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。     

TRIP590先进高强钢板的双向加载变形行为

为了探索TRIP590先进高强钢板的复杂变形行为,从试验、理论和有限元模拟三个方面对其在不同双向加载路径下的应力应变关系进行研究。针对TRIP590先进高强钢板料进行十字形试件的双向拉伸试验,获得了不同加载路径下的双向拉伸变形性能。基于弹塑性理论和广义胡克定律,采用Mises屈服准则和Hill48屈服准则(Hill屈服准则采用两种方法求解其参数)给出包含弹性和塑性应变在内的双向拉伸真实应力-真实应变关系曲线,并与试验结果进行对比,分析不同屈服准则的精度及误差原因。采用ABAQUS有限元软件,基于Mises和Hill48两种屈服准则对十字形试件不同加载路径下的双向拉伸试验进行有限元模拟。将试验直接采集到的不同加载路径下的双向拉伸载荷-位移数据与有限元模拟结果进行对比,进一步分析不同屈服准则的精度,同时验证采用本研究中的十字形试件的双向拉伸试验来计算双向应力-应变关系的可行性。研究结果可为TRIP590先进高强钢板在实际成形工艺中的应用提供重要的技术支撑。     

不同屈服准则与硬化模型对DP780双相高强钢拉延弯曲回弹预测影响规律研究

随着汽车车身对轻量化、高效节能等要求的提高,先进高强钢因其高比强度、比刚度等性能在汽车工业中应用呈上升趋势。因此,研究先进高强钢的回弹现象,总结其回弹规律,对改善先进高强钢零件的成形精度具有重要意义。目前的研究主要是基于U弯试验研究不同材料模型对回弹的影响规律,而屈服准则和硬化模型对Daw-bending回弹预测的适用性需要进一步研究。基于建立的Draw-bending试验平台,研究圆辊半径与名义张紧力对DP780回弹的影响规律。并利用PAM-STAMP有限元分析软件研究不同硬化模型(Hollomon模型、Y-U模型)和屈服准则(Mises、Hill48、Yld2000)对Draw-bending回弹预测的影响规律。研究表明,在试验方面,增大弯曲半径和张紧力都能减小侧壁卷曲回弹。在有限元仿真回弹预测方面,当采用双精度求解器求解Y-U模型材料参数时,可以提高Draw-bending回弹的预测精度。由于DP780各向异性的特殊性,采用Y-U硬化模型和Mises屈服准则或Yld2000屈服准则可以得到更高的回弹预测精度。对于厚度与截面半径的预测,采用Y-U硬化模型与Yld2000屈服准则可以得到更好的预测精度。     

板料屈服行为及强化规律的研究进展

研究板料塑性成形的理论基础是屈服准则、强化规律以及本构模型。随着新材料、新工艺的不断出现,温度和应变速率对塑性成形过程中的影响也不容忽视,原有的塑性理论已无法满足研究和工程应用的需求。从板料屈服准则研究、包辛格效应与强化模型研究、屈服强化规律试验方法研究以及涉及应变速率和温度的板料屈服强化研究4个方面阐述板料屈服行为及强化规律的研究进展,指出常用屈服准则的特点和不足,说明各种强化模型中组合强化模型仍然是研究重点。试验方法主要从研究屈服轨迹的双向拉伸试验及确定强化模型参数试验的2个方面进行介绍。此外,指出针对板料在复杂应力状态下应力张量与应变张量之间的涉及应变率和温度的屈服准则和相应的流动准则的本构关系还有待研究。提出随着新材料、新工艺的不断出现,涉及应变速率和温度的屈服准则和强化规律、试验方法以及在有限元模拟中的应用等研究将是未来的研究热点。     

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。     

汽车用高强度钢板的动态变形行为

对DP590钢板和CR340LA钢板在应变速率为0.003s-1(准静态)和20~700s-1(动态)下进行了室温拉伸试验,研究了试验钢板的动态拉伸变形行为、应变速率敏感性和动态断裂行为。结果表明:两种试验钢板的动态真应力-真应变曲线均无屈服平台,屈服后真应力随真应变的增加先快速增大后缓慢增大;应变速率对屈服强度的影响略高于对抗拉强度的影响,并且DP590钢板的应变速率敏感性和硬化指数均高于CR340LA钢板的;两种试验钢板的均匀伸长率均随应变速率的增加而降低;随应变速率的增加,DP590钢板中的位错密度增加,当应变速率不小于200s-1时出现位错胞;DP590钢板在准静态拉伸时发生明显颈缩,而动态拉伸时未发生颈缩,且随应变速率的增加,拉伸断口上的C形韧窝数量减少,等轴状韧窝数量增加。     

