松散耦合法建立耦合电磁场和结构场的大型复杂型面铝合金翻边件电磁成形有限元模型,研究采用1层、2层和3层平板线圈电磁翻边下的板料塑性流动行为,并采用试验研究揭示了不同压边力控制下板料法兰部分塑性流动规律。结果表明,当采用3层平板线圈时,翻边件的复杂型面部分完全贴膜,法兰部分材料进入凹模腔的部分更多,促使板料发生更多的塑性流动;不同压边力控制下,法兰部分由塑性流动产生不同的工件形式,在压边力不足时,法兰部分产生明显的起皱现象;通过合理的压边力控制,可得到贴膜性良好的大型复杂型面铝合金翻边件。     

平面应力条件下轴对称拉深成形法兰区起皱和破裂分析

分别采用平面应力和平面应变假设条件,对轴对称拉深成形法兰区的应力分布进行了分析比较,两种情况下的径向应力计算值相差较小,但周向应力计算值相差较大。有限元模拟表明,平面应力条件下得到的解析结果与模拟值非常接近,表明平面应力假设条件比平面应变假设条件更接近于实际情况。在平面应力条件下,建立了轴对称成形法兰区起皱失稳条件和圆筒形件破裂失稳条件,导出了临界压边力的计算式。对于某一具体的拉深成形问题,计算得到了临界压边力与拉深位置的关系曲线。分析结果有助于进一步认识拉深成形各变形区的变形特点,建立更符合实际的起皱、破裂准则,预测成形缺陷及临界压边力。     

圆筒形件不用压边拉深时的皱曲预报

在建立皱由模型的基础上，根据压缩塑性失稳临界载荷公式，导出圆筒形件不用压迫拉深时的皱曲临界切向压应力表达式。由不皱曲条件给出不皱曲的判定式，以及由皱曲确定的极限拉深系数。     

Flow characteristics of accelerating pump in hydraulic-type wind power generation system under different wind speeds

Influences of hydraulic pressure on forming features in micro hydro deep drawing are different from those in normal drawing due to the small size of specimens. In this study, micro hydro deep drawing of SUS304 sheets was carried out in order to study the impacts of the hydraulic pressure on the quality of the drawn cup. Experimental results indicate that there is a critical hydraulic pressure range from 3 to 6 % of the blank’s initial yield stress, where wrinkling and earing development trends change twice. The wrinkling and the earing of the drawn cup also reach their local extremes in the critical pressure range. The cup earing value moves in the opposite direction from the wrinkling value. Hydraulic pressure affects the wrinkling and the earing of the drawn cup through changes in the micro-frictional condition, the shape of the blank and its strain-stress state. Micro-finite element (FE) simulation which takes these factors as well as the material size effects into consideration showed similar results to the experimental ones, thus validating the experimental results and the suitability of the micro-simulation model for micro-forming FE simulation. The experimental and simulation results indicate that the critical hydraulic pressure based on the blank’s initial yield stress can restrict the wrinkling and the earing of the drawn cup. Ultra-high pressure has the potential to avoid the cup wrinkling and earing.     

轴对称拉深成形法兰区起皱失稳变形能及临界压边力

在平面应变假设条件下,对轴对称拉深成形法兰区的起皱失稳问题进行了理论分析。首先采用数学方法,将以积分形式表示的应力解析式进行了简化。在此基础上,进一步简化了起皱过程中变形能的计算式。给出的算例表明,对起皱过程中的变形能分别以简化后的计算式和以原积分式进行计算,其结果误差很小,相对误差小于0.8%。该起皱失稳临界压边力的计算和分析简化方法有助于给出简明和符合实际的起皱判据。     

Bifurcation analysis of wrinkling formation for anisotropic sheet

Surface distortions in the form of localized buckles and wrinkles are often observed in the sheet metal forming process. In many cases the presence of wrinkles in the final praduct is unacceptable for the purposes of assembly. Because of the trend in recent years towards thinner gauges and higher strength, wrinkling is increasingly becoming a more common and troublesome mode of failure in sheet metal forming. In this study, a numerical analysis for evaluating a wrinkling limit diagram (WLD) for an anisotropic sheet subjected to biaxial plane stress is presented. Here the scheme of plastic bifurcation theory for thin shells based on the Donnell-Mushtari-Viasov shell theory is used. The effects of the various material parameters (yield stress, strain hardening coefficient and normal anisotropy parameter) and geometric parameters on WLD are investigated numerically and compared with Kawai's and Havranek's experiment(1975).     

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。     

数值模拟的双层金属板拉深成形工艺研究

某轿车排气歧管保护罩采用双层镀铝钢板同步拉深工艺制成,为获得最佳成形工艺参数,避免拉深时产生严重减薄及起皱现象,采用Dynaform软件对双层金属板同步拉深成形过程进行了有限元数值模拟,分析了压边力对拉深成形过程的影响,获得了不同压边力下保护罩内、外层板的壁厚减薄与增厚分布规律。结果表明,与单层板拉深成形相似,对于复杂型面双层金属板拉深件而言,单纯增加压边力并不能完全避免拉深过程中的起皱现象;采用压边力及合理布置拉深筋,可以保证内、外层板材料塑性流动均匀,有效抑制起皱、拉裂等缺陷。根据数值模拟结果进行了产品试制,获得了质量合格的拉深件。     

WRINKLE LIMIT BLANK HOLDER FORCE MODELS IN SQUARE-BOX DEEP DRAWING WITH VARIABLE SEGMENT BLANK-HOLDERS

Constituting the reasonable control models of the wrinkle limit blank holder forces is the sticking point of the processes of the deep drawing with variable blank-holder forces, especially in the square-box forming. To begin with, a mode of segmenting flange of the square-box into eight zones is put forward according to the fact that the uniformity of flange deforming can be improved by controlling segment blank-holders. Considering the integral influence of shear stress, a new concept, strain relaxation factor is defined. Hereby, the law of distribution of stress and stain in the deforming flange of square-box is achieved. Then based on these mechanical analysis models and the energy principle, the wrinkling flexivity functions of the straight flange and the circle flange are given, and the corresponding formulae of wrinkling limit blank-holder force in these two situations are also educed. In these processes, ply-anisotropy, strain hardening, thickness and friction are considered. In the end, a calculating example is designed to validate the rationality of the formulae of wrinkling limit blank-holder force, at the same time, the influences of the ply-anisotropy exponent and the strain hardening exponent on the wrinkle limit blank holder forces are also analyzed.     

