板材多点成形过程的有限元分析

多点成形过程采用静力隐式格式进行数值模拟是比较合适的。本文建立了用于多点成形过程分析的静力隐式弹塑性大变形有限元方法 ,给出了对稳定迭代收敛过程效果较好的板壳有限单元模型、处理多点不连续接触边界的接触单元方法以及增量变形过程中应力及塑性应变计算的多步回映计算方法。基于这些方法编制了计算软件 ,应用该软件进行了矩形板的液压胀形过程及球形模具拉伸成形过程的有限元分析 ,数值计算结果与典型的实验结果及计算结果吻合很好。最后给出了球形、圆柱形目标形状的实际多点成形过程的数值模拟结果。     

适用于壳体h型自适应有限元分析的一组新单元

推导出一组适用于h型自适应分析的四边形蜕化壳元。对于大多数壳体结构,壳单元的刚度矩阵可分为薄膜、弯曲和剪切三部分。对薄膜部分本文采用杂交应力元方法进行设计,独立假设薄膜应力场以改善其精度;弯曲部分的刚度矩阵则依然由基于位移的应变来获得;而剪切部分则采用假设自然应变的方法来获得能克服薄壳下剪切自锁的新剪应变并用于计算此部...     

金属板材冲压成型过程的有限单元法模拟

用有限单元法模拟了金属板材的冲压成型过程。在模拟过程中，应用了同时考虑了薄膜力和弯矩的板壳大变形理论，考虑了板材在塑性阶段各向异性的强化性质，考虑了模具和工件的接触和摩擦条件，分析了金属板在冲压过程中的屈曲现象，建立了增量形式的变分原理。弹塑性薄壳单元被引入，它的位移模式在变分的意义上满足单元边界上一阶导数连续的条件，并有足够的秩来适应单元的有限拉伸、转动和弯曲，计算中采用了罚函数方法，即在模具和工件的接触面上，模具的表面被假设为文克尔地基，采用了修正的库伦摩擦定律，迭代法被用来决定模具与工件的接触条件和金属板的塑性行为。本文最后提供了一个算例。     

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets: Application to sheet springback

The constitutive model for the unusual asymmetric hardening behavior of magnesium alloy sheet presented in a companion paper (Lee, M.G., Wagoner, R.H., Lee, J.K., Chung, K., Kim, H.Y., 2008. Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheet, Int. J. Plasticity 24(4), 545–582) was applied to the springback prediction in sheet metal forming. The implicit finite element program ABAQUS was utilized to implement the developed constitutive equations via user material subroutine. For the verification purpose, the springback of AZ31B magnesium alloy sheet was measured using the unconstrained cylindrical bending test of Numisheet (Numisheet ’2002 Benchmark Problem, 2002. In: Yang, D.Y., Oh, S.I., Huh, H., Kim, Y.H. (Eds.), Proceedings of 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Jeju, Korea) and 2D draw bend test. With the specially designed draw bend test the direct restraining force and long drawn distance were attainable, thus the measurement of the springback could be made with improved accuracy comparable with conventional U channel draw bend test. Besides the developed constitutive models, other models based on isotropic constitutive equations and the Chaboche type kinematic hardening model were also considered. Comparisons were made between simulated results by the finite element analysis and corresponding experiments and the newly proposed model showed enhanced prediction capability, which was also supported by the simple bending analysis adopting asymmetric stress–strain response.     

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

This paper proposes an extension of the SHB8PS solid–shell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the “thickness” direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications—both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems.     

Simulation of springback: Through-thickness integration

The number of through-thickness integration points (N_IP) required for accurate springback analysis following sheet forming simulation using shell elements is a subject of confusion and controversy. Li and Wagoner recommended, in 1999, based on a finite element analysis (FEA) of draw-bending springback, the use of 25 integration points (IP), with up to 51 IP required to ensure accuracies of 1%. Several researchers have since reported that N_IP between 5 and 11 are adequate, or even that 7 or 9 IP are optimal, with reduced accuracy for more IP. These apparent contradictions are addressed with an analytical model of elasto-plastic bending under tension, followed by elastic springback. The fractional error in the evaluated bending moment, which is equal to the fractional error in springback, was determined by comparing three numerical integration schemes, with various N_IP, to the closed-form result. The results illustrate the oscillatory nature of numerical integration error with small parametric changes, such that fortuitous agreement can be obtained in isolated simulations where the number of integration points is inadequate. The concept of an assured error limit is introduced as well as a maximum error limit (for a range of generally unknown sheet tensions). The assured error limit varies with the integration scheme, N_IP, bending ratio (R/t), and sheet tension. Guidelines for the number of integration points required for given error tolerances are reported to allow practitioners to choose numerical parameters appropriately.     

Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity

The main objective of this paper is to develop a generalized finite element formulation of stress integration method for non-quadratic yield functions and potentials with mixed nonlinear hardening under non-associated flow rule. Different approaches to analyze the anisotropic behavior of sheet materials were compared in this paper. The first model was based on a non-associated formulation with both quadratic yield and potential functions in the form of Hill’s (1948). The anisotropy coefficients in the yield and potential functions were determined from the yield stresses and r-values in different orientations, respectively. The second model was an associated non-quadratic model (Yld2000-2d) proposed by Barlat et al. (2003). The anisotropy in this model was introduced by using two linear transformations on the stress tensor. The third model was a non-quadratic non-associated model in which the yield function was defined based on Yld91 proposed by Barlat et al. (1991) and the potential function was defined based on Yld89 proposed by Barlat and Lian (1989). Anisotropy coefficients of Yld91 and Yld89 functions were determined by yield stresses and r-values, respectively. The formulations for the three models were derived for the mixed isotropic-nonlinear kinematic hardening framework that is more suitable for cyclic loadings (though it can easily be derived for pure isotropic hardening). After developing a general non-associated mixed hardening numerical stress integration algorithm based on backward-Euler method, all models were implemented in the commercial finite element code ABAQUS as user-defined material subroutines. Different sheet metal forming simulations were performed with these anisotropic models: cup drawing processes and springback of channel draw processes with different drawbead penetrations. The earing profiles and the springback results obtained from simulations with the three different models were compared with experimental results, while the computational costs were compared. Also, in-plane cyclic tension–compression tests for the extraction of the mixed hardening parameters used in the springback simulations were performed for two sheet materials.     

A reliability study of springback on the sheet metal forming process under probabilistic variation of prestrain and blank holder force

This work deals with a reliability assessment of springback problem during the sheet metal forming process. The effects of operative parameters and material properties, blank holder force and plastic prestrain, on springback are investigated. A generic reliability approach was developed to control springback. Subsequently, the Monte Carlo simulation technique in conjunction with the Latin hypercube sampling method was adopted to study the probabilistic springback. Finite element method based on implicit/explicit algorithms was used to model the springback problem. The proposed constitutive law for sheet metal takes into account the adaptation of plastic parameters of the hardening law for each prestrain level considered. Rackwitz-Fiessler algorithm is used to find reliability properties from response surfaces of chosen springback geometrical parameters. The obtained results were analyzed using a multi-state limit reliability functions based on geometry compensations.     

Analytical springback model for lightweight hexagonal close-packed sheet metal

Experiments have shown that magnesium alloy sheet a common hexagonal close-packed metal, exhibits mechanical behavior unlike that of sheets made of cubic metals (X.Y. Lou et al., 2007, Int. J. Plasticity, 24, 44). The unique stress–strain response includes a strong asymmetry in the initial yield and subsequent plastic hardening. In other words, the stress–strain curves in tension and compression are significantly different. A proper representation of the constitutive relationships is crucial for the accurate evaluation of springback, which occurs due to the residual moment distribution through the sheet thickness after bending. In this paper, we propose an analytical model for asymmetric elasto-plastic bending under tension followed by elastic unloading in order to evaluate the bending moment, which is equivalent to the springback amount. To simplify the calculations, the experimentally measured stress–strain curve of the magnesium alloy sheet was approximated with discrete linear hardening in each deformation region, and the material properties were characterized according to several simplifying assumptions. The bending moment was calculated analytically using the approximate asymmetric stress–strain relationship up to the prescribed curvature corresponding to the radius of the tool in sheet metal forming operations. A numerical example showed an unusual springback increase, even with an increase in the applied force; this is an unexpected result for conventional symmetric materials. We also compared the calculated springback amounts with the results of physical measurements. This showed that the proposed model predicts the main trends of the springback in magnesium alloy sheets reasonably well considering the simplicity of the analytical approach.     

复合材料回转壳的有限元级数解

本文用有限元法和Fourier级数展开技术求解复合材料回转壳体在各种荷载作用下的弯曲问题,文中利用回转壳在几何上的轴对称性质,将各物理量在环向展开为Fourei级数,而在母线和壳厚方向分割单元,所采用的单元为6节点18自由度等参元,它考虑了剪切变形和挤压变形的影响,能计算厚度方向的挤压应力,数值算例表明,本文提出的单元性能优良,算法稳定收敛。     

冲压板材拉伸筋阻力的一种有效数值计算方法

将弹塑性有限变形的拟流动角点本构理论和厚向各向异性屈服函数引入弹塑性动力显式有限元列式,对板材通过拉伸筋的变形过程及拉伸筋阻力进行了数值模拟,并与有关实验结果进行了比较很好的一致性,表明了该计算方法的有效性。进而,数值研究了拉伸筋形状、界面摩擦状况以及材料的厚向各向异性对拉伸筋阻力的影响,为实际覆盖件冲压成形中拉伸筋的设置提供了重要的定量依据。     

