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.     

Evaluation of yield criteria for forming simulations based on residual stress measurement

Process induced anisotropy in sheet metal is accounted for in analytical modeling by anisotropic yield criteria. The suitability of a yield criterion for predicting sheet metal forming process is generally validated by way of its ability to predict surface strains. However, the sensitivity of surface strains to yield criteria is dependent upon strain modes, with plane strain mode exhibiting higher sensitivity. To eliminate dependency on strain modes, stresses are used to evaluate yield criteria, since forming stresses are less sensitive to strain modes. In the study, the residual stresses remaining in a hemispherical cup formed in plain strain mode is predicted using Hill48 and Barlat89 criteria. The residual stresses are experimentally characterized by using X-Ray diffraction method. Suitable yield criterion for forming simulation is validated based on the correlation of theoretical predictions with experimental residual stress values.     

Analytical and finite element simulation studies on earing profile of Ti-6Al-4V deep drawn cups at elevated temperatures

Rolled sheet metal alloys exhibit plastic anisotropy, which leads to the formation of ears during the deep drawing process. An analytical function proposed by Yoon et al. (Int J Plast 27(8):1165–1184, 2011) predicts earing profile based on yield stress and r value directionalities for circular cup drawing. In this study, this analytical approach is applied for a deep drawing of Ti-6Al-4V at elevated temperatures up to 400 °C. Three yield criteria namely, Hill 1948, Barlat 1989 and Barlat Yld2000-2d are used to obtain the directionality inputs for the analytical formula. The analytical model is validated using experimental results and FE simulations and is found to be closely matched while requiring very less CPU time. FE simulation has been also conducted with various yield functions. Barlat Yld2000-2d is considered to be the most suitable yield criterion for very accurate earing prediction in deep drawing of Ti-6Al-4V as the inputs for both the analytical and FEM models.     

屈服准则对不锈钢弯管变形预测精度影响

通过XRD衍射及不同方向单向拉伸试验验证,经过多道次拉拔生产出的304奥氏体不锈钢管材存在有明显的各向异性现象.采用Mises各向同性、Hill1948和Barlat1991各向异性屈服准则对不锈钢弯管过程进行有限元模拟,分析弯曲后管材内外侧壁厚分布、弯曲角度及管坯截面椭圆度的变化规律,通过模拟与实验结果对比发现,当实验数据较少时,采用Hill1948各向异性屈服准则,能够很好预测304奥氏体不锈钢管材弯曲成形过程,而Barlat1991各向异性屈服准则中的一些参数经过近似后,对成形行为的预测精度明显降低.     

Experimental and numerical investigation of anisotropic yield criteria for warm deep drawing of Ti–6Al–4V alloy

Accuracy of the finite element simulation of sheet metal forming is significantly dependent on the correctness of input properties and appropriate selection of material models. In this work, anisotropic yield criteria namely, Hill 1948, Barlat 1989, Barlat 1996, Barlat 2000 and Cazacu Barlat have been implemented for Ti–6Al–4V alloy at 400 °C. Material constants required for the yield criteria have been determined and deformation behavior in deep drawing process has been analyzed in finite element software. Also, deep drawing experiments on Ti–6Al–4V alloy have been performed at 400 °C to validate finite element simulation results. Further, comparison of yield criteria based on thickness distribution, earing profile, complexity in material parameter identification and computational time has shown Cazacu-Barlat to be well suited for deep drawing of Ti–6Al–4V alloy.     

各向异性板料屈服轨迹的研究

针对建立的十字形双向拉伸试验系统,利用有限元模拟优化得到的十字形试件,采用载荷控制方式对SPEN钢板和2024-O铝合金板进行了不同加载路径下的双向拉伸试验,得到了不同硬化阶段下的实验屈服轨迹,并与现有屈服准则Hill48、Hill79、Hill90、Hill93、Gotoh、Hosford、Barlat-Lian以及Mises的理论屈服轨迹进行了对比.结果表明:对于SPEN钢板,Hosford各向异性屈服准则得到的理论屈服轨迹与实验屈服轨迹符合得最好,其次是Mises屈服准则,Hill48屈服准则最差;对2024-O铝合金板,Barlat89、Hosford屈服轨迹与实验屈服轨迹符合得最好,Mises屈服准则最差.     

