Approximate yield criterion for voided anisotropic ductile materials

As most fractures of ductile materials in metal forming processes occurred due to the results of evolution of internal damage — void nucleation, growth and coalescence. In this paper, an approximate yield criterion for voided (porous) anisotropic ductile materials is developed. The proposed approximate yield function is based on Gurson’s yield function in conjunction with the Hosford’s non-quadratic anisotropic yield criterion in order to consider the characteristic of anisotropic properties of matrix material. The associated flow rules are presented and the laws governing void growth with strain are derived. Using the proposed model void growth of an anisotropic sheet under biaxial tensile loading and its effect on sheet metal formability are investigated. The yield surface of voided anisotropic sheet and void growth with strain are predicted and compared with the experimental results.     

On bend-stretch forming of aluminum extruded tubes — I: experiments

Tubular aluminum frame parts for automotive applications are best produced by extrusion. The tubes are then cold formed to the required shape by prestretching, pressurizing and bending them over rigid dies. Tension prevents buckling of the compressed side and significantly reduces the springback on unloading. An unwanted byproduct of the process is distortion of the cross section. It has been found that modest levels of pressure can reduce this distortion. The selection of the level of tension and pressure for optimum forming is presently empirical. The study discussed herein seeks to develop a scientific basis for optimizing forming processes such that buckling is avoided and distortion and springback are minimized. Part I describes a custom bend-stretch-pressure forming facility developed for the study. The facility is operated by one pneumatic and two servohydraulic closed-loop systems. This allows computer control of the process, and affords selectable loading histories. The planar forming process was modeled by approximating the tube as a nonlinear elastic–plastic beam which can undergo large rotations. The model was shown capable of reproducing accurately the loading history experienced by different sections along the length of the part during forming. Representative results from forming experiments involving rectangular aluminum are presented. The results are used to discuss the effect of friction, tension and pressure on the cross-sectional distortion, springback and net elongation of the part. Part II presents a model for establishing the cross-sectional distortion induced during forming. The model is used in conjunction with experimental results to establish ways of optimizing the process.     

Prediction of forming limits for anisotropic sheets containing prolate ellipsoidal voids

In sheet metal forming operations, the formability of sheet metals is limited by the occurrence of internal damage evolution that eventually yields a localized neck. Thus, designing and optimizing a sheet metal forming process, requires the precise prediction of the forming limits of the sheet materials. Accordingly, the current work attempts to theoretically predict the forming limit diagrams (FLDs) of voided anisotropic sheets using a new version of the Marciniak and Kuczynski (M–K) model. The analysis employs Gologanu–Leblond–Devaux's yield function for materials containing axisymmetric prolate ellipsoidal cavities with random orientations in conjunction with Barlat and Lian's 1989 anisotropic yield criterion. The effect of a void shape parameter on a ductile material under biaxial tensile loading is introduced and examined within the framework of the M–K model, along with the effect of including a first-order strain gradient term in the flow stress. To confirm the validity of the proposed M–K model, the predicted FLDs were compared with experimental results for steel sheets. The predicted forming limits for the voided sheets were found to agree well with the experimental data.     

Three-dimensional effects of the bend–stretch forming of aluminum tubes

Bend–stretch forming is commonly used to shape extruded tubular aluminum parts for automotive applications. The tubes are pre-stretched, pressurized and bent over rigid dies. Tension prevents buckling of the compressed side and significantly reduces springback during unloading. An unwanted byproduct of the process is distortion of the cross section. Small amounts of pressure applied during forming can reduce this distortion. A systematic study of how to select the appropriate amounts of tension and pressure for accurate forming with minimal distortion has been conducted. The problem was first studied experimentally using a custom forming facility. An efficient 2-D model of the process was previously developed which was shown capable of capturing the main deformation features of interest. Its efficiency made this model a useful design tool for optimally selecting the forming parameters. In this paper, a 3-D finite element model of the forming process is used to simulate the complete forming process. By using a specially calibrated non-quadratic yield function, the model accurately reproduces all aspects of the process. The model is used to study 3-D features of the problem such as variations of distortion and springback along the length, the effect of friction, the lifting of a section of the tube around the mid-span off of the die, the effect of post-tension, and forming over a variable radius die.     

