Evaluation of ductile fracture in sheet metal forming using the ellipsoidal void model

The ductile fracture in the simulation of sheet-metal-forming processes is evaluated by the ellipsoidal void model previously proposed by the author. In the present study, the simulation and experiment of the hole expansion test are performed using six types of metals. For an alloy, the relationship between prestrain and hole expansion ratio calculated using the ellipsoidal void configuration and ellipsoidal void shape and that calculated using the ellipsoidal void configuration and circular void shape agree with the relationship obtained experimentally. For a pure metal, the relationship between prestrain and hole expansion ratio calculated using the average void configuration and average void shape agrees with that obtained experimentally. Furthermore, the method of introducing prestrain to an as-rolled sheet is proposed, and the prestrain in this sheet is estimated.     

板料成形中韧性断裂准则应用研究进展

对板料成形中的成形极限应力图、最大变薄率、成形极限图以及韧性断裂准则等预测成形极限的方法,进行了综述和分析。指出利用韧性断裂准则,不但能够较好地预测塑性差的板料成形极限,而且还能考虑应变路径的变化。利用有限元方法模拟时,韧性断裂准则既可以应用到完全耦合的弹塑性损伤模型的增量方法中,也可以应用到一步有限元逆算法中。为了准确地预测成形极限,除了提高有限元模拟精度外,应找到一种本质地反映材料性能的韧性断裂准则。     

Experimental and numerical investigation of thickness effect on ductile fracture toughness of steel alloy sheets

Effect of thickness on ductile fracture toughness of plates made of steel alloy GOST 08Ch22N6T is investigated experimentally. Multiple specimen tests for determining fracture toughness have been conducted using compact tension (CT) specimens with thicknesses of 1.25, 1.64 and 4.06 mm according to standard test method ASTM E813. The results show the significant effect of thickness on fracture toughness. It is observed that in low thickness, J_c increases with the thickness increase until it reaches a maximum; however, further increase in the thickness causes the J_c-value to decrease. Two-dimensional finite element analysis is also performed to reproduce the experimental results. The comparison shows a very good agreement.     

Experimental and numerical investigation on ductile fracture mechanism of aluminium alloy using new modified model

In the present paper, the ductile fracture of aluminium alloy 5052P-H34 is studied by experiments and simulations. Then, the extension of the damage growth model, which captures both tension as well as shear, was employed in the present paper, and a modified Rousselier model was proposed. A stress integration algorithm based on the general backward Euler return algorithm was developed and implemented into finite element (FE) models in the ABAQUS/Explicit platform. The shear coefficient was calibrated by a FE analysis based on an inverse calibration procedure combined with the physical experiments. The predictive capability of this model was studied by comparing the experiments with the simulations, and the validity of this model was verified. The results show that the modified Rousselier model can give more accurate results for both tension and shear failure.     

Numerical Methodology for Metal Forming Processes Using Elastoplastic Model with Damage Occurrence

Ductile damage often occurs during metal forming processes due to the large thermo-elasto （visco） plastic flow Iocalisation. This paper presents a numerical methodology, which aims to virtually improve any metal forming processes. The methodology is based on elastoplastic constitutive equations accounting for nonlinear mixed isotropic and kinematic hardening strongly coupled with isotropic ductile damage. An adaptive remeshing scheme based on geometrical and physical error estimates including a kill element procedure is used. Some numerical results are presented to show the capability of the model to predict the damage initiation and growth during the metal forming processes.     

Assessment of forming parameters influencing spring-back in multi-point forming process: A comprehensive experimental and numerical study

Like all sheet metal forming methods, one of the main characteristics of parts formed by multi-point forming is dimensional deviation caused by elastic recovery that is known as spring-back. In this paper the effects of material property, sheet thickness and anisotropy ratio along with process parameters such as elastic layer thickness, elastic layer hardness and number of punch elements on spring-back are studied utilizing finite element simulations and experimental tests. Experimental tests are carried out under various conditions by forming V-shaped and Sin-shaped geometries. Aluminum alloy 3105, stainless steel 304 and pure copper were used as sheet materials for experiments. Likewise, black rubber with shore A hardness of 50 and polyurethane with hardness of 65 and 85 were allocated as elastic layers. The Abaqus® commercial code is employed for finite element simulations. The definition of yield behavior of utilized sheet materials is fulfilled by using three yield criteria of Barlat-89, Hill-48 and Von-Mises. Since the Barlat-89 is not adopted in Abaqus, VUMAT and UMAT user defined subroutines are provided and integrated with explicit simulation of forming process and implicit simulation of spring-back phenomenon respectively. The results indicate that parameters such as material property, blank thickness and anisotropy affect spring-back in multi-point forming. Also the thickness and hardness of elastic layers are novel ideas that should be considered in order to minimize the spring-back. In general, using the elastic layer with minimum possible thickness and greater hardness beside the maximum number of pins leads to minimum spring-back.     

