Finite element analysis of forming limit in bore expanding of aluminium alloy sheets

Summary A recently proposed method to predict the forming limit of sheet metals is applied to the problem of bore expanding. Axisymmetric bore-expanding processes of various aluminium alloy sheets are simulated by the rigid-plastic finite element method. From the calculated histories of stress and strain, the forming limit, i.e. the fracture initiation, is predicted by means of the ductile fracture criterion. The comparison with the experimental results shows that the fracture initiation site and the critical punch stroke are successfully predicted by the present approach. Received 23 February 1998; accepted for publication 12 May 1998     

Vibration analysis of a circular disk tensioned by rolling using finite element method

Summary The paper proposes a method in finite element analysis for estimating natural frequencies of a disk tensioned by rolling, without the use of eigenvalue analysis. The natural frequencies of a disk vary when the localized plastic deformation caused by roll-tensioning induces residual stresses. Tensioning is used for improving the dynamic stability of circular saws; the optimal condition of rolling can be predicted from natural frequency characteristics. In the proposed method, the natural frequencies after rolling are easily estimated from the mode shapes of the disk before rolling and the stress distribution after rolling. The method is based on ideas similar to thermal stress and sensitivity analysis rather than on eigenvalue analysis. The effectiveness of the method is shown by comparing the natural frequency characteristics obtained by this method with those by eigenvalue analysis. Received 18 June 1998; accepted for publication 8 April 1999     

厚板热轧中心气孔缺陷压合临界力学条件的证明与应用

利用上界三角形速度场推导了热轧条件下厚板中心气孔缺陷压合时内部缺陷开裂的判定条件。证明了动态临界几何条件当l／h≥0．518时坯料为压合轧制；当给定轧件入口厚度时，增加道次压下率ε、轧辊半径R、单位宽度轧制力P，将有利于厚板缺陷压合；升温和咬入时加后推力也有利于缺陷压合。此外，还提供实例首次对厚板压下规程的压合条件进行了分析计算，算例表明：特厚板轧制设计道次压下率时，应尽量使道次变形区不存在拉应力区、满足压合条件并避免表面变形，方能使中心区域有效压合，起到提高探伤合格率及改善内部质量的明显效果。本文提出了制定厚板轧制规程需考虑缺陷压合条件的新思路。     

A complete three-dimensional finite element analysis of the bar-bar tensile impact apparatus

A complete three-dimensional FEM model of the Bar-Bar Tensile Impact Apparatus (BTIA) is constructed, in which the slots in the bars and the glue layers between the bars and the flat-shaped specimen are included. For elastic-plastic specimen material, Ly12cz aluminum alloy, the process of tensile impact experiments is simulated and the matching relation between the specimen geometry and the bars is investigated. Based on the FEM analysis, an iterative method is proposed to design a reasonable specimen geometry for obtaining the true dynamic stress-strain relation for a certain specimen material. The project supported by the National Natural Science Foundation of China (19272061)     

Measurement of deformation gradients in hot rolling of AA3004

In this paper we describe an experimental technique developed to measure the deformation gradients and temperature in a single hot rolling pass of an AA3004 sample that was fitted with an insert. The insert had been previously hand engraved with a 1×1 mm grid pitch, and the analysis of the data digitally captured from the image of the deformed grid enabled the calculation of the components of the deformation gradient tensor. Four steel pins prevented relative motion between the insert and the rest of the sample. No detachment was observed between insert and sample after rolling. The temperature was measured during rolling using two embedded thermocouples, one close to the surface and the other in the centerline. The commercial finite element code ABAQUS was used to create a three-dimensional model of the rolling process. The recorded temperature was compared to the numerical values evaluated after tuning the heat transfer coefficient. The shape of the grid after rolling was checked against the deformed mesh using different fricition coefficients in order to obtain the optimum match. The unusually large length of the insert enabled the rolling process to be stopped halfway so that a picture of the roll-gap area could be obtained. This provided a partially deformed grid that represented the transient state during rolling. The experimentaily determined deformation gradient in this area as well as in the steady-state area agreed well with the finite element oredictions.     

