An enhanced constitutive material model for machining of Ti–6Al–4V alloy

Material failure due to adiabatic shear banding is a characteristic feature of chip formation in machining of Ti–6Al–4V material. In this paper, an enhanced Zerilli–Armstrong (Z-A) based material flow stress model is developed by accounting for the effects of material failure mechanisms such as voids and micro-cracks on the material flow strength during shear band formation. These effects are captured via a multiplicative failure function in the constitutive material flow stress model. The strain and strain rate dependence of the material failure mechanism are explicitly modeled via the failure function. The five unknown constants of the failure function are calibrated using cutting force data and the entire model is verified using separate force, chip segmentation frequency and tool–chip contact length data from orthogonal cutting experiments reported by 0035 and 0040. Model predictions of these quantities based on the enhanced material model are shown to be in good agreement with experiments over a wide range of cutting conditions.     

From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation

This paper proposes a methodology to identify the material coefficients of constitutive equation within the practical range of stress, strain, strain rate, and temperature encountered in metal cutting. This methodology is based on analytical modeling of the orthogonal cutting process in conjunction with orthogonal cutting experiments. The basic mechanics governing the primary shear zone have been re-evaluated for continuous chip formation process. The stress, strain, strain rate and temperature fields have been theoretically derived leading to the expressions of the effective stress, strain, strain rate, and temperature on the main shear plane. Orthogonal cutting experiments with different cutting conditions provide an evaluation of theses physical quantities. Applying the least-square approximation techniques to the resulting values yields an estimation of the material coefficients of the constitutive equation. This methodology has been applied for different materials. The good agreement between the resulting models and those obtained using the compressive split Hopkinson bar (CSHB), where available, demonstrates the effectiveness of this methodology.     

工业纯钛室温下的应变速率敏感性及Hollomon经验公式的改进

通过实验研究了工业纯钛TA2在室温下应变速率范围为1×10-4～1×10-2s-1的拉伸力学性能。发现TA2的拉伸力学性能存在显著的应变速率敏感性,随着应变速率的增加,材料的强度提高、塑性下降,应变速率敏感性指数较高。通过对Hollomon经验公式σ=Kεnεm的推导和TA2实验数据的分析发现应变速率敏感性指数m和应变硬化指数n分别会受到应变和应变速率的影响,并且它们之间均呈指数关系。因此对Hollomon经验公式提出了改进,得到了TA2在室温下改进的Hollomon模型。与传统的Hollomon经验公式及Johnson-Cook模型相比,改进的Hollomon模型的预测结果与实验结果更加吻合,能更准确地表现材料的拉伸力学性能。     

考虑应变补缩的6063铝合金高温流变应力本构方程(英文)

为了建立精确模拟6063铝合金高温流变应力的本构方程,在温度为573~773 K和应变速率为0.5~50 s-1的条件下,采用Gleeble-1500热模拟机进行等温热压缩实验。结果表明:可以采用参数Z描述温度和应变速率对6063铝合金热变形行为的影响,建立的本构方程中的材料常数(α,n,Q和A)可以表示成应变的4次多项式函数。模拟结果表明:所建立的本构方程能精确预测6063铝合金高温流变应力,因此,本构方程适合用于模拟热变形过程,如挤压和锻造,并且可以在工程应用中正确设计变形参数。     

Constitutive equations of flow stress of magnesium AZ31 under dynamically recrystallizing conditions

Constitutive equations for the relationship between flow stress, strain, strain rate and temperature for magnesium AZ31 alloy under hot working conditions where dynamic recrystallization is prevalent have been developed. Equation development data were obtained using isothermal plane strain compression (PSC) tests carried out at 300–500 °C with strain rates ranging from 0.5 to 50 s⁻¹, to an equivalent strain of 0.7. The predicted flow stress curves show good comparison with the experimental isothermal flow curves in terms of peak, steady state stress and flow softening behaviour but at higher Zener–Hollomon (Z) values (>10¹¹ s⁻¹) the predicted peak stress deviates from the isothermal value in the range of 14–25 MPa suggesting a breakdown in the hyperbolic sine equation at those Z values. The developed constitutive equations for the valid thermomechanical conditions were adopted in a finite element model to simulate the PSC conditions. The distributions of strain, strain rate and temperature qualitatively suggest higher strain rate at the centre of the sample which agrees well with that of the quantitative analysis of the dynamically recrystallized grain size.     