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.     

Non-local regularization for FE simulation of damage in ductile materials

The paper presents an application of the non-local regularization to the finite element modelling of ductile damage and tearing. In order to model the damage growth in ductile materials of structural components, integral limiters have been introduced. These integral limiters, which are spatial averaging operators, can prevent the problem of mesh-sensitivity of the finite element computations. Hence, it was important to establish the characteristic length l_c for spatial averaging operators of the non-local regularization. More formally, the in-plane distance l_c and the out-of-plane FE dimension have been specified, characterizing the volume over which averaging of stress and strain was carried out to ensure that the continuum theory can represent the physical process of damage.

In order to check the reliability and transferability of the method, FE simulations of various testing examples have been carried out, namely ductile fracture in notched tensile specimens, ductile crack growth in C(T) specimens and application to the pipe-bending test.     

基于FEA的板料成形工艺优化及评价函数研究

基于有限元和优化方法的板料成形工艺优化设计技术已经成为新的研究热点,建立合理的评价标准以形成目标函数,从而用于评价冲压件的成形性是其关键技术之一.提出局部成形性、整体成形性和综合成形性评价函数.基于试验设计法,结合方盒形件拉深以及发动机罩外板成形,验证了本文提出的评价函数具有良好的可靠性和易用性.     

An integrated continuous-discontinuous approach towards damage engineering in sheet metal forming processes

This paper addresses the simulation of ductile damage and fracture in metal forming processes. A combined continuous-discontinuous approach has been used, which accounts for the interaction between macroscopic cracks and the surrounding softening material. Softening originates from the degradation processes taking place at a microscopic level, and is modelled using continuum damage mechanics concepts. To avoid pathological localisation and mesh dependence and to incorporate length scale effects due to microstructure evolution, the damage growth is driven by a non-local variable via a second order partial differential equation. The two governing equations, i.e. equilibrium and non-local averaging, are solved in an operator-split manner. This allows one to use a commercial finite element software to solve the equilibrium problem, including contact between the tools and work piece. The non-local averaging equation is solved on a fixed configuration, through a special purpose code which interacts with the commercial code. A remeshing strategy has been devised that allows: (i) to capture the localisation zone, (ii) prevent large element distortions and (iii) accommodate the crack propagation. To illustrate the capabilities of the modelling tool obtained by combining these continuum mechanics concepts and computational techniques, process simulations of blanking, fine-blanking and score forming are presented.     

Anisotropic ductile fracture of Al 2024 alloys

The anisotropic fracture of the 2024-T351 aluminium alloy is investigated using a micromechanics-based damage model accounting for the effect of the void aspect ratio and void distribution. The 2024-T351 Al alloy contains precipitation free bands in which most void nucleating particles are located. The presence of these bands, which are parallel to the rolling direction, primarily controls the distribution of damage and overall fracture anisotropy. The primary void nucleating particles also present a preferential elongation in the rolling direction. These key microstructural features have been determined using quantitative characterisation methods. The effects of void shape and void spacing on the fracture behaviour are elucidated by means of FE cell calculations. FE simulations of cylindrical notched round bars loaded in different orientations are made and compared with experimental data, allowing a better understanding of the damage process as well as the limitations of the modelling approach.     

韧性断裂准则在高强钢板料成形中的应用

 针对板料成形中的韧性断裂准则预测成形极限的方法,进行了综述和分析,提出了利用韧性断裂准则能够较好地预测塑性差的板料成形极限,而且还能考虑应变路径的变化．将Cockroft和Latham准则应用到高强度钢板DP590的成形预测中．对高强钢DP590进行了单向拉伸试验,获得了相应的物性参数．同时对该高强钢进行了方盒件成形试验,并进行了相应的有限元模拟．通过对高强钢的极限试验,利用有限元模拟获得了该材料的Cockroft和Latham准则常数．最后利用该常数对方盒件的拉深过程进行了缺陷的预测,模拟结果和试验结果完全吻合．表明韧性断裂准则是可以应用到高强度钢板的成形中的．     

