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.     

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.     

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.     

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.     

Influence of Triaxial Stress State on Ductile Fracture Strength of Polycrystalline Nickel

In this contribution, the effect associated with stress triaxiality on ductile damage evolution in high purity nickel has been investigated from both experimental and theoretical points of view. Tensile tests on smooth and notched round bar specimens were performed to calibrate the fracture strain in a wide range of stress triaxiality. The capability of the Gurson model to reproduce and predict physical failure behaviour was examined. It was shown that stress triaxiality played a major role on damage evolution as demonstrated by the progressive reduction of material ductility under increasing triaxial states of stress.     

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。     

Stress triaxiality effect on void nucleation in ductile metals

The stress triaxiality effect on the strain required for void nucleation by particle‐matrix debonding has been investigated by means of micromechanical modelling. A unit‐cell model considering an elastic spherical particle embedded in an elastic‐plastic matrix was developed to the purpose. Particle‐matrix decohesion was simulated through the progressive failure of a cohesive interface. It has been shown that the parameters of matrix‐particle cohesive interface are correlated with macroscopic material properties. Here, a simple relationship for the maximum cohesive opening at interface failure as a function of material fracture toughness and yield stress has been derived. Results seem to confirm that, increasing stress triaxiality, the strain at which void nucleation is predicted to occur decreases exponentially in a similar way as for fracture strain. This result has substantial implications in modelling of ductile damage because it indicates that if the stress triaxiality is high enough, ductile fracture can occur at plastic strain lower than that necessary to nucleate damage for moderate or low stress triaxiality regime.     

Dynamic vs. quasi-static shear failure of high strength metallic alloys: Experimental issues

Ductile fracture of metals by void nucleation, growth and coalescence under positive stress triaxiality is well admitted. This is not the case when metals are submitted to negative stress triaxiality. The present work aims at contributing to a better understanding of the competition between micro-mechanisms at the origin of failure of metals when submitted to shear-pressure loading at low and high strain rates. With this aim in view, experiments were carried out on Ti–6Al–4V shear-compression samples involving a stress triaxiality range comprised between −0.2 and −0.5. Results show that the material failure is the consequence of a void growth induced process. At high strain rate, due to the localization of the deformation within adiabatic shear bands, the failure of the material occurs earlier, leading to maximum shear strain smaller at high strain rate than at low strain rate. Impact tests were also carried out on Kalthoff and Winkler type double notched plates. They showed that the interaction between tension and shear waves leads to a complex Mode I–Mode II crack propagation.     

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.     

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.     

Use of a modified Gurson model for the failure behaviour of the clinched joint on Al6061 sheet

This paper discusses the ductile fracture behaviour of the clinched joint on Alloy 6061 sheets. Failure behaviour of the clinched joint is associated with the nucleation, growth and coalescence of voids within the microstructure. Various corrections to the original Gurson model are proposed to allow for instability and final fracture of the material. This paper is concerned with the application of the modified Gurson–Tvergaard–Needleman damage developed by Ken Nahshon and Zhenyu Xue. The results of the tension tests are compared with those of numerical analysis to obtain the initial void volume fraction f₀ and the shear damage coefficients k_w. The modified Gurson–Tvergaard–Needleman model is used to describe the failure behaviour and the shear strength of the clinched joint. Good agreement is shown between the experiment results and the numerical results on the location of fracture and the maximum failure load.     

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.     

Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading

The present paper is concerned with multi-axial ductile fracture experiments on sheet metals. Different stress-states are achieved within a flat specimen by applying different combinations of normal and transverse loads to the specimen boundaries. The specimen geometry is optimized such that fracture initiates remote from the free specimen boundaries. Fracture experiments are carried out on TRIP780 steel for four different loading conditions, varying from pure shear to transverse plane strain tension. Hybrid experimental–numerical analyses are performed to determine the stress and strain fields within the specimen gage section. The results show that strain localization cannot be avoided prior to the onset of fracture. Through-thickness necking prevails under tension-dominated loading while the deformation localizes along a band crossing the entire gage section under shear-dominated loading. Both experimental and simulation results demonstrate that the proposed fracture testing method is very sensitive to imperfections in the specimen machining. The loading paths to fracture are determined in terms of stress triaxiality, Lode angle parameter and equivalent plastic strain. The experimental data indicates that the relationship between the stress triaxiality and the equivalent plastic strain at the onset of ductile fracture is not unique.     