基于不同失稳理论的DP780双相钢成形极限预测

采用板材综合成形试验机对DP780双相钢进行极限应变试验,分别基于C-H失稳理论和M-K凹槽失稳理论搭载Yld2000屈服准则和幂指数硬化模型对DP780双相钢成形极限曲线进行预测,并与试验结果进行对比。结果表明：基于M-K凹槽失稳理论和C-H失稳理论获得的成形极限曲线对成形极限的预测精度分别为97.97%和95.82%;初始厚度不均匀度越大,钢板表面越光滑,越有利于成形;当初始厚度不均匀度为0.992时,M-K凹槽失稳理论对DP780双相钢成形极限的预测精度最高,相对误差为0.66%,在实际冲压生产中,当初始厚度不均匀度取0.992时,该理论模型可作为获取DP780双相钢成形极限曲线的一种可靠方法。     

屈服准则和硬化模型对DC56D+Z钢汽车后背门内板成形仿真精度的影响

以DC56D+Z超深冲钢为研究对象,基于Ludwik、Swift和Hockett-Sherby硬化模型开展材料性能参数解析,确定能够精确表征其力学行为的硬化模型;利用最佳硬化模型,分别搭载Hill'48、Barlat'89和BBC-2005屈服准则对DC56D+Z钢汽车后背门内板进行冲压成形仿真,获得了材料流动量、最大主应变和最大减薄率等数据,并通过与试验结果的对比分析了不同屈服准则对仿真精度的影响.结果表明:Hockett-Sherby硬化模型对DC56D+Z钢力学行为的描述精度最高,拟合相关系数的平方为0.9979;基于Hockett-Sherby硬化模型并搭载BBC-2005屈服准则的仿真模型对材料流动量、最大主应变和最大减薄率的预测精度最高,最大相对误差分别为4.9％,5.6％,10.1％,更适用于DC56D+Z钢板的冲压成形仿真.     

先进高强钢DP780板料的温成形极限预测研究

为准确预测DP780钢板料在温成形条件下的成形极限曲线,将韧性断裂预测模型引入到数值模拟.基于DP780钢板料在温度范围573 K～873 K、应变率范围6.67× 10-4s-1～6.67×10-3s-1的单向拉伸试验结果分析,利用强塑积指标确定了温度为673 K、应变率为3.33× 10-3s-1条件下材料的温冲压成形性能较好.通过该变形条件下的简单拉伸试验和数值模拟,确定了影响DP780钢板料韧性断裂的主要因素.建立了可以预测DP780钢板料在不同应变路径下发生拉伸型断裂和剪切型断裂两种断裂机制的韧性断裂预测模型,并与温成形本构模型、Hill'48屈服准则相结合实现了刚模胀形试验的数值模拟,预测了DP780钢板料在温度为673 K下的成形极限曲线,并建立了成形极限数学模型.结果 表明,利用该方法预测的成形极限结果拥有较好的精度.     

复合型裂纹小范围屈服下裂尖塑性区统一解

采用俞茂宏统一强度理论,推导Ⅰ、Ⅱ复合型裂纹在小范围屈服条件下裂尖塑性区尺寸的统一解析解.给出材料参数在不同拉压比α、泊松比v和中间主应力影响参数b下的一族裂尖塑性区形状与大小的轨迹.讨论以上参数对裂尖塑性区变化的影响,其中拉压比α对塑性区影响较大,α≠1导致塑性区在裂纹上下表面处不连续,b=0和b=1分别对应裂尖塑性区的上限、下限边界.同Tresca准则、Mises准则的解进行比较分析,已有解均是它的特例或线性逼近,该理论解具有理论的统一性和对不同材料的普适性.     

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.     

Earing predictions for strongly textured aluminum sheets

Metallic alloy sheets develop crystallographic texture and plastic anisotropy during rolling. Deep drawing of a cylindrical cup from a rolled sheet is one of the typical forming operations where the effect of this anisotropy is most evident. Generally, in the finite element analyses of this process, the evolution of anisotropy during forming is neglected. In this paper, results of an experimental program carried out to quantify the anisotropy of aluminum alloy AA5042-H2 are reported. In addition to tensile tests along seven directions in the plane of the sheet, cup-drawing tests were conducted. It was observed that the material displays eight ears. The effects of the evolution in anisotropy and the directionality in hardening on the predictions of the earing profile for this material are investigated using a new methodology that incorporates multiple hardening curves corresponding to uniaxial tension along several orientations with respect to the rolling direction, and to biaxial tension. Yielding is described using the anisotropic yield function Yld2000-2D [1] and a form of CPB06ex2 yield function [2], which is tailored for metals with no tension–compression asymmetry. It is shown that even if distortional hardening is neglected, the latter yield function predicts a cup with eight ears as was observed experimentally. Consideration of distortional only leads to improved accuracy in prediction of the non-uniformity of the cup height profile.     

