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.     

Constitutive modeling of void shearing effect in ductile fracture of porous materials

Many solids, including geomaterials and commercially available metallic alloys, can be considered as a porous media. The Gurson-like model has been proposed to describe plastic deformation for such type of materials. It has attracted a great deal of attention and various modifications to this model have been proposed. The constitutive equations of Gurson-like model are governed by the first and second stress invariants and the current void volume fraction of the material. Tvergaard and Needleman included void nucleation, growth and coalescence to Gurson model in a phenomenological way [Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 1984;32(1):157–69] – thus suggesting the so called GTN model. Meanwhile, little attention was given to the dependence of the damage evolution on the third stress invariant. McClintock et al. [McClintock FA, Kaplan SM, Berg CA. Ductile fracture by hole growth in shear bands. Int J Fract Mechan 1966;2(4):614–27] proposed damage model based on the void evolution in localized shear banding. In the present paper, a separate internal damage variable which differs from the conventional void volume fraction is introduced. The GTN model is further extended to incorporate the void shearing mechanism of damage, which depends on the third stress invariant. Numerical aspects are addressed concerning the integration of the proposed constitutive relations. A unit cell is studied to illustrate the intrinsic mechanical behavior of the modified model. Computations of the deformation in axisymmetric and transverse plane strain tension are also performed. Realistic crack modes in these simulations are achieved for the modified GTN model.     

The effect of particle distribution on damage formation in particulate reinforced metal matrix composites deformed in compression

Image analysis results are reported on the generation of damage in particulate reinforced metal matrix composites during compressive deformation. The technique allows the automated collection of data on the incidence of particle fracture and void formation in the matrix as a function of important microstructural parameters such as local particle volume fraction and particle size. There is a strong relationship between damage and the local volume fraction of the reinforcement proving that damage formation is accentuated in regions of particle clustering. With the SiC reinforced materials examined, there was observed to be a change in dominance of damage mechanism from particle fracture at low local volume fractions to void formation in the matrix within strongly clustered regions. The results are compared with finite element (FE) modelling of the compressive deformation of clustered particles using a simple cluster of equi-spaced particles. The FE results suggest that plastic flow is generally inhibited in clustered regions. In certain highly clustered configurations shielding is such that flow does not occur in the heart of the cluster even at high levels of average plastic strain. The modelling suggests that the change in dominance of damage mechanism is related to the dramatic increase in tensile hydrostatic stresses in the matrix with higher levels of particle clustering.     

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。     

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.     

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.     

多孔材料剪切局部化中的尺寸效应

微孔洞的尺寸对于孔洞长大率的影响显著,研究了这种尺寸效应在延性材料的塑性流动局部化中的作用。在拓展的Gurson模型基础上,采用Rice提出的一个简单的模型,剪切带内外的材料在发生塑性流动局部化时分别为不同的响应,讨论了孔洞尺寸a和初始孔洞体积百分比f0的影响。结果表明:考虑孔洞尺寸后单轴拉伸曲线变化比较大,但剪切带角度几乎没有变化。     

Some contribution to process zone fracture mechanics

The mechanism of the ductile fracture is studied theoretically for the Al Alloy 7075-T6 specimens. A model for the interaction of a crack tip with a void nearby is analyzed by using the Modified Gurson's Model. Taking fracture criterion into consideration, the analysis of a crack propagation is carried out and besides the distribution of the equivalent plastic strain, the void volume fraction f and the localization are obtained. Microcracks nucleate on the ligament between crack and void, and grow and coalesce each other, and at last the main crack thus formed coalesces with the void and the coalescence of the crack and void is completed. And these phenomenon occurs in the localized region.The initiation of the microcrack of 7075 occurs at small J and the microcrack penetration between crack and void occurs at larger J, and the propagation does not occur smoothly. These results coincide with the results of the experiments by FRASTA (FRActure Surface Topographic Analysis) and Fractography.     

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.     

Localization of deformation in rate sensitive porous plastic solids

The effect of material rate sensitivity on the localization of deformation in a porous visco-plastic solid is examined under plane strain tension and axisymmetric tension conditions. The plastic flow rule proposed by Gurson [3], modified to account for material rate sensitivity, is adopted to model the plastic softening behavior that arises due to void nucleation and growth. An initial imperfection in the form of a planar band is assumed and a material instability is sought as the deformation proceeds. Comparisons are made with the results of a rate-independent analysis [10]. The present rate-dependent results show that the retardation effect on flow localization is larger when the material is more rate-sensitive, and that, with a given rate sensitivity, the retardation effect on flow localization is greater in plane strain tension than in axisymmetric tension. Results are also obtained by employing parameter values representative of spheroidized carbon steels studied by Fisher [21], and the predictions of the model are in good agreement with experimental observations.     