Thermo-mechanical modeling of orthogonal machining process by finite element analysis

A plane strain finite element method is used with a new material constitutive equation for 1020 steel to simulate orthogonal machining with continuous chip formation. Deformation of the workpiece material is treated as elastic–viscoplastic with isotropic strain hardening, and the numerical solution accounts for coupling between plastic deformation and the temperature field, including treatment of temperature-dependent material properties. To avoid numerical errors associated with large deformation of elements, automatic remeshing is used, with at least 15 rezonings required to achieve a satisfactory solution. Effects of the uncertainty in the constitutive model on the distributions of strain, stress and temperature around the shear zone are presented, and the model is validated by comparing average values of the predicted stress, strain, strain rate and temperature at the shear zone with experimental results. Parametric effects associated with cutting speed and initial work temperature are considered in the simulations.     

Extension of Oxley's predictive machining theory for Johnson and Cook flow stress model

This paper presents an extension of Oxley's predictive analytical model for forces, temperatures and stresses at primary (shear zone) and secondary (tool-chip interface zone) deformation zone for Johnson and Cook flow stress model. The effect of strain in addition to strain-rate and temperature at tool–chip interface, which is ignored by many researchers, is considered in the present analysis. The extension is made inline with Oxley's predictive machining theory by introducing the term n_eq for Johnson and Cook material flow stress model. The term n_eq becomes strain hardening exponent (n) for power law flow stress model used by Oxley and can be found for other material models too. Johnson and Cook flow stress model that considers the effect of strain, strain-rate, and temperature on material property is widely used nowadays in finite element method simulation and analytical modeling due to its simple form and easy to use. The extension of Oxley's theory is verified for orthogonal cutting test data from the available literature for 0.38% carbon steel [Oxley, P.L.B., 1989. The Mechanics of Machining: An Analytical Approach to Assessing Machinability. Ellis Horwood Ltd., England] and AISI 1045 steel [Ivester, R.W., Kennedy, M., Davies, M., Stevenson, R., Thiele, J., Furness, R., Athavale, S., 2000. Assessment of machining models: progress report. Machining Science and Technology 4, 511–538] and found in good agreement.     

On the Work-Hardening of AA 3104-H19 Aluminum Alloy

The aim of this study is to investigate the work-hardening of AA 3104-H19 aluminum alloy. Uniaxial tensile tests were carried out in both the rolling and transverse directions. In the past, some authors have used such uniaxial tensile test data and the Hollomon equation fitted to them to predict the forming limit curves. In a previous study, we showed experimentally that the Hollomon equation exponent, typically 0.07, used in such limit strain predictions is too high and should be approximately 0.04. Other authors have obviously used such a high value because they have compensated for the reduction of limit strains near the plane strain by increasing the Hollomon equation exponent. The reduction of limit strains near the plane strain occurs, as the Marciniak-Kuczynski theory, which the aforementioned authors have used, assumes a local inhomogeneity or a thinner section in the sheet to explain the local necking in stretch forming. In this study, it is shown experimentally that the Hollomon equation exponent in both the rolling and transverse directions is very close to 0.04. It is shown further that the Hollomon or Voce equations do not describe very well the work-hardening of the AA 3104-H19 alloy in either the rolling or transverse direction.     

钛合金TC4切削过程流动应力模型研究

运用有限元技术对切削过程进行仿真可以预测切削力、切削温度、应力分布,优化刀具参数和切削条件。建立适合于切削条件中大应变、高应变率条件下材料的流动应力模型,是切削过程有限元仿真的关键技术。文章通过正交切削实验和有限元迭代的方法,修正了难加工材料TC4在大应变、高应变率条件下的J-C流动应力模型,使修正模型能够适应切削仿真中的大应变、高应变率要求。计算结果表明,采用新的J-C流动应力模型进行计算,所得主切削力值与实验测量值的平均误差从36.28%降为12.06%,进给力的平均误差由原来的61.03%降为现在的25.57%。该修正的流动应力模型比用霍普金森实验所得到的流动应力模型更适合于切削过程的有限元仿真,可以提高切削仿真的计算精度。     

Constitutive relationship of IN690 superalloy by using uniaxial compression tests