Effects of process parameters on force reduction and temperature variation during ultrasonic assisted incremental sheet forming process

The incremental sheet forming (ISF) is an innovative dieless forming process featured with high formability and short lead time which is suitable for rapid prototyping and small volume production. The integration of ultrasonic (US) vibration into the ISF process can significantly reduce the forming force and bring other benefits. In this work, the impacts of process parameters including the sheet material, US power, feeding speed, and tool diameter, on force reduction and temperature increment were studied. The force reduction contains two components—the stress superposition-induced force reduction and acoustic softening-induced force reduction. The stress superposition-induced force reduction was analyzed by finite element simulation while the total force reduction was detected by experiments since currently, the unknown mechanism of the acoustic softening cannot be modeled. The temperature increment was measured by a high-speed infrared camera. The results show that the force reduction can go up to 56.58% and the temperature increment can be as high as 24.55 °C. In general, the material with a higher yield stress results in a higher force reduction and a higher temperature increment. A higher US power or a lower feeding speed can significantly enhance the force reduction and the interface temperature increment. The tool with a smaller diameter has a comparable effect as a larger tool, but a larger vibration amplitude is required.     

Formation mechanism and modeling of surface waviness in incremental sheet forming

Improving and controlling surface quality has always been a challenge for incremental sheet forming (ISF), whereas the generation mechanism of waviness surface is still unknown, which impedes the widely application of ISF in the industrial field. In this paper, the formation mechanism and the prediction of waviness are both investigated through experiments, numerical simulation, and theoretical analysis. Based on a verified finite element model, the waviness topography is predicted numerically for the first time, and its generation is attributed to the residual bending deformation through deformation history analysis. For more efficient engineering application, a theoretical model for waviness height is proposed based on the generation mechanism, using a modified strain function considering deformation modes. This work is favorable for the perfection of formation mechanism and control of surface quality in ISF.     

Thickness distribution and design of a multi-stage process for sheet metal incremental forming

Sheet incremental forming (ISF) is a promising technology. It is inexpensive and does not require particular dies. Sheet thinning, however, has always been one of the forming defects which impede the process’s wide application. Although a multi-stage forming process is supposed to be effective to deal with this problem, it is still uncertain how the process can reduce thickness thinning and there is no applicable rule to determine the favorable number of forming stages. In this work, based on a truncated cone, a finite element method (FEM) model for a double-pass forming was established first. Unlike simplifications in previous studies, with the process of the three-dimensional coordinates in numerical controlled (NC) machining code, the tool trajectory in this simulation model is the same as that in real work. With this approach, it was expected to gain reliability of the simulation result, and then this simulation result and a single-pass forming result were analyzed. The results of the analysis indicate that more uniform thickness distribution in the double-forming process largely benefits from the increase of the total plastic deformation zone. Finally, under the condition of constant volume in deformation, an equation was proposed to work out the right number of necessary forming stages and the rule of this equation was verified with a relatively complex product.     

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.     

Surface damage under dynamic loading

Experimental studies of surface damage resulting from high velocity impacts on a metal target, detonation spraying and impulsive laser loading of coatings reveal common features that can be understood within the framework of shock wave mechanics. The nature of dynamic damage is spallation caused by interference of rarefaction waves following the compression impulse and forming tensile stress regions. Focusing of rarefaction waves from the sides of impacting particles leads to longitudinal cracks. A system of less deep circular cracks is generated around the focusing spall crack during repeated loading of the contact zone. The removal of debris from the zone of multiple longitudinal spallation results in valleys on the target. The interference of rarefaction waves occurring on valley walls and face causes transverse face spallation. In this paper it is assumed that, since similar damage morphologies are reported in the erosion wear of ductile metals at lower velocities, in these cases too a shock physics analysis, rather than the commonly used quasi-static plasticity approach, is valid.     

