非线性路径下板料拉深成形过程中破裂预测

在优选模型参数和简化孔洞形核规律的基础上,采用Gurson-Tvergaard (GT) 多孔材料本构模型分析圆筒件拉深过程;根据金属成形工艺特点,综合考虑拉伸型和剪切型2种不同韧性断裂机制,提出一个统一的韧性断裂准则形式.对于未经过预变形和经过预变形的圆筒件拉深试验和数值模拟进行了比较,结果表明:相对于成形极限图,新的韧性断裂准则可以更加准确地预测非线性路径下圆筒件的拉深破裂.     

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。     

A new failure criterion for the Gurson-Tvergaard dilational constitutive model

In the Gurson-Tvergaard model a failure criterion has to be used to signify the void coalescence. In the literature, a constant critical void volume fraction criterion has been widely used. However, it is questionable whether the critical void volume fraction is a material constant and, furthermore, it is also difficult in practice to determine the constant. By modifying Thomason's plastic limit-load model, a new failure criterion which is fully compatible with the Gurson-Tvergaard model, is presented in this study. In the present criterion, the void coalescence failure mechanism by internal necking has been considered and the material failure is a natural result of the development of dual constitutive, stable and unstable, responses. In practical application of the present criterion, no critical void volume fraction needs to be pre-determined either numerically or experimentally. Furthermore, according to the new criterion, the void volume fraction corresponding to void coalescence is not a material constant, rather a function of stress triaxiality. The predictions using the present criterion have been compared with the finite element results by Koplik and Needleman, and very good agreement is observed. The potential advantage of this criterion and other related issues are discussed.     

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.

     

Three-dimensional cell model analyses of void growth in ductile materials

Three-dimensional micromechanical models were developed to study the damage by void growth in ductile materials. Special emphasis is given to the influence of the spatial arrangement of the voids. Therefore, periodical void arrays of cubic primitive, body centered cubic and hexagonal structure are investigated by analyzing representative unit cells. The isotropic behaviour of the matrix material is modelled using either v. Mises plasticity or the modified Gurson-Tvergaard constitutive law. The cell models are analyzed by the large strain finite element method under monotonic loading while keeping the stress triaxiality constant. The obtained mesoscopic deformation response and the void growth of the unit cells show a high dependence on the value of triaxiality. The spatial arrangement has only a weak influence on the deformation behaviour, whereas the type and onset of the plastic collapse behaviour are strongly affected. The parameters of the Gurson-Tvergaard model can be calibrated to the cell model results even for large porosity, emphasizing its usefulness and justifying its broad applicability.     

Modelling macroscopic imperfections for the prediction of flow localization and fracture

Ductile materials subjected to plastic deformation experience the different stages of void nucleation, growth and coalescence that eventually lead to ductile fracture. Several models have been proposed to assess the influence of this damage on flow localization and fracture. In general, the plastic behaviour is represented by a constitutive model for porous or damaged materials. It is typical to introduce a material imperfection, with porosity higher than average, which evolves up to localization and fracture. However, the void volume fraction in the imperfection is chosen more or less arbitrarily. In the present work, a model that evaluates this void volume fraction more rigorously is developed. The forming limit diagram (FLD) for a dual phase‐steel is calculated using the damage‐based imperfection calculation and validated with experimental results. The effect of void shape on the imperfection porosity level and limit strains in sheet forming is also assessed with the present method.     

A numerical analysis of failure characteristics of ductile layers in laminated composites

In this study, the failure of the ductile layers from collinear, multiple and delaminating cracks that occur in laminated composite systems was studied using a constitutive relationship that accounts for strength degradation resulting from the nucleation and growth of voids. The results indicate that, in laminated composites, void nucleation and growth ahead of the cracks occur at a much faster rate because of evolution of much higher stress values in the interface region. Except for short crack extensions, collinear and multiple cracks develop crack resistance curves similar to that seen for a crack in the ductile layer material as a homogenous isotropic cases. For delaminating crack cases, the fracture behaviour is strongly influenced by the delamination length. The resistance of the ductile layers to crack extension can be significantly reduced by short delamination lengths; however, for large delamination lengths the resistance to crack extension becomes greater than that seen for the ductile material. The results also show that, if the crack tip is at the interface, similar maximum stress values develop in the ductile layers as in the fracture test of the same ductile material, suggesting that ductile–brittle fracture transition behaviour of the ductile layers is dependent upon the extent of the cracks in the brittle layers and fracture characteristics of the brittle layers.     

