延性金属膨胀环的运动及断裂的三维数值模拟

利用LS-DYNA三维动力有限元软件对延性金属环的膨胀运动与断裂进行数值模拟。在膨胀环圆周加入泊松随机分布断裂成核点,利用J-C本构模型,研究诸如颈缩形成时间、颈缩区与均匀变形区的温度、应力、应变的对比等颈缩形成机理,以及讨论了环圆周上断裂成核点的泊松随机分布碎裂特性的影响。数值计算结果与实验结果、理论分析结果吻合较好,表明施加泊松随机断裂成核点的数值模拟方法是合理的。     

Mechanical modelling of ductile fracture

Mechanical models of material failure by void growth to coalescence are described to give a brief overview of methods applied in the analysis of ductile fracture. Approximate constitutive relations for porous ductile materials are discussed, modelling both the nucleation and growth of voids. The application of the material models is illustrated by numerical analyses for a tensile test specimen and for dynamic, ductile crack growth. Unstable void growth is a relevant mechanism in ductile materials subject to a high level of triaxial tension. The analysis of such cavitation instabilities in elastic-perfectly plastic materials is discussed for axisymmetric stress states, and the relevance to metal/ceramic components is emphasized.General Lecture presented at the 10th Italian National Congress of Theoretical and Applied Mechanics; AIMETA, Pisa, October 1990.     

The ductile fracture of polycarbonate

The fracture of a known ductile polymer (polycarbonate) is investigated. It is shown that polycarbonate obeys the Dugdale model of ductile yielding by comparing measured plastic-zone sizes and displacements to the theoretical predictions. Strain-energy release rates are calculated and the critical value is shown to be one or two orders of magnitude higher than critical values for brittle polymers. Photoelastic photographs of the fracture process are presented and it is shown that the photoelastic effect definitely enhances the definition of the yield zone. Microscopic photoelastic photographs are also presented which are used to give a new interpretation to the photoplastic effect. Finally, suggestions for future work are presented.     

Micromechanics of coalescence in ductile fracture

Significant progress has been recently made in modelling the onset of void coalescence by internal necking in ductile materials. The aim of this paper is to develop a micro-mechanical framework for the whole coalescence regime, suitable for finite-element implementation. The model is defined by a set of constitutive equations including a closed form of the yield surface along with appropriate evolution laws for void shape and ligament size. Normality is still obeyed during coalescence. The derivation of the evolution laws is carefully guided by coalescence phenomenology inferred from micromechanical unit-cell calculations. The major implication of the model is that the stress carrying capacity of the elementary volume vanishes as a natural outcome of ligament size reduction. Moreover, the drop in the macroscopic stress accompanying coalescence can be quantified for many initial microstructures provided that the microstructure state is known at incipient coalescence. The second part of the paper addresses a more practical issue, that is the prediction of the acceleration rate δ in the Tvergaard-Needleman phenomenological approach to coalescence. For that purpose, a Gurson-like model including void shape effects is used. Results are presented and discussed in the limiting case of a non-hardening material for different initial microstructures and various stress states. Predicted values of δ are extremely sensitive to stress triaxiality and initial spacing ratio. The effect of initial porosity is significant at low triaxiality whereas the effect of initial void shape is emphasized at high triaxiality.     

Modeling of ductile fracture: Significance of void coalescence

In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (E_c) as a function of the stress triaxiality parameter (T) and the Lode angle (θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E_c(T, θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E_c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.     

The ductile fracture of anisotropic materials

A theoretical solution is obtained which adapts the Dugdale model to anisotropic materials. The effect of anisotropy is shown to modify each isotropic field equation by amultiplicative constant which is a function of the anisotropic-material constants. A limit on the validity of a Dugdale-type solution is found using a von Mises' yield criterion which implies that the crack and plastic zone will extend along a direction other than the crack line. As long as the material is within pirescribed limits, the Dugdale finiteness condition is shown to be affected by material anisotropy only in the calculation of a yield stress. Experimental results on crack-opening displacements are presented which indicate that a large degree of anisotropy is necessary to cause significant deviations from isotropic theory. Results are presented which indicate that anisotropy does affect the direction of crack propagation.     

