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.     

圆筒形件拉深失稳及各因素影响分析

对板料成形中圆筒形件拉深的破裂失稳及产生破裂失稳的临界压边力进行研究.由于凸、凹模圆角及其间隙的存在,圆筒形件拉深的筒壁区实际为凸、凹模圆角之间的公切线部分.根据Mises-Hill屈服函数及Tresca准则求出凸缘变形区、凹模圆角区和筒壁区的应力分布,得到危险断面处的应力表达式,从而求出不产生破裂失稳的临界压边力的解析表达式,并进一步分析获得拉深比、硬化指数、厚向异性系数、摩擦因数以及径向推力等因素对临界压边力的影响规律.采用液压压边与周缘加径向推力的拉深模具对08Al板料进行拉深试验,试验结果与理论计算结果具有很好的一致性.     

比例/非比例加载路径下5754O汽车用铝合金板各向异性变形行为的精确解析

随着越来越高的汽车轻量化需求,铝合金板在现代汽车工业中的应用越来越广。在不同加载路径下,包括比例和非比例加载,5754O铝合金板在塑性成形过程中具有复杂的各向异性规律。试验表明5754O铝合金板的各向异性规律随变形量的增加会发生改变,因此在常参数屈服准则理论框架下,基于传统的单一曲线假设难以对5754O铝合金板在整个塑性变形过程中的各向异性行为进行精确描述。鉴于上述问题,并同时考虑到大变形过程中材料变形的稳定性,对Yld2000-2d屈服准则进行改进。基于改进的Yld2000-2d屈服准则和单一曲线假设推导不同方向的单向拉伸应力应变曲线,并与试验结果进行了对比。结果表明,与原始的Yld2000-2d屈服准则不同,基于改进的Yld2000-2d屈服准则,传统的单一曲线假设仍然适用于5754O铝合金板各向异性问题。给出不同强化方式在比例加载路径下的统一性和非比例加载路径下的分散性证明。基于改进的Yld2000-2d屈服准则和等向强化和混合两种强化方式,推导非比例加载路径下板料的应力应变曲线。基于试验结果,验证了推导的理论曲线的精度。实现了5754O铝合金板在比例和非比例加载路径下变形行为的精确描述,为其工业应用提供了重要的理论支撑。     

基于虚场法的铝合金各向异性屈服及硬化属性参数同步表征

变形铝合金板材因轻质、高比强和比模量等优点广泛应用于航空航天工业中,其轧制生产过程引起的塑性各向异性可显著影响板材的变形行为,加大零部件成形精度控制和服役行为数值模拟预测的难度。针对目前常规测试方法表征材料各向异性屈服及各向异性塑性硬化属性所需试验数量多、种类复杂、限制条件多的现状,结合全场变形测量和虚场法,通过一种桥型试件的循环拉伸-压缩试验,首次实现2024铝合金板材各向异性屈服与塑性硬化本构参数的同步表征,大幅减少试验数量,简化试验过程。研究表明,采用当前的加载构型,在参数优化目标函数中结合材料0°和90°两个拉伸加载方向的试验数据,并配合多虚场约束,可以在不同参数表征初始猜测值下产生稳定的Hill1948各向异性屈服参数表征结果,保证解的准确性;对于非线性运动硬化模型,采用单材料方向加载和单虚场的目标函数即可获得对应材料方向稳定可靠的非线性运动硬化参数表征结果。研究成果可为铝合金板材成形工艺分析提供理论依据、数据参考和便捷的测试技术支持。     

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。     

Calculations from texture of earing in deep drawing for FCC metal sheets

The present study aims to calculate the height at each peripheral position of a cup drawn from polycrystalline sheet using texture data. In the analytical treatment the polycrystalline sheet is simplified to an aggregation of many single crystals with various orientations, and the texture is represented by a three-dimensional crystallite orientation distribution function. The ear is calculated crystallographically using the orientation distribution function as a volume fraction of a certain oriented crystal. In the experiment aluminium, Al-Mg alloy and copper sheets which are treated under various conditions of cold rolling and heat treatment are used. The average textures over the thicknesses of the sheets are measured by the Schulz reflection method. The calculated ears based on the measured textures are compared with the experimental ears for each material. The results show that all the principal features of the ears of drawn cups are predicted satisfactorily by the calculation.     

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。     

不同强化模型下的板料成形极限

介绍Hill48屈服准则下基于不同强化模型的屈服方程。推导出能够用来确定随动强化模型和混合强化模型中参数的方程。采用单向拉伸曲线上所取得的数据,对所得方程进行拟合,得到参数值,并使用所得参数值得出三种强化模型下的单向拉伸曲线。结果表明采用上述方法能够准确地确定强化模型中的参数。给出随动强化模型和混合强化模型下成形极限的计算方法。基于三种强化模型,针对分散性失稳准则、Hill集中性失稳准则、凹槽失稳准则和平面应变漂移失稳准则,得到简单加载路径下的成形极限图和成形极限应力图。从这些图中可以看出,强化模型对成形极限图和成形极限应力图影响明显。因此应当确定板料在成形过程中的强化规律,选择合适的强化模型进行成形极限预测。     

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.     