齿轮接触有限元分析

通过接触仿真分析研究了通用接触单元在轮齿变形和接触应力计算中的应用。建立了一对齿轮接触仿真分析的模型，并使用新的接触单元法计算了轮齿变形和接触应力，与赫兹理论比较，同时也计算了摩擦力对接触应力的影响。计算分析了单元离散、几何、边界范围与加载或约束处理方式的误差，建立了一个计算轮齿变形和接触应力的标准，说明了新的接触单元法的精确法、有效性和可靠性。     

Finite element simulations on the mechanical properties of MHS materials

Finite element simulations are carried out to examine the mechanical behavior of the metallic hollow sphere (MHS) material during their large plastic deformation and to estimate the energy absorbing capacity of these materials under uniaxial compression. A simplified model is proposed from experimental observations to describe the connection between the neighboring spheres, which greatly improves the computation efficiency. The effects of the governing physical and geometrical parameters are evaluated; whilst a special attention is paid to the plateau stress, which is directly related to the energy absorbing capacity. Finally, the empirical functions of the relative material density are proposed for the elastic modulus, yield strength and plateau stress for FCC packing arrangement of hollow spheres, showing a good agreement with the experimental results obtained in our previous study. The project supported by the Hong Kong Research Grant Council (RGC) (HKUST 6079/00E) and the National Natural Science Foundation of China (10532020).     

滚压强化的残余应力的数值仿真及工艺分析

表面滚压强化,由于在表层引起加工硬化和残余压应力,可以十分有效地提高构件、零件疲劳强度,而滚压强化的有限元数值仿真,将成为分析优化滚压强化工艺的重要手段.本文建立了连续多、圈滚压工艺的有限元数值仿真模型,获得了比较合理的滚压变形与残余应力结果.在此基础上对滚压工艺做了进一步分析.结果表明,滚压变形的进给量太大.滚压的转速太快都容易造成工件表层残余应力分布的不均匀甚至形成残余拉应力;在滚压与未滚压的过度区域,从表面到心部的近1mm范围内,均未出现人们通常所担心的残余拉应力.这将在工程生产实践中,为滚压工艺制订提供重要的依据.     

Finite element simulation on the mechanical properties of MHS materials

Finite element simulations are carried out to examine the mechanical behavior of the metallic hollow sphere (MHS) material during their large plastic deformation and to estimate the energy absorbing capacity of these materials under uniaxial compression. A simplified model is proposed from experimental observations to describe the connection between the neighboring spheres, which greatly improves the computation efficiency. The effects of the governing physical and geometrical parameters are evaluated; whilst a special attention is paid to the plateau stress, which is directly related to the energy absorbing capacity. Finally, the empirical functions of the relative material density are proposed for the elastic modulus, yield strength and plateau stress for FCC packing arrangement of hollow spheres, showing a good agreement with the experimental results obtained in our previous study.     

Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material

Three-dimensional finite element analysis was used to study the effect of the angle between the loading direction and the axisymmetric direction on the indentation behavior of a transversely isotropic piezoelectric half-space by a cylindrical indenter of flat end. Two cases were considered in the analysis, which included (a) the indentation by an insulating indenter, and (b) the indentation by a conducting indenter. Both the indentation load and the indentation-induced potential were found to be proportional to the indentation depth. Using the simulation results and the analytical relationship for the indentation by a rigid, insulating indenter, semi-analytical relationships were developed between the indentation load and the indentation depth and between the indentation-induced potential on the indenter and the indentation depth for the conducting indenter, respectively. The proportionality between the indentation-induced potential and the indentation depth is only a function of the angle between the loading direction and the poling direction, independent of the type of indenters, which may be used to measure the relative direction of the loading axis to the axisymmetric axis of transversely piezoelectric materials from the indentation test.     

