THE EFFECT OF PRESSURE ON THE DUCTILITY OF THIN SHEET SUBJECTED TO SOME SIMPLE FORMING PROCESSES

Assuming a generalized strain hardening curve whose form is independent of the hydrostatic component of the stresses, the effect of pressure on the ductility of metal subjected to some simple sheet forming processes is calculated. The metal is assumed to be isotropic and to obey the v Mises yield criterion and its associated flow rule. In all cases considered, the ductility is increased by the presence of fluid pressure on the sheet surface.     

Effect of hardening models on different ductile fracture criteria in sheet metal forming

Prediction of the fracture is one of the challenging issues which gains attention in sheet metal forming as numerical analyses are being extensively used to simulate the process. To have better results in predicting the sheet metal fracture, appropriate ductile fracture criterion (DFC), yield criterion and hardening rule should be chosen. In this study, the effects of different hardening models namely isotropic, kinematic and combined hardening rules on the various uncoupled ductile fracture criteria are investigated using experimental and numerical methods. Five different ductile fracture criteria are implemented to a finite element code by the user subroutines. The criterion constants of DFCs are obtained by the related experimental tests. The in-plane principle strains obtained by the finite element analyses for different DFCs are compared with the experimental results. Also, the experimental results are used to evaluate the principle strain values calculated by the finite element analysis for different combinations of DFCs and hardening rules. It is shown that some DFCs give better predictions if the appropriate hardening model is employed.     

Development of a new failure prediction criterion in sheet metal forming

In industrial try-out processes in sheet metal forming usually the forming limit curve is used as failure criterion in order to describe the onset of localized necking. Forming limits, however, are strain-path dependent. Up to today many different approaches how the strain-path dependent behavior of the forming limit curve can be avoided have been published. Best known are the approaches based on forming limit stress curves published by Arrieux, and the approach of Müschenborn published in 1975. An overview over existing failure criteria is given in this contribution. The failure criterion forming limit stress curve as well as several failure criteria based on Müschenborn’s approach will be evaluated with newly recorded experimental data on forming limit curves for non-proportional loading. A new approach, that is in contrast to the two mentioned approaches not based on assumptions but on experimental observations, is presented herein. The suggested approach is presented as failure surface where strains above the surface indicate the onset of localized necking. The failure surface is given as function of the loading mode and the level of effective pre-stretching. Different suggestions how to use and simplify the new approach are given in this paper. The prediction accuracy of the addressed approaches as well as of the newly suggested approach is evaluated by transforming the data of the approaches back into the conventional forming limit curve for several non-linear strain paths. The comparison of the described approaches shows that forming limits for non-proportional loading can be well-predicted with the suggested approach.     

Thermo-mechanical sheet metal forming of aero engine components in Ti-6Al-4V—PART 2: Constitutive modelling and validation

In this work constitutive models suitable for thermo-mechanical forming of the titanium alloy Ti-6Al-4V are evaluated. A tool concept for thermo-mechanical forming of a double-curved sheet metal component in Ti-6Al-4V is proposed. The virtual tool design is based on finite element (FE) analyses of thermo-mechanical sheet metal forming in which two different anisotropic yield criteria are evaluated and compared with an isotropic assumption to predict global forming force, draw-in, springback and strain localisation. The shape of the yield surface has been found important and the accuracy of the predicted shape deviation could be slightly improved by including the cooling procedure. The predicted responses show promising agreement with the corresponding experimental observations when the anisotropic properties of the material are considered.     

Approximate yield criteria for anisotropic porous ductile sheet metals

An approximate macroscopic yield criterion for anisotropic porous sheet metals is developed under plane stress conditions in this paper. The metal matrices are assumed to be rigid perfectly plastic and incompressible. The Hill quadratic and non-quadratic anisotropic yield criteria are used to describe the matrix normal anisotropy and planar isotropy. The voids in sheet metals are assumed in the form of through-thickness holes. Under axisymmetric loading, a closed-form upper bound macroscopic yield criterion is derived as a function of the anisotropy parameter R, defined as the ratio of the transverse plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial loading conditions. The plane stress upper bound solutions for different in-plane strain ratios can be fitted well by the closed-form macroscopic yield criterion.     