Fracture modelling of WC-Co hardmetals using crystal plasticity theory and the Gurson model

The behaviour of edge cracks under Mode I loading in the WC–Co material system is studied using the finite element method (FEM). This work focuses on ductile failure mechanisms in the Co binder. A micromechanical approach is taken whereby Co layers are modelled explicitly. An embedding technique is employed. Crystal plasticity theory and J₂ flow theory are used to represent plastic deformation in Co ligaments. Areas of high hydrostatic stress, triaxiality and accumulated slip or effective plastic strain are identified within the binder material. The Gurson model is used to model crack growth in the Co ligaments. Fracture resistance curves are obtained giving a relationship between macroscopic material behaviour and microscopic failure mechanisms. Factors effecting the crack growth in single and multiple ligaments are identified.     

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.     

Numerical modeling of elasto-plastic porous materials with void shape effects at finite deformations

A new constitutive model for elasto-plastic (rate-independent) porous materials subjected to general three-dimensional finite deformations is presented. The new model results from simple modifications of an earlier model of Kailasam and Ponte Castañeda (1997, 1998) [40], [41] so that it reproduces the exact spherical and cylindrical shell solution (composite sphere and composite cylinder assemblage) under purely hydrostatic loadings, while predicting (by calibration) accurately the void shape evolution according to the recent “second-order” model of Danas and Ponte Castañeda [17]. Furthermore, the present model is based on a rigorous homogenization method which is capable of predicting both the constitutive behavior and the microstructure evolution of porous materials. The microstructure is described by voids of arbitrary ellipsoidal shapes and orientations and as a result the material exhibits deformation-induced (or morphological) anisotropy at finite deformations. This is in contrast with the well-known Gurson [32] model which assumes that the voids remain spherical during the deformation process and thus the material remains always isotropic. The present model is implemented numerically in a finite element program where a three-dimensional thin-sheet (butterfly) specimen is subjected to a combination of shear and traction loading conditions in order to examine the effect of stress triaxiality and shearing upon material failure. The ability of the present model to take into account the nontrivial evolution of the microstructure and especially void shape effects leads to the prediction of material failure even at low stress triaxialities and small porosities without the use of additional phenomenological damage criteria. At high stress triaxialities, the present model gives similar predictions as the Gurson model.     

Fracture Criteria for Automobile Crashworthiness Simulation of Wrought Aluminium Alloy Components

In automobile crashworthiness simulation, the prediction of plastic deformation and fracture of each significant, single component is critical to correctly represent the transient energy absorption through the car structure. There is currently a need, in the commercial FEM community, for validated material fracture models which adequately represent this phenomenon. The aim of this paper is to compare and to validate existing numerical approaches to predict failure with test data. All studies presented in this paper were carried out on aluminium wrought alloys: AlMgSi1.F31 and AlMgSiCu‐T6. A viscoplastic material law, whose parameters are derived from uniaxial tensile and compression tests at various strain rates, is developed and presented herein. Fundamental ductile fracture mechanisms such as void nucleation, void growth, and void coalescence as well as shear band fracture are present in the tested samples and taken into consideration in the development of the fracture model. Two approaches to the prediction of fracture initiation are compared. The first is based on failure curves expressed by instantaneous macroscopic stresses and strains (i. e. maximum equivalent plastic strain vs. stress triaxiality). The second approach is based on the modified Gurson model and uses state variables at the mesoscopic scale (i. e. critical void volume fraction). Notched tensile specimens with varying notch radii and axisymmetric shear specimens were used to produce ductile fractures and shear band fractures at different stress states. The critical macroscopic and mesoscopic damage values at the fracture initiation locations were evaluated using FEM simulations of the different specimens. The derived fracture criteria (macroscopic and mesoscopic) were applied to crashworthiness experiments with real components. The quality of the prediction on component level is discussed for both types of criteria.     

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.