Determination of friction models for metallic die–workpiece interfaces

A two-parameter friction model is used which combines the Coulomb friction model and the friction factor yield stress model. The drawback of this two-parameter model is the complex nature of its calibration. In this paper a new technique is proposed to calibrate the model, which utilizes two testpiece geometries, namely the solid cylindrical compression testpiece and the ring compression testpiece. In addition, a mathematical model is required of the true stress–true strain behaviour of the material, so that finite deformation/finite element techniques can be used to accurately predict the compression behaviour of both testpieces.By a combination of careful experimentation, carried out on aluminium alloy and copper testpieces, and of finite element analyses of the testpieces made using the two-parameter friction model, it has been shown that it is possible to derive the true stress–true strain curve for the workpiece materials; and, to calibrate the friction model. The geometrical changes of all testpieces, carefully measured throughout the tests, for a range of four different friction conditions, dry friction, lubricant, lead metal and nylon, have been predicted with good accuracy using the true stress–true strain constitutive models, the two-parameter friction model, and the finite-element analysis procedures. In this way, the proposed approach has been validated.     

Anand Parameters Determination for SnAgCu Solder Bearing Micro-amounts Rare Earth Ce

SnAgCu solder system with the addition of rare earth Ce,which has better thermo-mechanical properties compared to those of SnPb solder,is regarded as one of the promising candidates for electronic assembly.Moreover,the SnAgCuCe solder alloys can provide good quality joints with Cu substrates.However,there is few report of the constitutive model for SnAgCu solder beating micro-amounts rare earth Ce.In this paper,the unified viscoplastic constitutive model,Anand equations,is used to represent the inelastic deformation behavior for SnAgCu and SnAgCuCe solders.In order to obtain the acquired data for the fitting of the material parameters of this unified model,a series of experiments of constant strain rate test were conducted under isothermal conditions at different temperatures.The Anand parameters of the constitutive equations for SnAgCu and SnAgCuCe solder were determined from separated constitutive relations and experimental results.Nonlinear least-square fitting was selected to determine the model constants.And the simulated results were then compared with experimental measurements of the stress-inelastic strain curves:excellent agreement was found.The model accurately predicted the overall trend of steady-state stress-strain behavior of SnAgCu and SnAgCuCe solders for the temperature ranges from 25℃ to 150℃,and the strain rate ranges from 0.01 s-1 to 0.001 s-1.It is concluded that the Anand model can be applied for representing the inelastic deformation behavior of solders at high homologous temperature and can be recommended for finite element simulation of the stress-strain response of lead free soldered joints.Based on the Anand model,the investigations of thermo-mechanical of SnAgCu and SnAgCuCe soldered joints in fine pitch quad flat package by finite element code were done under thermal cyclic loading,it is found that the reliability of SnAgCu soldered joints can be improved remarkably with addition of rare earth Ce.The results may provide a theory guide for developing constitutive model for lead-free solders.     

Numerical modeling of dynamic recrystallization during nonisothermal hot compression by cellular automata and finite element analysis

In this study, dynamic recrystallization during nonisothermal hot compression was numerically simulated by cellular automata and finite element analysis. A modified cellular automata model was developed by introducing a new parameter for considering solute drag effect. The isothermal hot compression tests of pure copper were carried out to verify the modified cellular automata model by comparing material behavior and average grain size. The effect of solute drag was numerically considered and compared to the experimental data and the numerical data obtained by conventional cellular automata without solute drag effect. Then, the modified cellular automata model was applied to a nonisothermal hot compression by combining with a finite element analysis. The finite element analysis was conducted to acquire local parameters such as strain, strain rate, and temperature. These values were provided to the cellular automata model as input. The local changes of microstructure and average grain size were simulated by cellular automata and compared with nonisothermal hot compression results. The simulation results were in reasonably good agreement with experimentally determined microstructures by electron backscattering diffraction. The developed model was further applied to simulate a hot gear blank forging process to check its applicability. With the current approach, local microstructures can be determined for better understanding microstructural changes during the nonisothermal process.     

A short summary on finite element modelling of fatigue crack closure

This paper presents a short summary pertaining to the finite element modelling of fatigue crack closure. Several key issues related to finite element modelling of fatigue crack closure are highlighted: element type, mesh refinement, stabilization of crack closure, crack-tip node release scheme, constitutive model, specimen geometry, stress-states (i.e., plane stress, plane strain), crack closure monitoring. Reviews are presented for both straight and deflected cracks.     

