金属薄板循环塑性强化模型及实验研究进展

金属薄板塑性成形及回弹预测精度在很大程度上取决于所采用的强化模型能否对材料变形行为准确描述。梳理了各向同性强化模型、随动强化模型、旋转强化模型、畸变强化模型以及各类微观强化模型,对不同模型的特点及局限性进行了分析。同时,总结并讨论了标定强化模型中材料参数的各类循环加载实验方法。针对强化模型参数识别的问题,总结了常用的参数标定方法,分析了影响识别精度的因素。最后,介绍了不同强化模型在回弹预测方面的应用并分析了影响预测精度的因素。     

平面应变板料拉弯成形回弹理论分析

基于平面应变假设,采用服从Hill平方屈服准则和指数强化材料模型,建立了板料拉弯成形回弹量预测的理论模型。应用该模型计算了一个拉弯成形回弹实例,分析了单位宽度切向拉力、凸模圆角半径、摩擦因数及各向异性参数对板料回弹量的影响。分析结果表明,只有当中性层偏移距离超过板厚的四分之一时,增大切向拉力才能有效地控制板料回弹量,而且弯曲半径越大,增大切向拉力控制板料的回弹量越为有效,然而拉力不能无限制的增大,它的计算准则为板料最外层的等效应变应不大于极限应变。同时还表明,摩擦因数对板料回弹量的影响随切向拉力的增大变得更为显著,而各向异性参数对板料拉弯成形回弹量的影响也较为明显。与有限元数值模拟预测结果的对比表明,理论模型预测板料拉弯成形回弹量与有限元数值模拟结果很接近。     

基于Yoshida-Uemori材料模型的汽车结构件冲压回弹分析

Yoshida-Uemori随动硬化材料模型能够准确描述应变路径发生变化时材料性能的改变,从而较好地反映复杂加载情况下材料的各向异性.本文基于JSTAMP件分别采用Yoshida-Uemori随动硬化材料模型和各向同性硬化材料模型对汽车高强钢结构件的冲压成形进行了仿真分析与回弹预测,研究了不同材料硬化模型对回弹预测精度...     

基于混合硬化模型的TRIP780高强钢双C梁扭曲回弹仿真与试验

为了实现扭曲回弹的精确预测,在高强度钢板冲压成形中必须对工艺参数进行有效控制。基于试验数据,利用响应面法和遗传算法对Voce非线性各向同性硬化模型和Chaboche非线性随动硬化模型组成的混合硬化模型参数进行反求。基于三维空间两异面直线夹角,提出一种评价扭曲回弹的指标。利用液压机进行TRIP780高强钢双C梁扭曲回弹试验,并且利用三坐标测量仪测量扭曲回弹角。利用基于双C梁有限元模型建立的回弹角响应面模型预测值逼近回弹角的测量值,从而确定混合硬化模型参数。为了实现扭曲回弹的精确预测,在冲压成形中必须对有效的工艺参数进行控制。基于已验证的双C梁有限元模型,利用极差分析方法对相关因素进行分析,确定影响扭曲回弹的关键因素。研究结果表明,对扭曲回弹影响较大的因素依次为摩擦系数μ、压边力FN、凹模圆角半径R1和R2,为扭曲回弹的有效控制提供一定的理论依据。     

考虑初始残余应力的板料弯曲回弹理论分析

在实际弯曲加工过程中,板料内部如果带有初始残余应力,将与弯曲应力发生叠加,对板料的回弹产生一定的影响。由于传统的回弹理论都没有考虑初始残余应力的影响,该文基于平面应变假设,采用服从Mises屈服准则和线性强化材料模型,推导了考虑初始残余应力的板料弯曲回弹角近似公式并基于有限元软件ABAQUS进行了残余应力板料弯曲回弹仿真对比分析。理论计算与仿真结果具有较好的一致性,验证了理论模型的正确性。研究结果表明,残余应力和厚度对板料回弹均有较大影响:沿宽度方向,不同初始残余应力处的板料回弹并不均匀;增大初始残余应力峰值和减小板料厚度均使不同初始残余应力处板料的回弹差值增大。     

