21-6-9高强不锈钢管数控弯曲回弹的理论计算及有限元分析

为了研究几何参数和材料参数对回弹的影响,基于弹塑性理论推导了最终弯曲半径和回弹角度的近似计算公式,结合有限元模拟,分析几何参数和材料参数对21-6-9高强不锈钢管材数控弯曲回弹规律的影响,并对理论解析、有限元模拟和试验结果进行对比。结果表明：最终弯曲半径随着弯曲半径、强度系数的增大或弹性模量、硬化指数的减小而增大,且与弯曲角度无关;回弹角度随着弯曲角度、相对弯曲半径、强度系数的增大或弹性模量、硬化指数的减小而增大;有限元模拟结果和试验结果吻合良好,能够较精确地预测回弹;理论解析与试验结果对比误差较大,但能够反映回弹角的变化趋势。     

基于包辛格效应的回弹仿真分析

金属材料在一个方向上的应变硬化降低了反方向的屈服强度,材料包辛格效应的存在对车身成形仿真精度产生了重要影响,尤其现今高强钢和铝合金的大量应用,使车身成形件的回弹问题日益突出,车身模具制造对有限元回弹预测的准确性提出更高的要求。为了提高回弹的仿真精度有必要对材料的包辛格效应进行研究,利用一套夹具对DC06和DP600两种材料的薄板进行拉伸压缩试验,获得不同预应变下的位移加载曲线,通过拉伸压缩试验结果与仿真结果的对比分析,得到能反映材料包辛格效应的非线性混合硬化模型材料参数。开展U形件成形试验,并建立试验的仿真模型,计算DC06和DP600薄板的U形件成形回弹量,分析等向强化、混合强化和随动强化本构模型对回弹预测精度的影响,针对回弹仿真结果和试验结果的差别,对影响仿真精度的材料模型因素进行分析。结果表明,DC06和DP600的包辛格效应大小存在差别,考虑包辛格效应有助于回弹仿真精度的提高,但小曲率弯曲成形回弹计算对材料本构模型的敏感性,限制了回弹仿真精度的提高。     

On the modelling of the bending-unbending behaviour for accurate springback predictions

The prediction of springback is probably the area in sheet forming simulation where the least success has been achieved in terms of solution accuracy. The springback is caused by the release of residual stresses in the workpiece after the forming stage. An accurate prediction of residual stresses puts, in turn, high demands on material modeling during the forming simulation. Among the various ingredients that make up the material model, the hardening law is one of the most important ones for an accurate springback prediction. The hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behaviour, and permanent softening. The complexities of existing hardening laws do of course vary within quite wide ranges. One of the purposes of the present study was to try to identify a model of reasonable complexity that at the same time can fulfill the requirements concerning accuracy. Five different hardening models have been evaluated in the present investigation. The simplest model, the isotropic hardening one, involves only one history variable, while the most advanced model involves ten history variables and four additional material parameters. In the current report, results for four different materials will be accounted for. The kinematic hardening parameters have been determined by inverse modeling of a three-point bending test. A response surface method has been used as an optimization tool, together with a finite-element model of the bending test set-up. The springback of a simple U-bend has been calculated for one of the materials, and from the results of these simulations some conclusions regarding the choice of hardening law are drawn.     

Finite element simulation of springback for a channel draw process with drawbead using different hardening models

The objective of this work is to predict the springback of Numisheet’05 Benchmark#3 with different material models using the commercial finite element code ABAQUS. This Benchmark consisted of drawing straight channel sections using different sheet materials and four different drawbead penetrations. Numerical simulations were performed using Hill's 1948 anisotropic yield function and two types of hardening models: isotropic hardening (IH) and combined isotropic-nonlinear kinematic hardening (NKH). A user-defined material subroutine was developed based on Hill's quadratic yield function and mixed isotropic-nonlinear kinematic hardening models for both ABAQUS-Explicit (VUMAT) and ABAQUS-Standard (UMAT). The work hardening behavior of the AA6022-T43 aluminum alloy was described with the Voce model and that of the DP600, HSLA and AKDQ steels with Hollomon's power law. Kinematic hardening was modeled using the Armstrong-Frederick nonlinear kinematic hardening model with the purpose of accounting for cyclic deformation phenomena such as the Bauschinger effect and yield stress saturation which are important for springback prediction. The effect of drawbead penetration or restraining force on the springback has also been studied. Experimental cyclic shear tests were carried out in order to determine the cyclic stress-strain behavior. Comparisons between simulation results and experimental data showed that the IH model generally overestimated the predicted amount of springback due to higher stresses derived by this model. On the other hand, the NKH model was able to predict the springback significantly more accurately than the IH model.     