铝合金热轧变形抗力模型的试验研究

主要介绍用Gleeble-1500热模拟试验机测定铝合金材料7075热变形抗力的试验方法,分析不同应变速度和不同温度的流变应力曲线所显示的材料组织性能,总结出适合铝合金7075热轧的分段周纪华变形抗力模型,通过拟合曲线与实测数据的比较,证明拟合出的分段周纪华变形抗力模型能准确地反映7075的热变形抗力,适用于铝合金热轧轧制力的计算。     

A study on hot extrusion of Ti–6Al–4V using simulations and experiments

Hot extrusion of Ti–6Al–4V alloy has been studied using finite element simulation and the results are compared with those obtained experimentally. First, the constitutive behavior of the material and friction at the extrusion temperatures are established based on the results obtained through cylindrical and ring compression tests, respectively. While the flow stress below β transus temperature is expressed as a strain-dependent function, it is taken as strain-independent one at higher temperatures. The distribution of strain, temperature and effective stress has been simulated under different design and processing conditions. Simulation results show that heat generation due to deformation is significant (as much as 160°C) in the hot extrusion of Ti alloys, and it mainly occurs at the beginning of the extrusion process. This leads to reduction in flow stress which, in turn, leads to enlarged deformation zone. A fair agreement has been found between the experimental results and those obtained through simulations.     

金属切削变形本构方程的研究

金属切削过程的本构关系与应变、应变率、温度等多种因素有关,建立切削变形区内工件材料的本构方程是研究切削变形的关键。本文在文献综述的基础上,首先给出金属切削本构方程的试验研究方法,然后给出金属切削工件材料的典型本构方程,并给出Usui本构方程中不同工件材料的特性系数,以及同一工件材料AISI52100(HRC62)的不同本构方程。经对比分析可见,金属切削过程中变形区内的应力—应变关系除与试验方法、切削条件有关外,还与工件材料的组分和微观晶格结构密切相关。本文最后分析了金属切削变形本构方程研究中存在的问题,并指出发展趋势。     

ZGMn13高锰钢本构方程及仿真实验的研究

在有限元仿真中材料的本构方程对仿真结果有着重要的影响,利用压缩试验和分离式Hopkinson压杆试验得到的数据推导出ZGMn13高锰钢的Johnson-Cook本构方程中的参数,并依据此方程进行有限元仿真。     

Correlation between Single Factor Material Constitutive Model Parameters and Temperature for Ti6Al4V Alloy

Accurate material constitutive model is considered highly necessary to perform finite element simulation and analysis.However,it is difficult to establish the material constitutive model because of uncertainty of mathematical relationship and constraint of existing experimental condition.At present,there exists considerable gap between finite element simulation result and actual cutting process.Particular emphases were put on investigating the correlation between "single factor" material constitutive model parameters and temperature for Ti6Al4V alloy,and also establishment of material constitutive model for this kind of material.Theoretical analyses based on dislocation theory and material functional relations showed that material model was deeply affected by variation temperature.By the least squares best fit to the available quasi-static and high-speed impact compression experiment data,material parameters at various temperatures were found.Experimental curves analyses and material parameters comparison showed that the "single factor" material constitutive model parameters were temperature dependent.Using the mathematical mapping between material parameters and temperature,"single factor" material constitutive model of Ti6Al4V alloy was established,which was proven to be right by comparing with experimental measurements.This work makes clear that the "single factor" material constitutive model parameters of Ti6Al4V alloy are temperature dependent.At the same time,an accurate material constitutive model is established,which helps to optimize cutting process and control machining distortion for Ti6Al4V alloy aerospace parts.     

Hot shape forging of gas turbine disk using microstructure prediction and finite element analysis

The Waspaloy, a Ni-based superalloy, has been widely used for forging material of gas turbine disk since it requires the high tensile strength at high temperature and good resistance to low cycle fatigue. The purpose of this study is to develop a forging process of turbine disk that satisfies the hot deformation characteristics of Waspaloy. Generally, the hot forging of superalloy has been subjected to isothermal forging since the available temperature range of forging is narrow. However, the non-isothermal forging was used to make a turbine disk in this study. Therefore, the analyses of temperature variation and deformation behavior of the material were important to obtain the sound forging products. The hot compression test was carried out to know formability at high temperature and microstructure evolution during hot deformation. In order to define the optimum forging conditions including material temperature, strain rate, strain, microstructure evolution and forging load, the commercial finite element analysis code was used to simulate the forging procedure of turbine disk. The hot forged turbine disk was heat-treated for obtaining the high temperature properties. The cut-off tests on the heat-treated forged disks were carried out. Experimental results were compared with the simulation results by FE analysis. Test results were in good agreement with the simulations. This study shows that the superalloy turbine disk can be manufactured by the semi-closed die forging.     

