Prediction of forming limit diagrams for AL6111-T4 under non-proportional loading

In this paper, an anisotropic damage model for predicting FLDs is extended to predict the sheet metal formability under non-proportional loading involving changing directions of principal strain plane and damage plane. The material chosen for the prediction of FLDs is AL6111-T4 aluminum alloy. A satisfactory agreement between the model predictions and test results has been achieved.     

Characterization and modeling of the mechanical behavior and formability of a 2008-T4 sheet sample

A 2008-T4 sheet sample has been characterized and its mechanical behavior and formability have been modeled. Uniaxial tensile and equal biaxial tensile stress-strain data, compressive yield strengths, crystallographic texture, earing and the forming limit curve were experimentally determined. Bulge test specimen shape and thickness profiles were also measured after various amounts of biaxial strain. A recently developed phenomenological constitutive model of anisotropic mechanical behavior was used to predict the directionality of strength, plastic strain ratio (R) and shear strain ratio (Г) values. In addition, this model was used to predict the forming limit curve for this sample. Predictions made with the recent model generally compare favorably with experimental results and with predictions made using the Taylor/Bishop and Hill theory. According to the data obtained in hydraulic bulge testing, the 2008-T4 exhibited apparent isotropic behavior. However, in cup drawing—another axisymmetric deformation mode—this material exhibited anisotropic behavior, as indicated by the formation of ears and troughs.     

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.     

Formability evaluation of friction stir welded 6111-T4 sheet with respect to joining material direction

In order to evaluate the formability of friction stir welded (FSW) automotive TWB (tailor-welded blank) sheets with respect to base material direction, the aluminum alloy 6111-T4 sheet was joined with three different types of combination: RD||RD, TD||RD, TD||TD (Here, RD and TD mean the rolling direction and transverse direction, respectively). Formability performance was experimentally and numerically studied in three applications including the simple tension tests, hemisphere dome stretching and cylindrical cup drawing tests. For numerical simulations, the non-quadratic orthogonal anisotropic yield function, Yld2004-18p and the isotropic hardening law were implemented into the material constitutive model. As for the failure criterion, the forming limit diagram (FLD) was utilized to determine the failure strain.     

Finite element method for sheet forming based on an anisotropic strain-rate potential and the convected coordinate system

A variational formulation and the associated finite element (FE) equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-rate potential proposed by [11.]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes were efficiently considered. In order to check the validity of the present formulation, a cylindrical cup deep drawing test was modeled for a 2008-T4 aluminum alloy sheet sample. Eating simulations were performed and planar anisotropic material properties were experimentally determined. Even though quantitative agreement was not fully achieved, reasonably good agreement was found between the FE simulation and the experiment in thickness strain distribution and caring. No numerical difficulty due to planar anisotropy was encountered, and the computational procedure was found to be very stable, requiring only moderate computational time. The results have shown that the present formulation for planar anisotropic deformation can provide a good basis for the analysis of sheet metal forming processes for planar anisotropic materials, especially for aluminum alloy sheets.     

Prediction of sheet forming limits with Marciniak and Kuczynski analysis using combined isotropic-nonlinear kinematic hardening

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic-nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.     

Multi-scale parallel finite element analyses of LDH sheet formability tests based on crystallographic homogenization method

