Damage in dual phase steels and its constituents studied by X-ray tomography

Damage in a dual phase steel was measured using in situ high-resolution X-ray absorption tomography. A comparison with the behavior of its two constituents ferrite and martensite, taken separately, was also achieved in the present work. The method was particularly useful for analyzing the respective contribution of nucleation and growth of voids in the studied materials. Quantitative analysis of the damage events was carried out on a same 3D region inside the reconstructed volumes at different deformation steps for different samples cut from the three kinds of materials. Void number prediction and growth model, based on local stress triaxiality, show a good agreement with the experimental data.     

基于微孔贯通细观损伤模型的金属韧性断裂分析

韧性材料断裂过程通常可看作是材料内部微孔洞的形核、扩展及相互贯通的积累。经典的Gurson- Tvergaard (GT)模型能够很好地模拟具有变形均匀、各向同性的孔洞的萌生及扩展过程;但无法模拟由孔洞贯通而引起的局部变形过程,因此需要对其修正,引入相应的孔洞贯通准则。该文采用两种贯通准则对经典GT模型进行修正,即Thomason的塑性极限载荷准则和临界等效塑性应变准则。借助用户自定义程序UMAT将采用这两种贯通准则修正的GT本构关系嵌入至商用有限元软件ABAQUS中,从而可通过对金属材料应力状态和断裂机理的分析控制孔洞的贯通。以一组含有不同缺口根半径的圆棒拉伸试验件为例,分析了该类金属构件自孔洞萌生至最终断裂的整个损伤演化过程,并与试验数据进行了对比,验证了该模型的有效性。该文还讨论了金属断裂过程中应力三轴度对微裂纹萌生与扩展的影响。     

Void configuration under constrained deformation in ductile matrix materials

SiC particle reinforced Al 2025 aluminum alloy composite is used for tensile tests. The ductile fracture by nucleation, growth and coalescence of micro voids, particle cracking and the interfacial debonding under the different constraint conditions, which are obtained by changing the notch radius, is analyzed. The effect of the local constraint on the respective damage phenomenon is analyzed using the axi-symmetric unit cell FE model by changing the local stress triaxiality and side constraint. The results show that the fracture process of the notched tensile bar is simulated well and the damage phenomena agree qualitatively with the experimental ones. Finally the effect of constraint on the void configuration and coalescence is investigated experimentally using three-dimensional fracture surface observations using the SEM (scanning electron microscope) and three-dimensional imaging analysis method. The constraint effect is analyzed by changing the specimen’s shape. The experimental results show that the void aspect ratio is decreased with increases of SiC particle volume fraction in aluminum alloy. The final void volume fraction at fracture also changes by the specimen shape and the material’s structure.     

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.     

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.     

Use of a modified Gurson model approach for the simulation of ductile fracture by growth and coalescence of microvoids under low, medium and high stress triaxiality loadings

In the paper the modified Gurson model is developed for the simulation of damage growth and ductile fracture under low, medium and high stress triaxiality loadings. A new coalescence criterion is introduced based on a simple assumption that singular value of the effective stress triggers the coalescence of microvoids in materials. According to the introduced approach the void coalescence described by means of the modified Gurson model is not only determined by the so-called critical, constant void volume fraction but also by the stress triaxiality ratio. Computational simulations have been carried out for Al 2024–T351 aluminum specimens. In order to find some improvements of micromechanical damage models, two different approaches have been compared for modeling the shear driven microvoid coalescence under low stress triaxiality loadings.     

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.     

