Deformation processing of metal powders: Part I—Cold isostatic pressing

Analytical and numerical techniques are used to analyze in detail the stage I Cold Isostatic Pressing (CIPing) of metal powders. Plastic yielding is considered to be the only densification mechanism and the constitutive model developed recently by Fleck, Kuhn and McMeeking [(J. Mech. Phys. Solids40, 1139 (1992)] is used to describe the elastoplastic behavior of the metal powder. It is shown that, for the case of powder consolidation in a long cylindrical tube, a change in length is not possible, unless it is accompanied by some distortion (“shape change”) of the CIPed specimen. The numerical implementation of the constitutive elastoplastic equations in a finite element program is discussed. The finite element method is used to analyze the CIPing of titanium powder. The predictions of the finite element solution agree well with available experimental data.     

Precision radial turning of AISI D2 steel

This paper compares finite element model (FEM) simulations with experimental and analytical findings concerning precision radial turning of AISI D2 steel. FEM machining simulation employs a Lagrangian finite element-based machining model applied to predict cutting and thrust forces, cutting temperature and plastic strain distribution. The results show that the difference between the experimental and simulated cutting force is near 20%, irrespectively of the friction coefficient used in the simulation work (approximately 19.8% for a friction of 0.25% and 18.4% for the Coulomb approach). Concerning the thrust force, differences of about 22.4% when using a friction coefficient of μ?=?0.25 and about 56.9% when using the Coulomb friction coefficient (μ?=?0.378) were found. The maximum cutting temperature obtained using the analytical model is 494.07°C and the difference between experimentation and simulation methods is 15.2% when using a friction coefficient of 0.25 and when using the Coulomb friction only 3.1%. Regarding the plastic strain, the differences between analytical calculations and FEM simulations (for the presented friction values) suggest that the finite element method is capable of predictions with reasonable precision.     

冷挤压弹塑性有限元模拟中摩擦条件的处理

根据流体动力润滑理论,建立冷挤压流体动力润滑模型,并将该模型引入有限变形弹塑性有限元中,对摩擦边界条件进行处理,得到冷挤压工艺中工件内部应力、应变的分布。     

Strain and Stress Fields During Scratch Tests on Amorphous Polymers: Influence of the Local Friction

In this paper, we present results deduced from three-dimensional finite element simulations of scratching, with spherical indenter geometry at different imposed ratios, a/R in the range of 0.1–0.9. For each simulated ratio a/R, the local friction has been increased from 0 to 1. The paper aims at studying the tangential scratch behaviour of homogeneous polymeric substrates, considered in first approximation as elastic linear-hardening plastic material. For only elastic–plastic contacts, without any strain rate or temperature effects, it focuses on studying some characteristic response due to spherical scratching process as a function of scratching conditions (a/R, μ _loc ) such as the stress and plastic strain fields, including the plastic zone dimension and the definition of an volume average plastic strain.     

Finite element modelling of skeletal muscles coupled with fatigue

In this study, Hill's muscle theory coupled with fatigue was proposed to describe mechanical behaviours of skeletal muscles. The force developed by a fatigued muscle was described by a muscle fatigue formula which was a time function of the activation α_a and the stretch λ. The modified Hill's muscle theory was hence incorporated into a three-dimensional (3D) finite element model using the PAK finite element code. In this paper, the theoretical derivation of the 3D muscle model was firstly described. After presenting the method of establishing the finite element programme, a case example of studying the mechanical response of a frog gastrocnemius muscle was used to illustrate the applicability of the proposed methodology. The effects of the muscle fatigue on the deformation as well as the stress and strain distribution of the frog muscle subject to a cyclic activation function have been determined. An experiment capturing the real-time shape change of a frog muscle was also conducted to assess the applicability of the proposed method. A comparison between the deformed shapes of the predictive model and the frog muscles was also made. It was shown that the method is capable of providing a reasonable model for describing the mechanical behaviour of skeletal muscles.     

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.     

Upper-bound limit analysis of a rigid-plastic body with frictional interfaces

A finite element formulation of the upper-bound theorem for rigid-plastic solids, generalized to include interfaces with finite friction, is described. As proved by Collins [J. Mech. Phys. Solids 17, 323 (1969)], the usual definition of a kinematically admissible velocity field is unnecessarily restrictive when the upper-bound theorem is applied to many practical problems. This paper shows that a relaxed inequality can be used successfully to derive upper bounds in the presence of Coulomb friction on interfaces, provided one considers a wide enough class of “admissible” velocity fields.One of the major advantages of using a numerical formulation of the upper-bound theorem is that both complex loading geometry and inhomogeneous material behaviour can be easily dealt with. Using a suitable linear approximation of the yield surface, the application of the necessary boundary conditions, the plastic flow rule and the yield criterion lead to a large linear programming problem. The numerical procedure uses constant-strain triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the finite element mesh. During the solution phase, an active set algorithm is used to solve the linear programming problem.     

