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.     

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.     

Distortion,degeneracy and rezoning in finite elements — A survey

The results obtained from finite element analysis are significantly affected by the quality of elements. In certain applications like shape optimization, crash analysis, metal forming, fluid flow analysis, and large displacement analysis, the finite element mesh is systematically updated in an iterative process. In such situations, in spite of an ideal starting mesh, the quality of elements could deteriorate, causing severly distorted elements. In extreme cases, the elements become degenerate and further progress of analysis is restricted. An understanding of the methods of quantifying element distortion helps in identifying ‘bad’ geometry and in deciding when to remesh. Knowledge about geometric configurations which cause degeneracy assists in controlling degeneracy during the analysis. This paper contains a survey of available distortion measures and degeneracy conditions for various elements in two and three dimensions. It is a review of the literature in this field in the last two decades. A brief review of rezoning is also included, since it is one of the more popularly used methods to correct a distorted mesh.     

Adaptiver 3D-Vernetzungsalgorithmus zur FEM-Analyse von Massivumformvorgängen

In the numerical simulation of bulk metal forming process by the finite element method (FEM) extremely degenerated meshes result due to high local deformation. The finite elements distort so much that they lose their regular shape. Remeshing and rezoning techniques are necessary to avoid the resulting numerical problems. For remeshing it is important to create a new mesh with regular elements, and to refine the generated grid in dependency of geometric features. An automatic remeshing-module independent of the FE-code is developed at the Institute of Metal forming and Metal forming Machine tools (IFUM). This program creates a mesh that meets all requirements of the object by combination of adaptive meshing and optimisation of the correct grid distortion. In this paper an algorithm to mesh complex 3D geometries with tetrahedron elements is introduced, by taking into account the specific of metal forming processes and their implication in FE-Analysis.     

A fractal patch test

Element consistency is generally checked using the patch test on an element patch of finite size. This condition may in certain cases be too restrictive, and disqualifies elements that appear to be convergent. A method termed ‘fractal patch test’ is presented, in which the patch size is maintained constant while the distorted mesh is refined. Examples are given for four-node quadrilateral elements used in plane stress and strain analysis, and for plate bending elements.     

Localized remeshing techniques for three‐dimensional metal forming simulations with linear tetrahedral elements

The localized remeshing technique for three‐dimensional metal forming simulations is proposed based on a mixed finite element formulation with linear tetrahedral elements in the present study. The numerical algorithm to generate linear tetrahedral elements is developed for finite element analyses using the advancing front technique with local optimization method which keeps the advancing fronts smooth. The surface mesh generation using mesh manipulations of the boundary elements of the old mesh system was made to improve mesh quality of the boundary surface elements, resulting in reduction of volume change in forming simulations. The mesh quality generated was compared with that obtained from the commercial CAD package for the complex geometry like lumbar. The simulation results of backward extrusion and bevel gear and spider forgings indicate that the currently developed simulation technique with the localized remeshing can be used effectively to simulate the three‐dimensional forming processes with a reduced computation time. Copyright © 2006 John Wiley & Sons, Ltd.     

On the strain Assumption in a finite element model for plates and shells

Two different methods of assuming independent strain fields are examined for the nine node degenerate solid shell element. In the first case, the assumed strain field is chosen for the local orthogonal co-ordinate systems defined at the Gaussian integration points. In the second case, the independent strain is assumed for a local orthogonal co-ordinate system defined at the origin of the parent co-ordinates. The results of numerical tests involving simple example problems demonstrate that the second method is capable of exactly representing constant stress or moment states even when element geometries are distorted. In addition, both methods lead to a finite element model which is free of locking.     

Experimental and finite element simulation methods for rate-dependent metal forming processes

An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.     

Rigid-plastic boundary element analysis of the upsetting of slabs

This paper presents an innovative approach for analysing plane strain metal forming processes. The proposed approach is based on the rigid-plastic boundary element method for slightly compressible material models.The main advantage of the rigid-plastic boundary element method over existing numerical simulation methods is the necessity of requiring the unknowns to be mainly set at the contour of the workpiece, simplifying the analysis and offering additional computational advantages.A numerical example consisting of the frictionless upsetting of rectangular slabs between flat anvils under plane strain conditions is included to show the applicability of the proposed approach. Assessment with the analytically exact solution is made in terms of geometry, pressure and distribution of strain and stress inside the workpiece.     