The hot deformation behavior of IN690 superalloy was characterized in a temperature range of 1273-1473 K and a strain rate range of 0.01-10 s-1 using uniaxial compression tests on process annealed material.The constitutive relations between flow stress and effective strain,effective strain rate as well as deformation temperature were studied.It can be concluded that the flow stress significantly reduces with the deformation temperature of IN690 superalloy increasing.Whereas,there is a significant increase of flow stress when the strain rate increases from 0.1 s-1 to 10 s-1.Based on the hyperbolic-sine Arrhenius-type equation,a constitutive equation considering compensation of strain was developed.The activation energy and the material constants(Q,n and ln A) decrease as the deformation strain increases.The strain dependent term is successfully incorporated in the constitutive equation through a quartic equation.A good agreement between the experimental data and the predicted results has been achieved,indicating that the proposed constitutive equation and the methods of determing the material constants are suitable to model the high temperature deformation behavior of IN690 superalloy.     

35% SiC_p/2024A1复合材料的热变形行为(英文)

采用Gleeble-1500D热模拟试验机,对35%SiCp/2024A1复合材料在温度350~500°C、应变速率0.01~10s-1的条件下进行热压缩试验,研究该复合材料的热变形行为与热加工特征,建立热变形本构方程和加工图。结果表明,35%SiCp/2024A1复合材料的流变应力随着温度的升高而降低,随着应变速率的增大而升高,说明该复合材料是正应变速率敏感材料,其热压缩变形时的流变应力可采用Zener-Hollomon参数的双曲正弦形式来描述;在本实验条件下平均热变形激活能为225.4 kJ/mol。为了证实其潜在的可加工性,对加工图中的稳定区和失稳区进行标识,并通过微观组织得到验证。综合考虑热加工图和显微组织,得到变形温度500°C、应变速率0.1~1 s-1是复合材料适宜的热变形条件。     

7075铝合金热压缩变形流变应力

在Gleeble-1500热模拟试验机上,采用高温等温压缩试验,对7075铝合金在高温压缩变形中的流变应力行为进行了研究。结果表明,应变速率和变形温度的变化强烈地影响合金流变应力的大小,流变应力随变形温度升高而降低,随应变速率提高而增大;可用Zener-Hollomon参数的指数形式来描述7075铝合金高温压缩变莆时的流变应力行为。     

Hot deformation behavior of EA4T steel

The compressive deformation behavior of EA4T steel was investigated at temperatures ranging from 950 to 1150 C and strain rates from 0.1 to 20 s 1 on Gleeble-1500 thermo-simulation machine. The work hardening rate versus stress curves were used to determine the characteristic points of flow curves. The application of constitutive equations to determine the hot working constants of this material was discussed. Furthermore, the effect of Zener-Hollomon parameter (Z) on the characteristic points of flow curves was studied using the power law relation. The deformation activation energy of this steel was determined as 309.5 kJ/mol. Some behaviors were compared to other steels.     

Determination of workpiece flow stress and friction at the chip–tool contact for high-speed cutting

This paper presents a methodology to determine simultaneously (a) the flow stress at high deformation rates and temperatures that are encountered in the cutting zone, and (b) the friction at the chip–tool interface. This information is necessary to simulate high-speed machining using FEM based programs. A flow stress model based on process dependent parameters such as strain, strain-rate and temperature was used together with a friction model based on shear flow stress of the workpiece at the chip–tool interface. High-speed cutting experiments and process simulations were utilized to determine the unknown parameters in flow stress and friction models. This technique was applied to obtain flow stress for P20 mold steel at hardness of 30 HRC and friction data when using uncoated carbide tooling at high-speed cutting conditions. The average strain, strain-rates and temperatures were computed both in primary (shear plane) and secondary (chip–tool contact) deformation zones. The friction conditions in sticking and sliding regions at the chip–tool interface are estimated using Zorev's stress distribution model. The shear flow stress (k_chip) was also determined using computed average strain, strain-rate, and temperatures in secondary deformation zone, while the friction coefficient (μ) was estimated by minimizing the difference between predicted and measured thrust forces. By matching the measured values of the cutting forces with the predicted results from FEM simulations, an expression for workpiece flow stress and the unknown friction parameters at the chip–tool contact were determined.     

