Calculation of the forming limit diagram

A mathematical model is presented to help understand sheet metal deformation during forming. The particular purpose of this model is to predict the forming limit diagram (FLD). The present model is an extension of a previous analysis by Jones and Gillis (JG)^[1] in which the deformation is idealized into three phases: (I) homogeneous deformation up to maximum load; (II) deformation localization under constant load; (III) local necking with a precipitous drop in load. In phase III, the neck geometry is described by a Bridgman-type neck. The present model extends the JG theory, which was applied only to the right-hand side (RHS) of the FLD. The main difference in treating the two different sides of the FLD lies in the assumptions regarding the width direction deformations. For biaxial stretching (the RHS), the minor strain rate is assumed to be homogeneous throughout the process. However, for the left-hand side (LHS) of the FLD in the critical cross section, the minor strain rate is taken to be proportional to major strain rate. This is a critical difference from the JG approach and permits the LHS to be computed with good accuracy. Another important difference between this and the JG analysis is a more realistic neck geometry. At the inception of phase III, JG matched the phase II sheet thickness at the center of the neck, that is, at its minimum cross section. Here, the phase III neck matches the phase II sheet thickness at its ends, that is, at its maximum cross section. Although this may seem a minor point, it greatly improves the geometrical concept involved. Both the actual neck geometry and the criterion for determining the limit strain are modified from the earlier analysis in order to agree more closely with actual press shop practice. Results from this analysis are compared with the experimental ones for aluminum-killed (AK) steel and three aluminum alloys. These results are also compared to other theoretical calculations of the forming limit for AK steel. It is apparent that the present model is best. Unlike the other types of analyses, the present model predicts the limiting strain states for several materials very accurately without any adjustable parameters. This is certainly an unprecedented result. Using the mathematical model, the effects of varying material properties are studied. The properties considered are the strain-hardening exponent,n, the strain-rate sensitivity parameter,m, and the plastic anisotropy ratio,r, The important influence of these material properties upon the formability (level of the FLD) is affirmed.     

Influence of limit stress states and yield criteria on the prediction of forming limit strains in sheet metals

Several researchers have proposed analytical methods for predicting the forming limit curve (FLC), which has been successfully used as a diagnostic tool in sheetmetal forming. However, these approaches lack ease of adaptability to various situations and also involve considerable complexity. Sing and Rao proposed a new FLC modeling approach based on limit stress states derived from yield criterion and material properties from a simple tensile test. The first aspect of this study addresses the influence of the shape of the forming limit stress curve (FLSC) upon the FLC. The FLC modeled from a singly linear FLSC exhibits good agreement with the experimental curve, unlike those modeled from an elliptical or a piecewise linear FLSC. It is, thus, established that a linearized limit stress locus describes adequately the actural localized neck condition for the materials chosen in this study. Second, the study focuses on the suitability of the different cases of Hill’s yield criterion for satisfactory prediction of FLCs. The FLCs predicted using different cases of Hill’s criterion are compared with experimental FLCs in the case of steel and copper. Different cases of Hill’s criterion provide a wider choice for FLC modeling for different classes of materials. The sensitivity of Hill’s stress exponent is also thoroughly explored for achieving a close correspondence between the predicted and experimental FLCs.     

Finite element modeling simulation of in-plane forming limit diagrams of sheets containing finite defects

Finite element modeling (FEM) has been used to predict forming limit diagrams (FLDs) of thin sheets based on two-dimensional (2-D) finite thickness defects. The local growth of these defects is simulated until an arbitrary failure criterion is reached. Many aspects of this simulation re-produce the standard Marciniak-Kuczynski (M-K) results. For example, the plane strain intercept, FLD₀, is sensitive to the material work hardening,n, and the strain rate sensitivity,m, but is not affected by the normal anisotropy,r. The positive side of the FLD was characterized by a line of logarithmic slopeP. The value ofP decreases sharply asn andm increase. The effect ofr depends on the choice of yield function. The absolute location of the FLD, as given by the FLD₀, depends not only on the material properties, but also on the choice of failure criterion, defect geometry, and details of the simulative model (mesh size, number of defect dimensions,etc.). This is true of any measurement or simulation of the FLDs. Therefore, we propose that the FLD₀ be used as the single “fitting parameter” between modeling and experimental results: a more realistic approach based on what is actually measured in the FLD experiments. This method allows clarification of the role of material plasticity properties(e.g.,n, m, andr) vs fracture properties (contained in the FLD₀) in determining the shape of the FLDs.     