Growth and coalescence of penny-shaped voids in metallic alloys

The growth and coalescence of penny-shaped voids resulting from particle fracture is a common damage process for many metallic alloys. A three steps modeling strategy has been followed to investigate this specific failure process. Finite element cell calculations involving very flat voids shielded or not by a particle have been performed in order to enlighten the specific features of a damage mechanism starting with initially flat voids with respect to more rounded voids. An extended Gurson-type constitutive model supplemented by micromechanics-based criteria for both void nucleation and void coalescence is assessed for the limit of very flat voids towards the FE calculations. The constitutive model is then used to generate a parametric study of the effects of the stress state, the microstructure and the mechanical properties on the ductility. Based on these results, a simple closed-form model for the ductility is finally proposed. The main outcomes of this study are that (i) the ductility of metal alloys involving penny-shaped voids is primarily controlled by the relative void spacing; (ii) the definition of an effective porosity in terms of an equivalent population of spherical voids is valid for low particle volume fraction; (iii) the presence of a particle shielding the void does not significantly affect the void growth rates and void aspect evolution; (iv) early fracture by void coalescence can occur under very low stress triaxiality conditions if the particle volume fraction is large enough, explaining that some alloys and composites can fail through a transgranular ductile fracture mode under uniaxial tension condition before the onset of necking; (v) the fracture mechanism moves from void growth controlled to void nucleation controlled when increasing the void nucleation stress, lowering the stress triaxiality, and increasing the initial void aspect ratio.     

APPLICATION OF LOCAL DAMAGE MODELS TO THE NUMERICAL ANALYSIS OF DUCTILE RUPTURE

Abstract— Two damage models were implemented into the finite element program ADINA to study the correlation between microscopical damage and macroscopical material failure. In the first model, based on the Gurson yield function the nucleation, growth and the coalescence of voids were incorporated into the constitutive relations. In the second model the void growth was determined according to the Rice and Tracey model using the von Mises yield function, and material failure was simulated by eliminating the elements where the critical void growth ratio was exceeded. The numerical results for the local and global behaviour of the specimens were compared with experiments. The generality of the damage parameters was checked by investigating several specimen geometries. Both damage models deliver qualitatively consistent results with regard to the influence of the stress triaxiality on the void growth and on the beginning of the material failure. However, the Gurson model gives a more accurate numerical simulation because the damage development and the stress drop continue after the onset of void coalescence while the critical void growth model causes less convergence problems in the simulation of large crack extension. The J _n-curve was estimated on the basis of both models.     

Shock induced void nucleation during Taylor impact

Taylor impact experiments in the classic and symmetric configurations were used to study the plastic deformation and void nucleation in Al-6082-T6 rods. Deformation histories during impact were recorded using high-speed photography. X-ray computed tomography was used to visualize the extent of damage in recovered specimens. Above threshold velocities, void nucleation was observed along the central axis of the specimens, and reconstructed images from the tomography provide a 3-D mapping of the damaged region. The use of X-ray tomography is the first step in developing a method to characterise the damage process during impact using in-situ flash X-rays, which is also attempted in this study. Finite element simulations of these experiments are in good agreement with the experimental measurements, and confirm that void nucleation is due to the coalescence of lateral release waves at the centre of the specimen. The simulations also revealed that the time to failure is velocity dependent, and that the threshold velocity for void nucleation is sensitive to the properties and geometry of the target.     

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.     

Analysis of fracture limit curves and void coalescence in high strength interstitial free steel sheets formed under different stress conditions

Void formation, which is a statistical event, depends on inhomogeneities present in the microstructure. The analysis on void nucleation, their growth and coalescence during the fracture of high strength interstitial free steel sheets of different thicknesses is presented in this article. The analysis shows that the criterion of void coalescence depends on the d-factor, which is the ratio of relative spacing of the ligaments (δd) present between the two consecutive voids to the radius of the voids. The computation of hydrostatic stress (σ_m), the dominant factor in depicting the evolution of void nucleation, growth and coalescence and the dimensional analysis of three different types of voids namely oblate, prolate and spherical type, have been carried out. The ratio of the length to the width (L/W) of the oblate or prolate voids at fracture is correlated with the mechanical properties, microstructure, strains at fracture, Mohr’s circle shear strains and Triaxiality factors. The Lode angle (θ) is determined and correlated with the stress triaxiality factor (T), ratio of mean stress (σ_m) to effective stress (σ_e). In addition, the Void area fraction (V _a), which is the ratio of void area to the representative area, is determined and correlated with the strain triaxiality factor (T_o).     