A static friction model for tube bulge forming using a solid bulging medium

In a metal working process, the friction between the material and the tools influences the process by modifying the strain distribution of the workpiece. From a numerical point of view, a constant coefficient of friction (Coulomb’s friction) is commonly used in finite element simulations to model the frictional behaviour of contacting solids. However, friction coefficient varies in time and space with many parameters. We presented here a theoretical model of static friction in rubber/metal contact which allows the determination of the static coefficient of friction as a function of local contact conditions. Simulations using finite element software ABAQUS/Explicit were carried out for an axisymmetric tube bulging operation using the defined friction model. We compared the computed tube thickness related to the constant coefficient of static friction with the defined friction model. The results clearly showed that the new friction model provides better agreement between experiments (Girard, Grenier, Mac Donald, J Mater Process Technol 172:346–355, 2006) and results of numerical simulations.     

Analytical and numerical analyses of local loading forming process of T-shape component by using Coulomb,shear and hybrid friction models

The Coulomb friction model, shear friction model and hybrid friction model were employed to analyze the local loading forming process by using slab method (SM) and finite element method (FEM). The results indicated that predicted results by shear friction model and hybrid friction model are almost the same, but there exists a notable difference between Coulomb friction and the other two friction models. The rib cavity will be filled better under Coulomb friction model, and difference of rib height after forming process between Coulomb friction model and shear friction model increases at first and then decreases with the increase in width of local loading.     

A three-dimensional rigid-plastic finite element analysis of bevel gear forging by using a remeshing technique

A three-dimensional remeshing scheme implemented by using a modular concept is proposed for the finite element analysis of a complicated forging process. In order to show the effectiveness of the scheme, forging of a bevel gear is simulated by using several basic modules in the general rigid-plastic finite element code (Yoon and Yang, Int. J. Mech. Sci.30, 887, 1988; Yang et al., Int. J. Mech. Sci.31, 145, 1989) developed for cold forging. Criteria for remeshing as well as a scheme for the mapping of state variables are proposed for three-dimensional remeshing. The computational results are compared with experimental data in order to check the validity of the simulation. The computational results show that the computation can be effectively carried out by using the proposed remeshing scheme and that it can be extended to other more complicated product geometry.     

A friction model for dry contacts during metal-forming processes

In a metal-working process, the friction between the material and the tools influences the process by modifying the strain distribution of the workpiece. This frictional behavior is often taken into account by using a constant coefficient of friction in the finite element simulations. However, friction coefficient varies in time and space with many parameters. This paper aims at modeling of friction in dry contacts which happens at metal-forming processes in the lack of lubricant. The coefficient of dry friction in this model is a function of contact area ratio (which is a function of surface contact characteristics) and strain hardening exponent (material property). The V-bending process of aluminum alloy 6061-T4 sheets was studied experimentally and numerically using ABAQUS/Standard with two kinds of friction models: Coulomb friction and newly developed dry friction models. The results clearly showed that the developed dry friction model has better results in predicting load-stroke curves and springback compared to traditional Coulomb friction model. The FE prediction error for 6061-T4 AA is 16.9% using Coulomb friction model and 9.2% using dry friction model.     

考虑摩擦因数与滑动速度相关时的轮轨滚动接触有限元分析

使用与滑动速度相关的摩擦因数替代库伦摩擦定律中的常系数,结合mixed Lagrangian/Eulerian方法建立轮轨滚动接触有限元模型,分析牵引力主导的蠕滑工况下的干燥状态的轮轨滚动接触特性。通过与摩擦因数取值为常数的轮轨滚动接触分析结果对比发现:与滑动速度相关的摩擦因数对轮轨滚动接触最大接触应力和接触斑面积影响不大,均在1%以内;但是对轮轨接触斑内最大Mises应力、最大纵向切应力、最大横向切应力和最大等效塑性应变影响较大,特别是对最大纵向切应力影响幅度近20%;更需要引起注意的是对轮轨滚动接触摩擦力矢量分布和切向塑性应变分布影响明显,这对轮轨滚动接触疲劳损伤分析非常重要。     

Three-dimensional finite element modelling of the scratch test for a TiN coated titanium alloy substrate

A three-dimensional (3D) finite element (FE) simulation of a rigid Rockwell C indenter scratching a TiN/Ti-6Al-4V coating/substrate system is presented. Coulomb friction between the indenter and the surface of the coating/substrate system was considered. The material properties of the coating and substrate were assumed to be elastic–plastic following a bilinear law with isotropic strain hardening. The von Mises yield criteria was used to determine the onset of plastic deformations. The scratch depth profiles at different moving distances were studied. The distributions of the stress field at the contact surface, in the coating, and at the interface of the coating/substrate system were investigated. The finite element results can be used to explain the failure modes of coated materials at the scratch test.     