A model of one-surface cyclic plasticity and its application to springback prediction

This paper presents an elasto-plastic constitutive model based on one-surface plasticity, which can capture the Bauschinger effect, transient behavior, permanent softening, and yield anisotropy. The combined isotropic-kinematic hardening law was used to model the hardening behavior, and the non-quadratic anisotropic yield function, Yld2000-2d, was chosen to describe the anisotropy. This model is closely related to the anisotropic non-linear kinematic hardening model of Chun et al. [2002. Modeling the Bauschinger effect for sheet metals, part I: theory. International Journal of Plasticity 18, 571-95.]. Different with the model, the current model captures in particular permanent softening with a constant stress offset as well as the Bauschinger effect and transient behavior under strain path reversal. Inverse identification was carried out to fit the material parameters of hardening model by using uni-axial tension/compression data. Springback predicted by the resulting material model was compared with experiments and with material models that do not account for permanent softening. The results show that the resulting material model has a good capability to predict springback.     

Modeling of anisotropic plastic behavior of ferritic stainless steel sheet

Modeling of anisotropic plastic behavior of ferritic stainless steel sheet (Type 409) was investigated using the three yield functions of Hill [A theory of the yielding and plastic flow of anisotropic metals. Proceedings of Royal Society of London, Series A 1948;193:281–97.], Barlat and Lian [Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions. International Journal of Plasticity 1989;5:51–66] and Barlat et al. [Plane stress yield function for aluminum alloy sheet. Part I: Theory. International Journal of Plasticity 2003;19:1297–319.] (referred to as Yld2000-2d) criteria. Mechanical behaviors were characterized based on uniaxial tension, balanced biaxial bulge, and disk compression tests. Directionalities of yield stresses and r values were predicted from the three criteria and compared with experimental results. In order to verify the modeling accuracy of the three functions under complex loading conditions, cylindrical cup drawing and limiting dome height tests were carried out numerically and experimentally. It has been demonstrated that the result from Yld2000-2d criterion exhibits good agreement with experimental data. The effects of anisotropic hardening on earing and necking were also investigated based on the different levels of plastic work.     

Influence of constitutive model in springback prediction using the split-ring test

The aim of this paper is to compare several plastic yield criteria to show their relevance on the prediction of springback behavior for a AA5754-0 aluminum alloy. An experimental test similar to the Demeri Benchmark Test [Demeri MY, Lou M, Saran MJ. A benchmark test for springback simulation in sheet metal forming. In: Society of Automotive Engineers, Inc., vol. 01-2657, 2000] has been developed. This test consists in cutting a ring specimen from a full drawn cup, the ring being then split longitudinally along a radial plan. The difference between the ring diameters, before and after splitting, gives a direct measure of the springback phenomenon, and indirectly, of the amount of residual stresses in the cup. The whole deep drawing process of a semi-blank and numerical splitting of the ring are performed using the finite element code Abaqus. Several material models are analyzed, all considering isotropic and kinematic hardening combined with one of the following plasticity criteria: von Mises, Hill’48 and Barlat’91. This last yield criterion has been implemented in Abaqus. Main observed data are force-displacement curves during forming, cup thickness according to material orientations and ring gap after splitting. The stress distributions in the cup, at the end of the drawing stage, and in the ring, after springback, are analyzed and some explanations concerning their influence on springback mechanisms are given.     

Finite element simulation of earing defect in deep drawing

Deep drawing is an extensively used press working process since it eliminates expensive machining and welding operations and enables the production of components at a very high rate. The workpiece material used in a deep drawing process is anisotropic in nature, due to a prior thermomechanical treatment. Earing is one of the major defects observed in a deep drawing process due to the anisotropic nature of the sheet material. Knowledge about the ear formation in deep drawing allows a prior modification of the process, which can result in a defect-free final product with financial savings. In this paper, a recently proposed anisotropic yield criteria by Barlat et al. for rolled sheets is used to model the anisotropy for simulating the earing defect in square and circular cup drawing processes. The effect of the tooling geometry and process parameters on the ear formation is studied. It is shown that, in the square cup, the uneven metal flow rate, rather than the material anisotropy, is mainly responsible for the flange earing. Finite element formulation, based on the updated Lagrangian approach, is employed for the analysis. The stresses are updated in a material frame and the logarithmic strain measure is used, which allows the use of a large increment size. Isotropic hardening is assumed, and it follows a power law. Inertia forces are neglected due to small accelerations. The modified Newton–Raphson iterative technique is used to solve the nonlinear incremental equations.     