Assessment on the performance of distinct stress integration algorithms for complex non-quadratic anisotropic yield criteria

In this work, three distinct return mapping algorithms are presented and analyzed in detail: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique, which reduces to (ii) a fully-explicit algorithm and, finally, (iii) a semi-implicit algorithm,. In order to describe the complex anisotropic behaviour of some metals, such as aluminium alloys, two non-quadratic anisotropic yield criteria were implemented: the Yld91 and Yld2004-18p. The performance of the developed algorithms is inferred in a series of sheet metal forming benchmarks and the quality of the results is assessed when compared to experimental results presented in the literature. The numerical simulations show that the semi-implicit algorithm is quite efficient with the von Mises yield criterion. However, when anisotropy is taken into account, the algorithm requires several iterations to return the stresses to the yield surface, particularly when the stresses are located at corner regions of that surface. The semi-explicit algorithm proved to be the most robust and efficient algorithm with anisotropic yield criteria. The good agreement between the experimental data and the obtained numerical results demonstrate the high efficiency of the presented algorithms and the ability of the anisotropic criteria to predict the material’s complex anisotropic behaviour.     

大幅面板材渐进折弯成形的本构建模及模拟

为了提高大幅面板材成形的模拟精度,在板材折弯平面应变假设条件下,推导出基于Hill各向异性屈服准则的弹塑性本构方程.借助ABAQUS有限元软件本构模块用户子程序接口,通过编程将上述推导的应力-应变本构关系显示表达式嵌入ABAQUS分析平台.以超长大开口半椭圆形工件成形为例,建立了大幅面钢板渐进折弯的三维弹塑性有限元模型,并数值模拟了多道次渐进折弯成形及回弹全过程.模拟效果和工程应用结果表明,与传统的基于平面应力假设的本构关系模型相比,采用平面应变假设的本构关系模型的模拟结果更接近实验值.     

Effect of continuous strain path changes on forming limit strains of DP600

The strain path may change in actual sheet metal‐forming processes, so the determination of formability of sheet metal should consider the nonlinear strain path. For identifying the forming limit (FL) strains under nonlinear strain path, a conventional two‐step procedure with unloading is classically used to produce the strain path change, which results in no continuous measure of strain. The in‐plane biaxial tensile test with a cruciform specimen is an interesting alternative to overcome the drawbacks of conventional method. The strain path change can be made without unloading during a single test. In this work, the experimental FL strains of DP600 sheets under two types of nonlinear strain path are investigated and then compared with those under linear strain paths. The Oyane ductile fracture criterion is used in the finite element simulation to predict the experimental results.     

Influence of out-of-plane compression stress on limit strains in sheet metals

The prediction of the forming limits of sheet metals typically assumes plane stress conditions that are really only valid for open die stamping or processes with negligible out-of-plane stresses. In fact, many industrial sheet metal forming processes lead to significant compressive stresses at the sheet surface, and therefore the effects of the through-thickness stress on the formability of sheet metals cannot be ignored. Moreover, predictions of forming limit curves (FLC) that assume plane stress conditions may not be valid when the forming process involves non-negligible out-of-plane stresses. For this reason a new model was developed to predict FLC for general, three-dimensional stress states. Marciniak and Kuczynski (Int J Mech Sci 9:609-620, 1967) first proposed an analytical method to predict the FLC in 1967, known as the MK method, and this approach has been used for decades to accurately predict FLC for plane stress sheet forming applications. In this work, the conventional MK analysis was extended to include the through-thickness principal stress component (σ ₃), and its effect on the formability of different grades of sheet metal was investigated in terms of the ratio of the third to the first principal stress components (). The FLC was predicted for plane stress conditions (β = 0) as well as cases with different compressive through-thickness stress values (β ≠ 0) in order to study the influence of β on the FLC in three-dimensional stress conditions. An analysis was also carried out to determine how the sensitivity of the FLC prediction to the through-thickness stress component changes with variations in the strain hardening coefficient, in the strain rate sensitivity, in plastic anisotropy, in grain size and in sheet thickness. It was found that the out-of-plane stress always has an effect on the position of the FLC in principal strain space. However, the analysis also showed that among the factors considered in this paper, the strain hardening coefficient has the most significant effect on the dependency of FLC to the through-thickness stress, while the strain rate sensitivity coefficient has the least influence on this sensitivity.     