An exponential ductile continuum damage model for metals

In the frame of continuum damage mechanics an isotropic ductile plastic damage model is derived. The model is based on void damage variable, defined using effective stress concept and thermodynamics. The damage evolution from this model is exponential with equivalent plastic strain as experienced in some low carbon steel like AISI 1015. The damage model is sensitive to stress triaxiality and emulates the damage evolution as recorded in experiments conducted on such metals. The model is validated by comparison with the Rice-Tracey model and other experimental results published in the literature. This model can be used to study the growth and coalescence of micro voids, influence of stress triaxiality on strain to rupture and crack initiation phenomena.     

Micromechanics of room and high temperature fracture in 6xxx Al alloys

The micromechanics of ductile fracture has made enormous progress in recent years. This approach, which was mostly developed in the context of structural integrity analysis, is becoming a key tool for materials scientists to optimize materials fracture properties and forming operations. Micromechanical models allow quantitatively linking fracture properties, microstructure features at multiple lengths scales, and manufacturing conditions. After briefly reviewing the state of the art, this paper illustrates the application of the micromechanics-based methodology by presenting the results of an investigation on the damage resistance of 6xxx Al produced by extrusion.The presence of coarse, elongated, particles is the key microstructural feature affecting the fracture behaviour of 6xxx Al. The detrimental elongated β-type particles are transformed into rounded α-type particles by heat treatment. In situ tensile tests revealed that, at ambient temperature, the α particles and the β particles oriented with the long axis perpendicular to the main loading direction undergo interface decohesion, while the β particles oriented perpendicular to the loading direction break into several fragments. At high temperatures, only interface decohesion is observed. Uniaxial tensile tests on notched and smooth round bars were performed on two different alloys, at different temperatures ranging between 20 °C and 600 °C, under different loading rates, while systematically varying the content in β versus α particles. The ductility increases with decreasing amount of β particles, increasing temperature and strain rates, and decreasing stress triaxiality.A viscoplastic extension of the Gurson model has been developed for capturing the complex hierarchy of damage mechanisms, coupled with viscoplastic and stress state effects. Three populations of voids are modelled while accounting for the different void nucleation mechanisms leading to different initial void aspect ratio. Proper modelling of the initial void aspect ratio and of its evolution with void growth was the key to predict the effect of the β → α conversion on ductility. The void coalescence criterion takes into account the presence of secondary voids resulting from particle fragmentation. The characteristics of particles entering the model were all measured experimentally. The temperature and rate dependent flow properties of the matrix material have been obtained by inverse modelling. The only fitting parameters are the critical stresses for void nucleation. The model is validated by comparing the predictions to the experimental data involving different relative proportion of α and β particles, temperature, loading rate and stress triaxiality. This type of model opens the path for an “alloy by design” strategy which relates end-use properties to upstream manufacturing operations.     

Nanoscale void nucleation and growth and crack tip stress evolution ahead of a growing crack in a single crystal

A constrained three-dimensional atomistic model of a cracked aluminum single crystal has been employed to investigate the growth behavior of a nanoscale crack in a single crystal using molecular dynamics simulations with the EAM potential. This study is focused on the stress field around the crack tip and its evolution during fast crack growth. Simulation results of the observed nanoscale fracture behavior are presented in terms of atomistic stresses. Major findings from the simulation results are the following: (a) crack growth is in the form of void nucleation, growth and coalescence ahead of the crack tip, thus resembling that of ductile fracture at the continuum scale; (b) void nucleation occurs at a certain distance ahead of the current crack tip or the forward edge of the leading void ahead of the crack tip; (c) just before void nucleation the mean atomic stress (or equivalently its ratio to the von Mises effective stress, which is called the stress constraint or triaxiality) has a high concentration at the site of void nucleation; and (d) the stress field ahead of the current crack tip or the forward edge of the leading void is more or less self-similar (so that the forward edge of the leading void can be viewed as the effective crack tip).     