Finite element analysis of the dynamic response of clamped sandwich beams subject to shock loading

The finite element (FE) method is employed to analyse the response of clamped sandwich beams subject to shock loadings. Pressure versus time histories representative of shock loadings are applied uniformly to the outer face of the sandwich beam; an impulse applied uniformly to the outer face of the sandwich beam is shown to model adequately shock loadings. Material elasticity and strain hardening representative of structural steels have only a minor effect upon the beam response. Further, the magnitude of the compressive strength of the core has only a limited influence upon the dynamic response of the sandwich beam for the representative range of core strengths considered. The FE results for the deflections and structural response time agree well with the rigid ideally-plastic analytical predictions of Fleck and Deshpande (J. Appl. Mech. (2003), in press).     

Finite element analysis of tire traveling performance using anisotropic frictional interaction model

The traveling performance of off-the-road vehicles, such as construction machinery and exploration rovers, significantly depends on the interaction between the ground and the traveling mechanism, since inelastic ground deformation and frictional sliding phenomena are induced by the vehicle’s movement. In general, a tread surface causes anisotropic frictional interaction behavior on a macroscopic scale. In this study, an acceptable frictional interaction model was implemented to finite element method to rationally examine the anisotropic frictional interaction behavior between the tire and the ground. Finite element analysis of the single tire traveling performance, including certain slippage and side slip (skid), was then carried out to examine the effect of the anisotropic frictional interaction on the numerical results for the drawbar-pull and side force.     

钨球侵彻LY-12铝合金靶板的有限元分析

介绍了利用LS-DYNA进行球形破片侵彻靶板的网格划分方法,确定了钨球破片和LY-12铝合金的材料模型,利用不同尺寸的球形破片对不同厚度的靶板进行了仿真分析,得出了不同情况下破片对靶板的穿透曲线图、正向跳飞曲线图和破片穿透靶板时的临界入射角和正向跳飞时的临界入射角,并对破片的剩余速度和末角度进行了分析。     

Finite element analysis of thermo-elastic behavior of piezoelectric structures under finite deformation

It is noted that the behavior of most piezoelectric materials is temperature dependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in the case of finite deformation. On the other hand, for the purpose of precise shape and vibration control of piezoelectric smart structures, their deformation under external excitation must be ideally modeled. This demands a thorough study of the coupled piezo-thermo-elastic response under finite deformation. In this study, the governing equations of piezoelectric structures are formulated through the theory of virtual displacement principle and a finite element method is developed. It should be emphasized that in the finite element method the fully coupled piezo-thermo-elastic behavior and the geometric non-linearity are considered. The method developed is then applied to simulate the dynamic and steady response of a clamped plate to heat flux acting on one side of the plate to mimic the behavior of a battery plate of satelite irradiated under the sun. The results obtained are compared against classical solutions, whereby the thermal conductivity is assumed to be independent of deformation. It is found that the full-coupled theory predicts less transient response of the temperature compared to the classic analysis. In the steady state limit, the predicted temperature distribution within the plate for small heat flux is almost the same for both analyses. However, it is noted that increasing the heat flux will increase the deviation between the predictions of the temperature distribution by the full coupled theory and by the classic analysis. It is concluded from the present study that, in order to precisely predict the deformation of smart structures, the piezo-thermo-elastic coupling, geometric non-linearity and the deformation dependent thermal conductivity should be taken into account. Project supported by the National Natural Science Foundation of China (Nos. 10132010 and 50135030) and the Foundation of In-service Doctors of Xi'an Jiaotong University.     

