Stress based prediction of formability and failure in incremental sheet forming

A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is usually valid when the strain path is linear throughout the deformation process [1]. Strain path in incremental sheet forming is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is first used to model the necking limit in incremental sheet forming. The stress-based forming limit is also combined with the fracture limit based on maximum shear stress criterion to show necking and fracture together. A derivation for a general mapping method from strain-based FLC to stress-based FLC using a non-quadratic yield function has been made. Simulation model is evaluated for a single point incremental forming using AA 6022-T43, and checked the accuracy against experiments. By using the path-independent necking and fracture limits, it is able to explain the deformation mechanism successfully in incremental sheet forming. The proposed model has given a good scientific basis for the development of ISF under nonlinear strain path and its usability over conventional sheet forming process as well.     

Efficient implicit simulation of incremental sheet forming

In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment. Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6. Copyright © 2011 John Wiley & Sons, Ltd.     

Polymer incremental sheet forming process: Temperature analysis using response surface methodology

To reduce costs associated with the manufacturing of customized products, several innovative forming processes have been developed. Incremental sheet forming (ISF) is one of these new technologies, becoming, in the past decade, more interesting for the academic and industrial community. The influence of main process parameters, namely, tool diameter, spindle speed, feed rate, and step down, is studied in depth in this paper. The maximum temperature achieved during the forming process of a truncated pyramid frustum with a circular generatrix using three nonbiocompatible and two biocompatible polymer materials is measured. Box–Behnken design of experiments and the response surface methodology have been utilized to statistically analyze the results and to provide models able to predict the maximum temperatures.     

Thermal modeling in electricity assisted incremental sheet forming

A thermal model was built to account for the effects of geometrical parameters of sheet specimen, process parameters and material parameters on the temperature increase of the sheet specimen in Electricity-Assisted Incremental Sheet Forming (EISF). In the EISF, the local area of sheet specimen contacting with a forming tool is heated by direct current, which flows through the forming tool to the sheet specimen. EISF experiments of two high strength steel sheets were carried out to validate the thermal model. The thermal model can be integrated into the control program of EISF system to achieve more accurate temperature control.     

Experimental investigations and optimization of forming force in incremental sheet forming

Incremental sheet forming process has been proved to be quiet suitable and economical for job and batch type production, which exempts expensive and complex tooling for sheet forming. Investigation of forming forces becomes important for selecting the appropriate hardware and optimal process parameters in order to assure perfection and precision of process. Moreover, lack of available knowledge regarding the process parameters makes the process limited for industrial applications. This research paper aims at finding out effects of different input factors on forming forces in single-point incremental forming (SPIF) process. For operation sustainability and hardware safety, it becomes critical to optimize forming forces for a given set of factors to form a particular shape. In this study, optimization of input factors has been performed to produce conical frustums with helical tool path using Taguchi analysis as design of experiment (DOE) and analysis of variance (ANOVA). The optimal experimental conditions for forming forces have been calculated as sheet thickness (0.8 mm), step size (0.2 mm), tool diameter (7.52 mm), tool shape (hemispherical), spindle speed (1000 rpm), feed rate (1000 mm/min) and wall angle (50^o). Effects of tool shape and viscosity of lubricants have also been investigated. An intensive understanding of the mechanism of forming forces has been presented, which shows that force trend after peak values depends upon instant input factors that can be categorized as a safe, severe and crucial set of parameters.     

基于金属板材渐进折弯成形的闭环控制系统性能分析

为了解决板材成形回弹问题,将自动控制理论中反馈控制的思想引入到板材渐进折弯成形过程.利用先进的控制技术来解决板材工件的精确成形.然而,闭环控制的稳定性、准确性和快速性会直接影响到系统的正常工作.针对闭环系统稳定性对工件成形品质的影响,建立了渐进折弯成形闭环控制系统模型.通过理论推导,利用小线性化处理及模型简化方法求解闭环系统传递函数及特征方程.采用离散根轨迹法并进行了Matlab/Simulink仿真试验,其结果表明,系统总增益等于一时能确保成形工件形状稳定、快速、准确收敛到目标形状.     

Improving geometrical accuracy for flanging by incremental sheet metal forming

Incremental Sheet Forming (ISF) is a manufacturing technology for individualized and small batch production. Among the opportunities this technology provides there is the possibility of a short ramp-up time and to cover the whole production chain of sheet metal parts by using a single reconfigurable machine set-up. Since recent developments proved that manufacturing of industrial parts is feasible, finishing operations such as flanging and trimming gain importance, which are an integral part of manufacturing process chains of many sheet metal parts. This paper analyses the technological capabilities of performing flanging operations by ISF. Due to the localized forming zone and the absence of surrounding clamping devices, ISF exhibits a different material flow than conventional flanging processes. In this paper, the influence of the tool path characteristics, the flange length as well as the flange radius is analysed in order to establish a process window and to compare it to the process limits of conventional flanging operations. Since geometrical deviations occur when flanging operations are performed by ISF, a new adaptive blank holder is developed, which acts in the vicinity of the forming tool and reduces unwanted deformation outside the primary forming zone. The experimental results show the benefits of the adaptive blank holder with respect to geometric accuracy. The established process window and the adaptive blank holder hence contribute to the applicability of incremental flanging operations, such that ISF can be used for all forming and flanging operations along the process chain.     