A variational void coalescence model for ductile metals

We present a variational void coalescence model that includes all the essential ingredients of failure in ductile porous metals. The model is an extension of the variational void growth model by Weinberg et al. (Comput Mech 37:142–152, 2006). The extended model contains all the deformation phases in ductile porous materials, i.e. elastic deformation, plastic deformation including deviatoric and volumetric (void growth) plasticity followed by damage initiation and evolution due to void coalescence. Parametric studies have been performed to assess the model’s dependence on the different input parameters. The model is then validated against uniaxial loading experiments for different materials. We finally show the model’s ability to predict the damage mechanisms and fracture surface profile of a notched round bar under tension as observed in experiments.     

Locally enhanced Voronoi cell finite element model (LE‐VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions

Ductile heterogeneous materials such as cast aluminum alloys undergo catastrophic failure that initiates with particle fragmentation, which evolves with void growth and coalescence in localized bands of intense plastic deformation and strain softening. The Voronoi cell finite element model (VCFEM), based on the assumed stress hybrid formulation, is unable to account for plastic strain‐induced softening. To overcome this shortcoming of material softening due to plastic strain localization, this study introduces a locally enhanced VCFEM (LE‐VCFEM) for modeling the very complex phenomenon of ductile failure in heterogeneous metals and alloys. In LE‐VCFEM, finite deformation displacement elements are adaptively added to regions of localization in the otherwise assumed stress‐based hybrid Voronoi cell finite element to locally enhance modeling capabilities for ductile fracture. Adaptive h‐refinement is used for the displacement elements to improve accuracy. Damage initiation by particle cracking is triggered by a Weibull model. The nonlocal Gurson–Tvergaard–Needleman model of porous plasticity is implemented in LE‐VCFEM to model matrix cracking. An iterative strain update algorithm is used for the displacement elements. The LE‐VCFEM code is validated by comparing with results of conventional FE codes and experiments with real materials. The effect of various microstructural morphological characteristics is also investigated. Copyright © 2008 John Wiley & Sons, Ltd.     

Conditions for shear localization in the ductile fracture of void-containing materials

This paper investigates the possibility that ductile fracture occurs by the McClintock-Berg mechanism of localization of deformation within a narrow shear band, owing to the progressive softening of the material by increasing porosity due to void growth. The ductility predicted for a macroscopically homogeneous sample of a voided material is shown to be unrealistically large and hence an initial inhomogeneity of properties is considered, in the sense of an analysis by Marciniak and Kuczynski in the related problem of local necking in sheet metals. General conditions for a localization bifurcation with an initial inhomogeneity (imperfection), concentrating deformation to allow localization within it, are derived. The initial imperfection is taken in the form of a void-containing, thin slice of a material and is assumed to have a void volume fraction slightly larger than the outside of the imperfection. Elastic-plastic constitutive rate relations for void-containing materials proposed by Gurson are adopted to the conditions for the localization bifurcation. The critical conditions are analyzed numerically to discuss the sensitivity of localization conditions to an initial imperfection, in consideration of the implications for the theory of ductile fracture. The results suggest that the existence of an initial imperfection makes it possible for localization to occur at a reasonable strain, and the predictions from this analysis seem broadly consistent with reported experimental observations.

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Résumé Le mémoire étudie la possibilité que les ruptures ductiles se produisent par un mécanisme de Mc Clintock-Berg afférant à la localisation d'une déformation dans une bande de cisaillement étroite et ce en raison d'un adoucissement progressif du matériau par un accroissement de la densité de porosité associée à la croissance de lacunes. On montre que la ductilité prévue pour une éprouvette macroscopiquement homogène d'un matériau comportant des lacunes est irréellement grande et que dès lors, il y a lieu de considérer une inhomogénéité des propriétés dans le sens d'une analyse par Marciniak et Kuczynski effectuée dans le problème connexe du rétrécissement local des tôles minces. Les conditions générales pour une bifurcation de cette localisation en fonction d'une inhomogénéité initiale (imperfection) ainsi que pour une déformation concentrée qui permette une telle localisation dans cette inhomogénéité, sont déduites de cette analyse. L'imperfection initale est considérée sous la forme d'une mince couche de matériau comportant des lacunes, et est supposée présenter une fraction d'un volume lacunaire légèrement plus grande qu'en déhors de l'imperfection. Pour les conditions de la bifurcation de la localisation, on adopte les relations constitutives élastoplastiques proposées par Gurson dans le cas de matériaux comportant des lacunes. Les conditions critiques sont analysées par voie numérique afin de discuter la sensibilité aux conditions de localisation pour une imperfection initiale, considérant les implications que cela peut avoir pour la théorie de la rupture ductile. Les résultats suggèrent que l'existence d'une imperfection initiale rend possible une localisation sous une déformation raisonnable et les prédictions pour cette analyse paraissent largement consistantes avec les observations expérimentales publiées.

