Constitutive modeling for Ti-6Al-4V alloy machining based on the SHPB tests and simulation

A constitutive model is critical for the prediction accuracy of a metal cutting simulation. The highest strain rate involved in the cutting process can be in the range of 10~4–10~6 s~(–1). Flow stresses at high strain rates are close to that of cutting are difficult to test via experiments. Split Hopkinson compression bar(SHPB) technology is used to study the deformation behavior of Ti-6Al-4V alloy at strain rates of 10~(–4)–10~4s~(–1). The Johnson Cook(JC) model was applied to characterize the flow stresses of the SHPB tests at various conditions. The parameters of the JC model are optimized by using a genetic algorithm technology. The JC plastic model and the energy density-based ductile failure criteria are adopted in the proposed SHPB finite element simulation model. The simulated flow stresses and the failure characteristics, such as the cracks along the adiabatic shear bands agree well with the experimental results. Afterwards, the SHPB simulation is used to simulate higher strain rate(approximately 3×10~4 s~(–1)) conditions by minimizing the size of the specimen. The JC model parameters covering higher strain rate conditions which are close to the deformation condition in cutting were calculated based on the flow stresses obtained by using the SHPB tests(10~(–4)–10~4 s~(–1)) and simulation(up to 3×10~4 s~(–1)). The cutting simulation using the constitutive parameters is validated by the measured forces and chip morphology. The constitutive model and parameters for high strain rate conditions that are identical to those of cutting were obtained based on the SHPB tests and simulation.     

Subsurface deformation and damage accumulation in aluminum–silicon alloys subjected to sliding contact

The study of plastic deformation and damage accumulation below the contact surfaces is important in order to understand the dry sliding wear behaviour of aluminum alloys. Experimental evidence exists for the nucleation of voids and microcracks around second phase particles in the material layers adjacent to the contact surface. Propagation of these cracks at a certain depth below the surface may lead to the creation of long, thin plate-like wear debris particles. This work studied the deformation processes during sliding wear by means of metallographic observations of subsurface layers in an Al–7% Si (A356 Al) alloy and by finite element analyses. Specifically, the accumulation of subsurface stresses and strains was investigated, using a coupled structural-thermal finite element model based on the Voce-type exponential stress–strain relationship obtained from the sliding wear tests. Additionally, temperature and strain rate effects were taken into account using a constitutive equation based on Johnson–Cook and Cowper–Symonds models.Accordingly during sliding, the flow stress in subsurface layers increased rapidly and reached a saturation stress after a finite number of sliding contacts. The variation of hydrostatic pressure for different loading conditions was also determined as a function of sliding passes: as the sliding process progressed from the first to the seventh contacts, the hydrostatic pressure at the surface increased from 1150 to 1300 MPa. A total temperature increase of 45 K occurred at the surface after the seventh sliding contact. A debris formation model was proposed in which the presence of a maximum damage gradient at critical depth was considered. The model showed that, with a sliding velocity of 10 m/s, and a normal load of 150 N per unit thickness in mm, the material location where the maximum rate of damage occurred corresponded to a normalized depth (depth/counterface diameter) of 0.060. Increasing the load to 250 N/mm caused an increase in the critical depth of damage (a normalized depth of 0.085). Comparisons with the experimental subsurface crack observations indicate that the proposed damage rate calculations provide a good estimation of the subsurface crack propagation depth.     