金属韧性断裂准则的数值模拟和试验研究

对不同外形的45钢试件进行了拉伸、压缩和扭转等材料试验,对工程中常用的5个韧性断裂准则的适用范围进行了对比研究,并采用Gurson-Tvergaard(GT)多孔材料本构模型对试验过程进行了数值模拟.指出目前使用的断裂准则都不可能对材料在多种变形条件下给出一个固定临界值.根据金属成形工艺特点,综合考虑拉伸型和剪切型2种不同韧性断裂机制,提出一个统一的韧性断裂准则形式.试验和数值计算结果证明了该准则的有效性和普适性,进而利用单向拉伸和扭转试验确定的材料常数合理地预测压缩过程中的韧性断裂现象.     

MICROMECHANICAL MODELLING OF DAMAGE AND FRACTURE OF DUCTILE MATERIALS

A micromechanical model of ductile damage by void nucleation, growth and coalescence is widely and successfully applied to describe phenomena of ductile tearing. The model's fundamental principles, and especially the constitutive equations of Gurson, Tvegaard and Needleman (GTN-model), are briefly described. Some of the material parameters of the GTN-model are calibrated by performing cell model calculations, which is a method of determining the structural behaviour of a single void in a plastic material. The approach is used to study the dependence of material strength and toughness on microstructural features of nodular cast iron. The numerical simulations were realized within the FE-program ABAQUS by a user-supplied material model.     

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.     

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.     

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.     

An out-of-plane length scale for ductile crack extensions in 3-D SSY models for X65 pipeline materials

This paper investigates the ductile crack extension in the API 5L X65 pipeline steels in 3-D small-scale yielding (SSY) models using the Gurson-Tvergaard (GT) dilatational plasticity model implemented in the “computational cell” framework. The objective of the study targets at determining an out-of-plane length scale of the computational cell for 3-D crack extensions in fracture models with a through-thickness, straight crack front. The basic Gurson material parameters: the initial void volume fraction f ₀ and the in-plane size of the computational cell D, calibrate from a set of notched tension specimens fabricated using API X65 steels. Cell extinctions based on a critical void volume fraction facilitates the process of the void growth and void coalescence which leads to the final failure of the “cell” and thus crack extensions. This study examines two types of 3-D SSY models: the side-grooved model and the plane-sided model. The element size in the thickness direction imposes significant effects on the computed fracture resistance and crack extension. Converged predictions of the J-Δa curve requires the out-of-plane length scale near the side groove equal to the in-plane length scale D. Plane-sided models converge faster than does the side-grooved model and requires the out-of-plane length scale to be 2D near the free surface. The required out-of-plane length scale does not indicate strong dependence on the material hardening exponent and the initial void volume fraction of the material.     

A VIEW ON DUCTILE-FRACTURE MODELLING

Theoretical models of ductile fracture are reviewed in terms of experimental results from metallurgical studies of ductile fracture in metals and alloys. It is shown that the plastic limit-load model, which is based on a criterion of void coalescence by internal microscopic necking of the intervoid matrix, is fully consistent with scanning electron microscope (SEM) observations of both the ductile-fracture surface and the microstructure immediately adjacent to the fracture surface. On the other hand, the dilational-plastic models of ductile fracture, which are based on the dilational-growth of spherical voids to some arbitrary critical void-volume fraction, are inconsistent with the microstructural observations of ductile fracture. This inconsistency between the dilational-plastic models and experimental results is shown to be the combined effect of neglecting the controlling influence of extensional void-growth and the failure to incorporate a physically realistic criterion of void coalescence.
The problems of modelling the ductile crack-growth process by both analytical and numerical (finite element) studies, where problems of uniqueness of the plastic velocity field may occur, are also considered. The limitations of the finite-element method in modelling void-coalescence problems, where the equations of plasticity are of second-order hyperbolic form, are also discussed.     