修正GTN模型及其在预测硅钢冷轧边裂中的应用

考虑剪应变对微孔洞损伤演化的影响, 对GTN损伤模型的损伤演化机制进行修正, 建立了适用于不同应力三轴度水平的损伤模型. 结合隐式应力更新算法和显式有限元计算, 采用VUMAT子程序实现了修正GTN模型在有限元软件ABAQUS中的数值计算. 通过模拟纯剪切和剪切-拉伸两组试样的损伤演化和断裂行为, 验证了修正GTN模型在不同应力三轴度承载条件下的有效性. 运用修正GTN损伤模型模拟含边部缺口的带钢在轧制过程中裂纹的萌生和扩展行为, 模拟结果与实验相一致, 表明该模型可有效地用于带钢缺陷在轧制过程中扩展行为的分析和预测. 模拟和实验结果表明, 带钢边部缺口在轧制过程中, 缺口前沿和后沿均会萌生裂纹, 且后沿裂纹扩展更为明显.     

屈服准则和硬化模型对5052铝板回弹仿真的影响

为选择适合于5052铝合金回弹仿真的材料模型,对LS-Dyna软件中4个材料模型MAT_36、MAT_122、MAT_125和MAT_226所采用的屈服准则和硬化模型进行了分析,采用这4个模型对5052铝板U形件的回弹进行了仿真,对回弹过程中圆角区的应力释放进行了讨论.同时,进行了U形件的回弹试验,并与仿真结果进行了比较.结果表明,4个材料模型中,基于Yoshida-Uemori随动硬化模型和Barlat’89屈服准则的材料模型MAT_226具有最好的回弹预测精度,由各向同性硬化模型和Hill’48屈服准则组合的材料模型MAT_122的回弹预测结果与试验结果的偏差最大.硬化模型对回弹预测精度的影响大于屈服准则的影响.     

拼焊板U形件弯曲成形回弹补偿和焊缝移动规律研究

为了提高预测回弹的准确性,选用了拼焊板U形件作为研究对象,运用Dynaform软件,进行冲压成形和回弹的有限元数值模拟研究,得出了压边力、板料强度以及板料厚度对焊缝移动的影响规律,并探讨了焊缝、压边力、材料性能参数和板料厚度对回弹的影响,最终进行回弹补偿与实验验证.研究结果表明随着压边力的增大,焊缝向厚侧移动;板料强度不同时,焊缝向强度高的一侧移动;厚度不同时,焊缝向板料厚的一侧移动;焊缝会令板料的回弹量增大;随着压边力的增大,回弹量减小;弹性模量相同的条件下,材料屈服极限σs越高,回弹角越大;材料硬化指数n越小,回弹角越大;保持厚侧板料不变的情况下,另一侧板料越薄,回弹量越大.     

板料V形弯曲回弹的动力显式有限元分析

板料成形后的回弹对精度影响较大,在数值模拟时对回弹进行精确预测显得非常重要.基于连续介质力学及有限变形理论,建立了适合于三维板料成形分析的显式算法的有限元数学模型,采取集中质量矩阵,用动力显式积分的方法,使位移计算显式化,避免了由材料、几何、边界条件等高度非线性因素引起的计算收敛问题.根据该模型开发了动力显式算法的板料成形过程模拟的有限元分析程序DESSFORM3D,应用该软件模拟了包括回弹在内的整个板料V形弯曲的成形过程.通过3个不同凸模行程时计算与实验的板料几何形状对比以及计算结果与实验结果对比,验证了软件计算结果的准确性.     

板料V形弯曲回弹的动力烛式有限元分析

板料成形后的回弹对精度影响较大，在数值模拟时对回弹进行精确预测显得非常重要。基于连续介质力学及有限变形理论，建立了适合于三给板料成形分析的显式算法的有限元数学模型，采取集中质量矩阵，用动力显式积分的方法，使位移计算显式化，避免了由材料、几何、边界条件等高度非线性因素引起的计算收敛问题。根据该模型开发了动力显式算法的板料成形过程模拟的有限元分析程序DESSFORM3D，应用该软件模拟了包括回弹在内的整个板料V形弯曲的成形过程。通过3个不同凸模行程时计算与实验的板料几何形状对比以及计算结果与实验结果对比，验证了软件计算结果的准确性。     

