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.     

Parameter identification of a mechanical ductile damage using Artificial Neural Networks in sheet metal forming

In this paper, we report on the developed and used of finite element methods, have been developed and used for sheet forming simulations since the 1970s, and have immensely contributed to ensure the success of concurrent design in the manufacturing process of sheets metal. During the forming operation, the Gurson–Tvergaard–Needleman (GTN) model was often employed to evaluate the ductile damage and fracture phenomena. GTN represents one of the most widely used ductile damage model. In this investigation, many experimental tests and finite element model computation are performed to predict the damage evolution in notched tensile specimen of sheet metal using the GTN model. The parameters in the GTN model are calibrated using an Artificial Neural Networks system and the results of the tensile test. In the experimental part, we used an optical measurement instruments in two phases: firstly during the tensile test, a digital image correlation method is applied to determinate the full-field displacements in the specimen surface. Secondly a profile projector is employed to evaluate the localization of deformation (formation of shear band) just before the specimen’s fracture. In the validation parts of this investigation, the experimental results of hydroforming part and Erichsen test are compared with their numerical finite element model taking into account the GTN model. A good correlation was observed between the two approaches.     

Ductile shear failure or plug failure of spot welds modelled by modified Gurson model

For resistance spot welded shear-lab specimens, interfacial failure under ductile shearing or ductile plug failure are analyzed numerically, using a shear modified Gurson model. The interfacial shear failure occurs under very low stress triaxiality, where the original Gurson model would predict void nucleation and very limited void growth. Void coalescence would therefore be largely postponed. However, using the shear modification of the Gurson model, recently introduced by Nahshon and Hutchinson (2008) [1], failure prediction is possible at zero or even negative mean stress. Since, this shear modification has too large effect in some cases where the stress triaxiality is rather high, an extension is proposed in the present study to better represent the damage development at moderate to high stress triaxiality, which is known to be well described by the Gurson model. Failure prediction and tensile response curves for an interfacial shear failure or a ductile plug failure, are here compared when using either the original Gurson model, the shear modified model, or the extension to the shear modified model. The suggested extension makes it possible to use the shear modified model as a simple way of accounting for damage development under low triaxiality shearing, without further increasing the damage rate in regions of moderate to high stress triaxiality.     

Continuum damage mechanics modelling incorporating stress triaxiality effect on ductile damage initiation

Micromechanical modelling of void nucleation in ductile metals indicates that strain required for damage initiation reduces exponentially with increasing stress triaxiality. This feature has been incorporated in a continuum damage mechanics (CDM) model, providing a phenomenological relationship for the damage threshold strain dependence on the stress triaxiality. The main consequences of this model modification are that the failure locus is predicted to change as function of stress triaxiality sensitivity of the material damage threshold strain and that high triaxial fracture strain is expected to be even lower than the threshold strain at which the damage processes initiate at triaxiality as low as 1/3. The proposed damage model formulation has been used to predict ductile fracture in unnotched and notched bars in tension for two commercially pure α‐iron grades (Swedish and ARMCO iron). Finally, the model has been validated, predicting spall fracture in a plate‐impact experiment and confirming the capability to capture the effect of the stress state on material fracture ductility at very high stress triaxiality.     

A modified Gurson model and its application to punch-out experiments

Recent experimental evidence has reiterated that ductile fracture is a strong function of stress triaxiality. Under high stress triaxiality loading, failure occurs as a result of void growth and subsequent necking of inter-void ligaments while under low stress triaxiality failure is driven by shear localization of plastic strain in these ligaments due to void rotation and distortion. The original Gurson model is unable to capture localization and fracture for low triaxiality, shear-dominated deformations unless void nucleation is invoked. A phenomenological modification to the Gurson model that incorporates damage accumulation under shearing has been proposed. Here we further extend the model and develop the corresponding numerical implementation method. Several benchmark tests are performed in order to verify the code. Finally, the model is utilized to model quasi-static punch-out experiments on DH36 steel. It is shown that the proposed modified Gurson model, in contrast to the original model, is able to capture the through-thickness development of cracks as well as the punch response. Thus, the computational fracture approaches based on the modified Gurson model may be applied to shear-dominated failures.     