Analysis of shear localization in porous materials based on a lower bound approach

The conditions for shear localization in porous materials are examined based on the lower bound approach proposed by the present authors. The influence of void nucleation and material inhomogeneity on the critical strain to localization is investigated and an improved plastic strain controlled nucleation criterion is proposed which makes it possible to include the influence of hydrostatic stress and avoid the ambiguity caused by the non-normality flow rule. The constitutive behavior of porous materials (including the yield loci, the void growth rate and the stress-strain curve) is also examined and comparison is made between the theoretical result and the experiment. Finally the instability and fracture of sintered CP Ti alloy and AISI4340 steels is analyzed and results are compared with the experiment.     

On Using a Dual Bound Approach to Characterize the Yield Behaviour of Porous Ductile Materials Containing Void Clusters

Two constitutive models for porous ductile materials are employed together to predict the yield behaviour of ductile materials containing void clusters. In this dual bound approach, the upper and lower bound constitutive models of Gurson (1977) and Sun and Wang (1989) are each evaluated in order to obtain upper and lower estimates for the material behaviour. By combining these two solutions, a predictive band can be created to capture the experimental variation in the yielding behaviour. Although these constitutive models have been derived with the assumption of a periodic void distribution, real materials contain void clusters that can significantly alter the onset of yielding and fracture. Therefore it is of great interest to determine if using dual constitutive models can produce an acceptable first-order approximation of the yielding behaviour in these materials. In the present work, the upper and lower bound yield loci are superimposed over numerical data available in the literature for the yielding of materials containing void clusters. It is shown that the dual bound approach is able to capture the material behaviour over a wide range of practically encountered stress triaxialities.     

Numerical prediction of the structural failure of airbag inflators in the destructive testing phase

The aim of the present numerical study was to predict the structural failure of airbag inflators undergoing destructive bust tests, while accounting for the thermomechanical history of the constitutive material. For this purpose, the material was previously characterized under tension, compression, torsion and shear loading conditions at various strain rates. It was found to be elastic–viscoplastic and prone to ductile fracture. The behaviour of the material was then modelled using the Gurson–Tvergaard–Needleman (GTN) approach, and the material constants were identified via the gradient-based inverse method. The observed and predicted locations of the damage induced by void growth during the crimping process showed good agreement. In addition, the numerical simulations of the destructive testing phase (involving dynamic internal pressure loading) yielded a Mode I-like failure process, as observed experimentally. The burst pressure value predicted was found to be very similar to the experimental value, which confirms that the conservative method presented here could be usefully applied to industrial situations.     

Prediction of ductile failure using a local strain-to-failure criterion

In this article, we provide the details of the predictive simulations performed by the University of Texas team in response to the 2012 Sandia Fracture Challenge (Boyce et al. in The Sandia Fracture challenge: blind predictions of ductile tearing. Int J Fract. doi:10.1007/10704-013-9904-6, 2013). The material constitutive model was calibrated using the tensile test data through an optimization scheme. A modified Johnson–Cook failure criterion was also partially calibrated using the material characterization data obtained from a tension test and a compact-tension fracture test. These models are then embedded in a highly refined finite element simulation to perform a blind prediction of the failure behavior of the Sandia Fracture Challenge geometry. These results are compared with experiments performed by Sandia National Laboratories and additional experiments that were performed at the University of Texas at Austin with full-field three-dimensional digital image correlation in order to explore the different failure modes. It is demonstrated that a well-calibrated model that captures the essential elastic–plastic constitutive behavior is necessary to confidently capture the elasto-plastic response of challenging structural geometries; it is also shown that a simple ductile failure model can be used to predict ductile failure correctly, when proper calibration of the material model is established.