Two-directional toolpath correction in single-point incremental forming using model predictive control

Incremental sheet forming (ISF) is an emerging forming technology that promises high flexibility and formability. These properties make it suited for small-scale and customised production. However, the poor geometric accuracy of ISF limits the wide application of this flexible forming technology. This paper presents a two-directional toolpath correction approach to enhance ISF forming accuracy using a model predictive control (MPC) algorithm. A toolpath optimisation method for vertical toolpath correction has been validated in our previous work (Lu et al., Int J Adv Manuf Technol 72:1–14, 2015), and it helps to reduce errors in the base of the test shapes to a suitable level while its major limitation is that horizontal geometric errors are relatively large. This paper extends our previous work (Lu et al., Int J Adv Manuf Technol 72:1–14, 2015) by augmenting the vertical control module with a new control module for horizontal toolpath correction. The proposed control algorithm was experimentally validated in single-point incremental sheet forming (SPIF) using two forming case studies. In the first case study (a truncated pyramid), two control approaches with different assumptions for the horizontal springback distribution along the horizontal cross-sectional profile were tested and compared. Then, the developed MPC control algorithm was applied to form a more complex asymmetric shape. The results show that the developed strategy can reduce the forming errors in the wall and base of the formed shape compared to the existing works. The ISF process with MPC control leads to significant accuracy improvement in comparison with the typical ISF process that is without toolpath control.     

Comparison of Modified Mohr-Coulomb Model and Bai-Wierzbicki Model for Constructing 3D Ductile Fracture Envelope of AA6063

Ductile fracture of metal often occurs in the plastic forming process of parts.The establishment of ductile fracture cri-terion can effectively guide the selection of process parameters and avoid ductile fracture of parts during machining.The 3D ductile fracture envelope of AA6063-T6 was developed to predict and prevent its fracture.Smooth round bar tension tests were performed to characterize the flow stress,and a series of experiments were conducted to charac-terize the ductile fracture firstly,such as notched round bar tension tests,compression tests and torsion tests.These tests cover a wide range of stress triaxiality(ST)and Lode parameter(LP)to calibrate the ductile fracture criterion.Plas-ticity modeling was performed,and the predicted results were compared with corresponding experimental data to verify the plasticity model after these experiments.Then the relationship between ductile fracture strain and ST with LP was constructed using the modified Mohr-Coulomb(MMC)model and Bai-Wierzbicki(BW)model to develop the 3D ductile fracture envelope.Finally,two ductile damage models were proposed based on the 3D fracture envelope of AA6063.Through the comparison of the two models,it was found that BW model had better fitting effect,and the sum of squares of residual error of BW model was 0.9901.The two models had relatively large errors in predicting the fracture strain of SRB tensile test and torsion test,but both of the predicting error of both two models were within the acceptable range of 15％.In the process of finite element simulation,the evolution process of ductile fracture can be well simulated by the two models.However,BW model can predict the location of fracture more accurately than MMC model.     

Numerical simulation of electric hot incremental sheet forming of 1050 aluminum with and without preheating

Incremental sheet forming (ISF) consists of deforming the sheet, through a spherical punch, punctually and progressively until it reaches the desired geometry. Compared to the conventional process, the ISF can achieve much higher levels of formability. But the stresses and residual strains are often pushed to the limit on the path, producing a piece with brittle behavior, which is not desirable for applications in engineering. To work around this inconvenience, one solution would be to perform the conformation at high temperatures, a process known in engineering as hot forming. This study aims to evaluate the behavior of the state of stresses and strains in the hot incremental sheet forming of 1050 aluminum alloy, with and without pre-heating, using the finite element method. This behavior has been studied by numerical simulation, using the software RADIOSS, which has a suitable formulation for inserting the effects of temperature and strain rate in the material. The results show a decline in the forces for electric hot incremental sheet forming preheated (EHISFP) compared to the electric hot incremental sheet forming (EHISF). Moreover, for these same cases, there was a gain in relation to the geometric precision on average more than 4%.     

板材充液拉深动态加载系统开发与应用

液室压力和压边力加载路径是充液拉深工艺中决定零件成形质量的关键工艺参数。针对传统被动加压方式加载路径单一,液室压力较低,不能满足复杂结构零件和高强度材料的成形要求,提出采用闭环控制技术实时调节液室压力和压边力的动态加载方式。设计可控压边和高压增压系统,并应用基于上、下位机的检测控制系统实时调节凸模速度、压边力和液室压力满足设定的工艺参数。在动态加载系统上进行异型结构不锈钢零件的充液拉深试验,动态加载路径下试验件一次整体成形,且表面质量好,贴模精度高。结果表明,充液拉深动态加载系统能够实现复杂加载轨迹和局部高压,适用于复杂结构和高强度材料零件的成形制造。     

