Plastic behaviour of perforated sheets with slot-type holes under biaxial stress state

A yield criterion of sheets with slot-type holes under biaxial loading has been proposed in terms of apparent stresses. The yield criterion was confirmed by finite-element analysis results. In order to analyse stretching of a perforated sheet for slot-type shadow mask by finite-element method, a yield function which can incorporate the apparent yield stress and the apparent plastic contraction ratio has been obtained. The agreement between the measured and calculated results of stretch forming of the perforated sheet was satisfactory.     

Constitutive law for AZ31B Mg alloy sheets and finite element simulation for three-point bending

The constitutive law to describe the anisotropic and asymmetric mechanical behavior of AZ31B magnesium (Mg) alloy sheets at room temperature has been developed here for the plane stress condition, based on the orthotropic yield criterion proposed by Cazacu O, Plunkett B, Barlat F. [Orthotropic yield criterion for hexagonal closed packed metals. International Journal of Plasticity 2006;22:1171–94] and different isotropic hardening laws for tension and compression. Experimental procedures to obtain the material parameters of the yield surface and the hardening laws have been discussed for the AZ31B Mg alloy sheet. For verification purposes, finite element simulation results based on the developed constitutive laws have been compared with experimental results for a three-point bending test.     

参数求解方法对屈服准则的各向异性行为描述能力的影响

详细分析基于应力各向异性和变形各向异性两种求解Hill48屈服准则参数的方法。在给出两种各向异性参数求解表达式的基础上,具体分析Hill48屈服准则本身的局限性。以5754O铝合金板为研究对象,进行不同方向的单向拉伸试验。采用两种各向异性参数求解方法,基于Hill48屈服准则推导不同方向拉伸过程中的理论应力-应变曲线和拉伸过程中的变形规律。通过对比理论与试验结果具体分析参数求解方法对屈服准则精度的影响。基于两种参数求解方法,进行5754O铝合金板拉深试验的有限元模拟,讨论不同求解方法对凸耳现象的描述精度。得出结论：当对应力各向异性为主的问题进行分析时,应采用应力各向异性法求解;当对变形各向异性为主的问题进行分析时,则应采用变形各向异性法求解。研究结果对屈服准则在板料成形方面的合理应用具有重要的参考价值。     

Model for compaction of metal powders

A new yield criterion for metal powder compaction based on continuum mechanics has been proposed. It includes three parameters to characterize the geometric hardening of powder compact and strain hardening of incompressible metal matrix. The elasto-plastic finite element method to describe compaction of metal powders has been formulated using the new yield criterion. The values of parameters in the yield criterion could be determined through cold isostatic pressing (CIP). The finite-element method was used to simulate compaction behaviour of copper powders of different shape and mean particle size.     

基于重构核粒子法的带孔薄板模态分析研究

无网格法是一种新颖的工程数值计算方法,与有限元法相比,具有很多独特的优势。重构核粒子法具有变时-频特性和多分辨率特性等优点,在结构动力学中有广泛的应用。本文针对带孔薄板这一不连续问题,根据无网格法和板壳振动的基本理论,采用了可视性准则处理场函数的不连续性,编写了基于重构核粒子法的模态分析程序,得到了不同边界条件下带孔薄板的前五阶固有频率和模态,并和有限元分析结果进行了比较。算例表明该方法收敛性好、精度高,为带孔薄板的模态分析提供了一种新的求解方法。     

Simulation and experimental verification of flexible roll forming of steel sheets

Roll forming is a sheet metal forming process that has been used for decades. Usually roll-formed sections have a constant cross section. Flexible roll forming is a brand new forming process that produces parts with variable cross sections, in which the rollers translate back and forth in a direction that is perpendicular to the sheet feeding direction. Theoretical analysis gives an explanation of the plane strain state, compressive stresses, tensile stresses, and shear stresses in flexible roll forming. In order to analyze the mechanics and the deformation characteristics of flexible roll forming, the finite element method (FEM) model of a 17-step flexible roll forming process is established. The yield criterion used in the FEM simulation is Hill 48, and the parameters of which are solved with the yield stresses under different loading conditions and are firstly verified with a plane strain tensile test. The complicated roller paths are realized with data extracted from the computer-aided design (CAD) files with VC++ programs developed by the authors. We developed the first flexible roll forming prototype machine in China, with which the roll forming experiment of a side door beam is performed. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion that is solved with yield stresses agree well with the experimental results, which indicates that the simulation model can well reflect the real forming process. Detailed analysis of the distribution and history of plastic strain, longitudinal strain, shear strain, and thickness of both the constant cross section and the variable cross section is performed, which is of great help to understand this forming process.     

