An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming

In this paper, a combined experimental and numerical investigation of free hydroforming of aluminium alloy tubes is conducted. The tubes are subjected to different loading histories involving axial compression and internal pressure. The circumferential and axial strains experienced by the tubes are continuously recorded along with the pressure and axial load. The numerical simulations are carried out using both 2D axisymmetric and 3D finite-element formulations by applying the experimentally recorded axial load and internal pressure. In the latter, a geometric imperfection is introduced in the form of wall thickness reduction at the tube mid-length in order to trigger necking which happens after significant bulging and beyond the stage of peak pressure. The strain histories and peak pressures obtained from the simulations agree well with those determined from the experiments. Further, the forming limit curve predicted by the simulations as well as from a M–K analysis incorporating the computed strain paths corroborate well with the experimental data. The role of nonproportional straining on the mechanics of failure of the tubes due to bulging and necking is studied in detail.     

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.     

中小型内高压成形机液压系统的设计与仿真

为研发节能高效、经济实用的三侧缸内高压成形设备,设计了合模力可变且最大为10 MN,三轴向进给、组合式充液胀形且最高胀形压力为300 MPa的中小型内高压成形机液压系统,并对系统主要部件选型。将整机液压系统分为合模压机、充液胀形、轴向进给和下缸退料4个子系统,并基于AMESim对各子系统进行建模与仿真测试。在此基础上建立整机液压系统完整仿真模型,并应用工程成形实例进行仿真试验。仿真实验结果表明:系统设计合理,主要参数控制精度达到设计要求,设计的液压系统为研发此类装备提供参考。     

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 parametric study on residual stresses and forging load in cold radial forging process

In this work, a comprehensive study of radial forging process is presented through 2-D axisymmetric and 3-D finite element simulations while considering internal tube profile. The tube used in this investigation has four internal helical grooves along its length. The material is modeled with the elastic-plastic behavior, and sliding-sticking friction model is utilized to model the die-workpiece and mandrel-workpiece contacts. The numerical results in the 2-D case are compared with available experimental data. Residual stresses in the forged product, stress concentration around the grooves, pressure distribution on the hammers and mandrel and maximum forging load are studied. The effects of process parameters such as workpiece and die geometries, percentage of deformation, and workpiece motions on residual stresses and applied pressures on the hammers and mandrel are investigated. The results provide a valuable insight into the parameters affecting radially forged products and provide a useful tool for better design of this process.     

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.     

磨料流微去除力学分析与可控因素影响

研究了磨料流抛光中磨粒微去除力学建模方法以及可控因素影响抛光效果的问题。以力为纽带,提出磨粒去除工件表面微凸材料的动力来源于三个方面--介质作用力、磨粒挤压载荷和磨粒冲击载荷。利用建立的力学模型,分析了磨料流加工的内在因素,其中可控因素包括：加工温度、加工压力、活塞的移动速度、磨料黏度、磨粒物理性质（如尺寸、硬度）等;研究了各可控影响因素与工件表面抛光质量及效率的关系;量化了可控因素的大小对磨粒作用在工件表面的力的影响程度;将磨粒作用在工件表面的力合成并分解为与活塞运动方向相同的轴向力和垂直于工件壁面的切向力,指出微去除效果随轴向力与径向力的比值改变而发生变化,设计出简易的测量轴向力和径向力的方案。用试验验证了所建模型和可控因素对抛光效果影响,以及工件表面的加工纹理方向直接影响工件表面粗糙度的减小率和材料去除率的正确性。     

FEM INVESTIGATION FOR ORTHOGONAL CUTTING PROCESS WITH GROOVED TOOLS-TECHNICAL COMMUNICATION

Rigid-visco-plastic finite element models are used to simulate the chip formation and cracking in the turning processes with grooved tools. The Johnson-Cook constitutive equation and Johnson-Cook damage model, which are appropriate for high-speed machining, are assumed for the workpiece material properties. Thermal effects in cutting are considered. The tool material is considered as rigid, but heat-conducting, with the properties of tool material H11. The calculated chip back-flow angle, curling radius and thickness are analyzed as three typical chip shape parameters. The effects of land length and second rake angle of the grooved tool on chip formation, cracking and temperature are discussed. Some simulation results are compared with other published analytical and experimental results.     