屈服准则用于高强度热轧钢板的适用性分析

为确定适合描述高强度热轧钢板变形行为的屈服准则,采用Hollomon流动应力方程和三种屈服准则对几类高强度热轧钢板在不同应变路径下达到成形极限的成形过程进行了模拟.比较了Barlat(1989)、Hill(1948)、Barlat六参数3种屈服准则,对热轧酸洗板QStE340TM、SAPH370和热轧镀锌板ZStE260P在单向拉伸、平面应变和双向等拉3种应变路径下的变形过程进行了比较.结果表明,Barlat(1989)屈服准则能较好地描述单元的变形行为,且在平面应变路径下的模拟结果最符合实验结果.     

Formability prediction of high-strength steel sheet using experimental,analytical and theoretical analysis based on strain and stress forming limit curves and its application to automotive forming parts

In this work, the high-strength steel (HSS) sheet dual-phase 440 (DP440) were conducted to establish the forming limit curve (FLC) and analytical forming limit stress curve (FLSC) obtained from experimental forming limit curve. First, the Nakajima stretch forming examination was carried out to obtain forming limit curve of investigated sheet. Afterwards, the theoretical Marciniak–Kuczinsky (M–K) model was developed and calculated to evaluate localized necking limits both in strain and stress spaces combination with anisotropic yield criteria. Then, the analytical forming limit stress curves were plastically calculated by using experimental forming limit curve data combination with Swift hardening model and anisotropic yield criteria namely, Hill’48 and Yld2000-2d for representing anisotropic plastic deformation behavior on examined steel sheet. Finally, automotive stamping parts were performed in order to verify an applicability of all developed curves. It was observed that the analytical forming limit stress curves could more precisely predict the formability of automotive parts better than the forming limit curve based on strain. Particularly, the one based on Yld2000-2d predict better than the one based on Hill’48. Simultaneously, the experimental forming limit curve and analytical forming limit stress curve were also evaluated comparing with the theoretical calculated forming limit curve and forming limit stress curve using the Marciniak–Kuczinsky model. It should be noted again that the experimental forming limit curve and analytical forming limit stress curve are the best one. Therefore, the Yld2000-2d yield function better represented the anisotropic behavior of the high-strength steel sheet dual-phase 440 than Hill′ 48 yield function, and can suitable be used for the analysis prediction and design of bumper automotive parts under forming processes.     

Determination of Anisotropic Yield Coefficients by a Data-Driven Multiobjective Evolutionary and Genetic Algorithm

The texture induced anisotropy of yield strength in cold rolled sheet metals is modeled using anisotropic yield criteria. The classical and other optimization methods used so far to determine the yield coefficients are limited by fixed set of experimental data, initial guess values, and pre-determined weight factors. A robust multiobjective optimization based on evolutionary algorithm proposed in this paper minimizes the error in yield stress and plastic strain ratio simultaneously and thereby overcomes the limitations in the approaches used before. The new approach is tested using Hill48 and Barlat89 yield criteria for five different materials from literature. The new approach is observed to improve the prediction capability of yield coefficients when compared to earlier approaches. The Pareto frontier obtained in the new approach can serve as a comparative tool to evaluate the accuracy of different yield criteria.     

Approximate yield criteria for anisotropic porous ductile sheet metals

An approximate macroscopic yield criterion for anisotropic porous sheet metals is developed under plane stress conditions in this paper. The metal matrices are assumed to be rigid perfectly plastic and incompressible. The Hill quadratic and non-quadratic anisotropic yield criteria are used to describe the matrix normal anisotropy and planar isotropy. The voids in sheet metals are assumed in the form of through-thickness holes. Under axisymmetric loading, a closed-form upper bound macroscopic yield criterion is derived as a function of the anisotropy parameter R, defined as the ratio of the transverse plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial loading conditions. The plane stress upper bound solutions for different in-plane strain ratios can be fitted well by the closed-form macroscopic yield criterion.     