Constitutive law for AZ31B Mg alloy sheets and finite element simulation for three-point bending

The constitutive law to describe the anisotropic and asymmetric mechanical behavior of AZ31B magnesium (Mg) alloy sheets at room temperature has been developed here for the plane stress condition, based on the orthotropic yield criterion proposed by Cazacu O, Plunkett B, Barlat F. [Orthotropic yield criterion for hexagonal closed packed metals. International Journal of Plasticity 2006;22:1171–94] and different isotropic hardening laws for tension and compression. Experimental procedures to obtain the material parameters of the yield surface and the hardening laws have been discussed for the AZ31B Mg alloy sheet. For verification purposes, finite element simulation results based on the developed constitutive laws have been compared with experimental results for a three-point bending test.     

The effects of strain rate and anisotropy upon the sheet-stretching process

A rate-dependent elasto-plastic finite element formulation has been developed for the large-deformation sheet-stretching process. The formulation used was based on the power-form constitutive equation applied for the stress-strain-strain rate relation of the material and Hill's anisotropic yield criterion in the plastic range. A principle of virtual work rate applied towards a Lagrangian reference system was adopted. The resulting nonlinear equilibrium equations have been solved through usage of an incremental method with the R_min technique. Additionally, the location of fracture initiation in the material and the total punch stroke were predicted by the strain energy density criterion.Experimental tests were performed and have exhibited good agreement with numerical simulations. The method proposed here has been proven to be capable of evaluating the effects of various parameters on metal flow and could be modified for solving problems related to other manufacturing processes.     

Validation of constitutive models applicable to aluminium foams

An extensive experimental database has been established for the structural behaviour of aluminium foam and aluminium foam-based components (foam-filled extrusions). The database is divided into three levels, these are: (1) foam material calibration tests, (2) foam material validation tests and finally (3) structural interaction tests where the foam interacts with aluminium extrusions. This division makes it possible to validate constitutive models applicable to aluminium foam for a wide spectrum of loading configurations. Several existing material models for aluminium foam from the literature are discussed and compared. To illustrate the use of the database, four existing material models for foams in the explicit, non-linear finite element code LS-DYNA have been calibrated and evaluated against configurations in the database.     

Dynamics of a viscoelastic rotor shaft using augmenting thermodynamic fields—A finite element approach

Modelling viscoelastic materials is always difficult since such materials store energy as well as dissipate it to the thermal domain. Whereas modelling the elastic behaviour is easy, modelling the energy dissipation mechanism poses difficulty. This paper presents a theoretical study of the dynamics of a viscoelastic rotor-shaft system, where the internal material damping in the rotor-shaft introduces a rotary force well known to cause instability of the rotor-shaft system. An efficient modelling technique that assumes coupled (thermo-mechanical) augmenting thermodynamic field (ATF) to derive the constitutive relationships is found more suitable in comparison with the viscous and hysteric damping models, and is used to model the viscoelastic rotor material. Dynamic behaviour of an aluminium rotor is predicted through viscoelastic modelling of the continuum to take into account the effect of internal material damping. Stability limit speed (SLS) and unbalance response (UBR) amplitude are used as two indices to study the dynamics. It is observed that, the ATF approach predicts more reliable SLS and UBR amplitude in comparison with the viscous and hysteretic model of rotor-internal damping. Composite rotor-shaft assumed by reinforcing the aluminium matrix with carbon fibre is found to postpone the critical speeds and thus make available, higher speed of rotor operation and lower UBR amplitude in comparison with pure aluminium rotor-shaft. Finite element method is used for modelling and analysis.     