Identification of Constitutive Material Model Parameters for High-Strain Rate Metal Cutting Conditions Using Evolutionary Computational Algorithms

Advances in plasticity-based analytical modeling and finite element methods (FEM) based numerical modeling of metal cutting have resulted in capabilities of predicting the physical phenomena in metal cutting such as forces, temperatures, and stresses generated. However, accuracy and reliability of these predictions rely on a work material constitutive model describing the flow stress, at which work material starts to plastically deform. This paper presents a methodology to determine deformation behavior of work materials in high-strain rate metal cutting conditions and utilizes evolutionary computational methods in identifying constitutive model parameters. The Johnson-Cook (JC) constitutive model and cooperative particle swarm optimization (CPSO) method are combined to investigate the effects of high-strain rate dependency, thermal softening and strain rate-temperature coupling on the material flow stress. The methodology is applied in predicting JC constitutive model parameters, and the results are compared with the other solutions. Evolutionary computational algorithms have outperformed the classical data fitting solutions. This methodology can also be extended to other constitutive material models.     

金属体积成形的无网格Galerkin模拟

为避免金属体积成形有限元法模拟中网格畸变造成网格重划和模拟精度降低,采用无网格法模拟金属体积成形.利用无网格法近似位移场,建立金属体积成形的无网格法连续性控制方程,采用罚函数法施加本征边界条件和体积不变条件,基于Markov变分原理推导了金属体积成形的无网格Galerkin求解列式.用数值计算法求解该列式,实现金属体积成形的无网格模拟.数值结果表明,无网格法能有效处理金属体积成形中出现的大变形,避免了网格畸变和重划,具有较高的模拟精度.     

高速切削时摩擦系数对切削影响的数值模拟

高速切削加工中,刀屑间的摩擦系数对切削产生重要影响．由于刀屑接触的复杂性,它们之间的摩擦系数很难确定．为了探究高速切削时,刀具与切屑间摩擦系数对切削的影响,采用有限元通用程序ABAQUS／STANDARD对不同摩擦系数下切削过程进行数值模拟．通过对Mises应力和加工表面节点垂直方向位移的比较,得出刀屑间的摩擦系数对剪切角有较大影响,摩擦系数增大,剪切角随之减小．高速切削既能够提高切削效率,又能提高加工精度．     

Enhanced finite element formulations on the numerical simulation of tailor-welded hydroformed products

This work aims to assess the influence of different finite element formulations in the performance and quality of solution obtained by numerical simulation in the analysis of tailor-welded hydroformed tubular parts. Tube hydroforming represents a cost effective forming process for high-strength, low weight products on, as an example, automotive and airspace applications. On the other side, the use of tailor-welding in order to obtain custom-made combinations of thicknesses and materials - leading to a wide variety of user-defined products - can be introduced into conventional tubular hydroforming processes in order to further improve the applicability range of the later process. The main goal of the present work is to describe the state-of-the-art in the field, focusing on distinct finite element formulations and providing guidelines for the simulation of tubular hydroforming process combined with tailor-welded joining techniques. Hexahedral solid and solid-shell enhanced assumed strain elements, either with reduced and full numerical integration procedures, are analyzed in order to infer about the potentialities of the combined forming technology. Material characterization of the heat affected zone is included and the influence of finite element modeling on defects onset and prediction during forming is considered.     

金属热成形过程的综合数值模拟

金属在热成形过程中的微观组织演变是影响产品力学性能的关键因素,该演变过程取决于温度、应变和应变速率。本文基于有限变形理论和微观组织演变的数学模型,建立了能够模拟变形过程、温度变化过程和微观组织演变过程的有限元法,研制了通用的三维有限元计算软件,并在H型钢三维热轧模拟方面进行了深入开发,给出了原材料为C-Mn钢的H型钢热轧过程综合模拟结果。综合对比了8组不同工艺下的热轧实验结果和计算机模拟结果,二者均吻合良好,表明本文方法能够较好地预报金属热成形过程。     

隔热板冲压成形工艺参数优化

目的确定隔热板合理可行的成形方案。方法简要分析了零件的成形特点,并利用有限元软件对零件的拉延成形进行了数值模拟。设计正交实验时,以压边力、1号和3号拉延筋的完全锁模力、2号和4号拉延筋的完全锁模力及摩擦因数4个参数为自变量,以最大厚度减薄率、破裂情况以及未充分变形区大小为优化目标。结果 2号和4号拉延筋是该隔热板成形的主要影响因素,锁模力都为60 N/mm时,隔热板拉延成形效果较好。结论通过分析各因素对优化目标的影响,得出了优化的工艺参数值,为零件的实际生产提供指导。     