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.     

An evaluation of some recent yield criteria for industrial simulations of sheet forming processes

The present paper deals with material modeling in connection with sheet metal forming analyses. One purpose of the report is to discuss the special needs and demands of industrial analysts. With this in mind, in particular, the demands put on the yield condition are analyzed. Two recent yield criteria for anisotropic metal sheets, in the literature denoted Yld2000 and BBC2000, respectively, are found to be very well suited for industrial use. They do both belong to a group of yield criteria called the “Hosford family”. Practical issues with regard to these yield criteria, such as procedures for determining the parameters being part of the models, implementation issues, and numerical efficiency, are thoroughly discussed. A version of the above criteria, using a reduced set of parameters, is proposed, and is shown to offer a significantly reduced computing time at the cost of some loss of accuracy.     

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.     

The effect of doubly tapered strut morphology on the plastic yield surface of cellular materials

Although the literature on the mechanics of cellular materials is vast, there is no theoretical model to account for the effects of axial yielding of struts aligned to the applied loading direction on the plastic yield surface under multiaxial loading conditions. An anisotropic hexagonal model having tapered strut morphology is developed to show these effects on the plastic yield surface under multiaxial tensile loading condition. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square cellular materials, and three-dimensional (3D) hexagonal and rhombic cellular materials of rod-like columnar structure. A tetrahedral element with tapered strut morphology is also used for a foam model to illustrate these effects on the yield surface under axisymmetric loading condition. Plastic collapse due to bending moment in the inclined struts is a dominant mode. However, under multiaxial tensile loading, the collapse due to axial yielding of struts parallel to the loading direction is found to be an important mode. The shape of plastic yield surface was found to depend not only on relative density but also on the strut morphology.     

On constitutive modeling for springback analysis

The springback phenomenon that occurs in thin metal sheets after forming is mainly a stress driven problem, and the magnitude is roughly proportional to the ratio between residual stresses and Young's modulus. An accurate prediction of residual stresses puts, in turn, high demands on the material modeling during the forming simulation.A phenomenological plasticity model is made up of several ingredients, such as a yield condition, a plastic hardening curve, a hardening law, and a model for the degradation of elastic stiffness due to plastic straining.The authors of this paper have recently, [1], showed the importance of a correct modeling of a cyclic stress-strain behavior via a phenomenological hardening law, in order to obtain an accurate stress prediction. The main purposes of the present study are to study the influence of two other constitutive ingredients: the yield criterion and the material behavior during unloading. Three different yield criteria of different complexity are evaluated in the present investigation: the Hill’48 criterion, the Barlat-Lian Yld89 criterion, and the 8-parameter criterion by Banabic/Aretz/Barlat.The material behavior during unloading is evaluated by loading/unloading tension tests, where the material is unloaded/reloaded at specified plastic strain levels. The slope of the unloading curve is measured and a relation between the “unloading modulus” and the plastic stain is established.In the current study, results for four different materials are accounted for. The springback of a simple U-bend is calculated for all the materials in the rolling-, transverse- and diagonal directions. From the results of these simulations, some conclusions regarding constitutive modeling for springback simulations are drawn.     

Stress analysis of two-dimensional cellular materials with thick cell struts

Finite element analyses (FEA) were performed to thoroughly validate the collapse criteria of cellular materials presented in our previous companion paper. The maximum stress (von-Mises stress) on the cell strut surface and the plastic collapse stress were computed for two-dimensional (2D) cellular materials with thick cell struts. The results from the FEA were compared with those from theoretical criteria of authors. The FEA results were in good agreement with the theoretical results. The results indicate that when bending moment, axial and shear forces are considered, the maximum stress on the strut surface gives significantly different values in the tensile and compressive parts of the cell wall as well as in the two loading directions. Therefore, for the initial yielding of ductile cellular materials and the fracture of brittle cellular materials, in which the maximum stress on the strut surface is evaluated, it is necessary to consider not only the bending moment but also axial and shear forces. In addition, this study shows that for regular cellular materials with the identical strut geometry for all struts, the initial yielding and the plastic collapse under a biaxial state of stress occur not only in the inclined cell struts but also in the vertical struts. These FEA results support the theoretical conclusion of our previous companion paper that the anisotropic 2D cellular material has a truncated yield surface not only on the compressive quadrant but also on the tensile quadrant.     

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.