A multi-scale parallel finite element (FE) procedure based on the crystallographic homogenization method was applied to the LDH sheet formability test analysis. For the multi-scale structure, two scales are considered. One is a microscopic polycrystal structure and the other is a macroscopic elastic plastic continuum. The analysis code can predict the formability of sheet metal in macro-scale, simultaneously the crystal texture and hardening evolutions in the micro-scale (Nakamachi E et al. Int J Plasticity 2007;23:450-8). Since huge computation time is required for the nonlinear dynamic multi-scale FE analysis, parallel computing technique based on domain partitioning of FE model for macro-continuum is introduced into the multi-scale code using the message passing interface (MPI) library and PC cluster (Kuramae H et al. In: Proceedings of the eighth international conference on computational plasticity, Part 1, 2005. p. 622-5). The explicit time stepping solution scheme in the nonlinear multi-scale FE dynamic problem is well-suited for parallel computing on distributed memory environment such as PC cluster because solving simultaneous equation is not required. We measured crystal morphologies of four automotive sheet metals, aluminum alloy sheet metals A6022-T43 and A5182-O, an asymmetrically rolled aluminum alloy sheet metal A6022-ASR, and mild steel HC220YD, by using the scanning electron microscope (SEM) with electron back scattered diffraction (EBSD) analyses, and defined a three-dimensional representative volume element (RVE) of micro polycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. We evaluate not only macroscopic formability of the automotive sheet metals by the multi-scale LDH test analysis, but also microcrystalline texture evolution during plastic deformation. Furthermore, a relationship between the macroscopic formability and the microcrystal texture evolution was discussed through looking at multi-scale FE results. It is concluded that the mild steel HC220YD was the highest formability than the aluminum alloy sheet metals because of remaining and generating the γ-fiber texture, such as {1 1 1}〈1 1 0〉-{1 1 1}〈1 1 2〉 orientations, during plastic deformation.     

参数求解方法对屈服准则的各向异性行为描述能力的影响

详细分析基于应力各向异性和变形各向异性两种求解Hill48屈服准则参数的方法。在给出两种各向异性参数求解表达式的基础上,具体分析Hill48屈服准则本身的局限性。以5754O铝合金板为研究对象,进行不同方向的单向拉伸试验。采用两种各向异性参数求解方法,基于Hill48屈服准则推导不同方向拉伸过程中的理论应力-应变曲线和拉伸过程中的变形规律。通过对比理论与试验结果具体分析参数求解方法对屈服准则精度的影响。基于两种参数求解方法,进行5754O铝合金板拉深试验的有限元模拟,讨论不同求解方法对凸耳现象的描述精度。得出结论：当对应力各向异性为主的问题进行分析时,应采用应力各向异性法求解;当对变形各向异性为主的问题进行分析时,则应采用变形各向异性法求解。研究结果对屈服准则在板料成形方面的合理应用具有重要的参考价值。     

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlat's 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.     

An experimental and analytical investigation of in-plane deformation of 2036-T4 aluminum sheet

Sheet aluminum alloy (2036-T4) specimens of several geometries were photogrid-ded and pulled in a tensile testing machine while precision photographs were taken of the photogrid. This technique allowed determination of strain distributions and load-displacement points. These results are compared with corresponding results obtained by Finite Element Modeling based on Hill's anisotropic plasticity theory and experimental tensile stress-strain data. FEM predictions and experimental results are in excellent agreement; verifying Hill's model for the case of in-plane deformation of 2036-T4 aluminum alloy between the strain states of plane strain tension and uniaxial tension.     

Blank shape design for a planar anisotropic sheet based on ideal forming design theory and FEM analysis

A sequential design procedure to optimize sheet forming processes was developed utilizing ideal forming design theory, FEM analysis and experimental trials. For demonstration purposes, this procedure was used to design a blank shape for a highly anisotropic aluminum alloy sheet (2090-T3) that results in a deep-drawn, circular cup with minimal earing. All blank shape design methods require a certain number of iterations. However, the sequential procedure can be more effective than the other iterative methods based on FEM analysis in conjunction with experimental trials or on experimental trials alone. For this design demonstration, the anisotropic constitutive behavior of the 2090-T3 sheet was expressed using plastic potentials previously proposed by Barlat et al. The implementation of the anisotropic strain-rate potential in the ideal forming design code is also briefly summarized.     

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.     