Study on cutting temperature during milling of titanium alloy based on FEM and experiment

A finite element model of helix double-edge cutting was developed to study cutting temperature during milling of titanium alloy Ti6Al4V. To improve the accuracy of finite element simulation, a new method to construct material constitutive model was presented, and material constitutive model with big strain, high strain rate, and high-temperature characters for aeronautical titanium alloy in cutting process was established. Using this finite element model, milling process of titanium alloy was simulated. Cutting temperature change curves and values were obtained. An analysis indicates that the highest cutting temperature lies in tool-chip interface and is more close to cutting edge; moreover, the temperature is higher in rake face than flank face of the tool. The embedded semi-artificial thermocouple cutting temperature experiment was improved by substituting constantan band for constantan wire. By comparing the results obtained from finite element simulation and cutting temperature experiment results, a good agreement is found, showing finite element simulation analysis of cutting temperature for titanium alloy is correct.     

热冲压硼钢B1500HS高温本构方程的研究

硼钢的高温本构方程是热冲压数值模拟不可缺少的数学模型,它反映了流动应力与应变、应变速度以及温度之间的依赖关系。为了研究热冲压硼钢B1500HS高温时的流变力学行为,采用Gleeble 1500D热模拟试验机,在600～900℃温度区间,分别以0.01 s–1、0.1 s–1、1.0 s–1、10 s–1的应变速度对硼钢B1500HS试样进行等温单向拉伸试验,计算得到各相应测试条件下的正应力—应变曲线。采用包含变形激活能和变形温度的双曲正弦形式修正的Arrhenius关系来描述硼钢奥氏体组织的热激活变形行为。通过对试验数据进行拟合回归分析,得到与应变量相关的各材料参数,以及与应变速度、变形温度相关的流变应力关系式。试验结果显示,流动应力随着变形温度的降低而增大,随着形变速度的升高而增大。计算结果表明:流变应力关系式的计算结果与试验数据的吻合度较好。     

Damage and failure characterization of 7075 aluminum alloy hot stamping

7000 series high strength aluminum alloys are increasingly used in manufacturing automobile body parts to meet the more stringent demands for automobile lightweight. Hot stamping of 7000 series high strength aluminum alloys is a complex thermal-mechanical coupling process and precise simulation is needed to predict material fracture. To obtain damage model of 7075 aluminum alloy in hot stamping, five different stress triaxiality specimens were designed. The fracture strain, critical strain and average stress triaxiality of different specimens were obtained by the hybrid finite element simulation and experiment (FE-EXP) method. GISSMO model of 7075 aluminum alloy at 400 °C was established. Compared with the experimental results of U-shaped part hot stamping under different lubrication conditions, the calibrated GISSMO model was demonstrated to predict the damage behavior of 7075 aluminum alloy during high temperature deformation accurately.

     

列车车体SUS301L-HT不锈钢动态力学性能及其对结构吸能特性的影响

对SUS301L-HT不锈钢材料分别进行了准静态拉伸试验和动态冲击拉伸试验,以获得不同应变率下的材料本构关系。为准确地描述SUS301L-HT不锈钢材料的动态力学性能,采用了列表插值法,并通过对比有限元对标和试验数据来验证该方法的可靠性。以典型薄壁吸能结构为载体,采用2种材料参数,对比分析了SUS301L-HT不锈钢材料的动态力学性能对结构吸能特性的影响。研究结果表明：SUS301L-HT不锈钢具有明显的应变率强化效应,随着应变率的增大,材料的塑性硬化能力降低,表现出明显的温度软化效应;列表插值法相比动态本构模型能更好地描述SUS301L-HT不锈钢的动态力学性能,且采用列表插值法得到的结果与试验结果、有限元结果均有良好的一致性;列车碰撞的应变率属于中低应变率范围,对于SUS301L-HT不锈钢制成的车体吸能结构,考虑应变率效应的结构的实际吸能量要比不考虑应变率效应的相同结构的吸能量高,但初始峰值力相对较大。     

选区激光熔化Ti-6Al-4V合金在高应变速率下力学性能的有限元模拟

采用选区激光熔化(SLM)技术制备Ti-6Al-4V合金,经真空退火热处理和热等静压处理后,研究了合金准静态和高应变速率(500~3000s^-1)下的力学性能;对双线性材料模型进行标定,将所得到的材料参数应用于霍普金森压缩试验的有限元模拟中,并将模拟结果与试验结果进行对比。结果表明:经真空退火和热等静压处理后,SLM成形合金的组织为α相和β相,呈网篮组织形貌;与准静态条件下的相比,在高应变速率下SLM成形合金的断后伸长率得到明显提高;模拟得到的归一化真应力-真应变曲线与试验得到的相吻合,平均相对误差为2.5%,其材料参数可用于后续的瞬态冲击仿真分析中。