热成形淬火对QP1180/22MnB5激光拼焊板组织与性能的影响

目的 对QP1180和22MnB5激光拼焊板进行热成形试验,以解决超高强钢板材焊后的软化问题。方法 选择QP1180和22MnB5异种高强钢作为母材进行激光自熔焊,对焊后的激光拼焊板进行热成形试验,通过体式显微镜、扫描电子显微镜、液压拉伸试验机和维氏硬度计等手段,分析热成形前后激光拼焊板微观组织和力学性能的变化。结果 与焊态拉伸试样相比,热成形试样抗拉强度提高了135%,断后伸长率降低了55%,拉伸试样都在22MnB5母材处断裂,均为塑性断裂。在热成形后,对焊接接头进行组织分析,发现QP1180母材区马氏体含量增加,22MnB5母材区和临界热影响区组织由珠光体和铁素体转变为马氏体,焊接接头热影响区各亚区的组织均转变为大小不同的板条马氏体。硬度测试结果表明,焊态试样焊接接头的QP1180临界区存在软化现象,硬度值最低为335HV,22MnB5侧硬度值由母材处向焊缝升高,母材硬度最低为170HV;而在热成形后,QP1180临界区软化现象消失,硬度值趋于平缓,22MnB5母材处硬度比焊态试样硬度高了2倍。结论 与焊态试样相比,经热成形后激光拼焊板的焊后软化问题得到了解决。     

Interaction between anisotropic plastic deformation and damage evolution in Al 2198 sheet metal

Deformation anisotropy of sheet aluminium alloy 2198 (Al-Cu-Li) has been investigated by means of mechanical testing of notched specimens and Kahn-type fracture specimens, loaded in the rolling direction (L) or in the transverse direction (T). Fracture mechanisms were investigated via scanning electron microscopy. Contributions to failure are identified as growth of initial voids accompanied by a significant nucleation of a second population of cavities and transgranular failure. A model based on the Gurson-Tvergaard-Needleman (GTN) approach of porous metal plasticity incorporating isotropic voids, direction-dependent void growth, void nucleation at a second population of inclusions and triaxiality-dependent void coalescence has been used to predict the mechanical response of test samples. The model parameters have been calibrated by means of 3D unit cell simulations, revealing the interaction between the plastic anisotropy of the matrix material and void growth. The model has been successfully used to describe and predict direction-dependent deformation behaviour, crack propagation and, in particular, toughness anisotropy.     

Investigation on fracture mechanisms of metals under various stress states

Fracture mechanisms for widely used metal materials are investigated under various loading conditions. Several specimens and different loading methods are deliberately designed to produce various stress states. The stress triaxiality is used to rate the level of tension and compression under various stress states. The stress triaxiality increases with adding a notch in the specimen under tension loading and decreases by changing the loading from tension to compression. Scanning electron microscopes are used to observe the microscopic features on the fracture surfaces. The fracture surfaces observed in the tests indicate that with the decreasing stress triaxiality the fracture mechanism for a given metal material includes intergranular cleavage, nucleation, growth, void coalescence, and local shear band expansion. With the fracture mechanisms changing from intergranular cleavage to nucleation, growth, and coalescence of voids, and expansion of a local shear band, four possible fracture modes can be observed, which are quasi-cleavage brittle fracture, normal fracture with void, shear fracture with void, and shear fracture without void. Quasi-cleavage brittle fracture and normal fracture with void are both normal stress-dominated fracture modes; however, their mechanisms are different. Shear fracture with and without void are both shear stress-dominated fracture, and shear fracture with void is also influenced by the normal stress. To a certain metal material, under high stress triaxiality, quasi-cleavage brittle fracture and normal fracture with void tend to occur, and under low stress triaxiality, shear fracture with and without void tend to occur. In addition, the critical positions and fracture criteria adapted to each fracture mode will also be different.     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

修正GTN模型及其在预测硅钢冷轧边裂中的应用

考虑剪应变对微孔洞损伤演化的影响, 对GTN损伤模型的损伤演化机制进行修正, 建立了适用于不同应力三轴度水平的损伤模型. 结合隐式应力更新算法和显式有限元计算, 采用VUMAT子程序实现了修正GTN模型在有限元软件ABAQUS中的数值计算. 通过模拟纯剪切和剪切-拉伸两组试样的损伤演化和断裂行为, 验证了修正GTN模型在不同应力三轴度承载条件下的有效性. 运用修正GTN损伤模型模拟含边部缺口的带钢在轧制过程中裂纹的萌生和扩展行为, 模拟结果与实验相一致, 表明该模型可有效地用于带钢缺陷在轧制过程中扩展行为的分析和预测. 模拟和实验结果表明, 带钢边部缺口在轧制过程中, 缺口前沿和后沿均会萌生裂纹, 且后沿裂纹扩展更为明显.     