Modeling of ductile fracture: Application of the mechanism-based concepts

This paper summarizes our recent studies on modeling ductile fracture in structural materials using the mechanism-based concepts. We describe two numerical approaches to model the material failure process by void growth and coalescence. In the first approach, voids are considered explicitly and modeled using refined finite elements. In order to predict crack initiation and propagation, a void coalescence criterion is established by conducting a series of systematic finite element analyses of the void-containing, representative material volume (RMV) subjected to different macroscopic stress states and expressed as a function of the stress triaxiality ratio and the Lode angle. The discrete void approach provides a straightforward way for studying the effects of microstructure on fracture toughness. In the second approach, the void-containing material is considered as a homogenized continuum governed by porous plasticity models. This makes it possible to simulate large amount of crack extension because only one element is needed for a representative material volume. As an example, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a modified Gologanu–Leblond–Devaux model [Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290–297; Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson’s model for porous ductile metals. In: Suquet, P. (Ed.) Continuum Micromechanics. Springer-Verlag, pp. 61–130] is used to describe the evolution of void shape and void volume fraction and the associated material softening, and the material failure criterion is calibrated using experimental data. The calibrated computational model successfully predicts crack extension in various fracture specimens, including the compact tension specimen, middle crack tension specimens, multi-site damage specimens and the pressurized cylindrical shell specimen.     

Impact fracture characterization of polymer with ductile behavior

The characterization of ductile polymers with ductile fracture behavior is still a controversial subject. Presently, two approaches based on fracture mechanics have been proposed for the evaluation of impact failure of plastics, i.e., the method using the concept of essential fracture work, and the crack initiation and propagation approach. This paper discusses the validity of the fracture parameters used in these approaches. Additional experimental results and evidence are presented; they indicate that the concept of essential work of fracture cannot be used to characterize the fracture property of plastics. At high loading rates, the fracture energy of plastics can decrease with crack extension, resulting in a variable essential work of fracture. It is also found that the work dissipated in the outer plastic zone as formulated in the concept does not only reflect the non-essential work but is also related to the fracture process.Instead, the approach based on two material parameters should be used to evaluate the impact fracture behavior. Crack initiation and propagation energies should be considered to account for the variation of material's fracture behavior during crack propagation so as to include time rate and size scale effects.     

The size dependence of micro-toughness in ductile fracture

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.     

Plasticity and ductile fracture of IF steels: experiments and micromechanical modeling

If one aims at the simulation of plasticity and failure of multiphase materials, the choice of an appropriate material law is of major importance. Plasticity models for porous metals contain, in addition to the yield surface and the flow potential, also functions describing the void nucleation, dependent on some macroscopically observable quantities, and the growth of these voids. In this paper, a micromechanically based method to develop a void nucleation function for porous plasticity models is proposed which is valid for all possible microstructures as long as the amount of second phase particles is low (i.e. the particles do not interact with respect to the stress and strain fields), and as long as the particles are large enough (above 0.1 μm) justifying a continuum mechanical approach. The method described consists of two stages: In the first stage, the microstructure is investigated via a finite element model. The FE model implicitly contains the effects of the shape of the precipitates, of the material parameters of both the matrix and the precipitates, of the void nucleation hypothesis (by the assumption of “nucleation limits” for characteristic damage-related quantities), and of the applied stress state. In the second stage, during postprocessing, the volume fraction of precipitates as well as the influences of the particle orientation distribution, size distribution, and size dependence of the damage-related quantities are taken into account. The model is applied to the microstructure of IF (Interstitially Free) steel, a material with a ductile matrix and rigid second phase particles of cubical shape. This microstructure is particularly suited for investigating shape and size effects. The model shows that either the size effect or the shape effect dominate the void nucleation behavior: in the case of particles of roughly the same size, the size distribution will hardly alter the nucleation strain distribution obtained by taking into account only the shape and orientation effects. For particles of very different sizes, the size effect will completely override the rather “sharp” original distribution regarding particle shape and orientation.     