板料屈服行为及强化规律的研究进展

研究板料塑性成形的理论基础是屈服准则、强化规律以及本构模型。随着新材料、新工艺的不断出现,温度和应变速率对塑性成形过程中的影响也不容忽视,原有的塑性理论已无法满足研究和工程应用的需求。从板料屈服准则研究、包辛格效应与强化模型研究、屈服强化规律试验方法研究以及涉及应变速率和温度的板料屈服强化研究4个方面阐述板料屈服行为及强化规律的研究进展,指出常用屈服准则的特点和不足,说明各种强化模型中组合强化模型仍然是研究重点。试验方法主要从研究屈服轨迹的双向拉伸试验及确定强化模型参数试验的2个方面进行介绍。此外,指出针对板料在复杂应力状态下应力张量与应变张量之间的涉及应变率和温度的屈服准则和相应的流动准则的本构关系还有待研究。提出随着新材料、新工艺的不断出现,涉及应变速率和温度的屈服准则和强化规律、试验方法以及在有限元模拟中的应用等研究将是未来的研究热点。     

基于成形应力极限的管材液压成形缺陷预测

基于塑性应力应变关系及Hill79屈服准则,推导出极限应力与极限应变间转化关系,进而建立2008T4铝合金的成形应力极限图(Forming limit stress diagram,FLSD)。采用LS-DYNA软件对三通管液压胀形过程进行模拟,应用FLSD预测胀形过程中破裂的发生及成形压力极限,并与传统成形极限图(Forming limit diagram,FLD)结果进行了对比。研究表明,FLD与FLSD预测结果中破裂缺陷位置相同,但极限内压力值存在很大差别,而FLSD预测结果与物理试验结果较吻合。考虑到FLD受应变路径影响显著的因素,将FLSD作为管材液压成形等复杂应变路径下的成形极限的判据更加方便可靠。     

高参数换热器管板热应力分析模型的研究

常规的管板设计方法是用等效无孔实心板来代替多孔管板,采用比较简单的公式、曲线、图表进行设计计算,但是这些计算无法准确考虑管板温度差引起的热应力。目前常用有限元方法,通过施加温度载荷和对流载荷计算得到管板的温度场,进而求出管板的温差应力,但计算结果的准确性一直是许多研究者关注的问题。采用有限元方法,以U型管式换热器管板为例,分别按给定管板表面温度、给定流体温度和管板表面传热膜系数、包含温度场在内的流固耦合三种分析模型计算得到管板的温度场,进而对比分析了不同模型对管板热应力计算结果的影响。研究结果为管板强度的精确设计提供了借鉴。     

Finite element analysis of limit strains in biaxial stretching of sheet metals allowing for ductile fracture

To predict limit strains in biaxial stretching of sheet metals, a criterion for ductile fracture is combined with the finite element simulation. The limit strains are determined by substituting the values of stress and strain obtained from the finite element simulation into the ductile fracture criterion. Material constants in the criterion are obtained from the fracture strains measured in the biaxial stretching tests. Calculations are carried out for various strain paths from balanced biaxial stretching to uniaxial tension of aluminium alloy sheets, and compared with the experimental results. The predicted limit strains are in good agreement with the measured ones not only just at the fracture site but also at outside of the fracture site. It is demonstrated that the forming limit diagrams are successfully predicted by the present approach.     

Effect of sheet anisotropy on the wear in deep-drawing process of a cylindrical cup

In the present investigation, the deep-drawing process of a cylindrical cup is simulated using the finite element method, with the aim of investigating the effect of sheet anisotropy on wear depth in the die which is exposed to the most severe tribological condition in this process. Both the blank and the die are assumed to be deformable. For the blank, the elasto-plastic behavior is considered, while the die material is assumed to be elastic. The sheet is anisotropic, so Hill quadratic yield criterion is employed. Two kinds of anisotropy, i.e. planar anisotropy and normal anisotropy are considered in this study. To study the effects of sheet anisotropy on the wear depth on the die shoulder qualitatively a parameter called relative wear depth (RWD) is introduced. Different distributions of Lankford coefficients are chosen and several conclusive results are presented.     