新型铝锂合金板材塑性流动与各向异性性能试验研究

通过单向拉伸试验,研究了新型Al-Li-Cu-Mg合金板材的基本成形性能.针对材料显著的各向异性性能,选取屈服强度、抗拉强度、延伸率以及厚向异性指数等材料性能参数进行对比分析,绘制了7个不同取样方向的单向拉伸曲线,研究了材料各向异性的规律.基于对本构方程、各向异性屈服准则的研究及对比,建立了新型Al-Li-Cu-Mg合金的本构模型,并根据实验曲线计算得到Hill48、Barlat89屈服准则中的各向异性参数,结合各屈服准则绘制了新型Al-Li-Cu-Mg合金屈服轨迹.对比分析各试件的断口方向,并结合第一、第三强度理论,分析了材料的各向异性.利用SEM观察试样的断口形貌,分析对比试件断口的韧窝特征及带状特征.研究发现:试件的延伸率越大,其韧窝特征越明显;反之,其带状特征越明显.从微观角度印证了Al-Li-Cu-Mg合金板材存在的各向异性.     

The equivalent plastic strain-dependent Yld2000-2d yield function and the experimental verification

An equivalent plastic strain-dependent anisotropic material model was developed for 5754O aluminum alloy sheet. In the developed model, the anisotropy coefficients for Barlat’s Yld2000-2d anisotropic yield function were established as a function of the equivalent plastic strain. The developed anisotropic material model was implemented into the commercial FEM code ABAQUS as a user material subroutine (UMAT) for simulations. In order to evaluate the accuracy of the developed material model, biaxial tensile tests were carried out using cruciform specimens and a biaxial loading testing machine. The results show that the developed material model predicts the experimental results better than the other three material models (Yld2000-2d, Mises and Hill48 yield functions). It is also found that the developed material model describes the uniaxial tensile test curves better than Yld2000-2d yield function. The deep drawing test for 5754O aluminum alloy sheet was carried out and was simulated with different material models. The comparison between the experimental and simulation results indicates that the developed material model predicts the earing profile better than other material models. It is concluded that the equivalent plastic strain-dependence of the material coefficients should be considered for the accurate prediction of the anisotropic deformation behavior of materials.     

Using genetic algorithm-back propagation neural network prediction and finite-element model simulation to optimize the process of multiple-step incremental air-bending forming of sheet metal

Using neural network to predict punch radius based on the results of air-bending experiments of sheet metal is a high efficiency work in spite of little error. A three-layer back propagation neural network (BPNN) is developed to best fit this discrete engineering problem involving many parameters of air-bending forming. A genetic algorithm (GA) is used to optimize the weights of neural network for minimizing the error between the predictive punch radius and the experimental one. Then, with the predicted punch radius and other geometrical parameters of a tool, 2D and 3D ABAQUS finite-element models (FEM) are established, respectively. The original forming process of multiple-step incremental air-bending of sheet metal, obtained from geometric planning for semiellipse-shaped workpiece, is simulated using the FEM. This process is further adjusted with simulation-optimization results, because of existing large errors in the workpiece simulated with the original forming process. Finally, a semiellipse-shaped workpiece, with average errors of +0.61/−0.62 mm, is manufactured with the optimized adjustment process. The experimental results show that the punch design method is feasible with the prediction model of GA-BPNN, and the means of optimizing process with FEM simulation is effective. It can be taken as a new approach for punch and process design of multiple-step incremental air-bending forming of sheet metal.     

正交异性板料拉深件快速展开与成形模拟

针对板件初始毛坯形状计算以及正交异性板的快速有限元分析问题,依据拉深件的UG模型,导出了零件的三角网格数据,并采用几何映射方法得到了用于快速有限元分析的拉深件初始展开毛坯.在此基础上,基于理想变形假设以及Hill’48正交异性屈服准则,给出了用于拉深件成形过程快速分析的一步法数学公式和有限元表达,并在Unigraphics系统中进行了有限元分析的后置处理.此外,对TC1钛板筒型拉深件毛坯初始形状进行了优化,并对成形中拉深件厚向应变分布进行了分析,得到了满意结果.     

Experimental and theoretical investigation of forming limit diagram for Ti-6Al-4 V alloy at warm condition

Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It is useful tool to access the forming severity of a drawing or stamping processes. In the present work, FLD has been determined experimentally for Ti-6Al-4 V alloy at 400 °C by conducting a hemispherical dome test with specimens of different widths. Additionally, theoretical FLDs have been determined using Marciniak Kuczynski (M-K) model. Various yield criteria namely: Von Mises, Hill 1948, Hill 1993 and Cazacu Barlat in combination with different hardening models viz., Hollomon power law (HPL), Johnson-Cook (JC), modified Johnson-Cook (m-JC), modified Arrhenius (m-Arr.), modified Zerilli–Armstrong (m-ZA) have been used in M-K analysis for theoretical FLD prediction. The material properties required for determination of yield criteria and hardening models constants have been calculated using uniaxial tensile tests. The predicted theoretical FLDs results are compared with experimental FLD. It can be observed that influence of yield criterion in M-K analysis for theoretical FLD prediction is predominant than the hardening model. Based on the results; it is observed that the theoretical FLD using Cazacu Barlat and Hill 1993 yield criteria with m-Arr. hardening model has a very good agreement with experimental FLD.     