Finite element analysis of the superplastic forming of thick sheet using the incremental flow formulation

The paper discusses the finite element analysis of the superplastic forming of thick sheet components. The incremental formulation proposed is based on a geometrical approximation of the flow type of constitutive equations that describe the behaviour of the alloy during forming. The spatial discretization is achieved using eight-noded finite elements. An algorithm capable of predicting the correct forming pressure is also presented in a form consistent with the incremental flow formulation. Some experimental validation of these techniques will be shown together with a number of more realistic applications which will illustrate the generality of these techniques and their ability to simulate the forming of complex components. Most of the material in this section is standard but has been included for the purpose of completeness and to introduce the reader to the notation used in the paper. © 1997 John Wiley & Sons, Ltd.     

板料渐进成形数值模拟与实验研究

为提高渐进成形的成形效率和成形质量,了解板料渐进成形的变形规律及工艺参数对成形的影响,采用有限元方法对板料渐进成形过程进行了数值模拟研究,分析了斜壁盒形件渐进成形过程应力分布和厚度变化趋势,通过对不同进给量和不同成形路径进行数值模拟,分析了工艺参数对成形的影响.结果表明,斜壁盒形件最大应力和最大厚度减薄发生在底面拐角处;成形过程中工具头运动轨迹应尽量采用走螺旋线的方式,可以提高成形件的成形能力和成形质量.渐进成形实验表明,数值模拟结果与实验结果基本吻合.     

Optimised tool-path design to reduce thinning in incremental sheet forming process

Rising energy prices and customers’ increasing ecological awareness pushed energy efficient manufacturing to the top position in industrial interests. Actually, companies want to identify the most effective measures to increase energy efficiency in manufacturing processes looking at the sustainability of their product as a point of strength and not only as an extra-cost according to an ancient production vision. For the above considerations, the scientific community introduced in the last years newer technological alternatives to improve the global efficiency in production processes. Incremental Sheet Forming belongs to this family and can be classified as a flexible solution for the modern market requirement. Nowadays, if the points of strength of the above process are widely recognized, more efforts are still necessary to enhance the product performance allowing a wider industrial suitability. In particular, a significant problem which penalizes the quality of the manufacture parts, is the not homogeneous thickness distribution. The research here presented can be placed in this frame: a promising analytical model is highlighted and a user friendly procedure is set up to simplify the design phase with the aim to optimise the thickness distribution along the profile. Satisfactory experimental results which validate the proposed technique are also presented.     

Substructuring in the implicit simulation of single point incremental sheet forming

This paper presents a direct substructuring method to reduce the computing time of implicit simulations of single point incremental forming (SPIF). Substructuring is used to divide the finite element (FE) mesh into several non-overlapping parts. Based on the hypothesis that plastic deformation is localized, the substructures are categorized into two groups: the plastic—nonlinear—substructures and the elastic—pseudo-linear—substructures. The plastic substructures assemble a part of the FE mesh that is in contact with the forming tool; they are iteratively updated respecting all nonlinearities. The elastic substructures model the elastic deformation of the rest of the FE mesh. For these substructures, the geometrical and the material behaviour are assumed linear within the increment. The stiffness matrices and the internal force vectors are calculated at the beginning of each increment then they are statically condensed to eliminate the internal degrees of freedom (DOF). In the iteration process the condensed stiffness matrices for the elastic substructures are kept constant. The condensed internal force vectors are updated by the multiplication of the condensed stiffness matrices and the displacement increments. After convergence, any geometrical and material nonlinearity for the elastic substructures are nonlinearly updated. The categorization of substructures in plastic and elastic domains is adapted during the simulation to capture the tool motion. The resulting, plastic and condensed elastic, set of equations is solved on a single processor. In an example with 1600 shell elements, the presented substructuring of the SPIF implicit simulation is 2.4 times faster than the classical implicit simulation.     

Fast simulation of incremental sheet metal forming by adaptive remeshing and subcycling

In order to use incremental sheet forming (ISF) in an industrial context, it is necessary to provide fast and accurate simulation methods for virtual process design. Without reliable process simulations, first-time right production seams infeasible and the process loses its advantage of offering a short lead time. Previous work indicates that implicit finite element (FE) methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires a very small time step. Finite element methods based on explicit time integration can be sped up using mass or time scaling to enable the simulation of large-scale sheet metal forming problems. However, AISF still requires dedicated adaptive meshing methods to further reduce the calculation times. In this paper, an adaptive remeshing strategy based on a multi-mesh method is developed and applied to the simulation of AISF. It is combined with subcycling to further reduce the calculation times. For the forming of a cone shape, it is shown that savings in CPU time of up to 80 % are possible with acceptable loss of accuracy, and that the simulation time scales more moderately when the part size is increased, so that larger, industrially relevant parts become feasible.     

