Dynamic ductile fracture in aluminum round bars: experiments and simulations

The application of rate-dependent cohesive elements is validated in simulation of ductile fracture in aluminum round bars under dynamic loading conditions. Smooth and notched round bars made of AA6060-T6 are tested and simulated under quasi-static and dynamic loadings. The smooth round bar is modeled using finite elements that obey Gurson–Tvergaard–Needleman (GTN) formulation as the constitutive equation. Comparing with experimental results, corresponding GTN parameters and rate-dependent plasticity of the alloy are obtained. A single strain rate-dependent GTN element with the obtained parameters is examined under different values of stress triaxiality and loading rates. The resulting stress-elongation curves represent the traction separation law (TSL) for cohesive elements and the variations of the maximum traction and the energy absorbed are investigated. The notched round bars are modeled by axisymmetric continuum and cohesive elements. The undamaged bulk material is elastic-visco plastic and the cohesive elements obey the TSL defined from the single element calculations. The experiments are simulated by these models in which the cohesive elements are rate sensitive and automatically obtain the values of the total strain rate from their adjacent continuum elements to update the values of the cohesive strength during the analysis. The results of the analysis, including maximum load, time of failure and diameter reduction are validated with the experimental results. The effects of element size, rate-dependent plasticity of the material and stress triaxiality are also discussed.     

Plane strain finite element simulation of shear band formation during metal forming

A plane strain finite element formulation and solution procedure for shear band failure during the plane strain metal forming process are developed and presented. The large strain elastic-plastic formulation includes a 5-node 10-degree-of-freedom (d.o.f.) ‘crossed-triangle’ element, a 4-node 8-d.o.f. element with selective reduced integration, an 8-node 16-d.o.f. element and a 4-node 8-d.o.f. element with an embedded shear band. The formulation includes an elastic-plastic material model with a modified Gurson yield function and combined isotropic-kinematic hardening. The solution procedure is based on a Newton–Raphson incremental-iterative method with an orthogonal projection of zero or negative eigen-modes when required. Two different examples of plane strain tension test are studied with results compared with available numerical solutions to evaluate the present formulation and solution procedure of the four different elements. The results demonstrate that both types of the 4-node quadrilaterals are comparable to the 5-node crossed-triangle element as well as the 8-jiode element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples are investigated. The first application is a numerical simulation of a sheet-stretching test with results compared with experimental data for a commercially pure aluminium–magnesium 5182-O sheet. The load vs. extension history and the through-thickness strain are compared. The good agreement suggests that it is possible to numerically determine the parameters needed for the modified Gurson yield function. The second application is a numerical simulation of the formation of dead metal zones in the extrusion process. A plane strain extrusion of a short aluminium billet through straight-sided dies is presented and characteristic features of the formation of dead metal zone are observed.     

On the influence of kinematic hardening on plastic anisotropy in the context of finite strain plasticity

The paper discusses the application of a newly developed material model for finite anisotropic plasticity to the simulation of earing formation in cylindrical cup drawing. The model incorporates Hill-type plastic anisotropy, nonlinear kinematic and nonlinear isotropic hardening. The constitutive framework is derived in the context of continuum thermodynamics and represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime. Plastic anisotropy is described by means of second-order structure tensors which are used as additional tensor-valued arguments in the representation of the yield criterion and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that fullfils plastic incompressibility and preserves the symmetry of the internal variables. The numerical examples investigate the influence of the hardening behaviour on an initially anisotropic yield criterion. In particular, the influence of using the kinematic hardening component of the model in addition to isotropic hardening in the earing simulations is examined. Comparisons with test data for aluminium and steel sheets display a good agreement between the finite element results and the experimental data.     

Computational and experimental study of high-speed impact of metallic Taylor cylinders

High-speed impact of metallic Taylor cylinders is investigated computationally and experimentally. On the computational side, a modular explicit finite element hydrocode based on updated Lagrangian formulation is developed. A non-classical contour integration is employed to calculate the nodal forces in the constant strain axisymmetric triangular elements. Cell and nodal averaging of volumetric strain formulations are implemented on different mesh architectures to reduce the incompressibility constraints and eliminate volumetric locking. On the experimental side, a gas gun is designed and manufactured, and Taylor impact tests of cylinders made of several metallic materials are performed. Computational predictions of the deformed profiles of Taylor cylinders and experimentally determined deformed profiles are compared for verification purposes and to infer conclusions on the effect of yield strength, strain hardening and strain rate on the material response. The article also compares the performance of different plastic flow stress models that are incorporated into the hydrocode with the experimental results and results provided by previously reported simulations and tests.     

On modeling anisotropy in deformation processes involving textured polycrystals with distorted grain shape

A mathematical formulation is presented which uses rate-dependent polycrystalline plasticity to model the development of plastic anisotropy in bulk forming processes. The formulation assumes that underlying a material point on a continuum scale is a collection of anisotropic, contiguous grains. The mechanical response at a continuum level is derived from the response of individual grains suitably averaged over all grains in the aggregate. The effects of preferred orientation (texture) and of the evolving grain shape on the directionality to the flow properties of the polycrystal are included. A general numerical framework is described for incorporating this complex material behavior in a finite element formulation. As an application, texture development during the flat rolling of aluminum sheets is presented. The simulation predictions have been compared with reported experimental data and with a previous study where the effects of grain shape were neglected.     