Experimental characterization and numerical modeling of micromechanical damage under different stress states

The use of HSLA steels for the manufacture of automotive components is interesting from an engineering point of view. This family of steels, while possessing high strength, also has good formability and can be used in forming manufacturing processes. In some forming processes such as blanking, shear strain localization occurs, which causes damage and results in the final fracture of the material. This paper presents an experimental study based on in situ tests to understand and identify the physical mechanisms of ductile damage under two stress states: tension and shear. Different macroscopic tests were performed to calibrate a damage model based on a micromechanical approach. This damage model is based on the Gurson–Tvergaard–Needleman theory and presents recent improvements proposed by Nahshon and Hutchinson and by Nielsen and Tvergaard so as to better predict fracture under a wide range of stress states, especially with low levels of stress triaxiality. These extensions have made the identification of the material parameter more complicated. In this work an identification strategy has been proposed using tests on specimens with different shapes. The identified parameter values are validated and the fracture model show good predictive capability over a wide stress state range.     

Determination of the Gurson–Tvergaard damage model parameters for simulating small punch tests

The objective of the final small punch test (SPT) is to determine the fracture properties of materials, such as fracture toughness, when not enough material is available for the conduct of conventional fracture tests. The damage model developed by Gurson, and subsequently modified by Tvergaard and Needleman (GTN), allows for the numerical simulation of the elastic‐plastic behaviour until fracture. This model is based on several constitutive material parameters that must be calibrated if the model is to be properly applied. In this paper, we develop a consistent methodology for the identification of the GTN damage parameters based on the adjustment of the load‐displacement curve obtained in the SPTs. The methodology presented is applicable to simulating other different SPTs with different thicknesses and test temperatures. Also, the three‐dimensional modelling developed will be useful in the future for analysing the possible anisotropy exhibited by some materials. The next step in the simulation will be to determine its validity in other stress fields with different triaxiality ratios, like the one present in CT specimens, the ultimate goal being to allow for the estimation of the material fracture toughness.     

高强钢板热冲压成形热力耦合数值模拟

为研究高强钢板的热冲压成形性,采用ABAQUS软件对高温下22MnB5高强钢板沟槽形件冲压成形进行了数值模拟研究.建立了基于热力耦合的弹塑性有限元模型和热成形下的材料模型,通过对沟槽形件热成形进行数值模拟,考察了压边力、模具间隙和凹模圆角半径等工艺参数对热成形时温度分布和回弹的影响,给出了热成形中产生回弹的机理,确定了合适的工艺参数,通过热成形试验验证了数值结果的可靠性.     

Effects of the stress state on plastic deformation and ductile failure: Experiment and numerical simulation using a newly designed tension‐shear specimen

The stress state is one of the most notable factors that dominates the initiation of ductile fracture. To examine the effects of the stress state on plasticity and ductile failure, a new tension‐shear specimen that can cover a wide range of stress triaxialities was designed. A fracture locus was constructed in the space of ductility and stress triaxiality for two typical steels based on a series of tests. It is observed that the equivalent plastic strain at failure exhibits a nonmonotonic variation with increasing the value of stress triaxiality. A simple damage model based on the ductility exhaustion concept was used to simulate the failure behaviour, and a good agreement is achieved between simulation results and experimental data. It is further shown that consideration of fracture locus covering a wide range of stress triaxialities is a key to an accurate prediction.     

Extension of the modified Bai‐Wierzbicki model for predicting ductile fracture under complex loading conditions

The ductile fracture behaviour of metallic materials is strongly dependent on the material's stress state and loading history. This paper presents a concept of damage initiation and failure indicators and corresponding evolution laws to enhance the modified Bai‐Wierzbicki model for predicting ductile damage under complex loading conditions. The proposed model considers the influence of stress triaxiality and the Lode angle parameter on both damage initiation and the subsequent damage propagation. The model parameters are calibrated for C45E + N steel using a series of mechanical tests and numerical simulations. The enhanced approach is applied to the modelling of various mechanical tests under proportional and non‐proportional loading conditions and successfully predicts the ductile damage behaviour in these tests.     