粉煤灰漂珠/聚氨酯复合泡沫铝材料压缩性能与本构关系研究

采用压力渗透法制备出了铝基复合泡沫材料,填充材料是以粉煤灰漂珠为主要组分、硬质聚氨酯泡沫为粘结剂的复合泡沫材料.通过准静态实验和分离式霍普金森压杆(Split Hopkinson pressure bar,SHPB)动态压缩的方法研究了复合泡沫铝的压缩力学响应,然后建立了动态本构关系.研究表明,复合泡沫铝的压缩应力-应变曲线与其它泡沫材料的应力-应变曲线类似,文中的两种铝基复合泡沫具有应变率效应,复合泡沫铝较密度相近未填充前的泡沫铝基具有更高的压缩强度与能量吸收能力.但由于漂珠尺寸的不同,导致两种复合泡沫铝的动态压缩结果不尽相同,且小颗粒复合泡沫铝在动态冲击下吸能效果最好.在本研究实验的应变率和密度范围内,本文建立的本构模型曲线与实验曲线吻合较好.     

粉煤灰漂珠/聚氨酯复合泡沫铝材料压缩性能与本构关系研究

采用压力渗透法制备出了铝基复合泡沫材料,填充材料是以粉煤灰漂珠为主要组分、硬质聚氨酯泡沫为粘结剂的复合泡沫材料.通过准静态实验和分离式霍普金森压杆(Split Hopkinson pressure bar,SHPB)动态压缩的方法研究了复合泡沫铝的压缩力学响应,然后建立了动态本构关系.研究表明,复合泡沫铝的压缩应力-应变曲线与其它泡沫材料的应力-应变曲线类似,文中的两种铝基复合泡沫具有应变率效应,复合泡沫铝较密度相近未填充前的泡沫铝基具有更高的压缩强度与能量吸收能力.但由于漂珠尺寸的不同,导致两种复合泡沫铝的动态压缩结果不尽相同,且小颗粒复合泡沫铝在动态冲击下吸能效果最好.在本研究实验的应变率和密度范围内,本文建立的本构模型曲线与实验曲线吻合较好.     

High-temperature dynamic deformation of aluminum alloys using SHPB

This paper investigates the dynamic deformation behavior of two aluminum alloys, 2024-T4 and 6061-T6, using a modified split Hopkinson pressure bar (SHPB) with a pulse shaper technique at both elevated and room temperatures. An experimental strategy is proposed, and the dynamic deformation behaviors of two alloys are evaluated with the modified high-temperature SHPB apparatus. The experiments were carried out under varying strain rates and temperatures. The reflected waves modulated by the pulse shaper, the flow stress-strain relationships, the strain rates, the front- and back-ends stresses during the dynamic deformation period were measured at varying high temperatures. Experimentally obtained data were used to evaluate the parameters in the material constitutive equation, such as the Johnson-Cook (JC) constitutive model.     

Deformation temperature and material constitutive model of cupronickel B10

Cupronickel B10—an important material used in aircraft carriers—exhibits excellent electrochemical and mechanical properties, such as high corrosion resistance and weldability. The Split-Hopkinson pressure bar (SHPB) test is a classical method to obtain the dynamic mechanical properties of solid materials. However, the deformation temperature has long been ignored in SHPB studies, which results in low accuracy of the material constitutive model. Thus, in this study, a new method for obtained the deformation temperature was proposed and the modified material equation was validated using experimental data. Quasi-static compression and SHPB experiments were conducted with a thermocouple. The results revealed that the deformation temperature of the quasi-static tests was nearly zero, whereas that of the SHPB experiments ranged from 40 to 90 °C. Therefore, the method developed to describe the deformation temperature can be used to improve the precision of SHPB experiments, as demonstrated for the case of cupronickel B10.     

考虑成形方向的航空铝合金修正本构模型的构建

为了能够准确地反映材料成形方向对其动态力学性能的影响,利用电子万能试验机及分离式霍普金森压杆（SHPB）装置,对航空铝合金7050-T7451板材沿不同成形方向（法向ND,横向TD,轧向RD）取样,并进行准静态加载试验和动态冲击剪切试验。结果表明：成形方向是影响材料准静态和动态力学性能的重要因素之一,在动态冲击剪切过程中,铝合金7050-T7451表现出一定的应变率敏感性和正应变率强化效应。基于材料的成形方向影响规律,构建包含应变率敏感函数项的修正的Johnson-Cook本构模型,并对比验证修正模型与试验数据的结果,证明了修正的、包含应变率函数项的材料本构模型更适用于描述不同成形方向下的材料动态力学性能,该模型能够为建立精确可靠的各向异性材料仿真模型提供数据支持。     

