Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y₀ and tangent modulus E_T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point (ε_c, σ_c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ_c at the specific true strain ε_C lead to the same loading and unloading indentation curve. We show that the true strain ε_c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ_c/ε_c is directly related to the elastic modulus of the indented material and the tip geometry.     

Coupled buckling and plastic instability for tube hydroforming

In this paper, the hydroforming limit of isotropic tubes subjected to internal hydraulic pressure and independent axial load is discussed.Swift's criterion is often used in this case for the prediction of diffuse plastic instability. Here, we first highlight the existence of two different Swift's criteria (for sheets and for tubes).Then, we recall that these types of approaches do not take into account buckling induced by axial loading. In fact, buckling may obviously occur before plastic instability; consequently, Swift's criteria must not be used alone to predict instability in the case of tube hydroforming.Numerical simulation was used to confirm these points and to analyse both the buckling and striction phenomena together. The two types of instability must be treated together in a reasonable approach to the hydroforming process.In this paper, the material verifies a “J2-flow” constitutive rate constitutive law. Jaumann's derivative was chosen and the Prandtl–Reuss equations with von Mises’ yield criterion and the associated flow rule were used. Isotropic hardening was taken into account.     

Contact analysis of impact in magnetic head disk interfaces

Three-dimensional finite element analysis of head and disk contact effects induced by impact in magnetic head disk interface (HDI) are presented. Elastic–plastic contact simulations are performed using . The entire contact–impact procedures during head disk collision under the dynamic loading of half-sine pulse acceleration with profiles of 300 and 500 g amplitude and 1.0 ms in duration are described in detail. Simulation results for the contact pressure distribution at HDI, von Mises equivalent stress, and equivalent plastic strain fields are examined and interpreted in terms of impact history. A comprehensive history of head disk relative displacement and von Mises equivalent stresses within contact region are provided and the evolution of plasticity are discussed. It is shown that finite element method can provide the simulation of the contact behavior resulting from the dynamic loading.     

晶须长径比对树脂基复合材料力学行为影响的数值模拟

在单向晶须增强树脂基复合材料的轴对称模型和已有研究成果基础上,利用有限元分析方法,研究该类复合材料中晶须长径比的变化对材料整体力学行为的影响.结果表明:晶须长径比对晶须应力作用明显大于对基体的影响;晶须的长径比h/r≤30时,随着晶须长径比的增大,发生在晶须端部处的集中应力急剧增加;但当长径比h/r＞30时,长径比的进一步增加对集中应力影响不大;随着晶须长径比的增大,界面剪切应力减小,分布曲线下移;但当长径比h/r＞30时,长径比的进一步增加对剪切应力影响不大;随着晶须长径比的增加,复合材料的拉伸强度逐渐增大.     

Numerical study of the flange earring of deep-drawing sheets with stronger anisotropy

A Barlat–Lian anisotropy yield function is introduced into a quasi-flow corner theory of elastic–plastic finite deformation and the elastic–plastic large deformation finite element formulation based on the principle of virtual velocity and the discrete Kirchhoff triangle plate shell element model. The focus of the present researches is on the numerical simulation of the flange earring of deep-drawing process of circular sheets with stronger anisotropy, based on which, the schemes for controlling the flange earring are proposed.     

Substepping algorithms with stress correction for the simulation of sheet metal forming process

The finite element analysis of the sheet metal forming process involves various nonlinearities. To predict accurately the final geometry of the sheet blank and the distribution of strain and stress and control various forming defects, such as thinning, wrinkling and springback, etc., the accurate integration of the constitutive laws over the strain path is essential. Our objective in this paper is to develop an effective and accurate stress integration scheme for the analysis of three-dimensional sheet metal forming problems. The proposed algorithm is based on the explicit “substepping” schemes incorporating with the stress correction scheme. The proposed algorithms have been implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform. The algorithms are then employed to analyze a typical deep-cup drawing process and the accuracy of these algorithms has been compared with the implicit “return” algorithm and explicit forward algorithm. The results indicate that the explicit schemes with local truncation error control, together with a subsequent check of the consistency conditions, can achieve the same or even better level of accuracy as “return” algorithm does for integrating large plastic problems like sheet metal forming process.     

热障涂层在多次热循环作用下残余应力的模拟

采用热弹塑性有限元方法,对热障涂层多次热循环降温过程中由于热梯度和材料参数不匹配而产生的残余应力进行了数值模拟,分析了平面和曲面的界面形貌对界面残余应力的影响.结果表明,在相同材料参数情况下,陶瓷层与粘接层的界面形状对残余应力及结构稳定状态有显著的影响,凹凸不平的界面将会使界面残余应力发生突变,不利于增强界面结合强度和涂层结构的热稳定性.该结果对分析涂层寿命及失效机制有指导意义.     

温度梯度对热障涂层影响的模拟

采用热弹塑性有限元法,对热障涂层在不同温度梯度作用的过程中,由于材料系数不匹配而引起的应力和位移进行了模拟分析.结果表明,等效应力的大小随温度梯度的大小单调递减;界面最大位移随温度梯度单调递增.同时也发现,模型在不同温度梯度下存在一个最小位移;当材料属性和载荷一定时,将存在一个最佳涂层厚度,使得涂层总的位移最小.该结果对分析涂层寿命及失效机制有指导意义.     