Microstructure and texture evolution during incremental sheet forming of AA1050 alloy

In incremental sheet forming higher limiting strain can be achieved compared to the conventional sheet metal forming process, which results in increased formability. The higher level of strain may be accompanied by non-uniform thinning. Thus, the different sections in a component may undergo different levels of deformation. In the present work a truncated cone of AA1050 H14 alloy was formed using the incremental sheetmetal forming (ISF) technique. The deformation mechanism during ISF was studied by investigating the microstructural and texture evolution in the truncated cone along the thickness of the cone wall. High resolution electron backscatter diffraction was performed at different sections of the formed truncated cone. The results show the formation of subgrains in different sections of the cone. At higher strains, grains become thin and elongated which results in grain fragmentation and formation of small grains. These small grains undergo complete recovery process and new grain boundaries (low and high angle) are formed within the thin elongated grains. Further, the evolution of shear texture shows the evidence of shear mode of deformation during incremental sheet forming. Thus, the presence of through thickness shear could be used for understanding the higher forming limit in the ISF process.

     

大幅面板材渐进折弯成形的本构建模及模拟

为了提高大幅面板材成形的模拟精度,在板材折弯平面应变假设条件下,推导出基于Hill各向异性屈服准则的弹塑性本构方程.借助ABAQUS有限元软件本构模块用户子程序接口,通过编程将上述推导的应力-应变本构关系显示表达式嵌入ABAQUS分析平台.以超长大开口半椭圆形工件成形为例,建立了大幅面钢板渐进折弯的三维弹塑性有限元模型,并数值模拟了多道次渐进折弯成形及回弹全过程.模拟效果和工程应用结果表明,与传统的基于平面应力假设的本构关系模型相比,采用平面应变假设的本构关系模型的模拟结果更接近实验值.     

多点复合渐进成形与单点渐进成形的对比分析

为提高金属板材渐进成形的成形质量、成形精度、成形效率和成形极限,了解不同渐进成形工艺对制件成形性能的影响,本文以典型方锥台制件为研究对象,利用有限元软件MSC.Marc对2种渐进成形工艺进行了三维建模,对比分析了单点渐进成形和多点复合渐进成形对制件等效塑性应变、厚度分布和成形精度的影响.数值模拟结果表明:单点渐进成形的等效塑性应变和厚度减薄主要集中在制件相邻侧壁间的拐角处,而多点复合渐进成形的等效塑性应变和厚度减薄均匀地分布在制件成形区;相同成形工艺参数下,相比单点渐进成形,多点复合渐进成形更有利于制件的成形效率、成形质量、成形精度和成形极限的提高,更有利于抑制破裂等失稳现象的产生.2种渐进成形工艺的成形试验表明,数值模拟结果与试验相符.     

渐进成形A3003铝板减薄带分析及数值模拟研究

研究渐进成形过程中板料减薄带的变化,可以提供合理的加工参数,提高板料的成形性能和加工利用率,减少零件破裂失效.基于渐进成形过程中金属板料轮廓的变化与理想情况下轮廓的区别,对渐进成形初始成形阶段A3003铝板减薄带的产生原因和剪切力的变化过程进行了理论分析,并通过有限元模拟分别从未变形区金属板料的长度和强度两个角度对板料渐进成形过程中未变形区下沉的影响,以及成形角度和杨氏模量对变形区回弹的影响两个方面,对减薄带的产生原因进行研究.结果表明:板料未变形区的下沉和变形区的回弹使板料在初始加工阶段形成一段平缓区域,工具头在平缓区域的变形性质发生了变化,平缓区域发生剪切变形导致了板料在初始加工阶段形成了减薄带;渐进成形时减小板料未变形区的长度,增大板料与垂直方向的角度可以一定程度上阻碍减薄带的产生,模拟结果与理论分析相符合.     

Rigid plastic model of incremental sheet deformation using second‐order cone programming

This paper describes a method for numerically modelling the incremental plastic deformation of shells and applies the method to incremental sheet forming (ISF). An upper bound finite element shell model is developed based on sequential limit analysis under the rigid plastic assumption, which is solved by manipulating the problem into the form of a second‐order cone program (SOCP). Initially, the static upper bound plate problem is investigated and the results are compared with the existing literature. The approach is then extended to a shell formulation using a linearized form of the Ilyushin yield condition and two methods for treating the Ilyushin condition are presented. The model is solved efficiently using SOCP software. The resulting model shows good geometric agreement when validated against an elasto‐plastic model produced using existing commercial software and with measurements from a real product produced using ISF. Copyright © 2008 John Wiley & Sons, Ltd.