An energy approach for predicting springback of metal sheets after double-curvature forming, Part I: axisymmetric stamping

In our previous study (Xue P, Yu TX, Shu E. International Journal of Materials Processing Technology 1999; 89-90:65-71.), based on the membrane theory of shells of revolution and an energy method a mechanics model and corresponding analytical procedure have been proposed to predict springback of circular and square metal sheets after a double-curvature forming operation. The strain hardening of the material is incorporated into the mechanics model. In the present paper, the method is extended to the cases, in which bending effect, as well as bending-and-unbending effect are taken into account. It is shown that the procedure developed is capable of quantitatively predicting the strain distribution and springback of metal sheets after axisymmetric stamping with a relatively minor effort of calculation and a good accuracy. The effect of stretching force applied at the edge of the plate on springback is also considered. Excellent agreement is found between the theoretical prediction of springback and experiment results.     

Numerical simulation of the effects of elastic anisotropy and grain size upon the machining of AA2024

Turning modeling and simulation of different metallic materials using the commercially available Finite Element (FE) softwares is getting prime importance because of saving of time and money in comparison to the costly experiments. Mostly, the numerical analysis of machining process considers a purely isotropic behavior of metallic materials; however, the literature shows that the elastic crystal anisotropy is present in most of the ‘so-called’ isotropic materials. In the present work, the elastic anisotropy is incorporated in the FE simulations along with the effect of grain size. A modified Johnson-Cook ductile material model based on coupled plasticity and damage evolution has been proposed to model the cutting process. The simulation results were compared with experimental data on the turning process of Aluminum alloy (AA2024). It was found that the elastic anisotropy influences the average cutting force up to 5% as compared to the isotropic models while the effect of grain size was more pronounced up to 20%.     

Shakedown analysis of beams using nonlinear kinematic hardening materials coupled with continuum damage mechanics

The nonlinear kinematic hardening theory of plasticity based on the Armstrong-Fredrick model and isotropic damage was used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. Damage and inelastic deformation were incorporated and they were used for the beam shakedown and ratcheting analysis. The beam material was assumed to follow the nonlinear strain hardening property coupled with isotropic damage. The effect of the damage phenomenon coupled with the elastoplastic nonlinear kinematic hardening was studied for deformation and load control loadings. The Bree's diagram was obtained for two different types of loading, and all numerical results confirmed the reduction of the safe loading domain due to material damage.     

Optimisation of springback in bending processes using FEM simulation and response surface method

The aim of this work includes the springback optimisation of bending processes using the concept of experimental design and response surface methodology (RSM). The optimisation method includes two phases. The first involves the objective function prediction using design of experiments and response surface method, while the second is an optimisation process using a FORTRAN gradient algorithm. Springback of sheet parts during bending processes is simulated using finite element model (FEM) including damage evolution effects within the sheet. The numerical simulation of the damage evolution has been modelled by means of continuum damage approach. The Lemaitre damage model, taking into account the influence of triaxiality, has been implemented into ABAQUS/Standard code in order to predict the external fibres rupture evolution during the process and the material characteristics changes after bending. The simulation included die corner radius and punch-die clearance as the main variables.     

Numerical modelling of cyclic plasticity and fatigue damage in cold-forging tools

Industrial cold-forging tools with complex geometry are very likely to be exposed to local plastic deformation near stress concentrating details. The accumulation of plastic deformation resulting from the cyclic loading conditions leads to fatigue damage and eventually to generation of a crack in the surface of the die. To study the effect of die prestressing on fatigue damage development, a plane strain finite element model of a cold-forging die is analysed. A complex material model, combining kinematic and isotropic hardening with continuum damage mechanics, is used to simulate the elastic–plastic material behaviour and damage development. Furthermore, a range of uncoupled damage measures are applied in the comparison of conventional and new prestressing concepts.     