基于有限元极限平衡法的三维边坡稳定性

提出了一种基于有限元弹塑性应力场和极限平衡状态的三维边坡稳定分析方法——三维有限元极限平衡法。首先,考虑三维空间中滑动方向,提出滑动面上一点在滑动方向上的极限平衡条件,并证明滑动面上土体整体达到极限平衡状态与滑动面上土体各处在滑动方向上处于极限平衡状态等价。再通过刚体极限平衡假定计算主滑方向和滑动面上各点滑动方向。最后,定义局部安全系数为抗剪强度与滑动方向上剪应力投影的比值,基于三维边坡整体极限平衡条件将局部安全系数通过积分中值定理转变为整体安全系数。该方法计算简单,消除了剪应力比形式定义安全系数滑动面形状限制,具备合理性与有效性。算例验证结果表明,该方法滑动方向假设合理,安全系数与严格三维极限平衡法结果一致。      

基于有限元法异型坯动态二冷控制模型开发与应用

建立了异型坯连铸凝固传热数学模型,并利用有限元法进行离散求解.在此基础上开发了异型坯连铸动态二冷控制模型,模型以5s为周期动态计算整个铸坯实时温度场,并采用有效拉速和表面目标温度法对二冷水量进行设定和优化.用可视化编程工具Visual C++6.0编制了异型坯连铸动态二冷控制系统.在相同工况情况下,动态二冷控制系统仿真结果与大型商业软件Marc计算结果一致,可用于在线控制或异型坯连铸二冷工艺离线设计优化.     

The effects of strength ratio on the forming limit diagram of tailor-welded blanks

In the present study, the influences of strength ratio (SR) are studied on the formability and forming limit diagram (FLD) of tailor-welded blanks (TWBs). AISI 340, St 12 and St 14 steel sheets with equal thickness of 1?mm were used as different kinds of steel to make TWB with different SR. TWBs were obtained by CO₂ laser welding of different steel sheets. Limit strength ratio (LSR) is introduced as a new useful factor to predict the FLD of TWB with different SR. Results of this research show that with increasing of difference of TWB’s SR and LSR, formability and the level of FLD will decrease. By SR increasing, limit dome height decreases and some defects such as weld line movement increase. The experimental findings show that the SR of TWB can effect on the position of fracture in the TWB products.     

Development and validation of a three-dimensional finite element model of the pelvic bone

Due to both its shape and its structural architecture, the mechanics of the pelvic bone are complex. In Finite Element (FE) models, these aspects have often been (over)simplified, sometimes leading to conclusions which did not bear out in reality. The purpose of this study was to develop a more realistic FE model of the pelvic bone. This not only implies that the model has to be three-dimensional, but also that the thickness of the cortical shell and the density distribution of the trabecular bone throughout the pelvic bone have to be incorporated in the model in a realistic way. For this purpose, quantitative measurements were performed on computer tomography scans of several pelvic bones, after which the measured quantities were allocated to each element of the mesh individually. To validate this FE model, two fresh pelvic bones were fitted with strain gages and loaded in a testing machine. Stresses calculated from the strain data of this experiment were compared to the results of a simulation with the developed pelvic FE model.     

热轧机有限元与神经网络集成建模

以某钢厂1580热连轧生产数据为基础,提出一种有限元与神经网络集成建模的方法.该方法首先对轧制过程的塑性变形进行有限元建模,然后结合有限元数值分析方法和智能技术的优点,实现有限元和神经网络的集成建模.集成模型中的神经网络模型为有限元模型提供参数调整的依据,并且在神经网络训练过程中使用改进的混沌粒子群优化算法对神经网络进行优化.通过与现场实际生产数据进行比较,验证了该模型的有效性.     

A finite element model of a persistent slip band based upon electron microscopic evidence

The initial stage of the fatigue process is the formation of persistent slip bands (psb’s). Recently, it was discovered that psb’s in large grains of an aluminum alloy elongate at a constant rate. This report describes a new model of a psb which accounts for this result. It is proposed that the material within a psb has a wide variation in yield strength: it is very small near the tip, but increases with distance from the tip reaching a maximum value at the initiatory site. This distribution results from softening of the matrix near the tip of the psb due to precipitate dispersal, followed by cyclic hardening of the softened material. The material parameters describing this distribution are based upon microstructural information contained in electron micrographs. Finite element calculations of the strain field show that the plastic strains in the matrix, in a small damage zone near the tip of a psb, are independent of the length of the psb, as required for a constant rate of elongation. Furthermore, the absolute values of plastic strain are consistent with the observed growth rates, while the calculated strains within the psb are in excellent agreement with interferometric data.     

Role of yield criteria and hardening laws in the prediction of forming limit diagrams

Forming limit diagrams (FLDs) are calculated based on an extension of previous analyses by Jones and Gillis,^[1] Choi et. al. ^[2] and Pishbin and Gillis.^[3] They considered the plastic behavior of sheet metals in three deformation phases using a generalized flow law and using the commonly used power hardening law to describe the stress-strain behavior. In the present study, however, the yield criterion proposed by Hosford is used in conjunction with both power-law and Voce material constitutive equations to develop a model. This model is capable of predicting the forming limit strains achievable during sheet metal forming operations for sheets having planar isotropy. The predictions from Voce and power-law equations have been compared with the experimental forming limits determined by hemispherical punch stretching of gridded blanks of AA3105 and AA8011 aluminum alloys. The results indicate good prediction of limit strains for the two alloys when the Voce equation is applied.     