Thermal and non-Newtonian analysis on mixed liquid–solid lubrication

A mixed liquid–solid lubrication theory is proposed which concerns the effect of solid particle, liquid lubricant and rubbing surface topography. Especially, it focuses on the circumstances when particle diameter, surface composite roughness and oil film thickness are in the same order of magnitude. A mathematical model containing Reynolds equation, particle load carrying equation, asperity contact equation and heat balance equation is constructed to simulate the mixed liquid–solid lubrication. Moreover, the introduction of non-Newtonian constitutive equation and the rheological parameters related to heat and pressure makes the model closer to practical application. Some typical examples have been analyzed to explore the characteristics of mixed liquid–solid lubrication. In these examples, the effects of the mixed liquid–solid lubricant, the particle diameter and mass concentration, the surface composite roughness, and the material properties are discussed. The simulating results are accordant with early experimental researches, which indicated that the mathematical model is in agreement with the practical mixed liquid–solid lubrication. The input parameters in the examples can be adjusted to adapt to versatile applications.     

Finite element modeling of residual stresses in machining induced by cutting using a tool with finite edge radius

A thermal elastic-viscoplastic finite element model is used to evaluate the residual stresses remaining in a machined component. An improvement in the accuracy of the predicted residual stresses is obtained by: (a) using a modified Johnson–Cook material model that is augmented by a linearly elastic component to describe the material behavior as non-Newtonian fluid; (b) using a remeshing scheme to simulate the material flow in the vicinity of the rounded cutting tool edge without the use of a separation criterion; (c) properly accounting for the unloading path, and (d) considering the thermomechanical coupling effect on deformation. Case studies are performed to study the influence of sequential cuts, cutting conditions, etc., on the residual stresses induced by orthogonal machining.     

Calibration and evaluation of seven fracture models

Over the past 5 years, there has been increasing interest of the automotive, aerospace, aluminum, and steel industries in numerical simulation of the fracture process of typical structural materials. Accordingly, there is a pressure on the developers of leading commercial codes, such as ABAQUS, LS-DYNA, and PAM-CRASH to implement reliable fracture criteria into those codes. Even though there are several options to address fracture in these and other commercial codes, no guidelines are given for the users as to which fracture criterion is suitable for a particular application and how to calibrate a given material for fracture. The objective of the present paper is to address the above issues and present a thorough comparative study of seven fracture criteria that are included in libraries of material models of non-linear finite element codes. A set of 15 tests recently conducted by the authors on 2024-T351 aluminum alloy is taken as a reference for the present study. The plane stress prevails in all these tests. These experiments are compared with the constant equivalent strain criterion, the Xue–Wierzbicki (X–W) fracture criterion, the Wilkins (W), the Johnson–Cook (J–C) and the CrachFEM fracture models. Additionally, the maximum shear (MS) stress model, and the fracture forming limit diagram (FFLD) are included in the present evaluation. All criteria are formulated in the general 3-D case for the power law hardening materials and then are specified for the plane stress condition. The advantage of working with plane stress is that there is one-to-one mapping from the stress to the strain space. Therefore, the fracture criteria formulated in the stress space can be compared with those expressed in the strain space and vice versa. Fracture loci for all seven cases were constructed in the space of the equivalent fracture strain and the stress triaxiality. Interesting observations were made regarding the range of applicability and expected errors of some of the most common fracture criteria. Besides evaluating the applicability of several fracture criteria, a detailed calibration procedure for each criterion is presented in the present paper. It was found rather unexpectedly that the MS stress fracture model closely follows the trend of all tests except the round bar tensile tests. The X–W criterion and the CrachFEM models predict correctly fracture in all types of experiments. The W criterion is working well in certain ranges of the stress triaxiality.     