轴对称压缩流动应力-应变曲线有限元修正方法的研究

材料的本构关系是塑性成形过程数值模拟分析模型的基础。通过不同变形参数下的轴对称压缩实验获取材料流动应力曲线 ,是建立本构关系的常用方法。材料在压缩过程中 ,由于试样和工具接触面上存在摩擦 ,不可避免地出现鼓形 ,所以试样内部的应变和应力分布都不是均匀的 ,由此测得的流动应力曲线精度有限。本文提出了一种新的修正方法 ,该方法使用平均等效应变的概念 ,利用有限元法模拟材料压缩过程得到的数据对实测曲线进行修正 ,降低了流动应力的误差。以镁合金AZ31B材料为例 ,使用该方法对压缩实验测得的流动应力曲线进行修正 ,经两次修正后 ,就达到较高的精度 ,说明该方法具有简单、实用的特点。     

A mathematical theory of plasticity for the upsetting of compressible P/M materials

A mathematical equation for the calculation of the flow stress in the case of the simple compression test is proposed for the P/M sintered preforms. A new yield function developed by Doraivelu et al. taking into account the hydrostatic stress, is considered for the development of the above equation. Similarly, another equation for the determination of the hydrostatic stress in the case of the simple compression test is proposed for P/M sintered preforms. Both of the above two equations depend upon two factors, namely: (i) the value of Poisson’s ratio; and (ii) the relative density of the P/M preform; during the compression test. Because there exists a relationship between Poisson’s ratio and the relative density for P/M preforms, it is proposed that the flow stress or the hydrostatic stress equations can be written in terms of either Poisson’s ratio or the relative density. It is observed that at relative densities of below 0.71 the aggregate is geometrically unstable and crumbles during deformation. In the range 0.71 ≤ R ≤ 1.0, the strain transferred to the matrix increases continuously until it asymptotically approaches the strain applied to the aggregate.     

Ti(C,N)基金属陶瓷刀具切削加工有限元模拟

介绍了本课题组研制的一种新的刀具材料--T(iC,N)基金属陶瓷的成分组成及其力学性能;基于大变形-大应变理论、增量理论以及更新拉格朗日算法、采用几何断裂分离准则,建立了二维弹塑性金属正交切削有限元模型,对金属正交切削过程进行了数值模拟;改变刀具前角,得出在不同的刀具前角下T(iC,N)基金属陶瓷刀具在正交切削过程中切削力以及刀具后刀面等效应力变化;分析了切削力、刀具表面等效应力对刀具磨损的影响;模拟结果与相关研究的实验数据吻合。本文的研究为后期研制新的刀具材料提供了理论依据,降低实验成本。     

Re-evaluation of the basic mechanics of orthogonal metal cutting: velocity diagram, virtual work equation and upper-bound theorem

This paper re-evaluates the known velocity relationships expressed in the form of a velocity diagram in orthogonal metal cutting, arguing that the metal cutting process be considered as cyclic and consisting of three distinctive stages. The velocity diagrams for the second and third stages of a chip-formation cycle are discussed. The fundamentals of the mechanics of orthogonal cutting, which are the upper-bound theorem applied to orthogonal cutting and the real virtual work equation, are re-evaluated using the proposed velocity diagram and corrected relationships are proposed. To prove the theoretical results, the equation for displacements in the deformation zone is derived using the proposed velocity relationships. To prove that the displacements in the deformation zone follow the derived equation and that this zone consists of two unequal parts, a metallographical study of chip structures has been carried out. To estimate the variation of stress and strain in the deformation zone quantitatively, a microhardness scanning test was conducted.Because it is proved that the chip formation process is cyclic, its frequency is studied. It is shown that when the noise due to various inaccuracies in the machining system is eliminated from the system response and thus from the measuring signal, and when this signal is then properly processed, the amplitude of the peak at the frequency of chip formation is the largest in the corresponding autospectra.     

A finite element analysis for the characteristics of temperature and stress in micro-machining considering the size effect

In this paper, a finite element method for predicting the temperature and the stress distributions in micro-machining is presented. The work material is oxygen-free-high-conductivity copper (OFHC copper) and its flow stress is taken as a function of strain, strain rate and temperature in order to reflect realistic behavior in machining process. From the simulation, a lot of information on the micro-machining process can be obtained; cutting force, cutting temperature, chip shape, distributions of temperature and stress, etc. The calculated cutting force is found to agree with the experiment result with the consideration of friction characteristics on the chip–tool contact surface. Because of considering the tool edge radius, this cutting model using the finite element method can analyze micro-machining with a very small depth of cut, almost the same size of tool edge radius, and can observe the ‘size effect' characteristic. Also, the effects of temperature and friction on micro-machining are investigated.