Springback prediction of the vee bending process for high-strength steel sheets

The precise prediction of springback is a key to assessing the accuracy of part geometry in sheet bending. A simplified approach is developed by considering the thickness ratio, normal anisotropy, and the strain-hardening exponent to estimate the springback of vee bending based on elementary bending theory. Accordingly, a series of experiments is performed to verify the numerical simulation. The calculation of the springback angle agrees well with the experiment, which reflects the reliability of the proposed model. The effects of process parameters such as punch radius, material strength, and sheet thickness on the springback angle are experimentally tested to determine the dominant parameters for reducing the springback angle in the sheet bending process for high-strength steel sheets. Moreover, the effects of the thickness ratio, normal anisotropy, and the strain-hardening exponent on the springback angle in the vee bending process for high-strength steel sheets are theoretically studied. Therefore, improving understanding on and control of the springback reduction of the vee bending process in practical applications is possible.     

3D FE modelling of high-speed ball nose end milling

The paper details research and development of a Lagrangian-based, 3D finite element (FE) model to simulate the high-speed ball nose end milling of Inconel 718 nickel-based superalloy using the commercial FE package ABAQUS Explicit. The workpiece material was modelled as elastic plastic with isotropic hardening and the flow stress defined as a function of strain, strain rate and temperature. Workpiece material data were obtained from uniaxial compression tests at elevated strain rates and temperatures (up to 100/s and 850°C, respectively) on a Gleeble 3500 thermo-mechanical simulator. The data were fitted to an overstress power law constitutive relationship in order to characterise flow behaviour of the material at the level of strain rates found in machining processes (typically up to 10⁵/s). Evolution of the chip was initially seen to progress smoothly, with the predicted machined workpiece contour showing good correlation with an actual chip profile/shape. Cutting force predictions from the FE model were validated against corresponding experimental values measured using a piezoelectric dynamometer, while modelled shear zone/chip temperatures were compared with previously determined experimental data. The model was successful in predicting the forces in the feed and step-over direction to within 10% of corresponding experimental values but showed a very large discrepancy with the thrust force component (～90%). Modelled shear-plane temperatures calculated at the point of maximum cutting force were found to demonstrate very good agreement with measured values, giving a discrepancy of ～5%. The simulation required a computational time of approximately 167 h to complete one full revolution of the ball end mill at 90 m/min cutting speed.     

Comparison between Gurson and Lemaitre damage models in wiping die bending processes

This paper is devoted to a finite element prediction of material damage distribution within the workpiece during wiping die bending processes. The damage mechanics approach has been used in this investigation in order to describe the progressive damage evolution within the sheet. A comparative study between the results obtained by the simulations using the Lemaitre and Gurson damage models is presented and discussed. The elastoplastic constitutive laws are integrated by means of an incremental formulation which has been implemented in the finite element code ABAQUS. The punch load, influenced by the friction coefficient, is investigated for different cases of die radius. The springback angle, which depends on the elastic properties of the material, is computed for all cases. Both models give similar results in the modelling of bending operations. The Gurson one is shown to have more flexibility for applications.     

Modelling of kinetic friction in V-bending of ultra-high-strength steel sheets

The Stribeck friction model was investigated in this study to predict springback of high-strength steel sheets. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The plane-strain bending process is simulated in ABAQUS/Standard. The influence of forming speed, over-pressing and holding time on springback behaviour of sheets was studied numerically. By plotting the variation of bending angle with punch stroke, we found that the loading curve of finite element analysis showed similar results to the experiments. The unloading curves of FE analysis with friction models based on Stribeck curve and Coulomb law showed good agreement with experiments with error less than 1.5%. Forming speed of up to 50 mm/s does not have significant effect on springback. The effect of holding time on reducing springback is small, but over-press has large effect on reducing springback. The results showed that Stribeck model is suitable for sheet metal forming simulations, especially at higher forming speeds and pressures.     