GH2132高温高应变率下力学性能分析与Johnson-Cook本构模型的建立

对铁基高温合金GH2132进行了准静态压缩试验和分离式霍普金森压杆(SHPB)试验,获得了该材料在不同温度和应变率下的应力应变曲线,分析了其力学行为.GH2132在准静态压缩过程中出现加工硬化且没有明显的屈服阶段.在SHPB试验中,GH2132有明显的温度软化效应,当应变率在4000～8000 s-1之间时表现出应变率...     

6061-T651铝合金动态力学性能及J-C本构模型的修正

为合理描述6061-T651铝合金的应力流动行为,利用万能材料试验机和霍普金森压杆,分别进行准静态、高温和高应变率下的材料力学性能测试,获得材料在不同条件下的应力应变曲线。基于试验结果,修正Johnson-Cook本构模型得到MJC(Modified Johnson-Cook)模型,并标定MJC模型各项参数。为校验MJC模型及参数的有效性,利用一级气炮发射直径为5.95mm的圆柱弹体冲击刚性靶的Taylor杆试验以及直径为12.68mm的刚性弹撞击厚度为2mm靶板的试验。最后,采用ABAQUS/Explicit有限元软件建立Taylor杆和弹靶冲击试验的三维模型,基于MJC本构模型进行Taylor杆冲击、以及结合MMC(ModifiedMohr-Coulomb)断裂准则进行弹靶冲击的数值模拟计算。研究结果表明,修正的MJC本构模型能够有效地描述6061-T651铝合金材料在大应变、高应变率和高温下材料的应力流动行为和变形行为。     

Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram

Based on the mathematical formulations for predicting forming limits induced by buckling, wrinkling and bursting of free-expansion tube hydroforming, a theoretical “Process Window Diagram” (PWD) is proposed and established in this paper. The theory developed in the first part of the present work was formulated within the context of free-expansion tube hydroforming with both combined internal pressure and end feeding. The PWD is designed to provide a quick assessment of part producibility for tube hydroforming. The predicted PWD is validated against experimental results conducted for 6260-T4 60×2×320 (mm) aluminum tubes. An optimal loading path is also proposed in the PWD with an attempt to define the ideal forming process for aluminum tube hydroforming. Parametric studies show that the PWD has a strong dependency on tube geometry, material property and process parameters. To the authors’ knowledge, this is the first attempt that a PWD is being formulated theoretically. Such a concept can be advantageous in deriving design solutions and determining optimal process parameters for tube hydroforming processes.     

A continuum plasticity model for the constitutive and indentation behaviour of foamed metals

A yield surface is proposed that can be fitted to the plastic flow properties of a broad class of solids exhibiting plastic compressibility and different yield points in tension and compression. The yield surface is proposed to describe cellular solids, including foamed metals, and designed to be fitted to three experimental results: (1) the compressive stress–strain response (including densification), (2) the difference between the tensile and compressive yield points and (3) the degree of compressibility of the foam, as measured by the lateral expansion during a uniaxial stress compression test. The model is implemented using finite elements and used to study the effects of plastic compressibility on two problems: the compression of a doubly notched specimen and indentation by a spherical indenter. The model is then fitted to the properties of a typical closed cell aluminum foam and used to study indentation into a dense aluminum face sheet on a foam foundation. The dependence of the indentation load–displacement curve on the relevant material and geometric parameters is determined, and a single load–displacement relation is presented which approximates the behaviour of a wide range of practical designs. These results can be used to design against indentation failure of sandwich panels.     