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。     

Crystal plasticity analysis of texture development in magnesium alloy during extrusion

The texture development mechanism during the extrusion of magnesium alloy is investigated by experimental observation and numerical analysis. First, we perform a finite element analysis of a full extrusion process using a phenomenological constitutive equation, and it is confirmed that the loading condition of the extrusion process near the central axis of the billet is approximated by an equi-biaxial compression mode. Then, the equi-biaxial compression problem is adopted as a simplified boundary value problem to be solved using a crystal plasticity model to clarify the detailed texture development mechanism during the extrusion process. The crystal plasticity analysis of equi-biaxial compression successfully reproduces the texture development from an initial random texture to the final experimentally observed texture. The effects of the deformation modes (i.e. slip and twinning systems) implemented in the calculation and the reference stress ratio of basal to nonbasal slip systems on texture development are studied in detail. Finally, the mechanism of texture development during the extrusion process is discussed in terms of the lattice rotation caused by the activated slip systems.     

考虑刚体运动与弹性运动耦合影响的旋转叶片振动有限元分析

本文研究了旋转叶片的纵向振动和双向横振动,考虑了刚体运动和弹性振动的耦合关系,利用有限元法推导出离散系统动力学方程,从而引出陀螺特征值问题。本文就某一特例了计算了在不同转速时叶片振动的自然频率,讨论了转速对振动频率的影响。     

Finite element analysis of air flow around permeable sand fences

A numerical study of the turbulent air flow in a trench trap and the turbulent flow around a permeable sand fence is reported in this paper. The two-dimensional modified k–ε turbulence model proposed by Kato and Launder is used to predict the turbulent characteristics of the air flow. The discretization method for the governing equations is the three-step Taylor/Galerkin finite element method proposed by the authors. For the flow in a trench trap the numerical results are compared with experimental data obtained under realistic conditions using a large wind tunnel. For the air flow around a permeable sand fence a pressure loss model is used to represent the effect of the porosity of the fence on the flow field. © 1997 John Wiley & Sons, Ltd.     

Crystal-plasticity finite-element analysis of inelastic behavior during unloading in a magnesium alloy sheet

A crystal-plasticity finite-element analysis of the loading-unloading process under uniaxial tension of a rolled magnesium alloy sheet was carried out, and the mechanism of the inelastic response during unloading was examined, focusing on the effects of basal and nonbasal slip systems. The prismatic and basal slip systems were mainly activated during loading, but the activation of the prismatic slip systems was more dominant. Thus the overall stress level during loading was determined primarily by the prismatic slip systems. The prismatic slip systems were hardly activated during unloading because the stress level was of course lower than that during loading. On the other hand, because the strength of the basal slip systems was much lower than that of the prismatic slip systems, the basal slip systems would be easily activated under the stress level during unloading in the opposite direction when their Schmid’s resolved shear stresses changed signs because of the inhomogeneity of the material. These results indicated that one explanation for the inelastic behavior during unloading was that the basal slip systems were primarily activated owing to their low strengths compared to that of the prismatic slip systems. Numerical tests using the sheets with random orientations and with the more pronounced texture were conducted to further examine the mechanism.     

Finite element analysis of two- and three-dimensional flows around square columns in tandem arrangement

Two- (2D) and three-dimensional (3D) finite element analyses for flow around two square columns in tandem arrangement were performed with various column spacings and Reynolds numbers. The computed values were compared with the wind-tunnel results in terms of the aerodynamic characteristics of the leeward column. In most 2D computations, strong vortices were formed behind the windward column, irrespective of widely changed Reynolds numbers. This was different from the experimental phenomena of equivalent spacing, so that the computed time-averaged pressure coefficients were not identical to the experimental values except when the distance between the two columns was adequately wide or narrow. On the other hand, in 3D computation, distinct differences in flow structures behind the column were observed between Reynolds numbers of 10³ and 10⁴ and the pressure coefficient in the 3D analysis with Re=10⁴ agreed well with the experimental value. Thus, the effectiveness of 3D computations and Reynolds number effects on the flow around two square columns have been confirmed. © 1998 John Wiley & Sons, Ltd.