FEM INVESTIGATION FOR ORTHOGONAL CUTTING PROCESS WITH GROOVED TOOLS–TECHNICAL COMMUNICATION

Rigid-visco-plastic finite element models are used to simulate the chip formation and cracking in the turning processes with grooved tools. The Johnson-Cook constitutive equation and Johnson-Cook damage model, which are appropriate for high-speed machining, are assumed for the workpiece material properties. Thermal effects in cutting are considered. The tool material is considered as rigid, but heat-conducting, with the properties of tool material H11. The calculated chip back-flow angle, curling radius and thickness are analyzed as three typical chip shape parameters. The effects of land length and second rake angle of the grooved tool on chip formation, cracking and temperature are discussed. Some simulation results are compared with other published analytical and experimental results.     

Inelastic wrinkling and collapse of tubes under combined bending and internal pressure

The problem of inelastic bending and collapse of tubes in the presence of internal pressure is investigated using experiments and analyses. The experiments involve 1.5-inch diameter, D/t=52 stainless steel tubes bent to failure at fixed values of pressure. The moment-curvature response is governed by the inelastic characteristics of the material. Bending induces some ovalization to the tube cross section while, simultaneously, the internal pressure causes the circumference to grow. Following some inelastic deformation, small amplitude axial wrinkles appear on the compressed side of the tube, and their amplitude grows stably as bending progresses. Eventually, wrinkling localizes, causing catastrophic failure usually in the form of an outward bulge. Internal pressure stabilizes the structure, it increases the wavelength of the wrinkles and can increase significantly the curvature at collapse. The onset of wrinkling is established by a custom bifurcation buckling formulation. The evolution of wrinkling and its eventual localization are simulated successfully using a FE shell model. The material is represented as an anisotropic elastic-plastic solid using the flow theory, while the models are assigned initial geometric imperfections with the wavelength of the wrinkling bifurcation mode. It is demonstrated that successful prediction of collapse requires very accurate representation of the material inelastic properties including yield anisotropies, and that as expected, the collapse curvature is sensitive to the imperfection amplitude and wavelength imposed.     

The investigation of mechanism of serrated chip formation under different cutting speeds

Chip type is determined by the coupled effects of workpiece material property, cutting speed, uncut chip thickness, feed rate, and tool edge geometry. The understanding of chip formation plays a critical role in studying surface integrity and optimization of machining process variables. Serrated chip, one of the major important chip type, is usually formed in hard cutting at high speed. In this study, a new analytical model has been proposed to better understand the formation of serrated chip, and the simulations have been acquired using ABAQUS/Explicit in machining AISI 1045 during different speeds (from 60 to 6000 m/min). The workpiece material property is modeled with the Johnson-Cook model, and the experiments have been conducted with AISI 1045 during speeds from 60 to 1200 m/min. It has been shown that flow stress is influenced simultaneously by the strain rate hardening and temperature softening. When the speed reaches very high, the temperature softening will fail, and the strain rate hardening will play a more important role. Also, it can be found that the hardening ratio increases when the cutting speed rises. The results of the simulations and experiments correlated well. The cutting force and thrust force both decrease as the cutting speed increases, and the difference between them will shrink when the machining speed reaches a high level.     

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.     

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.     

ANALYTICAL MODELING OF MICRO END-MILLING FORCES WITH EDGE RADIUS AND MATERIAL STRENGTHENING EFFECTS

The study aims at developing a predictive analytical force model for the micro end-milling operation taking into account the material strengthening as well as the edge radius effects that come into play at the micro level. The mechanistic models for macro end-milling process have been extensively reported in literature and such models predominantly use milling force coefficients which are empirically determined from end-milling experiments. The proposed model for micro end-milling is based on determination of milling force coefficients from fundamental oblique cutting approach. The edge radius effect has been accounted by analyzing the rubbing action similar to the rolling of a cylinder over work surface. Johnson-Cook material model has been modified based on the strain gradient plasticity theory incorporating the increase in material strength with decreasing uncut chip thickness. From the micro orthogonal cutting experiments, a good agreement between the experimental and predicted shear strength values is observed. The force model is validated against measured forces in end-milling experiments carried out on the KERN Evo 5 axis micro machining center. The feed and lateral forces are predicted within 10% deviation on an average.     

Comparisons of friction models in bulk metal forming

A friction model is one of the key input boundary conditions in finite element simulations. It is said that the friction model plays an important role in controlling the accuracy of necessary output results predicted. Among the various friction models, which one is of higher accuracy is still unknown and controversial. In this paper, finite element analyses applying five different friction models to experiments of upsetting of AA 6082 lubricated with four lubricants are presented. Frictional parameter values are determined by fitness of data of friction area ratio from finite element analyses to experimental results. It is found that calibration curves of the friction area ratio for all of the five chosen friction models used in the finite element simulations do fit the experimental results. Usually, calibration curves of the friction area ratio are more sensitive to friction at the tool/workpiece interface than those of the normal pressure.     