From formal solutions to computational methods avoiding passages to the limit

Before the advent of digital computers, the so-called formal solutions were the only available solutions to differential equations. Formal solutions can be closed solutions, or solutions involving infinite algorithms. The latter involve an infinite number of algebraic operations. Truncation becomes thus necessary, and the concepts of truncation error and convergence become vital. Once digital computers became available, other kinds of computational methods could be used and it became convenient to distinguish between computational methods like finite difference and finite element methods, in which numerical analysis starts before integration, and those like classical integral methods and boundary element methods, in which numerical analysis starts after integration. The classical finite difference method, in which a mesh is required, is a particular case of the generalised difference methods, characterised by a local interpolation around each node together with the collocation technique. The generalised difference method may be regarded as a modality of the meshless techniques. The finite element method differs of the finite difference method in that the approximate solution is generated respectively by variational and by collocation techniques. Hybrid and block elements are dual generalisations of the finite element method in which compatibility and equilibrium are respectively allowed within each element. Also in what concerns the methods in which numerical analysis starts after integration, bold steps have been given toward their generalisation, like those avoiding passages to the limit.     

Polynomial approximation of shape function gradients from element geometries

A method is presented for the polynomial approximation of shape function gradients based solely on the geometry of finite element boundaries. The method is founded on a least squares approach which leads to an integration scheme satisfying a necessary condition for convergence. In its simplest form the method reduces to the well‐known uniform strain approach for finite elements. The method is applicable to a broad class of problems such as connecting dissimilar meshes, mesh adaptivity and transitioning, and the construction of finite elements with variable topologies. Finite elements based on the polynomial approximations are shown to pass patch tests of various orders. In contrast to standard elements, higher‐order patch tests are passed without the need for nodes internal to element boundaries. Less sensitivity to volumetric locking under plane strain conditions is demonstrated through comparisons with a standard element formulation. Copyright © 2001 John Wiley & Sons, Ltd.     

Detailed experimental and numerical analysis of a cylindrical cup deep drawing: Pros and cons of using solid-shell elements

The Swift test was originally proposed as a formability test to reproduce the conditions observed in deep drawing operations. This test consists on forming a cylindrical cup from a circular blank, using a flat bottom cylindrical punch and has been extensively studied using both analytical and numerical methods. This test can also be combined with the Demeri test, which consists in cutting a ring from the wall of a cylindrical cup, in order to open it afterwards to measure the springback. This combination allows their use as benchmark test, in order to improve the knowledge concerning the numerical simulation models, through the comparison between experimental and numerical results. The focus of this study is the experimental and numerical analyses of the Swift cup test, followed by the Demeri test, performed with an AA5754-O alloy at room temperature. In this context, a detailed analysis of the punch force evolution, the thickness evolution along the cup wall, the earing profile, the strain paths and their evolution and the ring opening is performed. The numerical simulation is performed using the finite element code ABAQUS, with solid and solid-shell elements, in order to compare the computational efficiency of these type of elements. The results show that the solid-shell element is more cost-effective than the solid, presenting global accurate predictions, excepted for the thinning zones. Both the von Mises and the Hill48 yield criteria predict the strain distributions in the final cup quite accurately. However, improved knowledge concerning the stress states is still required, because the Hill48 criterion showed difficulties in the correct prediction of the springback, whatever the type of finite element adopted.     

Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test

We present a geometrically non‐linear assumed strain method that allows for the presence of arbitrary, intra‐finite element discontinuities in the deformation map. Special attention is placed on the coarse‐mesh accuracy of these methods and their ability to avoid mesh locking in the incompressible limit. Given an underlying mesh and an arbitrary failure surface, we first construct an enriched approximation for the deformation map with the non‐linear analogue of the extended finite element method (X‐FEM). With regard to the richer space of functions spanned by the gradient of the enriched approximation, we then adopt a broader interpretation of variational consistency for the construction of the enhanced strain. In particular, in those elements intersected by the failure surface, we construct enhanced strain approximations which are orthogonal to piecewise‐constant stress fields. Contrast is drawn with existing strong discontinuity approaches where the enhanced strain variations in localized elements were constructed to be orthogonal to constant nominal stress fields. Importantly, the present formulation gives rise to a symmetric tangent stiffness matrix, even in localized elements. The present modification also allows for the satisfaction of a discontinuous patch test, wherein two different constant stress fields (on each side of the failure surface) lie in the solution space. We demonstrate how the proposed modifications eliminate spurious stress oscillations along the failure surface, particularly for nearly incompressible material response. Additional numerical examples are provided to illustrate the efficacy of the modified method for problems in hyperelastic fracture mechanics. Copyright © 2003 John Wiley & Sons, Ltd.