Plastic buckling of circular tubes under axial compression—part I: Experiments

Elastic buckling of cylindrical shells due to axial compression results in sudden and catastrophic failure. By contrast, for thicker shells that buckle in the plastic range, failure is preceded by a cascade of events, where the first instability and failure can be separated by strains of 1–5%. The first instability is uniform axisymmetric wrinkling that is typically treated as a plastic bifurcation. The wrinkle amplitude gradually grows and, in the process, reduces the axial rigidity of the shell. This eventually leads to a limit load instability, beyond which the cylinder fails by localized collapse. For some combinations of geometric and material characteristics, this limit load can be preceded by a second bifurcation that involves a non-axisymmetric mode of deformation. Again, this buckling mode localizes resulting in failure.The problem is revisited using a combination of experiments and analysis. In Part I, we present the results of an experimental study involving stainless steel specimens with diameter-to-thickness ratios between 23 and 52. Fifteen specimens were designed and machined to achieve uniform loading conditions in the test section. They were subsequently compressed to failure under displacement control. Along the way, the evolution of wrinkles was monitored using a special surface-scanning device. Bifurcation buckling based on the J₂ deformation theory of plasticity was used to establish the onset of wrinkling. Comparison of measured and calculated results revealed that the wrinkle wavelength was significantly overpredicted. The cause of the discrepancy is shown to be anisotropy present in the tubes used. Modeling of the postbuckling response and the prediction of the limit load instability follows in Part II.     

柱形件在边角受压下的三向起皱行为

塑性失稳、分叉引起的起皱是材料加工和成形工艺中的常见现象,起皱的出现将影响零部件的成形质量和性能。已有的工作主要集中在一维和二维的起皱行为,为对开模挤压成形初期以及某些低刚度零件的装配过程中出现的三向起皱现象有更深的认识,设计一种通过改变锥模角度以获得皱曲特征的试验方案,得到局部应力集中下的三向皱曲形貌,描述各个方向起皱的特点,系统地分析锥模角度和试样晶粒大小对皱曲的影响。结果表明:柱面凸起高度、凸起距离和起皱波延伸距离随挤压角度的增大而增大;端面凸起高度和起皱波长、延伸距离均随着挤压角度的增大先增加后减小,凸起距离随角度增大单调减小;波长越长时对应起皱延伸越远;试样表面层晶粒越大,起皱波长和延伸距离越大,起皱形貌越明显。     

Wrinkling initiation and growth in modified Yoshida buckling test: Finite element analysis and experimental comparison

Wrinkling is one of the major defects in sheet metal products and may also play a significant role in the wear of the tool. The initiation and growth of wrinkles are influenced by many factors such as stress ratios, mechanical properties of the sheet material, geometry of the workpiece, contact condition, etc. It is difficult to analyze the wrinkling initiation and growth considering all the factors because the effects of the factors are very complex and the wrinkling behavior may show a wide scatter of data even for small deviations of factors. In this study, the bifurcation theory is introduced for the finite element analysis of wrinkling initiation and growth. All the above-mentioned factors are conveniently considered by the finite element method. The wrinkling initiation is found by checking the determinant of the stiffness matrix at each iteration and the wrinkling behavior is analyzed by successive iteration with the perturbed guess along the eigenvector. The effect of magnitude of perturbation on the wrinkling behavior can be avoided by the Newton-type iteration method. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. The finite element analysis is carried out using the continuum-based resultant shell elements considering the anisotropy of the sheet metal. For the verification of the analysis, the postbuckling of columns and circular plates are analyzed by finite element analysis using the bifurcation algorithm introduced in the study, and the results are compared with the exact solutions. In order to investigate the effects of geometry and stress ratio on the wrinkling initiation and growth, a modified Yoshida buckling test is proposed as an improved effective buckling test. In the modified Yoshida buckling test, the dimensions of the sheet specimen are varied to change the stress ratio and the degree of constraint. The finite element analysis is carried out for the modified Yoshida buckling test and compared with the experimental results.     

On the prediction of side-wall wrinkling in sheet metal forming processes

Prediction and prevention of side-wall wrinkling are extremely important in the design of tooling and process parameters in sheet metal forming processes. The prediction methods can be broadly divided into two categories: an analytical approach and a numerical simulation using finite element method (FEM). In this paper, a modified energy approach utilizing energy equality and the effective dimensions of the region undergoing circumferential compression is proposed based on simplified flat or curved sheet models with approximate boundary conditions. The analytical model calculates the critical buckling stress as a function of material properties, geometry parameters and current in-plane stress ratio. Meanwhile, the sensitivities of various input parameters and integration methods of FEM models on the prediction of wrinkling phenomena are investigated. To validate our proposed method and to illustrate the sensitivity issue in the FEM simulation, comparisons with experimental results of the Yoshida buckling test, aluminum square cup forming and aluminum conical cup forming are presented. The results demonstrate excellent agreements between the proposed method and experiments. Our model provides a reliable and effective predictor for the onset of side-wall wrinkling in sheet metal forming processes.