数控车削刀具圆弧半径对切削过程影响的数值分析

数控车削加工中刀具的圆弧半径对切削力,切屑的断屑,切屑的形状,加工表面质量、加工变形以及已切削表面的残余应力的大小,状态,分布有着很大的影响.本文采用有限元分析方法,利用有限元增量理论,建立了二维金属切削仿真模型,分析中采用网格自适应准则,模拟了典型零件车削二维切削过程中切屑的形成,得到了加工后已加工表面的残余应力的大小,状态以及分布状况,对于工程中的实际应用具有重要的意义.     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

Investigations on the effects of friction modeling in finite element simulation of machining

Accurately predicting the physical cutting process variables, e.g. temperature, velocity, strain and stress fields, plays a pivotal role for predictive process engineering for machining processes. These predicted field variables, however, are highly influenced by workpiece constitutive material model (i.e. flow stress), thermo-mechanical properties and contact friction law at the tool-chip-workpiece interfaces. This paper aims to investigate effects of friction modeling at the tool-chip-workpiece interfaces on chip formation process in predicting forces, temperatures and other field variables such as normal stress and shear stress on the tool by using advanced finite element (FE) simulation techniques.For this purpose, two distinct FE models with Arbitrary Lagrangian Eulerian (ALE) fully coupled thermal-stress analyses are employed to study not only the effects of FE modeling with different ALE techniques but also to investigate the influence of limiting shear stress at the tool-chip contact on frictional conditions, which was never done before. A detailed friction modeling at the tool-chip and tool-work interfaces is also carried by coupling sticking and sliding frictions. Experiments and simulations have been performed for machining of AISI 4340 steel using tungsten carbide tooling and the simulation results under increasing limit shear stress have been compared to experiments. The influence of limiting shear stress on the tool-chip contact friction was explored and validity of friction modeling approaches was examined. The results presented in this work not only provide a clear understanding of friction in FEM modeling of machining but also advance the process knowledge in machining.     

A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels)

The determination of residual stresses induced by welding or heat treatment operations requires the use of complex models taking into account thermal, metallurgical and mechanical phenomena. In this paper, we propose a mechanical model in which each phase can follow its own constitutive law. This model also takes into account phase transformation plasticity, which is treated independently of the behavior of each phase. This model has been implemented into the French FEM code Castem 2000. The interest of the proposed method is that it allows one to mix any type of nonlinear behavior using Taylor homogenization hypothesis. There is no need to develop a theory to get the equations of the homogenized material law. Two numerical examples demonstrate the efficiency and the flexibility of this approach. The results obtained are compared to experimental values for a typical welding situation and a high-temperature response. This comparison seems to indicate that viscous effects in the materials have a significative influence on the residual stresses produced by welding.     

A modification of the Jones–Harris method for deep-groove ball bearings

This study presents a modification of the Jones–Harris method (JHM) for the determination of deflection in deep-groove ball bearings. The finite element method (FEM) and curve fitting have been utilized to modify the load–deflection relationships of Hertz contact formulas in JHM. Several cases of deep-groove bearings are simulated to determine contact deflection. Results obtained from the modified JHM (MJHM) are more accurate than the JHM results demonstrated by the comparison between FEM and experimental results.     

The effect of hard coated metals on the thermo‐oxidative stability of a branched perfluoropolyalkylether lubricant

M‐50 and carburized Pyrowear 675® (Carpenter Technology, Reading PA, USA) steel coupons deposited with commercially available physical vapour deposited TiN, TiCN, TiAlCN, TiCrCN/TiB₄C multilayer, electroless Ni (E‐Ni) TiN and E‐Ni TiCN coatings were immersed in a branched perfluoropolyalkylether (PFPAE), Krytox AC® (E.I. du pont de Nemours and Company, Wilmington DE, USA), in an oxidative environment at temperatures ranging from 315 to 360 °C for a duration of 24 hours and compared with uncoated coupons. Coated and uncoated Pyrowear 675® coupons demonstrated superior corrosion resistance compared with coated and uncoated M‐50 respectively. The coatings most resistant to chemical attack in the PFPAE fluid were TiCN, E‐Ni TiN and E‐Ni TiCN. Copyright © 2006 John Wiley & Sons, Ltd.     

Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios (a/c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J–Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances (r/(J/σ₀)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/σ₀) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ_e, the hydrostatic stress σ_m and the stress triaxiality R_σ, the three-parameter J–Q_T–T_z approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor T_z and the Q_T term, which is determined by matching the finite element analysis results, the J–Q_T–T_z solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/c and n. Finally, the empirical formula of T_z and the stress components are provided to predict the stress state parameters effectively.     

Simulation of springback

Springback, the elastically-driven change of shape of a part after forming, has been simulated with 2-D and 3-D finite element modeling. Simulations using solid and shell elements have been compared with draw-bend measurements presented in a companion paper. Plane-stress and plane-strain simulations revealed the dramatic role of numerical tolerances and procedures on the results. For example, up to 51 integration points through the sheet thickness were required for accuracy within 1%, compared with 5–9 typically acceptable for forming simulations. Improvements were also needed in the number of elements in contact with the tools, and in the numerical tolerance for satisfying equilibrium at each step. Significant plastic straining took place in some cases upon unloading; however the choice of elastic–plastic unloading scheme had little effect on the results. While 2-D simulations showed good agreement with experiments under some test conditions, springback discrepancies of hundreds of percent were noted for one alloy with sheet tension near the yield stress. 3-D simulations provided much better agreement, the major source of error being identified as the presence of persistent anticlastic curvature. Most of the remaining deviation in results can be attributed to inaccuracies of the material model. In particular, the presence of a Bauschinger effect changes the results markedly, and taking it into account provided good agreement. Shell elements were adequate to predict springback accurately for R/t greater than 5 or 6, while solid elements were required for higher curvatures. As R/t approaches 2, springback simulated with solid elements tends to disappear, in agreement with measurements presented in the companion paper and in the literature.     

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlat's 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.