高速硬态切削温度场和切削力动态变化的数值模拟

基于大型有限元软件ABAQUS仿真平台,建立了高速加工的有限元模型。该模型采用Johnson—Cook（JC）模型作为工件材料模型,采用JC破裂模型作为工件材料失效准则,刀-屑接触摩擦采用可自动识别滑动摩擦区和黏结摩擦区的修正库仑定律,并采用任意拉格朗日一欧拉方法实现切屑和工件的自动分离。通过有限元方法对AISI4340（40CrNiMoA）淬硬钢高速直角切削过程进行了数值模拟。通过改变刀具前角的大小,对高速硬态切削过程中刀具的温度场及切削力的动态变化进行了研究,探讨了它们各自的变化规律,研究结果有助于优化高速切削工艺,研究刀具磨损机理和建立高速切削数据库。     

Numerical simulation of the effects of elastic anisotropy and grain size upon the machining of AA2024

Turning modeling and simulation of different metallic materials using the commercially available Finite Element (FE) softwares is getting prime importance because of saving of time and money in comparison to the costly experiments. Mostly, the numerical analysis of machining process considers a purely isotropic behavior of metallic materials; however, the literature shows that the elastic crystal anisotropy is present in most of the ‘so-called’ isotropic materials. In the present work, the elastic anisotropy is incorporated in the FE simulations along with the effect of grain size. A modified Johnson-Cook ductile material model based on coupled plasticity and damage evolution has been proposed to model the cutting process. The simulation results were compared with experimental data on the turning process of Aluminum alloy (AA2024). It was found that the elastic anisotropy influences the average cutting force up to 5% as compared to the isotropic models while the effect of grain size was more pronounced up to 20%.     

薄壁深抛物线形零件固体颗粒介质成形工艺

薄壁抛物线形壳体成形过程为拉深和胀形两种变形模式的复合,极易发生起皱和破裂。固体颗粒介质成形是采用固体颗粒代替刚性凸模或凹模(或弹性体、液体)对板料进行成形的工艺。板材在颗粒介质内压的作用下成形,可以有效防止抛物线形件拉深成形过程中侧壁的起皱;由于颗粒内压是非均匀分布的,故可以有效控制抛物线形件成形过程中的破裂,提高板材的成形极限。根据固体颗粒介质成形工艺的特点,提出了两次成形薄壁深壳体零件的工艺,建立了数值分析模型,通过数值模拟和试验对该成形过程和工艺参数进行了分析。结果表明,采用固体颗粒介质成形工艺过程简单、成形工件壁厚分布均匀、表面质量好、回弹小。     

0Cr18Ni9不锈钢本构模型及其对切削力预测影响分析

利用MTS材料试验机和分离式Hopkinson压杆(SHPB)实验装置对经过1100℃固溶处理后的0Cr18Ni9不锈钢的静态力学性能和动态力学性能进行了测量,用Johnson-Cook模型拟合了材料的本构关系,用正交切削实验识别了Johnson-Cook模型材料参数。将SHPB实验和切削实验两种方法得到的Johnson-Cook材料模型应用于切削力的预测,分析了不同实验方法得到的材料模型在切削力的预测中的适用性,为不锈钢切削研究中的分析模型和数值计算中的材料流动应力模型选择提供参考。     

Numerical and experimental investigation of inward tube electromagnetic forming

In this work, experimental and numerical simulation of high-speed inward forming of tubes on a die in electromagnetic forming (EMF) system using a compression coil is presented. A 2D axi-symmetric electromagnetic model is used to calculate magnetic field and magnetic forces. Modified loose-coupled simulations of electromagnetic and structural aspects of EMF process are reported and emphasized in this paper. During the simulation, in each time step, the transient magnetic forces are obtained from the electromagnetic model and used as input load to the mechanical model. Based on the calculated deformation, in each step, the tube geometry in the electromagnetic model is updated to calculate the electromagnetic forces in proceeding step. Tube material, AA 6061-T6, is assumed to obey the Johnson-Cook (J-C) rate-dependent model. Displacement and thickness variations of workpieces along the tube length are presented and discussed experimentally and numerically. The results demonstrate that various workpiece zones could be thickened or thinned based on various process parameters. In addition, it is seen that the increase of discharge voltage decreases the thickness at die radius and reverses the thickening trend at tip of the bead.