Springback simulation and analysis of strong anisotropic sheet metals in U-channel bending process

The springback phenomenon of strong anisotropic sheet metals with U-channel bending as well as deep-drawing is numerically studied in detail by using Updating Lagrange FEM based on virtual work-rate principle, Kirchhoff shell element models and the Barlat-Lian planar anisotropic yield function. Simulation results are compared with a benchamark test. Very good agreement is obtained between numerical and test results. The focus of the present study is on the numerical simulation of the springback characteristics of the strong anisotropic sheet metals after unloading. The effects of the planar anisotropy coefficients and yield function exponent in the B-L yield function on the springback characteristics are discussed in detail. Some conclusions are given. The project supported by the National Natural Science Foundation of China (No. 19832020) and Provincial Natural Science Foundation of Jilin China (No.20000519)     

Anticlastic curvature in draw-bend springback

Draw-bend springback shows a sudden decline as the applied sheet tension approaches the force to yield the strip. This phenomenon coincides with the appearance of persistent anticlastic curvature, which develops during the forming operation and is maintained during unloading under certain test conditions. In order to understand the mechanics of persistent anticlastic curvature and its dependence on forming conditions, aluminum sheet strips of widths ranging from 12 to 50 mm were draw-bend tested with various sheet tensions and tool radii. Finite element simulations were also carried out, and the simulated and measured springback angle and anticlastic curvature were compared. Analytical methods based on large deformation bending theory for elastic plates were employed to understand the occurrence and persistence of the anticlastic curvature. The results showed that the final shape of a specimen cross-section is determined by a dimensionless parameter, which is a function of sheet width, thickness and radius of the primary curvature in the curled region of an unloaded sample. When the normalized sheet tension approaches 1, this parameter rapidly decreases, and significant anticlastic deflection is retained after unloading. The retained anticlastic curvature greatly increases the moment of inertia for bending, and thus reduces springback angle.     

Springback analysis for sheet forming processes by explicit finite element method in conjunction with the orthogonal regression analysis

A new method to evaluate the amount of springback in sheet forming processes based on the explicit finite element method and the orthogonal regression analysis is presented in this paper. To calculate springback accurately, a simple but effective contact searching algorithm is described and Lagrangian multiplier method was used to evaluate the contact force. The loading and unloading process could be simulated within one code. The numerical results by the present method were compared with the results by the commercial dynamic explicit code LS-DYNA3D, also with the experimental results and very good agreement was drawn. In order to obtain the springback conveniently for the purpose of practical use, the orthogonal regression analysis was implemented to establish the explicit relationship between the springback and some design parameters. The present method has been applied to the analysis of some actual sheet forming processes and very good agreement between the numerical results and the experimental results in the final geometry was obtained.     

Shaping a thin-walled cylindrical shell on a three-roll bending machine

We use the Bernoulli-Euler kinematic hypothesis to model the steady-state process of shaping a thin-walled cylindrical shell by bending an elastoplastic strengthening parent sheet on a three-roll bending machine. We determine the curvilinear shape of the moving parent sheet in the bending area and the displacement of the central roll axis needed to obtain the prescribed curvature of the cylindrical shell when leaving the bending area. One- and multitransition shell shaping processes are considered. The computational model is in satisfactory agreement with experiments.     

A general analytic solution for plane strain bending under tension for strain-hardening material at large strains

A new analytic solution for plane strain bending under tension of a sheet is proposed for elastic-plastic, isotropic, incompressible, strain-hardening material at large strains. Numerical treatment is only necessary to calculate ordinary integrals and solve transcendental equations. No restriction is imposed on the hardening law. All governing equations and boundary conditions are exactly satisfied. The only exception is that the actual stress distribution over the ends of the sheet is replaced with a concentrated force and a concentrated bending moment. The through-thickness distribution of residual stresses and a measure of springback are also found. The range of validity of the solution is determined. An illustrative example is provided for Swift’s hardening law.     

Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method简

An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.     

覆盖件冲压仿真中的网格形态优化技术

覆盖件冲压仿真计算模型中网格密度分布的合理性与网格单元形态的优劣,对仿真结果的准确性有很大的影响.提出了一种改进的全四边形网格细分方法,使网格的密度分布适于覆盖件冲压分析计算要求,可保证细分后网格的协调性,并将算法推广以处理非结构化四边形网格和三角形四边形混合网格的细分.提出的网格细分策略,有助于提高细分后网格的质量.提出了适用于细分后四边形网格和非结构四边形网格的拓扑形态优化操作,可有效的提高网格模型的形态质量.