金属板材屈服行为与塑性失稳力学模型在微尺度下的应用

板材屈服准则与塑性失稳模型是精准描述高性能构件成形或服役过程的基础与前提。在板材塑性成形过程中,试样几何尺寸、材料晶粒大小、自由表面粗化和织构分布等都会对材料的塑性变形行为产生不可忽略的影响,导致单一尺度下的本构模型和断裂准则不能有效预测微观尺度下的材料变形行为和各种缺陷,大大限制了合金板材在航空、航天、汽车、医疗等工业上的应用。对现有屈服准则的研究进展进行了较为全面的回顾,从Hill、Hershey-Hosford和Drucker这3个系列出发,分别进行了对比分析,并总结了目前国内外用于验证屈服准则的金属板材双向拉伸实验机发展状况。基于不同的破裂失稳机理,将失稳模型分为宏观失稳准则、韧性断裂准则和耦合材料损伤演化的韧性断裂准则,并分别进行了归纳和阐述。此外,随着微成形技术的逐步推广,也对宏观塑性成形理论在微尺度下的应用进展进行了说明,指出了宏观屈服准则和失稳模型在微尺度下的不足和缺陷。最后讨论了宏观屈服准则和失稳模型今后的发展趋势以及宏观塑性成形理论在微尺度下的应用前景。     

Full-field measurement technique and its application to the analysis of materials behaviour under plane strain mode

The purpose of the paper is to provide a comprehensive experimental and numerical analysis of one of the encountered and critical state modes in sheet metal forming processes. The study is carried out with the help of the full-field measurement techniques. In order to confer some generality to the proposed work, several materials and different specimen shapes are considered that exhibit more or less homogeneous strain field. The proposed experimental study of the plane strain test is completed by a preliminary identification of the material parameters for non-linear behaviour at finite strains, using heterogeneous strain field.     

Limit Strains Comparison during Tube and Sheet Hydroforming and Sheet Stamping Processes by Numerical Simulation

Hydroforming is a manufacturing process that uses a fluid medium to form a component by using high internal pressure. Tube and sheet hydroforming has gained increasing interest in the automotive and aerospace industries because of its many advantages such as part consolidation, good quality of the formed parts etc. The main advantage is that the uniform pressure can be transferred to every where at the same time. Forming limit is the limit of the component up to that extent it can be formed safely. While analyzing hydroforming process, it is often assumed that the limit strains are identical as that of stamped sheet metal of equivalent material properties. It is not clear if such an assumption is valid. In this paper the forming limit strains during hydroforming is predicted. A series of tube bulge tests for tube hydroforming and limiting dome height test for sheet hydroforming and sheet stamping processes are simulated by a commercial finite element solver to predict the limit strains. Numerical simulation of forming limit strains in tube hydroforming with different internal pressure and different simulation set up with or without axial feeding, while in sheet hydroforming and sheet stamping, by changing the specimen geometry are considered to develop wide range of strain paths in the present work. The effects of process conditions on the forming limit strains are detailed. The comparison of limits strains during hydroforming and stamping processes is presented. Prediction of limits strains is based on a novel thickness based necking criterion.     

Strain evolution in the single point incremental forming process: digital image correlation measurement and finite element prediction