基于刚塑性模型的钨基合金喂料螺杆挤压成形有限元仿真及工艺优化

钨基合金喂料的螺杆挤压具有可生产直径较大,挤压比较大,且生产效率高等优点。利用Deform-3D软件,通过采用刚塑性模型对钨基合金喂料在挤压温度为60℃、70℃、80℃和挤压速度为3 mm/s、5 mm/s、7 mm/s的挤压条件下进行有限元模拟,分析了每种条件下速度场、温度场、损伤及应力场变化,并将最优结果与螺杆挤压实验相验证。结果表明:在挤压温度为70℃,挤压速度为5 mm/s下,得到直径为30 mm的棒坯表面光亮无缺陷;模拟结果与实验结果吻合。     

Three-dimensional finite element analysis of powder compaction process for forming cylinder block of hydraulic pump

Abstract

A three-dimensional finite element analysis of a powder compaction process was undertaken to determine the optimum manufacturing conditions for the complex cylinder block found in the hydraulic pump of an excavator. A porous material model was used to ascertain the material behaviour. The finite element predictions for both the density distribution and compaction load were in good agreement with experimental results.     

A finite element method on the basis of texture components for fast predictions of anisotropic forming operations

This paper introduces a novel method of including and updating texture‐based elastic‐plastic anisotropy during large‐strain metal forming operations. The approach is particularly designed for industrial use since it can be assembled by integrating existing software solutions from crystallography and variational mathematics. The approach is based on feeding spherical crystallographic texture components directly into a non‐linear finite element model. The method is used to perform fast simulations of industrial‐scale metal forming operations of textured polycrystalline materials including texture update. Instead of yield surface concepts or large sets of discrete grain orientations, a small set of discrete and mathematically compact Gaussian texture components was used to map the orientation distribution function discretely onto the integration points of a viscoplastic crystal plasticity finite element model. This method drastically enhances the computing speed and precision compared to previous crystal plasticity finite element approaches. The publication gives a brief overview of the different anisotropy concepts, provides an introduction to the new texture component crystal plasticity finite element method, and presents examples.     

一种基于深度神经网络的烧结料层透气性预报模型

为了保证整个烧结生产过程的顺利进行,通过对承钢2号烧结厂数据库中的数据进行采集、整合和预处理,运用相关性分析筛选出与料层透气性相关的重要特征变量,基于深度神经网络算法建立料层透气性预报模型,以即时为现场操作人员提供科学的操作指导。通过测试并与随机森林模型、支持向量机模型进行性能对比,结果表明,深度神经网络具有很好的预测效果,可实现对料层透气性的精准预测,对优化烧结现场的操作效果具有很好的指导意义。     

Analysis of synaptic transmission in the neuromuscular junction using a continuum finite element model

There is a steadily growing body of experimental data describing the diffusion of acetylcholine in the neuromuscular junction and the subsequent miniature endplate currents produced at the postsynaptic membrane. To gain further insights into the structural features governing synaptic transmission, we have performed calculations using a simplified finite element model of the neuromuscular junction. The diffusing acetylcholine molecules are modeled as a continuum, whose spatial and temporal distribution is governed by the force-free diffusion equation. The finite element method was adopted because of its flexibility in modeling irregular geometries and complex boundary conditions. The resulting simulations are shown to be in accord with experiment and other simulations.     

A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures

A three-dimensional (3-D) model for the prediction of dendritic grain structures formed during solidification is presented. This model is built on the basis of a 3-D cellular automaton (CA) algorithm. The simulation domain is subdivided into a regular lattice of cubic cells. Using physically based rules for the simulation of nucleation and growth phenomena, a state index associated with each cell is switched from zero (liquid state) to a positive value (mushy and solid state) as solidification proceeds. Because these physical phenomena are related to the temperature field, the cell grid is superimposed to a coarser finite element (FE) mesh used for the solution of the heat flow equation. Two coupling modes between the microscopic CA and macroscopic FE calculations have been designed. In a so-called “weak” coupling mode, the temperature of each cell is simply interpolated from the temperature of the FE nodes using a unique solidification path at the macroscopic scale. In a “full” coupling mode, the enthalpy field is also interpolated from the FE nodes to the CA cells and a fraction of solid increment is computed for each mushy cell using a truncated Scheil microsegregation model. These fractions of solid increments are then fed back to the FE nodes in order to update the new temperature field, thus accounting for a more realistic release of the latent heat (i.e., the solidification path is no longer unique). Special dynamic allocation techniques have been designed in order to minimize the computation costs and memory size associated with a very large number of cells (typically 10⁷ to 10⁸). The potentiality of the CAFE model is demonstrated through the predictions of typical grain structures formed during the investment casting and continuous casting processes.