Finite element analysis of the effect of sequential cuts and tool–chip friction on residual stresses in a machined layer

A thermo-elastic–viscoplastic model using explicit finite element code Abaqus was developed to investigate the effect of sequential cuts and tool–chip friction on residual stresses in a machined layer. Chip formation, cutting forces and temperature were also examined in the sequential cuts. The affected layer from the first cut slightly changes the chip thickness, cutting forces, residual strain and temperature of the machined layer, but significantly affects the residual stress distribution produced by the second cut. Residual stress is sensitive to friction condition of the tool–chip interface. Simulation results offer an insight into residual stresses induced in sequential cuts. Based on simulation results, characteristics of residual stress distribution can be controlled by optimizing the second cut.     

Flaring and nosing process for composite annoy tube in circular cone tool application

An elasto-plastic incremental finite element computer code based on an updated Lagrangian formulation was developed to simulate the flaring and nosing processes of a metal tube in the asisymmetric condition. The extended r _min technique was used to treat the elastic–plastic stress state and to solve contact problems at the tool–metal interface. A modified Coulomb’s friction law was introduced to treat the alternation of the sliding–sticking state of friction at the contact interface. The forming performed analysis using the finite element method and experiment. To examine the influence of the thickness ratio and the optimum punch semi-angle and friction on the forming load of the two-ply metal tubes consisting of soft aluminum, hard aluminum, and copper. The calculated tube geometries and the relationship between punch load and stroke are in good agreement with the experimental data.     

金属板料冲压成形的数值模拟

本文采用有限元动力显式算法模拟金属板料冲压成形的加工过程。四结点蜕化壳单元和刚体壳单元分别用来建立权和模具的有限元模型;更新Ｌａｇｒａｎｇｅ法和速率型本构关系被用来处理板料变形中的大应变和大转动;材料模型采用塑性各向异性屈服与等向强化模型;通过主从面模型定义板料和模具的接触,接触算法采用运动约束法,摩擦力用库仓定律计算;并利用动力松弛法对回弹过程进行了计算。模拟结果和实际零件比较,证明模型合理,算法稳定,结果可靠,具有良好的应用价值。     

Mechanistic and Finite Element Model for Prediction of Cutting Forces During Micro-Turning of Titanium Alloy

Titanium alloy Ti-6Al-4V is commonly used in biomedical applications due to its superior properties such as biocompatibility, high strength-to-weight ratio and corrosion resistance. To understand the mechanics of the micro-turning process of these alloys, a mechanistic model has been developed for predicting the cutting forces. A modified Johnson–Cook material model with strain gradient plasticity is used to represent the flow stress of work material. The micro-turning experiments were conducted to verify the cutting forces predicted by mechanistic model. A finite element model is also developed with different shear friction factors and calibrated using experimental results to confirm and interpret the results of mechanistic model. It is inferred that strain rate increases by increasing cutting speed, whereas it decreases with increase in the feed rate due to increase in adiabatic shear band spacing. Since Ti-6Al-4V has low thermal conductivity, when cutting speed increases, there is an increase in the tool-chip interface temperature that leads to decrease in cutting forces. When cutting speed increases, chip morphology changes from discontinuous to continuous, and there is significant deterioration in the surface finish. It is observed that the average cutting force prediction errors for mechanistic and finite element models are 9.69% and 11.45% respectively.     

A Mixed Lubrication Model for Computer Simulation of Extrusion Processes

A mixed lubrication/friction model for extrusion process is developed in the present research. The model combines a rigid-plasticity finite element code to simulate the interface condition between the tooling and workpiece in the extrusion operation. The influence of surface roughness on lubricant flow is treated by using the average Reynolds equation. The active lubrication regime and appropriate friction factor were determined from the current local values of interface variables such as mean lubricant film thickness and workpiece and tooling roughness, in addition to the more traditional external variables such as interface pressure, node sliding velocity and strain rate of the workpiece. Numerical results using the coupled code include friction stress and normal pressure under different lubrication conditions are compared with experimental investigation. The discrepancy is very small and the proposed model proved to be very efficient in predicting interface friction condition in the extrusion processes.     

Near-net-shape forming of 316L stainless steel powder under hot isostatic pressing

Near-net-shape forming of 316L stainless steel powder is investigated under hot isostatic pressing (HIPing). A stainless steel powder compact and an insert were encapsulated by a stainless steel container and hot isostatically pressed to produce an axisymmetric near-net-shape part. To simulate densification and deformation of a powder compact in the container during HIPing, the constitutive model of Abouaf et al., and that of McMeeking and co-workers were implemented into a finite element analysis. The thickness effect of the container on densification was also studied for the axisymmetric part during HIPing. Densification of a three-dimensional asymmetric part during HIPing was also investigated by comparing finite element calculations with experimental data by Eisen et al.