Springback prediction in sheet metal forming of high strength steels

Both increased weight reduction and improved passive safety have been simultaneously required for components of new vehicle generation. Thus, advanced high strength Dual Phase (DP) steels have been progressively used when making automotive parts. During each sheet metal forming process the high strength steels exhibit distinct springback effect, which is governed by strain recovery of material after load removal. The springback is variably sensitive to materials and process parameters. Considering springback occurred in a formed part is significant for designing tools and dies. In this work, both experiments and Finite Element Analyses (FEA) of a U-shape forming test were performed and compared for investigating the springback effect. Two DP steels (JSC590R and JSC780Y) with different strengths and a mild steel (JSC270C) were taken into account. The planar anisotropic material model according to Hill’s 1948, Barlat’s yield 2000, and Yoshida–Uemori kinematic hardening model were applied in the simulations. Various mechanical testing as hydraulic bulge test, disk compression test, and in particular cyclic test under tension and compression load were carried out in order to determine required materials parameters of the models. Obviously, steel with higher yield and tensile strength definitely showed an increasing in magnitude of both springback and curling. All presented material models restricted ability to predict springback effect of the examined steels, although the Yoshida–Uemori criterion provided more accurate results than other ones. The model is therefore preferred for describing the strain recovery mechanism of high strength steels, while parameter determination plays a decisive role. The cyclic test was verified to successfully describe the kinematic behaviour of material.     

2D adaptive mesh methodology for the simulation of metal forming processes with damage

In this work, a fully adaptive 2D numerical methodology is proposed in order to simulate with accuracy various metal forming processes. The methodology is based on fully coupled advanced finite strain constitutive equations accounting for the main physical phenomena such as large plastic deformation, non-linear isotropic and kinematic hardening, ductile isotropic damage and contact with friction. The adaptivity concerns the space discretization using FEM as well as the applied loading sequences. Mesh size distribution is based on various error indicators making use of the hessian of the plastic strain rate combined with a specific damage error function and a specific local curvature error function evaluated at contact boundaries. 2D mesh size can be refined or coarsened when necessary according to these error indicators. Particularely, the smallest size is found to be inside the zones where the damage is highly active. The applied loading paths are also adaptively decomposed into various sequences depending on both number and size of the fully damaged elements. The adaptive procedure is validated through various sheet and bulk metal forming examples. In this paper, a plane stress tensile test, an axisymmetric blanking process of two materials with different ductilities and a cold extrusion process are presented.     

Simulation of stretch forming with intermediate heat treatments of aircraft skins

In the aerospace industry stretch forming is often used to produce skin parts. During stretch forming a sheet is clamped at two sides and stretched over a die, such that the sheet gets the shape of the die. However for complex shapes it is necessary to use expensive intermediate heat-treatments in between, in order to avoid Lüders lines and still achieve large deformations. To optimize this process FEM simulations are performed. The accuracy of finite element analysis depends largely on the material models that describe the work hardening during stretching and residual stresses and work hardening reduction during heat treatments due to recovery and particle coarsening. In this paper, a physically based material modeling approach used to simulate the stretch forming with intermediate heat treatments and its predictive capabilities is verified. The work hardening effect during stretching is calculated using the dislocation density based Nes model and the particle coarsening and static recovery effects are modeled with simple expressions based on physical observations. For comparison the simulations are also performed with a phenomenological approach of work hardening using a power law. The Vegter yield function is used to account for the anisotropic and biaxial behavior of the aluminum sheet. A leading edge skin part, made of AA 2024 has been chosen for the study. The strains in the part have been measured and are used for validation of the simulations. From the used FEM model and the experimental results, satisfactory results are obtained for the simulation of stretching of aircraft skins with intermediate heat treatments and it is concluded that the physics based material modeling gives better results.