Position deviation in V-die bending process with asymmetric bend length

Novel finite element analyses and a series of experiments are performed to clarify basic characteristics of high-strength steel sheet metal during fabrication by asymmetric V-die bending processes. The proposed strategy for elastic–plastic FE simulation is used to simulate asymmetric V-die bending process to test its viability for friction contact processes. Accordingly, a series of experiments is performed to verify the numerical simulation. The calculation agrees well with the experiment. The effects of process parameters such as lubrication (contact friction), material properties, and process geometries on position deviation in bending point were experimentally tested to determine the dominant parameters for minimizing position deviation in sheet metal bending processes. Moreover, springback phenomenon is also discussed to minimize bending defects and to obtain a precise asymmetric bent component. This study could be used as a process design guideline for asymmetric bending of high-strength steel sheets.     

10CrMo910钢的疲劳损伤演变与寿命估算

对在周期加载条件下运行的锅炉、压力容器、压力管道等设备,不可避免地产生低周疲劳的失效。本文从损伤力学基本理论出发,以10CrMo910钢作为研究对象,采用应力幅法测量材料的低周疲劳损伤,提出了低周疲劳各向同性连续损伤模型,在有效应力和应变等价假设基础上建立了低周疲劳损伤演变和寿命估算式。     

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.     

Springback evaluation in hot v-bending of Ti-6Al-4V alloy sheets

In this paper, v-bending of Ti-6Al-4V alloy sheet was conducted from room temperature to 850 °C at a fixed velocity of 0.1 mm/s. Punches with punch radii of 1, 2, 4, and 6 mm, as well as several holding times were used. V-bending and springback behaviors were numerically analyzed with an isotropic hardening model that considered rate-dependent effects. Using a punch radius of 1 mm always leads to negative springback in the temperature range of 550–750 °C. This behavior occurs because an arc formed in the transition side near the end of bending and flattened at the end of bending, leading to an internal bending moment which causes specimen to bow inward after unloading. At a punch radius of 2 mm, positive springback occurs at 300–650 °C, while negative springback occurs at 700–750 °C. At punch radii of 4 and 6 mm, positive springback occurs at 600–750 °C, and the angle decreases as temperature increases. At 850 °C, negative springback occurs at a punch radius of 4 mm due to the decrease in yield strength. At a punch radius of 1 mm, cracking occurs at room temperature and 500 °C, while at 2 mm, it occurs only at room temperature. This discrepancy is ascribed to the greater plastic deformation caused by the smaller punch. As holding time increases, the shape of the deformed specimen more closely matches the desired shape.     

两种强化模型在拉伸筋阻力计算中的比较

将等向强化模型与运动中化模型分别引入逐级更新Ｌａｇｒａｎｇｅ有限元列式,采用八节点平面 应变单元,对拉伸筋阻力进行了数值计算,并将两种模型的计算结果进行了比较与讨论,运动强化模型更好地反映了板料在拉伸筋处的弯曲反弯过程,可以更准确地预测拉伸筋阻力。     

Parameter study for the finite element modelling of long bones with computed-tomography-imaging-based stiffness distribution

Four radii of different horses were tested in three-point bending and in pure torsion. Detailed finite element (FE) models of these long bones were established by means of computed-tomography (CT) images and tests simulated for both load cases. For the allocation of the local isotropic material stiffness, individual exponential functions were applied whose factor and exponent were determined solely by fitting them to the measured torsional stiffness and bending stiffness of the entire bones. These stiffness functions referring directly to the CT number and having exponents between 1.5 and 2 were in good agreement with Young's moduli subsequently measured from small samples cut from the investigated bones. Based on a model with local orthotropic material definition, an additional parameter study was conducted to verify the sensitivities of the FE analysis results on single variations in the orthotropic elastic constants. This study revealed that the bending test simulations could be enhanced by substantial reduction in Young's moduli in the directions perpendicular to the bone axis; thus, orthotropic material definition is preferable for the FE analysis of long bones.