Modeling the material behavior of magnesium alloy AZ31 using different yield criteria

Nowadays, the finite element analysis (FEA) is playing a main rule in fields of sheet metal forming for designing processes and dimensioning parts. The most frequent yield criteria used in the FE commercial programs for the sheet-metal-forming simulation, like AUTOFORM, PAMSTAMP, etc., are Hill’48 for common steels or Barlat’89 and various BBC models for some aluminum alloys. In this paper, different yield loci for biaxial tensile stress conditions of the magnesium sheet metal alloy AZ31 are investigated. The experimental investigations have been done using the specimen geometry for the experimental setup developed at the Chair of Manufacturing Technology (LFT) of the University of Erlangen. The yielding behavior is determined basing exclusively on real material data out of experiments so that no FE calculations are necessary to detect strains and stresses. Using these data, several yield criteria are applied to approximate the real material characteristics, whereas the model of BBC’2005 leads to the best agreement for uniaxial yield stresses, the anisotropy coefficients, and the yield locus.     

Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method

To reduce the computational time of finite element analyses for sheet forming, a 3D hybrid membrane/shell method has been developed and applied to study the springback of anisotropic sheet metals. In the hybrid method, the bending strains and stresses were calculated as post-processing, considering the incremental change of the sheet geometry obtained from the membrane finite element analysis beforehand. To calculate the springback, a shell finite element model was used to unload the sheet. For verification purposes, the hybrid method was applied for a 2036-T4 aluminum alloy square blank formed into a cylindrical cup, in which stretching is dominant. Also, as a bending-dominant problem, unconstraint cylindrical bending of a 6111-T4 aluminum alloy sheet was considered. The predicted springback showed good agreement with experiments for both cases.     

Wrinkling control in aluminum sheet hydroforming

In this paper, the wrinkling behavior of 6111-T4 aluminum alloys during sheet hydroforming process was numerically and experimentally investigated. In sheet hydroforming, one or both surfaces of the sheet metal are supported with a pressurized viscous fluid, while a punch forms the part. In sheet hydroforming the use of a matching female die is not needed. The use of the pressurized fluid delays the onset of material rupture (International Journal of Mechanical Science 2003;45:1815–48) and also acts as an active blank-holding force to control wrinkling in the flange area. To form a wrinkle-free deep-drawn hemispherical cup with sheet hydroforming, a theoretical analysis based on the work of Lo et al. (Journal of Materials Processing Technology 1993;37:225–39) was initially used to predict the optimum fluid pressure profile. Simplifying geometrical assumptions and Tresca material model used in the theoretical analysis provided a fluid pressure profile that resulted in premature rupture of the sheet metal. However, an optimum fluid pressure profile generated by the finite element method, using Barlat's anisotropic yield function (Journal of Mechanical Physics and Solids 1997;45(11/12):1727–63), was successfully applied in sheet hydroforming to make the deep-drawn hemispherical cup without tearing and with minimal wrinkling in the flange area. The finite element model was also capable of accurately predicting the location of the material rupture in pure stretch, and wrinkling characteristics of the aluminum alloy sheet in the draw-in process.     

软包锂电池电芯封装铝塑膜外壳拉深工艺

通过拉深试验对铝塑膜材料特性进行分析,在DYNAFORM软件中定义铝塑膜材料属性并进行仿真试验。结合单因素试验和正交试验对影响铝塑膜拉深成形性能的各工艺参数进行显著性分析,采用响应曲面法、拉丁超立方试验设计和多目标粒子群优化算法相结合的方法对影响铝塑膜成形性能显著的参数（如压边力、模具圆角半径、摩擦因数和拉深速度）进行优化,优化后的铝塑膜拉深成形时,其壳体最薄处厚度为55 μm。试验验证了铝塑膜拉深成形工艺优化的结果可行。     

An experimental and theoretical analysis on the application of stress-based forming limit criterion