Experimental and finite element predictions of residual stresses due to orthogonal metal cutting

The development and implementation of a finite element method for the simulation of plane-strain orthogonal metal cutting processes with continuous chip formation are presented. Experimental procedures for orthogonal metal cutting and measurement of distributions of residual stresses using the X-ray diffraction method are also presented. A four-node, eight degree-of-freedom, quadrilateral plane-strain finite element is formulated. The effects of elasticity, viscoplasticity, temperature, friction, strain-rate and large strain are included in this formulation. Some special techniques for the finite element simulation of metal cutting processes, such as element separation and mesh rezoning, are used to enhance the computational accuracy and efficiency. The orthogonal metal cutting experiment is set-up on a shaper, and the distributions of residual stresses of the annealed 1020 carbon steel sample are measured using the X-ray diffraction method. Under nominally the same cutting conditions as the experiment, the cutting processes are also simulated using the finite element method. Comparisons of the experimental and finite element results for the distributions of residual stresses indicate a fairly reasonable level of agreement. The versatility of the present finite element simulation method allows for displaying detailed results and knowledge generated by orthogonal metal cutting processes, such as the distribution of temperature, yield stress, effective stress, plastic strain, plastic strain-rate, hydrostatic stress, deformed configuration, etc. Such knowledge is useful to provide physical insights into the process as well as to better design the process for machining parts with improved performance.     

Numerical analysis of superplastic blow forming of Ti–6Al–4V alloys

The superplastic blow forming of a Ti–6Al–4V sheet into a cylindrical cup has been numerically analysed based on the actual forming process using ABAQUS. A detailed element type study has been performed to eliminate the element dependency in the finite element analysis. The accuracy and reliability of the proposed finite element model has been validated in comparison with experimental data. The validation proves that, there is a good agreement between the simulation and the experiment. In addition, the best prediction of the thickness distribution can be obtained using the continuum element. Furthermore, the effects of major factors such as friction coefficient and the strain rate sensitivity index upon the optimum forming pressure-time and thickness distribution of the component have been studied systematically using the proposed finite element model.     

Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms, elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate the efficiency of the algorithm.     

Adaptive 2D finite element simulation of metal forming processes

The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large-strain, elastic–plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.     

多台阶深筒形件成形工艺设计及仿真

根据塑性成形理论分析、计算确定某电器产品的阶梯圆筒件成形工艺,并建立有限元模型,实现多道次拉深过程的仿真.最后对仿真结果进行分析和试验验证.     

Numerical simulation for stress/strain distribution and microstructural evolution in 42CrMo steel during hot upsetting process

Based on experimental results, the dynamic recrystallization mathematical models of 42CrMo steel were derived. The effects of strain rates on the strain/stress distribution and microstructural evolution in 42CrMo steel during hot upsetting process were simulated by integrating the thermo-mechanical coupled finite element model. The results show that the deformation of the specimen is inhomogeneous, and the degree of the deformation inhomogeneity decreases with the increase of strain rates. The distribution of the effective stress in the specimen is also inhomogeneous, and the locus of the maximum effective stress changes with the variations of strain rates. The dynamic recrystallization volume fraction decreases with the increase of strain rates. The distribution of the dynamic recrystallization grain is inhomogeneous in the deformed specimen, and the average dynamic recrystallization grain size decreases as the strain rate is increased. A good agreement between the predicted and experimental results confirmed that the derived dynamic recrystallization mathematical models can be successfully incorporated into the finite element model to predict the microstructural evolution in the hot upsetting process for 42CrMo steel.     

Experimental research and numerical simulation of the dynamic cylinder upsetting

In order to study the dynamic effects under impulsive load, experimental and numerical investigations on the dynamic upsetting process of lead cylinder were conducted. Experiments were carried out on a drop hammer impact test machine. The results show that the dynamic effects on the forming load is related to the hammer velocity, radius–height ratio of specimen and drop mass. The forming load increases with the increase of the hammer velocity or radius-to-height ratio. The fluctuation of load–displacement curve becomes obvious with the increase of the hammer velocity and drop mass. The deformation processes were simulated by the finite element program ANSYS/LS-DYNA. The deformed configuration, velocity vector field and equivalent strain distribution were obtained. The results show that the deformed geometry exhibits mushroom, the material points in the upper region flow faster than that in the lower region, and a strain concentration zone appears in the upper center region.     