     

Influence of damage on the plastic instability of sheet metals under complex strain paths

During the sheet metal forming operation, internal damage occurs as a result of nucleation growth and coalescence of cavities around particles. This phenomenon limits the strains which can be achieved before the appearence of localized necking. In this paper, damage is represented by initially equi-axed cavities and a void growth model is extended and linearized for complex strain paths. For a given void distribution, a statistical study pointed out the existence of weak sections in the material leading to localized plastic flow. The influence of the physical parameters of voids on the forming limit diagrams is shown.     

THE COALESCENCE OF VOIDS IN PRESTRAINED NOTCHED ROUND COPPER BARS

Notched round copper bars are prestrained to various extents, recrystallized, and finally strained until fracture. Void nucleation and growth during prestraining cause a decrease in the macroscopic void coalescence strain. Modelling of this experiment requires a proper account of the changes in void sizes and their interdistances during prestraining. Modelling based on the Gurson–Leblond–Perrin model for void growth and the Thomason model for void coalescence is proposed. Comparison with experimental results allows a demonstration of the validity of the Thomason model and the inadequacy of models based on a critical porosity value. Porosity at coalescence is found to depend on the initial void volume fraction, the flow properties and the stress state.     

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.     

Triaxial tension-induced damage behavior of nanocrystalline NiTi alloy and its dependence on grain size

This study focused on the effect of grain size(GS)on dynamic damage performance of nano-crystalline nickel titanium(NC NiTi)alloy.Molecular dynamics simulations were conducted to triaxially expand it at a high strain rate(4×109 s-1),while the temperature and initial pressure remained 300 K and 0 bar,respectively.It was discovered that the superelastic NiTi alloy exhibited the similar damage response as ductile metallic materials,which was vividly characterized by void nucleation,growth,and coalescence.The stress-strain curves demonstrated that the void nucleations always occurred near the start of the strain softening region at various grain sizes.Interestingly,it was discovered that the void evolution was characteristic of an almost double-linear behavior,and the piecewise linearity became more prominent for the void volume fraction increase at larger grain size.More importantly,the fracture behavior was found to be strongly dependent upon the grain size in the NC NiTi alloy.For small grain size,the existing voids propagated along the grain boundaries and in the grains,leading to intergranular and transgranular fracture.Contrarily,the intergranular-dominated fracture was responsible for the void propagation in the large grain.In addition,the starting time,ending time,and threshold of void nucleation were found to be weak sensitivity to GS,and a reverse effect was appropriate to the void growth.The results highlighted that as the GS increased,more complete stress relaxation and shorter duration time were produced,leading to larger void volume fraction and faster growth rate.     

An analysis of deformation and failure in rectangular tensile bars accounting for void shape changes

A three-dimensional finite deformation study of necking and failure in rectangular tensile bars is carried out using a constitutive relation for porous material plasticity. The fully dynamic formulation accounts for void nucleation and growth along with thermal and rate effects, but here focus is on quasi-static response with a specified initial void volume fraction. The constitutive relation takes into account void shape changes and associated void rotations for three-dimensional voids. The constitutive update is carried out using a generalized rate tangent scheme for an elastic-viscoplastic solid. The sensitivity of necking and failure patterns to the aspect ratio of the rectangular bar is investigated with focus on the plane strain limit and a square tensile bar. The calculations predict the well-known slant fracture in plane strain tension and the emergence of a cup-cone like failure region for a square cross-section. Details are provided for the development of porosity in the bar with a square cross-section, including void shape changes and void rotations. The numerical examples show the capability of a constitutive relation for porous plasticity that can model details of void evolution, thus paving the way for advanced analyses of ductile failure under arbitrary loadings.

     

Influence of ductile damage on the bending behaviour of aluminium alloy thin sheets

Sheet metal forming involves planar stress states, in the sheet plane, like in tension and simple shear, or stress states characterized by a gradient in the thickness, like in bending. In this latter case, material limit prediction derived from an instability criterion is no longer valid. In this work, a criterion based on a critical void volume fraction, identified from macroscopic tests, is applied to the case of bending of square samples of aluminium alloy AA6016-T4. Mechanical tests are performed at two aging times to quantify its influence on the mechanical behaviour and only the hardening law is modified to take it into account. It is shown that a good correlation is obtained between the critical void volume fraction obtained from tension on notched samples and biaxial expansion, and the onset of crack development in the bent zone. Moreover, macroscopic load recorded during bending is sensitive to ductile damage, which makes this test particularly interesting for damage investigation.     

Creep Failure Analysis of Bars Sustaining Constant Tensile Loads

Life time and failure modes are predicted for metallic barssustaining tensile creep. Experimental results show that a ductile or a`brittle' mode of fracture occurs depending respectively on whether thenominal applied stress is large or small. The analysis is based on amodeling of void nucleation and growth in which damage evolution iscontrolled by two mechanisms of plastic flow in the matrix material.Fracture is supposed to occur when the porosity attains a critical valuewhich depends on the mode of fracture considered. Experimental resultsare explained and described in terms of the proposed model.