The effect of stress invariants on ductile fracture limit in steels

It is widely accepted that damage due to plastic deformation and ductile fracture in metals greatly depends on the triaxiality level (T) of the stress tensor, but according to recent developments described in the literature, it has been observed that the fracture limit ε_f may depend also on the deviatoric parameter (X) of the stress state. In the present paper, several special fracture tests comprising tensile, torsion, flattening and bending have been devised for the specific purpose of investigating as much wide as possible region of the T, X domain. In addition, numerical simulations of each test have been set up to provide additional information whenever direct measures could not be feasible. Three steel grades for cold working applications, each characterized by two different heat treatments have been investigated in the experimental campaign.The results state that fracture limits in the ε_f - T plane can be confined between two boundary curves, characterized by the values X = 0 and X = 1. The paper proposes that this evidence is a consequence of the application of Tresca criterion for shear failure. It is furthermore theoretically derived and experimentally verified that the two limits are linked together through the material hardening behaviour. Finally, it is discussed that an asymmetry between tension and compression states could exist as a consequence of the proposed approach.     

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

In this paper, an anisotropic material model based on a non‐associated flow rule and nonlinear mixed isotropic‐kinematic hardening is developed. The quadratic Hill48 yield criterion is considered in the non‐associated model for both yield function and plastic potential to account for anisotropic behavior. The developed model is integrated based on fully implicit backward Euler's method. The resulting problem is reduced to only two simple scalar equations. The consistent local tangent modulus is obtained by exact linearization of the algorithm. All numerical development was implemented into user‐defined material subroutine for the commercial finite element code ABAQUS/Standard. The performance of the present algorithm is demonstrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Models for ductile damage and fracture prediction in cold bulk metal forming processes: a review

Ductile damage and fracture prediction in real size structures subjected to complex loading conditions has been of utmost interest in the scientific and engineering community in the past century. Numerical simulations with nonlinear finite element (FE) codes allow investigating various complicated problems for damage and fracture prediction in real scale models, which is an important topic in many industries, including metal forming industry. For all industrial cold forming processes, the ability of numerical modeling to predict ductile fracture is crucial. However, this ability is still limited because of the complex loading paths (multi-axial and non-proportional loadings) and important shear effects in several forming processes. The development robust damage and fracture prediction models is essential to obtain realistic results for both geometry precision and mechanical properties. The present article reviews the models in three approaches of ductile damage, namely: uncoupled phenomenological model (or fracture criteria), coupled phenomenological models, and micromechanics-based models, which have been developed to predict ductile fracture in metal forming processes. The objective is to supply to engineers and scientists an overview on a “top-down” procedure to be able to construct predictive tools for metal forming processes.     

Gurson model parameters for ductile fracture simulation in ASTM A992 steels

This study is concerned with the modelling the ductile fracture in ASTM A992 steels using the Gurson‐Tvergaard‐Needleman (GTN) model for high stress triaxiality regime. The GTN model for ASTM A992 structural steels is calibrated from the experiments performed on axisymmetrically notched tensile specimens. The experiments are designed to obtain a range of stress triaxiality and different fracture initiation locations. The non‐uniqueness in the constitutive parameters of the GTN model is illustrated in this study. The choice of a unique set of GTN constitutive parameters is made by choosing the nucleation strain (?_N) as a material constant. The process of estimating this material specific nucleation strain is provided. All the other GTN model parameters corresponding to the material specific nucleation strain (?_N) are evaluated to best fit the experimental results. The calibrated GTN model is shown to predict the load displacement behaviour, ductility and fracture initiation locations in the notched specimens. The calibrated GTN parameters are used to successfully predict the ductility of structural components: (a) bars with a hole; (b) plate with reduced section and (c) plate with holes; that are typically found in structural engineering applications.     

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.     

基于Oyane韧性断裂准则的板料成形极限预测

本文基于Oyane韧性断裂准则,结合数值模拟方法,预测板料不同应变状态下的极限应变.准则中的材料参数通过单向拉伸和平面应变拉伸试验确定.在模拟胀形试验获得每一时间步应力、应变值的基础上,应用韧性断裂准则预测板料的成形极限.模拟结果表明用韧性断裂准则和数值模拟相结合的方法能成功获得板料的成形极限图.     

Interfacial heat transfer during hot metal forming operations assuming scale failure effects

Analysis of real contact area and thermal resistance combined with experimentally derived interfacial heat transfer coefficient values led to the development of an advanced finite element based model to simulate the heat transfer at the oxidised tool/workpiece interface during hot steel rolling. An extensive progress review and building on the Sellars 1990's core assumptions are discussed. Today, oxide scale failure is predicted, taking into account the main physical phenomena such as stress directed diffusion, fracture and adhesion of the oxide scale. The separation loads within the scale metal/system are measured during testing. They are sensitive to the chemical composition of steel. The assumption of several parallel heat flow systems at the roll/stock interface remains the core model for today's research.