Numerical simulation of forging a ball from a cylindrical billet

Abstract

Rigid‐viscoplastic finite element equations are used for the analysis of metal forming process. With the view of solution accuracy and computation efficiency, the possible overconstraint of the incompressibility condition is avoided by modifying the penalty method in the variational formulation; and both the direct iterative method and Newton‐Raphson iterative method are combined to solve the finite element equations. The forging process of a ball from a cylindrical workpiece is completely simulated by a remesh procedure. The computed results agree well with the experimental measurements. It is shown, during the early stage of plastic deformation, the effect of friction is small, but gradually increases with further plastic deformation. In the finishing stage, the shear plastic deformation is found mainly in the flash portion. As the shape factor of workpiece increases, the filling of the die cavity is more complete, but the required forming energy increases and the variation of microstructure within the final forged product is intensified. The effect of die velocity also improves die cavity filling.     

Modeling fatigue crack and spalling for rolling die under hot milling

In hot milling process, rolling die is subjected to nonsteady conditions which can rise the combinations of fatigue and spalling damage mechanism. An understanding about the failure mechanism of the rolling die is essential under hot rolling process. Fatigue crack growth and spalling process are governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic‐plastic fracture mechanics, an analytical model are presented in this paper to determine the elliptical crack growth rate and spalling damage mechanism. The model includes new proposed constitutive equations for fatigue and spalling crack growth. To verify the models, finite element simulation and experimental data are considered. The results show good agreement with finite element simulation and experimental data.     

多拐曲轴镦挤成形过程轴向流动模拟分析与试验验证

目的 解决多拐曲轴镦挤复合成形过程中,轴向流动导致尺寸精度低的问题。方法 从坯料加热、成形过程、成形后冷却等全流程模拟出发,以建立镦挤成形装置运动学、成形过程热力学、曲轴材料本构模型、几何模型等为基础,建立有限元模型,分析产生轴向偏差的原因。结果 有限元模拟分析表明,坯料体积、飞边厚度是镦挤成形过程产生轴向流动的关键性因素,可以通过优化台阶轴毛坯几何形状,控制轴向异常流动。结论 试验表明,多拐曲轴的轴向流动得到有效控制,单拐轴向长度偏差控制在±1 mm,成品率提高至90%以上。     

动态镦粗过程的动力显式有限元分析

为了研究金属的三维动态锤锻成形过程,基于连续介质力学及有限变形理论,建立了一种有限元模型.采用动力分析方法,在运动方程中加入惯性力项考虑锤锻中显著的惯性效应;根据设备的工作原理按照能量守恒定律计算变形期间的锤头速度;同时,将变形视为一个绝热过程计算变形期间试样内部的温度升高.基于建立的模型开发了动力显式有限元分析程序,模拟了铅块试样在落锤打击下的动态镦粗过程,给出了试样内部的位移、等效应变、等效应力和温度分布规律.将变形后试样几何形状、成形载荷-时间曲线和锤头速度-时间曲线的计算结果与实验结果相对比,表明了开发程序计算结果的准确性.     

Modeling of hot isostatic pressing of metal powder with temperature–dependent cap plasticity model

In this paper, the coupled thermo–mechanical simulation of hot isostatic pressing (HIPing) is presented for metal powders during densification process. The densification of powder is assumed to occur due to plastic hardening of metal particles. The constitutive model developed is used to describe the nonlinear behavior of metal powder. The numerical modeling of hot powder compaction simulation is performed based on the large deformation formulation, powder plasticity behavior, and frictional contact algorithm. A Lagrangian finite element formulation is employed for the large powder deformations. A modified cap plasticity model considering temperature effects is used in numerical simulation of nonlinear powder behavior. The influence of powder-tool friction is simulated by the use of penalty approach in which a plasticity theory of friction is incorporated to model sliding resistance at the powder-tool interface. Finally, numerical examples are analyzed to demonstrate the feasibility of the proposed thermo–mechanical simulation using the modified cap plasticity model in the hot isostatic forming process of powder compaction.     

UOE焊管成形三维有限元模拟

建立了UOE焊管成形过程的三维有限元模型,模拟具有大变形和复杂接触的成形过程,分析板料各个成形段的回弹,获得了不同成形段板料的变形构形、等效塑性应变分布以及成形载荷的变化。研究结果可为UOE工艺设计以及评估成形机组制管能力提供指导。     

An ALE hydrodynamic lubrication finite element method with application to strip rolling

A method that incorporates the hydrodynamic lubrication analysis into the arbitrary Lagrangian Eulerian (ALE) finite element analysis is developed for steady-state strip rolling simulation. By employing the ALE formulation, only part of the workpiece, which is subjected to large plastic deformation within the roll-bite region, is modelled, so that the computational cost is substantially reduced. In the hydrodynamic lubrication formulation, the effect of surface roughness on the lubricant flow is taken into consideration by the use of an average flow model. The friction stress is expressed in terms of forming variables such as surface roughness, lubricant and workpiece properties, film thickness, forming speed and process geometry. Furthermore, the elastic deformation of rolls is also analysed by the boundary element method to avoid the finite element discretization inside the rolls. Two numerical examples, aluminium and steel strip rolling processes, are presented to demonstrate the merits of the proposed method.