On the numerical implementation of a shear modified GTN damage model and its application to small punch test

Gurson-type models have been widely used to predict failure during sheet metal forming process. However, a significant limitation of the original GTN model is that it is unable to capture fracture under relatively low stress triaxiality. This paper focused on the fracture prediction under this circumstance, which means shear-dominated stress state. Recently, a phenomenological modification to the Gurson model that incorporates damage accumulation under shearing has been proposed by Nahshon and Hutchinson. We further calibrated new parameters based on this model in 22MnB5 tensile process and developed the corresponding numerical implementation method. Lower stress triaxiality were realized by new-designed specimens. Subsequently, the related shear parameters were calibrated by means of reverse finite element method and the influences of new introduced parameters were also discussed. Finally, this shear modified model was utilized to model the small punch test (SPT) on 22MnB5 high strength steel. It is shown that the shear modification of GTN model is able to predict failure of sheet metal forming under wide range of stress state.     

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.     

3D modelling of plug failure in resistance spot welded shear-lab specimens (DP600-steel)

Ductile plug failure of resistance spot welded shear-lab specimens is studied by full 3D finite element analysis, using an elastic-viscoplastic constitutive relation that accounts for nucleation and growth of microvoids to coalescence (The Gurson model). Tensile properties and damage parameters are based on uni-axial tensile testing of the basis material, while the modelled tensile response of the shear-lab specimens is compared to experimental results for the case of a ductile failure near the heat affected zone (HAZ). A parametric study for a range of weld diameters is carried out, which makes it possible to numerically relate the weld diameter to the tensile shear force (TSF) and the associated displacement, u _TSF , respectively. Main focus in the paper is on modelling the localization of plastic flow and the corresponding damage development in the vicinity of the spot weld, near the HAZ. For decreasing weld diameter, localization of plastic flow may be observed to occur in the weld nugget, introducing significant shearing. Due to these competing mechanisms a critical transition radius of the weld may be found. However, due to the limitation of the Gurson model in describing ductile failure at very low stress triaxiality, further analysis of the shear failure is omitted.     

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.     

基于电磁超声的塑性损伤铝材抗拉强度预测

针对电磁超声信号信噪比低这一问题,在利用相对非线性系数预测抗拉强度的同时引入应力三轴度来提升塑性损伤试件抗拉强度预测的准确性.建立了电磁超声非线性检测塑性损伤试件的有限元三维仿真模型,计算两个特征参量:应力三轴度和相对非线性系数,研究试件的内部应力状态特征和电磁超声检测信号的频谱特征.仿真分析结果表明这两个特征参量敏感...     

Damage evolution in experiments and simulation in a construction steel

Results from the modelling of the initiation and the evolution of microvoids governed by triaxiality and effective plastic strain in heterogeneous materials are presented. In particular, the damage evolution in a microalloyed thermomechanically treated steel consisting of brittle hard phases embedded in a ductile matrix is studied. Results obtained by numerical simulations using the finite element method are compared with experimental investigations of a notched cylindrical tensile bar. For this, two kinds of continuum damage models are used: the model of Rousselier, which assumes the yield stress as function of damage, and the concept of effective strains and stresses proposed by Lemaitre.     

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.     

Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500 °C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.     

Simulation of elevated temperature fatigue damage evolution using the finite element method for near alpha titanium alloy

The numerical estimation of evolving damage under low cycle fatigue loading condition has been performed in the near‐α titanium alloy IMI‐834 at 823 K temperature. By using the experimentally determined parameters as input, numerical simulation of fatigue damage has been performed on round specimens using finite element analysis. Coupled deformation‐damage model has been established for this alloy for simulation of damage evolution in a three‐dimensional cylindrical low cycle fatigue test specimen. The fatigue damage estimates from numerical simulation are observed to be in close agreement with the experimental results.     

考虑罗德角参数的钢材薄板延性断裂标定方法

在钢结构中钢梁腹板的断裂表现出很强的剪切断裂特征,因此在预测其断裂行为时除了考虑应力三轴度以外,还应考虑与剪切状态有关的罗德角参数的影响。该文提出了一种适用于钢材薄板延性断裂预测的标定方法。共设计了5组试件,分别为平板试件、开孔平板、开槽平板、90°剪切平板和45°剪切平板。利用平板试件和停机平板试件单向拉伸试验,结合有限元反演得到钢材的全过程真实应力-应变曲线。然后将其代入各试件有限元模型进行计算,标定出各试件对应的等效断裂应变、平均应力三轴度和平均罗德角参数。最后利用Matlab优化工具箱对断裂模型进行优化拟合,确定模型中的各项待定参数。     

Experimental and Numerical Investigation on the Size of Damage Process Zone of a Concrete Specimen under Mixed-Mode Loading Conditions

The characteristic length of a gradient-dependent damage model is a key parameter, which is usually regarded as the length of damage process zone (DPZ). Value and evolution of the size of DPZ were investigated by both a numerical method and an experimental manner. In the numerical study, the geometrical model adopted was a set of four-point shearing beams; the numerical tool used was the Abaqus/Explicit software. The distance between the front and end of a complete DPZ was obtained. Values of strain components at these points were given out at given time points. The experimental study of the evolution process of a damage process zone was investigated with a set of concrete specimens under mixed-mode loading conditions by using a white-light speckle method. The geometrical parameters of the damage process zone were measured. Double-notched specimens under four-point shear loading conditions were adopted. A series of displacement fields for points on the surface of the specimen were measured and further transferred into a strain field of these points during loading process. With reference to the strain values that occurred at both the front and end of a numerically-obtained DPZ, the length of the DPZ was determined with the experimental results. These results provide an experimental basis for the determination of the value of an internal length parameter for a gradient-enhanced and/or area-averaged non-local model.     