珠光体球墨铸铁损伤力学性能的研究

利用损伤力学原理，研究了球光体球墨铸铁在疲劳和拉伸载荷作用下的损伤演变规律。结果表明：珠光体球墨铸铁在循环应力作用下，损伤变量呈指数规律变化；当拉伸应力大于损伤阈值后，损伤变量随应力的提高而增加，且球化率愈低，增加愈快；损伤阈值低于屈服强度，随球化率呈直线增加。     

Micro/nano Indentation and Single Grit Diamond Grinding Mechanism on Ultra Pure Fused Silica

The existing research about ductile grinding of fused silica glass was mainly focused on how to carry out ductile regime material removal for generating very smoothed surface and investigate the machining-induced damage in the grinding in order to reduce or eliminate the subsurface damage.The brittle/ductile transition behavior of optical glass materials and the wear of diamond wheel are the most important factors for ductile grinding of optical glass.In this paper,the critical brittle/ductile depth,the inf...     

On bend-stretch forming of aluminum extruded tubes — II: analysis

Part II describes a two-dimensional model of the bend-stretch-pressure forming process, which assumes that the tube shape and all applied loads are uniform along the length. This simplification results in a significant improvement in computational time over corresponding three-dimensional models. The model is validated through comparisons with experimental results discussed in Part I and its application to the design process is illustrated. The model is then used to study the current manufacturing process and to evaluate some possible alternative loading histories. The effect of tension and pressure on the cross-sectional distortion, springback and net elongation are discussed in light of the predictions. Additionally, the merits of changing the tension and pressure after forming are discussed. The simulations and corresponding experiments are used as the basis for a design methodology for selecting the order and magnitude of the loads applied during the forming process.     

An approach to eliminate stepped features in multistage incremental sheet forming process: Experimental and FEA analysis

Incremental sheet forming (ISF) is a recently developed manufacturing technique. In ISF, forming is done by applying deformation force through the motion of Numerically controlled (NC) single point forming tool on the clamped sheet metal blank. Single Point Incremental sheet forming (SPISF) is also known as a die-less forming process because no die is required to fabricate any component by using this process. Now a day it is widely accepted for rapid manufacturing of sheet metal components. The formability of SPISF process improves by adding some intermediate stages into it, which is known as Multi-stage SPISF (MSPISF) process. However during forming in MSPISF process because of intermediate stages stepped features are generated. This paper investigates the generation of stepped features with simulation and experimental results. An effective MSPISF strategy is proposed to remove or eliminate this generated undesirable stepped features.     

Thermography in incremental forming processes at elevated temperatures

Temperature measurement is essential for several forming processes at elevated temperatures. It serves to determine and control the workpiece temperature. Thermography as a non-contact-based technology offers the possibility to capture thermograms of complete workpieces without any time-offset. However, the application of thermography requires the knowledge of the fundamentals of radiation thermometry, in particular the emissivity. This paper presents the results of the application of thermography in incremental sheet forming (ISF) with Joule heating and radial–axial ring rolling as a bulk forming process. Using thermography for the determination of the temperature of the forming zone allows for a real-time closed loop control in ISF with Joule heating. Additionally, the results of the temperature measurement of the surface temperature of radial–axial rolled rings are presented, which can be used as a starting point to make a forecast of the rings’ dimensions in cold state.     

Numerical simulation and experimental validation of a ductile damage model for DIN 1623 St14 steel

St14 steel (DIN 1623) is widely used in sheet metal forming industries because of its remarkable formability and also its low price. In this paper, damage behaviour of St14 steel is studied in order to be used in complex forming conditions with the goal of reducing the number of costly trials. Damage parameters of St14 steel have been determined by using standard tensile and Vickers micro-hardness tests. A fully coupled elastic-plastic-damage model has been developed and implemented into an explicit code. With this model, damage propagation and crack initiation, and ductile fracture behaviour of drilled and notched specimens are predicted. The model can quickly predict both deformation and damage behaviour of the part because of using plane stress algorithm, which is valid for thin sheet metals. Experiments are also carried out to validate the results. It is concluded that finite element analysis (FEA) in conjunction with continuum damage mechanics (CDM) can be used as a reliable tool to predict ductile damage and fracture of St14 steel.