ANALYSIS OF CAST STEEL FRACTURE MECHANISMS FOR DIFFERENT STATES OF STRESS

The process of fracture in a low-carbon cast steel was studied for different states of stress. As a result of heat treatment, two different microstructures have been obtained: ferritic-pearlitic and bainitic. The triaxial states of stress were realised by tensile tests on specimens with various notch configurations and on smooth specimens subjected to different hydrostatic pressures.
During tensile tests carried out under triaxial stress states, the following quantities at fracture were determined: the effective strain, effective stress, stress state components, mean stress and stress triaxiality factor. Fractography of the specimens was carried out to observe the fracture mechanisms and relate them to the state of stress. The fracture mechanism depended on the state of stress and microstructure. With a decreasing stress triaxiality factor, the failure mechanism changed from ductile to shear. The fracture mechanism changed across the diameter of the sample and also depended on the microstructure. The small, smooth samples fractured at a higher stress than the larger samples. Ductile fracture in the ferritic-pearlitic microstructure was controlled by cracking of the matrix–precipitate boundary. Samples with the bainitic microstructure fractured by shear, and fracture depended mainly on the effective stress, although void growth (which is controlled by stress triaxiality) reduced the critical effective stress at positive values of mean stress.     

Assessment of different ductile damage models and experimental validation

The tough fuel economy and emissions standards facing automotive industry creates the need for lightweight construction and the use of new generation of materials. However, the use of non-conventional materials leads to difficulties in the prediction of material behaviour during sheet metal forming processes, including damage and formability limits, thus challenging the numerical simulation. This paper seeks to contribute in the prediction of fracture on sheet metal alloys. Three constitutive damage models are used, GTN, Johnson Cook and Lemaitre, to simulate, as realistically as possible, the mechanical behaviour of the sheet metal material. The corresponding parameters of damage models are identified using an inverse analysis procedure, based on experimental test data. Finally, to validate and verify the applicability of the studied damage models to predict fracture, experiments are compared with FE simulations.     

A fracture locus for a 50 volume-percent Al/SiC metal matrix composite at high temperature

The effect of the stress state on the fracture locus function of the 50 vol.% Al/SiC metal matrix composite at high temperature is studied. The value of fracture locus function is quantitatively characterized by the amount of shear strain accumulated prior to the moment of failure. Nondimensional invariant parameters are used as characteristics of the stress state, namely, the stress triaxiality k and the Lode-Nadai coefficient μ _σ showing the form of the stress state. Besides conventional testing for tension, compression and torsion of smooth cylindrical specimens, the complex of mechanical tests includes a new type of testing, namely, that for bell-shaped specimens. These kinds of testing enable one to study fracture strain under monotonic deformation in the ranges μ _σ ?=?0?…?+?1 and k?=???1.08...0 without using high-pressure technologies. The stress–strain state during specimen testing is here evaluated from the finite element simulation of testing in ANSYS. The tests were performed at a temperature of 300 °C and shear strain rate intensity Η?=?0.1;?0.3;?0.5 1/s. The test results have offered a fracture locus, which can be used in models of damage mechanics to predict fracture of the material in die forging processes.     

On fracture mechanics under complex stress

The majority of linear elastic fracture mechanics investigations since the pioneering work of Irwin and Paris have been carried out under tension-tension loading conditions in sheet metal. However, built up structures have generally been under complex stress conditions and to date very scanty information is available on fracture mechanics parameters under complex stress conditions. The current stale of the art for mixed mode crack tips deformation is reviewed.In order to use linear elastic fracture mechanics methodology to predict crack growth rate in shear webs, an experimental program was initiated. Initial tests on 7075-T6 Aluminum alloy sheet, using a picture frame type specimen, were conducted. The critical stress intensity factors and the rate of crack growth under aforementioned condition are established.     

一种韧性断裂模型的理论研究和实验验证

为研究高强钢板成形过程中的损伤破裂机理,更准确地预测高强钢的断裂失效行为,基于细观损伤力学的空穴理论,并在屈服函数就是塑性势函数的通用性假设基础上推导了各向同性的韧性断裂模型;同时引入Lode参数以反映不同应变状态下空穴形核、长大以及聚合的差异,提出了一种包含应力三轴度和Lode参数的新模型.在Hill正交各向异性屈服假设下,描述了平面应力状态下应力比值、r值与应力三轴度、等效塑性应变的关系.最后,针对DP590进行了参数确定和实验验证.结果表明:应力三轴度在高强钢韧性断裂中仍然起主导因素,在低应力三轴下,材料主要是剪切型破坏,空穴的长大及聚合方式主要受剪应力影响,高应力三轴下,空穴损伤主要受拉应力影响,断裂是韧窝形的;Lode参数决定了应力组成形式,也间接地反映了应变状态,它与应力三轴度共同决定了空穴损伤的发展.新的模型能较准确地预测DP590的成形极限.