TC4-DT钛合金材料动态力学性能及其本构模型

利用同步组装的高温分离式Hopkinson压杆试验装置,对TC4-DT钛合金材料分别进行了常温下不同应变率（930~9700s-1）和应变率为5000s-1时不同温度下（20~800℃）的动态力学性能测试,获得了各种冲击载荷下的应力-应变曲线。试验数据表明,TC4-DT材料具有应变率增塑效应且存在着临界应变率值,当应变率高于此值时应变率敏感性增强明显,此外随着材料加热温度的升高,软化效应减弱。利用试验所得的数据拟合了基于Power-Law和Johnson-Cook两种热-黏塑性本构方程且获得这两种动态本构模型参数,并将所得的两种拟合曲线与试验所得数据进行对比分析,结果表明两曲线吻合度都较好,此外还对这两种曲线的拟合精度进行对比,对比结果表明两种模型的拟合误差相差不大,但是Power-Law模型拟合精度要略优于Johnson-Cook模型的拟合精度。     

6061-T6铝合金薄板剪切试件设计及动态剪切力学特性分析

车身结构影响了整车的碰撞安全性,其中车身承载部件在碰撞过程中主要表现为剪切失效,因此需要对车身材料的动态剪切力学特性展开研究。为了描述6061-T6铝合金材料在复杂工况下的力学特性,进行了准静态和动态力学性能试验。基于不同应力状态和应变率下铝合金力学性能的测试数据,标定了材料的本构模型和断裂模型参数,并通过对比试验与仿真结果验证了材料参数的准确性。为了实现拉伸试验机开展铝合金薄板剪切试验,设计四种形状的薄板剪切试件,采用数值模拟对比所设计剪切试件的应力及应变分布,并分析不同剪切应变率对6061-T6铝合金材料剪切力学特性的影响规律。结果表明：圆形开口对称试件适用于研究塑性变形阶段的失效断裂,而圆形开口偏置试件适用于研究弹性变形阶段的应力应变关系。在低剪切应变率范围内,6061-T6铝合金无显著的应变率强化效应,然而随着应变率的增加敏感性有所提高。     

高速切削钛合金Ti6Al4V切屑的形成及其数值模拟

应用Hopkinson压杆实验装置,确定了航空用钛合金Ti6Al4V高应变和高温条件下的应力-应变关系,结合Ti6Al4V合金准静态试验数据,建立了适合高速切削仿真的Johnson-Cook本构模型;通过有限元数值模拟,仿真了高速切削Ti6Al4V合金的锯齿状切屑形成过程,分析了整个锯齿状切屑形成过程的切削力、切削温度、等效塑性应变的变化,深入探讨了锯齿状切屑的形成机理;将模拟计算得到的切削力和切削温度与试验结果进行了比较,两者具有较好的一致性。
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考虑热塑性变形的316H不锈钢Johnson-Cook本构参数逆向识别

本构模型能表征材料变形过程中的动态响应,其精度对机械加工中切削力、切削温度的解析预测具有决定性作用.针对316H不锈钢本构模型缺失问题,提出一种基于切削理论的Johnson-Cook本构参数逆向识别方法.通过建立的不等分主剪切区的应力、应变、应变率及温度分布的数学模型,以及准静态压缩试验和正交切削试验的数据,采用粒子群...     

Passivity-based current controller design for a permanent-magnet synchronous motor

The control of a permanent-magnet synchronous motor is a nontrivial issue in AC drives, because of its nonlinear dynamics and time-varying parameters. Within this paper, a new passivity-based controller designed to force the motor to track time-varying speed and torque trajectories is presented. Its design avoids the use of the Euler–Lagrange model and destructuring since it uses a flux-based dq modelling, independent of the rotor angular position. This dq model is obtained through the three-phase abc model of the motor, using a Park transform. The proposed control law does not compensate the model’s workless force terms which appear in the machine’s dq model, as they have no effect on the system’s energy balance and they do not influence the system’s stability properties. Another feature is that the cancellation of the plant’s primary dynamics and nonlinearities is not done by exact zeroing, but by imposing a desired damped transient. The effectiveness of the proposed control is illustrated by numerical simulation results.