On strength criteria of fillet welds

A comparison between two widely used strength criteria (ISO and Eurocode 3) for welding design is carried out in this paper. Limit analysis theorems are applied for analysis of collapse load of a fillet weld using von Mises yield criterion, generalizing a previous methodology in which Tresca criterion was used. Using von Mises criterion, lower bounds of collapse load can be found by solving a quartic equation, thus avoiding the numerical sweep needed with Tresca criterion. The results of limit analysis fit much better with those of Eurocode 3 criterion, and this criterion also reasonably fits experimental results for side-fillets, but experimental results on end-fillets agree with ISO criterion and not with Eurocode 3 criterion and limit analysis. A numerical finite element analysis shows that this apparent contradiction is originated by the influence of overlapping between the welded plates, which gives rises to the transmission of part of the internal moment through contact forces between plates and not through the throat. The results support the use of Eurocode 3 criterion instead of ISO, and this is confirmed by the analysis of a varied set of welded layouts using the former in a general numerical method developed previously, which gives results that show a very reasonable agreement with experimental results found in the bibliography.     

Non-quadratic yield criterion for orthotropic sheet metals under plane-stress conditions

The paper presents a new yield criterion for orthotropic sheet metals under plane-stress conditions. The criterion is derived from the one proposed by Barlat and Lian (Int. J. Plasticity 5 (1989) 51). Three additional coefficients have been introduced in order to allow a better representation of the plastic behaviour of the sheet metals. The predictions of the new yield criterion are compared with the experimental data for an aluminium alloy sheet and a steel sheet.     

Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method

To reduce the computational time of finite element analyses for sheet forming, a 3D hybrid membrane/shell method has been developed and applied to study the springback of anisotropic sheet metals. In the hybrid method, the bending strains and stresses were calculated as post-processing, considering the incremental change of the sheet geometry obtained from the membrane finite element analysis beforehand. To calculate the springback, a shell finite element model was used to unload the sheet. For verification purposes, the hybrid method was applied for a 2036-T4 aluminum alloy square blank formed into a cylindrical cup, in which stretching is dominant. Also, as a bending-dominant problem, unconstraint cylindrical bending of a 6111-T4 aluminum alloy sheet was considered. The predicted springback showed good agreement with experiments for both cases.     

An anisotropic damage-based plastic yield criterion and its application to analysis of metal forming process

Based on the continuum damage mechanics (CDM), both the total damage growth force and the damage equivalent stress has been firstly derived. Material and damage are considered to be anisotropic in this theoretical model. A new damage-based plastic yield criterion, where the damage equivalent stress is taken as the yield function, and the corresponding damage evolution equation has been established. A relation between the damage variable and the plastic deformation has been proposed. This relation can be applied to obtain the damage history in terms of Moiré photo-mechanics technology in this work. In addition, from the anisotropic damage-based plastic yield criterion presented, the large-scale finite element codes ABAQUS/Explicit in conjunction with the damage experimental results has been then used to calculate some mechanical variable fields in metal forming process. It has finally been verified that the position corresponding to the maximum value in damage equivalent stress field accurately coincides with the initial place of macro-crack given by Erichsen cupping tests carried out by authors.     

A general forming limit criterion for sheet metal forming

The forming limit of sheet metal is defined to be the state at which a localized thinning of the sheet initiates during forming, ultimately leading to a split in the sheet. The forming limit is conventionally described as a curve in a plot of major strain vs. minor strain. This curve was originally proposed to characterize the general forming limit of sheet metal, but it has been subsequently observed that this criterion is valid only for the case of proportional loading. Nevertheless, due to the convenience of measuring strain and the lack of a better criterion, the strain- based forming limit curve continues to play a primary role in judging forming severity. In this paper it is shown that the forming limit for both proportional loading and non-proportional loading can be explained from a single criterion which is based on the state of stress rather than the state of strain. This proposed criteria is validated using data from several non-proportional loading paths previously reported in the literature for both aluminum and steel alloys. In addition to significantly improving the gauging of forming severity, the new stress-based criterion is as easy to use as the strain-based criterion in the validation of die designs by the finite element method. However, it presents a challenge to the experimentalist and the stamping plant because the state of stress cannot be directly measured. This paper will also discuss several methods to deal with this challenge so that the more general measure of forming severity, as determined by the state of stress, can be determined in the stamping plant.     