Numerical investigation of factors affecting creep damage accumulation in ASME P92 steel welded joint

The present study mainly investigated Type IV cracking occurring in the fine grained heat affected zone (FGHAZ) in the welded joint of ASME P92 steel at high temperature and low applied stress by numerical simulation method. Based on the modified Karchanov–Rabotnov constitutive equation, the user defined material subroutine (UMAT) was complied and the creep damage accumulation was carried out by finite element method using ABAQUS codes for the welded joint at 650 °C and 70 MPa. Calculated results revealed that the most severe creep damage and the highest equivalent creep strain occurred in the FGHAZ because of high maximum principle stress and high maximum principle stress. Furthermore, the effect of groove angle and HAZ width on the creep damage accumulation was investigated. It indicated that a small groove angle and a narrow FGHAZ width could deteriorate the creep damage accumulation because of the degradation of maximum principle stress and stress triaxiality in the FGHAZ.     

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.     

一种改进型方钢管柱与钢梁连接节点抗震性能研究

该文主要讨论了一种改进型方钢管柱与钢梁连接节点的抗震性能。通过对3个试件进行低周反复荷载试验,研究了是否采用T型件和梁截面高度比两个设计参数对节点域剪切承载力和变形能力的影响。在试验基础上,采用MSC.Marc 2012有限元软件进行了数值模拟分析,有限元模型能够较好地模拟试验试件的各项性能。试验和有限元分析结果表明:改进型高低梁柱异型节点试件应力集中主要发生在T型连接件与梁2的焊接处;虽然两种节点各部分的变形分担率十分接近,但改进型高低梁柱异型节点的剪切承载力和耗能能力分别提高了20%和200%。文末提出了T型连接装置的计算模型和设计方法,为今后实际工程应用提供了参考依据。     

Low‐cycle fatigue delamination initiation and propagation in fibre metal laminates

The aim of this paper is to develop an elastic–plastic‐damage constitutive law and a tool for simulation of delamination initiation and propagation in fibre metal laminates (FMLs) under low‐cycle fatigue loading regime. In the previous studies, the significance of plasticity in delamination growth and modelling of FMLs was not considered. Hence, cohesive zone law that combines the damage evolution with plasticity is developed. The new fatigue damage model is implemented as user‐written subroutines that links with ansys based on the cohesive finite element method. The cohesive zone model constitutive law has been verified by modelling of the delaminated adhesively bonded aluminium joint under normal and shear loadings and compared with the available results in the literature. The developed procedure and tool have been used for the analyses of DCB and ENF specimens under uniform and variable loadings. The obtained results for progressive damage and delamination and stress–strain curves are discussed in this paper.     

Effect of Reaction Layers on the Residual Stress of the Brazed TiC Cermets/Steel Joints

For the first time, considering the effect of reaction layers, numerical simulation calculation of residual stress on brazed TiC cermets/steel joint was studied by finite element method (FEM). The calculation results show that, when the joint is brazed at 1123 K for 300 s (low brazing parameters), the maximum shear stress value occurs on (Cu, Ni) layer near TiC cermets, which is 92.16 MPa as the temperature is 300 K. When the joint is brazed at 1273 K for 900 s (high brazing parameters), the maximum shear stress value occurs on (Cu,Ni)+(Fe, Ni) layer, which is 39.18 MPa as the temperature is 300 K. The fracture sites of the joints obtained from numerical simulation calculation accord with experimental results.     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

Experimental study of cavity growth in ductile rupture

Composite materials made of a steel matrix and spherical alumina particles were prepared to study the growth of cavities nucleated from Al₂O₃ inclusions during deformation at room temperature. Two materials containing different volume fractions of Al₂O₃ particles, i.e. ƒ = 0.5% and 2%, were investigated. Axisymmetric notched specimens were employed to determine the effect of stress triaxiality on cavity growth rate. These specimens were calculated by finite element method. They were predeformed at room temperature and subsequently broken at − 196°C. The experimental results are in broad agreement with the theoretical results derived from Rice and Tracey model. In particular it is observed that the cavity growth is proportional to the local strain obtained from the finite element calculations. Moreover the effect of stress triaxiality intervenes exponentially as predicted by the Rice and Tracey model. However, the theoretical proportionality factor in front of the exponential term is lower than the experimental one. The reasons for this discrepancy, especially the effect of interactions between neighbouring inclusions which are not taken into account in this model, are briefly discussed.     

Evaluation of the interfacial strength of carbon-fiber-reinforced temperature-resistant polymer composites by the micro-droplet test

This paper presents an evaluation method for the fiber/matrix interfacial strength. The interfacial strength is determined by comparing experimental data with numerical simulations. The micro-droplet test is conducted, and the fiber axial stress at the point of interface debonding is obtained. A numerical simulation is performed with ABAQUS using an axisymmetric finite-element model. In the numerical simulation, an accurate value of the thermal residual stress based on the thermo-viscoelasticity and the damage to the resin around the blade-contacting point is considered to simulate the experimental phenomena ideally. In the thermal residual stress analysis, the actual thermal residual stress is calculated by considering the relaxation modulus and the time–temperature superposition principle for the resin. Damage initiation criteria for both dilatational and shear cases, based on continuum damage mechanics, are considered for the resin. Interfacial debonding is simulated using a cohesive zone model, and the interfacial strength is taken as the strength of the cohesive zone element at the simulated fiber maximum stress corresponding to the experimental value.     

A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous Galerkin‐cohesive band model framework

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a nonlocal elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality‐dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D state, mandatory to incorporate the in‐plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction‐separation law is then built from the underlying damage model. The method is numerically shown to capture the stress triaxiality effect on the crack initiation and propagation.