In this paper, a detailed study on the stress-based forming limit criterion (FLSD) during linear and complex strain paths is developed. The calculation of stress-based forming limits based on experimental strain data is performed by using the method proposed by Stoughton [A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 2000;42:1–27]. By applying several combinations of different constitutive equations on the required plastic calculation, an analysis on the experimental forming stress limits is performed. The necking phenomenon is simulated by Marciniack–Kuczinsky (M–K) model using a more general code for predicting the forming limits. The selected materials are a bake-hardened steel (BH steel) and an AA6016-T4 aluminium alloy. Several yield criteria such as Von Mises isotropic yield function, quadratic and non-quadratic criterion of Hill (A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London 1948;A193:281–97; Theoretical plasticity of textured aggregates. Mathematical Proceedings of the Cambridge Philosophical Society 1979;85:179–91) and the advanced Barlat Yld96 yield function are used to show the influence of the constitutive law incorporated in the analysis on the stress-based forming limits. The effect of the hardening model on the FLSD is analysed by using two hardening laws, namely Swift law and Voce law. The influence of work hardening coefficient, strain rate sensitivity and the balanced biaxial yield stress on the theoretical FLSD is also presented. The effect of strain path changes on the stress-based forming limits is analysed. Some relevant remarks about stress-based forming limit criterion concept are presented.     

A theoretical prediction of the strain path of anisotropic sheet metal deformed under uniaxial and biaxial stress state

A model based on a combination of the micro- and macroscopic theories of plasticity has been built to predict the strain path of a textured sheet metal for a given imposed stress state. By applying the flow rule to a crystallographically based anisotropic continuum yield locus, the deformation strain tensor is determined. For each small increment of deformation, the change in the crystal rotation of each grain is followed and the strain tensor recalculated. The successive changes in the strain state with strain increment give the strain path followed by a material element. Analyses are made for different crystallographic orientations and typical sheet textures of commercially pure aluminium and a Cu-20% Zn alloy deformed in either the uniaxial or equibiaxial stress states. It is found that the simulated strain paths often deviate from those based on isotropic assumptions. The significance of the finding to the study of the formability of sheet metal is discussed.     

利用激光局部硬化效应提高2B06铝合金板材拉深成形性研究

针对2B06铝合金复杂零件成形困难问题,提出了利用激光热处理局部硬化提高板材成形性的思路。在通过激光热处理试验研究了铝合金板的激光硬化效应的基础上,采用数值模拟计算了铝合金板激光热处理过程中激光光斑路径和其周边热影响区域的峰值温度场,并通过实际测温验证了其准确性。提出并构建了耦合性能梯度的差性坯料模型,对激光局部硬化的杯形件拉深成形性进行了模拟和试验研究。结果表明,激光扫描方式可以形成稳定的梯度温度场并对周边非加热区影响较小,且可以通过多道次扫描方式设计不同宽度范围的大梯度差性板材坯料。力学性能试验表明激光热处理可以有效地提高铝合金的局部加工硬化能力,这种效应可以有效抑制杯形件拉深时圆角大变形区的减薄,从而提升了板材的拉深性能。在上述基础上,将激光局部热处理用于2B06铝合金航空复杂口框零件的成形,通过设计激光处理路径和参数,获得合理的局部硬化区域,可有效地避免在加强筋处出现过度减薄导致的破裂,大大提高复杂零件的成形性。     

耦合温度和应变率的铝合金板成形极限预测方法

为了提高铝合金板成形能力,一些先进成形工艺已经被开发。温成形是实现铝合金高成形能力和高成形精度的一种有效方法。温度和成形速度是影响铝合金板温成形工艺的重要参数,对其成形性能影响十分显著。提出一种综合考虑温度和应变率影响的铝合金板成形极限预测方法。采用响应面法建立铝合金板应变硬化指数n、应变率敏感度指数m与成形温度、应变率条件之间的力学性能函数关系;基于M-K理论,并结合Logan-Hosford屈服函数,推导出耦合温度和应变率的铝合金板成形极限图计算模型。模型检验表明力学性能响应面方程具有较高精度。成形极限的计算结果与已有的试验值对比表明,二者吻合较好,这证实耦合温度和应变率的铝板成形极限预测方法是正确和可靠的。