Three-dimensional finite-element method simulations of stamping processes for planar anisotropic sheet metals

A three-dimensional finite-element method (FEM) was developed to simulate forming processes with arbitrarily shaped tools for planar anisotropic sheet metals. An implicit, updated Lagrangian formulation based on an incremental deformation theory was employed along with a rigid-viscoplastic constitutive equation. Contact and friction were considered using the mesh-normal scheme which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relationships, which includes the equilibrium equation and mesh-normal geometric constraints, was appropriately linearized. Based on membrane approximation, linear triangular elements were used to describe formed sheets. The non-quadratic strain-rate potential previously developed by Barlat et al. was employed to account for the in-plane, anisotropic properties of sheets. Numerical simulations were performed for the deep drawing of a cylindrical cup and the stamping of an automotive front fender panel to test the planar anisotropic finite element code. In the cup-drawing analysis of a 2090-T3 aluminium alloy sheet sample, the predicted earing profile and cup height were compared with experiments. The predicted and experimental thickness strains were in relatively good agreement, even though thinning trends between rolling and transverse directions were reversed. In the fender stamping analyses of both the aluminum alloys and a mild steel sheet, the numerical stability, accuracy, and usefulness of the formulation were confirmed for automotive applications. In-plane, anisotropic effects on the forming limit curves are also discussed.     

润滑条件下铝合金板成形模拟中摩擦模型的研究

对润滑条件下铝合金薄板筒形件拉深成形过程进行了工艺分析，在作出一些简化和假设的基础上，建立了基于流体润滑的筒形件拉深成形过程摩擦模型；将该模型运用到板料成形过程有限元分析中，计算出筒形件成形时摩擦系数动态变化的数值；开发出基于探针测试的铝合金板温成形动态过程摩擦测试系统，并对筒形件成形时的摩擦系数进行了测试实验。计算结果与实验数据表明，板料成形过程中的摩擦系数不是一个常数，随着凸模行程的增加，摩擦系数具有增加的趋势。     

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.     

不同硬化模型对铝合金板冲压成形模拟结果的影响

研究不同塑性变形硬化模型对汽车5182-O铝合金板材冲压成形模拟结果的影响。采用材料单向拉伸试验得到应力应变关系曲线,基于Hollomom、Krupskowsky与Power方程对曲线进行拟合,建立材料室温下塑性变形硬化模型,对厚度为1.5 mm和0.85 mm的5182板材进行冲压试验和有限元模拟分析,对比分析冲压试验与模拟结果。试验与模拟结果显示,当板料厚度为1.5 mm时,板料冲压试验的成形力最大为42.95 kN,板料拉深深度为30.58 mm,基于Power方程计算得到的最大成形力为41.5kN与试验结果比较接近,Hollomom方程计算得到的拉深深度为30.546 mm,板材成形厚度分布与试验结果比较接近;当板料厚度为0.85 mm时,板料冲压试验的成形力最大为34.47kN,板料拉深深度为33.792 mm,基于Power方程计算得到的最大成形力为34.27 kN与试验结果比较接近,Hollomom方程计算得到的拉深深度为33.636 mm,板材成形厚度分布与试验结果比较接近。基于三种硬化模型铝合金冲压成形过程的计算模拟分析结果,并通过与试验对比得到不同硬化模型对铝合金板材冲压成形计算模拟的影响,进一步为汽车铝合金覆盖件在成形工艺的研究分析提供理论指导。     

The use of a shear instability criterion to predict local necking in sheet metal deformation

A shear instability criterion can provide a consistent approach to the onset of local necking in sheet metal forming under biaxial stretching. The neck is anticipated to initiate in the direction of pure shear when the shear stress attains some critical value. The yield function proposed by Hill is employed and the material is assumed to display only normal anisotropy. Empirically it is found that the additional material parameter required by this yield function is simply related to R, the coefficient of normal anisotropy, for a number of materials. This allows the limit strain to be predicted in terms of three well established plastic properties, viz. work hardening coefficient, coefficient of normal anisotropy and initial pre-strain. The influence of these on the limit strain curve is analysed and the coefficient of work hardening shown to play the most important role. Data available in the literature are employed in a comparison of the present theory with that due to Marciniak. In general the predicted limit strains are in reasonable agreement with the trend of experimental results for a wide range of materials. In the case of isotropic materials with work hardening coefficients in the range 0·2-0·6 predictions from the present theory are almost identical with those from that presented by Stören and Rice. The theory presented here exhibits a good correlation with experimental limit strains for materials with high work hardening coefficients, of approx. 0·4 or more. Generally, for low work hardening materials, with coefficients of 0·25 or less, the shear instability theory tends to an underestimate of limit strains and a Marciniak type of analysis may be more appropriate. However, bearing in mind the scatter of the experimental data the present theory constitutes a safe lower bound on limit strains and, in addition, has the advantage of simplicity in the mathematical calculation required.     

Constitutive law for AZ31B Mg alloy sheets and finite element simulation for three-point bending

The constitutive law to describe the anisotropic and asymmetric mechanical behavior of AZ31B magnesium (Mg) alloy sheets at room temperature has been developed here for the plane stress condition, based on the orthotropic yield criterion proposed by Cazacu O, Plunkett B, Barlat F. [Orthotropic yield criterion for hexagonal closed packed metals. International Journal of Plasticity 2006;22:1171–94] and different isotropic hardening laws for tension and compression. Experimental procedures to obtain the material parameters of the yield surface and the hardening laws have been discussed for the AZ31B Mg alloy sheet. For verification purposes, finite element simulation results based on the developed constitutive laws have been compared with experimental results for a three-point bending test.