Analysis of drawbead process by static-explicit finite element method

The problem analyzed here is a sheet metal forming process which requires a drawbead. The drawbead provides the sheet metal enough tension to be deformed plastically along the punch face and consequently, ensures a proper shape of final products by fixing the sheet to the die. Therefore, the optimum design of drawbead is indispensable in obtaining the desired formability. A static-explicit Finite element analysis is carried out to provide a perspective tool for designing the drawbead. The finite element formulation is constructed from static equilibrium equation and takes into account the boundary condition that involves a proper contact condition. The deformation behavior of sheet material is formulated by the elastic-plastic constitutive equation. The finite element formulation has been solved based on an existing method that is called the static-explicit method. The main features of the static-explicit method are first that there is no convergence problem. Second, the problem of contact and friction is easily solved by application of very small time interval. During the analysis of drawbead processes, the strain distribution and the drawing force on drawbead can be analyzed. And the effects of bead shape and number of beads on sheet forming processes were investigated. The results of the static explicit analysis of drawbead processes show no convergence problem and comparatively accurate results even though severe high geometric and contact-friction nonlinearity. Moreover, the computational results of a static-explicit finite element analysis can supply very valuable information for designing the drawbead process in which the defects of final sheet product can be removed.     

An analytical study on prediction of effective elastic constants of perforated plate

In this study, the validity of the Eshelby-type model for predicting the effective Young’s modulus and in-plane Poisson’s ratio of the 2-dimensional perforated plate has been investigated in terms of the porosity size and its arrangement. The predicted results by the Eshelbytype model are compared with those by finite element analysis. Whenever the ratio of the porosity size to the specimen size becomes smaller than 0.07, the effective elastic constants predicted by finite element analysis are convergent regardless of the arrangement of the porosities. Under these conditions, the effective Young’s moduli of the perforated plate can be predicted within the accuracy of 5% by the Eshelby-type model, which overestimates and underestimates the effective Poisson’s ratios by 10% and 6% for the plates with periodically and non-periodically arranged porosities, respectively.     

变幅单/多轴混合加载下GH4169光滑件的弹塑性有限元分析

对承受变幅单轴和变幅非比例多轴加载的镍基合金GH4169光滑薄壁管进行了有限元分析。使用ANSYS有限元分析软件进行有限元建模,采用Von Mises屈服准则和多线性随动强化准则来描述变幅弹塑性特性。结合三角波加载,在柱坐标系下对试样一端加载轴向位移和周向位移来实现拉扭应变加载。通过对光滑薄壁管件的有限元分析结果与试验结果进行比较,说明此方法对变幅单多轴加载弹塑性分析的正确性和实用性。     

Sectional finite element analysis of forming processes for aluminum-alloy sheet metals

The sectional finite element analysis of the forming processes for the aluminum-alloy sheet metal known to be planar anisotropic was performed. The two-dimensional rigid-viscoplastic FEM formulation based on the bending augmented membrane theory as well as the anisotropic yield criteria was introduced. For modeling the anomalous behavior of aluminum-alloy sheet metals, Barlat's strain rate potential and Hill's (Journal of the Mechanics and Physics of Solids 1990;38:405–17) non-quadratic yield theory with an isotropic hardening rule were employed. Furthermore, a new method to determine anisotropic coefficients of Barlat's strain rate potential was proposed. For evaluating bending effects in the forming process of aluminum-alloy sheet metals, the bending equivalent forces were calculated in terms of the changes in the interior angle at a node between two linear finite elements and were augmented to the membrane stretch forces. In order to verify the validity of sectional finite element formulation based on the bending augmented membrane theory, the plane strain stretch/draw forming processes of a square cup test were simulated and simulation results are compared with experimental measurements. Friction coefficient was obtained from drawbead friction test. The properties of selected material were obtained from uniaxial tensile tests. Simulation shows good agreement with measurements. For the application of the sectional finite element formulation introduced in this research, the drawing process of a rear seat back upper bracket of passenger cars is simulated assuming plane strain condition. The thinning distribution of the simulation agreed well with that of the measurement, so that the sectional analysis is acceptable in the design and analysis of aluminum-alloy sheet stamping dies.