Incremental Sheet Forming (ISF) is a relatively new class of sheet forming processes that allow the manufacture of complex geometries based on computer-controlled forming tools in replacement (at least partially) of dedicated tooling. This paper studies the straining behaviour in the Single Point Incremental Forming (SPIF) variant (in which no dedicated tooling at all is required), both on experimental basis using Digital Image Correlation (DIC) and on numerical basis by the Finite Element (FE) method. The aim of the paper is to increase understanding of the deformation mechanisms inherent to SPIF, which is an important issue for the understanding of the high formability observed in this process and also for future strategies to improve the geometrical accuracy. Two distinct large-strain FE formulations, based on shell and first-order reduced integration brick elements, are used to model the sheet during the SPIF processing into the form of a truncated cone. The prediction of the surface strains on the outer surface of the cone is compared to experimentally obtained strains using the DIC technique. It is emphasised that the strain history as calculated from the DIC displacement field depends on the scale of the strain definition. On the modelling side, it is shown that the mesh density in the FE models plays a similar role on the surface strain predictions. A good qualitative agreement has been obtained for the surface strain components. One significant exception has however been found, which concerns the circumferential strain evolution directly under the forming tool. The qualitative discrepancy is explained through a mechanism of through-thickness shear in the experiment, which is not fully captured by the present FE modelling since it shows a bending-dominant accommodation mechanism. The effect of different material constitutive behaviours on strain prediction has also been investigated, the parameters of which were determined by inverse modelling using a specially designed sheet forming test. Isotropic and anisotropic yield criteria are considered, combined with either isotropic or kinematic hardening. The adopted constitutive law has only a limited influence on the surface strains. Finally, the experimental surface strain evolution is compared between two cones with different forming parameters. It is concluded that the way the plastic zone under the forming tool accommodates the moving tool (i.e. by through-thickness shear or rather by bending) depends on the process parameters. The identification of the most determining forming parameter that controls the relative importance of either mechanism is an interesting topic for future research.     

Yield criteria for amorphous glassy polymers

Three amorphous polymers, polymethyl methacrylate, polystyrene and polycarbonate were tested in uniaxial tension, uniaxial compression, plane strain compression and simple shear, over a range of temperatures. In each test, the yield point was precisely determined via residual strain measurements after unloading. With the yield stresses determined for these four different stress states, two pressure dependent shear yield criteria, i.e, the modified Von Mises and the modified Tresca criteria, were checked and compared. It is shown that (i) in each case (material, temperature, initial ageing state), the yield locus is satisfactorily described by either one or the other of the two criteria, and (ii) each criterion can be associated with a specific deformation mode (either homogeneous or localized in shear bands). As for the temperature dependence of the yield stress sensitivity to the hydrostatic pressure, it appears to be related to the glass transition temperature (Tg) and more precisely to the α and β relaxations. Finally, the pressure dependence of the yield stress can be possibly explained as being due to two effects: (i) the influence of pressure on molecular motions leading to yielding and (ii) the influence of pressure on the microstructural state. This revised version was published online in November 2006 with corrections to the Cover Date.     

考虑初始残余应力的板料弯曲回弹理论分析

在实际弯曲加工过程中,板料内部如果带有初始残余应力,将与弯曲应力发生叠加,对板料的回弹产生一定的影响。由于传统的回弹理论都没有考虑初始残余应力的影响,该文基于平面应变假设,采用服从Mises屈服准则和线性强化材料模型,推导了考虑初始残余应力的板料弯曲回弹角近似公式并基于有限元软件ABAQUS进行了残余应力板料弯曲回弹仿真对比分析。理论计算与仿真结果具有较好的一致性,验证了理论模型的正确性。研究结果表明,残余应力和厚度对板料回弹均有较大影响：沿宽度方向,不同初始残余应力处的板料回弹并不均匀;增大初始残余应力峰值和减小板料厚度均使不同初始残余应力处板料的回弹差值增大。     

On the identification of an effective cross section for a cruciform specimen

Biaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm² for the considered specimen.     

An analytical model for bending and springback of bimetallic sheets

Springback is an inevitable phenomenon due to elastic redistribution of internal stresses occurring in sheet metal forming operations. Most of the research reported in this area has been concerned with the components formed from single metal. This article deals with the analytical solution for prediction of springback in bending of bimetallic sheets. A mathematical model is derived based on Woo and Marshall's constitutive equation, considering logarithmic strain (nonlinear) distribution across the thickness and thickness change during bending. Analytical modeling, based on logarithmic strain distribution across the thickness, can be used for accurate springback predictions in the case of smaller bend radius to the thickness ratio. The results of the springback and thickness change are validated using experimental results for the aluminum sheet layered with steel. Further, springback variation in bimetallic sheets is studied, with a change in material properties and thickness of each layer.