Local approach to ductile fracture and dynamic strain aging

Experiments on smooth and notched round specimens on a C–Mn steel used in nuclear industry are performed at different temperatures under quasi-static loadings, revealing dynamic strain aging (DSA). The behavior is highly dependent on temperature and strain rate, and a drop in fracture strain is observed. Fracture surface observation on notched tensile specimens shows classical ductile fracture mechanisms with growth and coalescence of voids. The apparent strain hardening behavior at each temperature and strain rate is taken into account to compute the void growth with the Rice and Tracey model and with a damage law developed from unit cell computations. It is shown that the apparent strain hardening at large strains is of major importance to correctly predict fracture with the Rice and Tracey model, but its influence on the void growth law is of minor importance. In particular, the stress triaxiality ratio within the notch is increased due to the negative strain rate sensitivity. The ductility drop observed in DSA domain is then partly explained, but void nucleation and void growth in presence of strain bands should be included in the fracture modeling of such materials.     

Numerical modeling of damage evolution of DP steels on the basis of X-ray tomography measurements

In order to couple the damage evolution and the stress state of DP steel grades, a new advanced GTN (Gurson-Tvergaard-Needleman) model was developed and implemented into a finite element code. This model is an extension of the original one. It takes into account the plastic anisotropy and the mixed (isotropic + kinematic) hardening of the matrix. Two different methods to compute the void volume fraction were developed and used within the constitutive equations. The first method is new and allows the accurate modeling of the observations of damage initiation and growth in DP steels measured using high-resolution X-ray absorption tomography ( [Bouaziz et al., 2008] and [Maire et al., 2008]). The second method is classic and assumes the additive decomposition of the total void volume fraction into a nucleation and a growth part. A parametric study is carried out to assess the effect of the kinematic hardening on some mechanical parameters such as the equivalent plastic strain, the triaxiality and the porosity. The numerical predictions are favorably compared to the experimental results.     

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...     

Effect of shear cutting on ductility of a dual phase steel

Both an experimental investigation with an especially designed setup and a mechanical FE analysis of the cutting process showed that for the laboratory dual phase steel investigated, cutting involves positive stress triaxiality and ductile fracture mainly due to void nucleation and coalescence at ferrite-martensite interfaces. Tensile tests on as-cut strip specimens showed a large reduction in ductility due to the presence of damage on the edges of the strips. Tensile tests on strip specimens containing short precracks and mechanical analysis showed that the cutting affected area behaves as a precrack during subsequent mechanical testing.     

Void growth and coalescence during high velocity impact

The extent of void growth and cracking due to ductile fracture occurring during symmetric Taylor cylinder impact tests on leaded brass has been determined experimentally. Void growth occurs within these predominantly compressively-loaded specimens through the development of large tensile hydrostatic stresses along the specimen axis near the impact face during expansion of the cylinder, termed “mushrooming”.

The measured porosities have been compared to predictions using a constitutive model based on the Gurson (1975, Ph.D. Thesis, Brown University) yield function, implemented within the DYNA2D finite element code. The initiation of void coalescence and subsequent crack development was also predicted using the approach of Tvergaard and Needleman (1984, Acta Metall. 32, 157) based on a critical porosity criterion.

The calculations were able to qualitatively predict the development of the porous zone and void coalescence within the impact specimens; however, the predicted void growth exceeded that observed experimentally and the predicted extent of void coalescence was too large. It is suggested that the primary source of error lies in excessively high predicted void growth rates using the Gurson yield function at high stress triaxiality levels.