Predicting damage and failure under low cycle fatigue in a 9Cr steel

Experimental data have been generated and finite element models developed to examine the low cycle fatigue (LCF) life of a 9Cr (FB2) steel. A novel approach, employing a local ductile damage initiation and failure model, using the hysteresis total stress–strain energy concept combined with element removal, has been employed to predict the failure in the experimental tests. The 9Cr steel was found to exhibit both cyclic softening and nonlinear kinematic hardening behaviour. The finite element analysis of the material's cyclic loading was based on a nonlinear kinematic hardening criterion using the Chaboche constitutive equations. The models’ parameters were calibrated using the experimental test data available. The cyclic softening model in conjunction with the progressive damage evolution model successfully predicted the deformation behaviour and failure times of the experimental tests for the 9Cr steels performed.     

Simulations of stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

The residual stresses due to fillet rolling and the bending stresses near the fillets of crankshaft sections under bending fatigue tests are important driving forces to determine the bending fatigue limits of crankshafts. In this paper, the residual stresses and the bending stresses near the fillet of a crankshaft section under fillet rolling and subsequent bending fatigue tests are investigated by a two-dimensional plane strain finite element analysis based on the anisotropic hardening rule of Choi and Pan [Choi KS, Pan J. A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials (in preparation)]. The evolution equation for the active yield surface during the unloading/reloading process is first presented based on the anisotropic hardening rule of Choi and Pan (in preparation) and the Mises yield function. The tangent modulus procedure of Peirce et al. [Peirce D, Shih CF, Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 1984;18:875–87] for rate-sensitive materials is adopted to derive the constitutive relation. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule, the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress–strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress–strain data for the nonlinear kinematic hardening rule. Then, a two-dimensional plane-strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted based on the anisotropic hardening rule of Choi and Pan (in preparation) and the nonlinear kinematic hardening rule of ABAQUS. In general, the trends of the stress distributions based on the two hardening rules are quite similar after the release of roller and under bending. However, the compressive hoop stress based on the anisotropic hardening rule is larger than that based on the nonlinear kinematic hardening rule within the depth of 2 mm from the fillet surface under bending with consideration of the residual stresses of fillet rolling. The critical locations for fatigue crack initiation according to the stress distributions based on the anisotropic hardening rule appear to agree with the experimental observations in bending fatigue tests of crankshaft sections.     

Springback simulation of advanced high strength steels considering nonlinear elastic unloading–reloading behavior

The stress–strain response of some materials, such as advanced high strength steels, during unloading is nonlinear after the material has been loaded into the plastic deformation region. Upon reloading, the response shows a nonlinear elastic response that is different from that in unloading. Therefore, unloading–reloading of these materials forms a hysteresis loop in the elastic region. The Quasi-plastic–elastic model (Sun and Wagoner, 2011) was modified and combined with both isotropic-nonlinear kinematic hardening and two-surface plasticity models to simultaneously describe the nonlinear unloading response and complex cyclic response of sheet metals in the plastic region. The model was implemented as user-defined material subroutines, i.e. UMAT and VUMAT, for ABAQUS/Standard and ABAQUS/Explicit finite element codes, respectively. Uniaxial loading-unloading tests were performed on three common grades of automotive sheet steel: DP600, DP980 and TRIP780 steel. The model was verified by comparing the predicted material response with the corresponding experimental response. Finally, the model was used to predict the springback of a U-shape channel section formed in a plane-strain channel draw process. The results showed that the model was able to considerably improve springback predictions compared to the usual assumption of linear elastic unloading.     

Effect of hardening models on different ductile fracture criteria in sheet metal forming

Prediction of the fracture is one of the challenging issues which gains attention in sheet metal forming as numerical analyses are being extensively used to simulate the process. To have better results in predicting the sheet metal fracture, appropriate ductile fracture criterion (DFC), yield criterion and hardening rule should be chosen. In this study, the effects of different hardening models namely isotropic, kinematic and combined hardening rules on the various uncoupled ductile fracture criteria are investigated using experimental and numerical methods. Five different ductile fracture criteria are implemented to a finite element code by the user subroutines. The criterion constants of DFCs are obtained by the related experimental tests. The in-plane principle strains obtained by the finite element analyses for different DFCs are compared with the experimental results. Also, the experimental results are used to evaluate the principle strain values calculated by the finite element analysis for different combinations of DFCs and hardening rules. It is shown that some DFCs give better predictions if the appropriate hardening model is employed.     

Development and application of the material constitutive model in springback prediction of cold-bending

The accuracy for cold-bending springback prediction is determined by the sensitivity and accuracy of the material constitutive model. Thus, the material constitutive model is developed and improved by many researchers, and the improved models are applied in the springback calculation with various materials in finite element simulation or theoretical analysis. To provide a reference for the researchers studying cold-bending springback problems, a review of the development and application of the material constitutive models is presented in this paper, which conducts from the elastic behavior, the anisotropy, and the work-hardening. It can be summarized as: (1) Springback prediction result is higher and more accurate when the variable elastic modulus and the nonlinear recovery are considered. (2) The isotropic hardening leads to an overestimation of the springback, which can be avoided by a hardening model describing the Bauschinger effect. (3) The hardening model has greater impact on springback than the yield criterion. (4) Good accuracy of the springback prediction can be achieved when the variable elastic modulus effect, the material anisotropy and the nonlinear hardening are considered together. It is also found the theory development and practical application of the material constitutive models are out of line, due to lacking further experiment, or that the stress loading–reloading history within a bending part may be not so complex as that “ratchetting behavior” discussed.     

A coupled FE–EFG approach for modelling crack growth in ductile materials

In this work, a coupled finite element–element free Galerkin approach has been used to model crack growth in ductile materials under monotonic and cyclic loads. In this approach, a small discontinuous domain near crack is modelled by EFG method, whereas the rest of the domain is modelled by FEM to exploit the advantages of both the methods. A ramp function has been used in the transition region to maintain the continuity between FE and EFG domains. Two plasticity models (GTN and von‐Mises) and three hardening rules (isotropic, kinematic and mixed) have been used to model the nonlinear material behaviour. Four different problems, i.e. single edge notched tension specimen, double edge notched tension specimen, compact tension specimen and three‐point bend specimen, are solved under plane strain condition using J–R curve approach. Finally, a CT specimen problem is also solved by coupled approach using three hardening rules and two plasticity models under cyclic loading.     

An analytical model for predicting springback and side wall curl of sheet after U-bending

An analytical model for predicting sheet springback after U-bending is proposed in this paper based on Hill48 yielding criterion and plane strain condition. The model takes into account of the effects of deformation history, thickness thinning and neutral surface shift on the sheet springback of U-bending. Three rules for material hardening – kinematic, isotropic and combined hardening – have been used to consider the effect of complex deformation history that has undergone stretching, bending, and unbending deformations on the sheet springback. The model is applied to the benchmark of NUMISHEET’93 2-D draw bending problem. It indicates that the springback is overestimated when isotropic hardening is applied, while is underestimated when kinematic hardening is applied. For reverse loading problem, the combined hardening is a good approach to the practical material. In addition to that, the effects of blank holding force, friction coefficient between sheet and tools, sheet thickness and anisotropy have been investigated. When the shifting distance of neutral surface exceeds one-fourth of sheet thickness, the springback can be reduced effectively by increasing the blank holding force and friction between sheet and die. And the springback increases with anisotropy and friction between sheet and punch, and decreases with the sheet thickness.     

On the influence of kinematic hardening on plastic anisotropy in the context of finite strain plasticity

The paper discusses the application of a newly developed material model for finite anisotropic plasticity to the simulation of earing formation in cylindrical cup drawing. The model incorporates Hill-type plastic anisotropy, nonlinear kinematic and nonlinear isotropic hardening. The constitutive framework is derived in the context of continuum thermodynamics and represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime. Plastic anisotropy is described by means of second-order structure tensors which are used as additional tensor-valued arguments in the representation of the yield criterion and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that fullfils plastic incompressibility and preserves the symmetry of the internal variables. The numerical examples investigate the influence of the hardening behaviour on an initially anisotropic yield criterion. In particular, the influence of using the kinematic hardening component of the model in addition to isotropic hardening in the earing simulations is examined. Comparisons with test data for aluminium and steel sheets display a good agreement between the finite element results and the experimental data.