Preliminary study on ductile fracture of imperfect lattice materials

The ductile fracture behavior of two-dimensional imperfect lattice material under dynamic stretching is studied by finite element method using ABAQUS/Explicit code. The simulations are performed with three isotopic lattice materials: the regular hexagonal honeycomb, the Kagome lattice and the regular triangular lattice. All the three lattices are made of an elastic/visco-plastic metal material. Two typical imperfections: vacancy defect and rigid inclusion are introduced separately. The numerical results reveal novel deformation modes and crack growth patterns in the ductile fracture of lattice material. Various crack growth patterns as defined according to their profiles, “X”-type, “Butterfly”-type, “Petal”-type, are observed in different combinations of imperfection type and lattice topology. Crack propagation could induce severe material softening and deduce the plastic dissipation of the lattices. Subsequently, the effects of the strain rate, relative density, microstructure topology, and defect type on the crack growth pattern, the associated macroscopic material softening and the knock-down of total plastic dissipation are investigated.     

The effects of void cluster size on ductile fracture

The effects of void clustering on ductile fracture are studied by modeling a discrete set of randomly distributed clusters. Each cluster consists of four, equally-spaced, cylindrical voids. The spacing between the clusters is held constant while the spacing between the voids is varied. A Eulerian finite element program is used to numerically solve the boundary value problems. A salient feature of the previous investigations is that both the ultimate stress and the fracture strain are functions of the void distribution. In contrast, the ultimate stress remains constant while the fracture strain changes with the void cluster diameter in the current investigation.     

Dynamical evolution of fracture process region in ductile materials

The aim of this paper is to investigate the dynamics of evolving finite fracture process regions in ductile material taking into account the dislocation motion.     

Numerical simulation of fracture mode transition in ductile plates

Fracture mode of ductile solids can vary depending on the history of stress state the material experienced. For example, ductile plates under remote in-plane loading are often found to rupture in mode I or mixed mode I/III. The distinct crack patterns are observed in many different metals and alloys, but until now the underlying physical principles, though highly debated, remain unresolved. Here we show that the existing theories are not capable of capturing the mixed mode I/III due to a missing ingredient in the constitutive equations. We introduce an azimuthal dependent fracture envelope and illustrate that two competing fracture mechanisms, governed by the pressure and the Lode angle of the stress tensor, respectively, exist ahead of the crack tip. Using the continuum damage plasticity model, we demonstrate that the distinctive features of the two crack propagation modes in ductile plates can be reproduced using three dimensional finite element simulations. The magnitude of the tunneling effect and the apparent crack growth resistance are calculated and agree with experimental observations. The finite element mesh size dependences of the fracture mode and the apparent crack growth resistance are also investigated.     

A multiresolution continuum simulation of the ductile fracture process

With the advancement in computational science that is stepping into the Exascale era and experimental techniques that enable rapid reconstruction of the 3D microstructure, quantitative microstructure simulations at an unprecedented fidelity level are giving rise to new possibilities for linking microstructure to property. This paper presents recent advances in 3D computational modeling of ductile fracture in high toughness steels. Ductile fracture involves several concurrent and mutually interactive mechanisms at multiple length scales of microstructure. With serial sectioning tomographic techniques, a digital dataset of microstructure features associated with the fracture process has been experimentally reconstructed. In this study, primary particles are accurately and explicitly modeled while the secondary particles are modeled by a two scale multiresolution continuum model. The present numerical simulation captures detailed characteristics of the fracture process, such as zigzag crack morphology, critical void growth ratios, local stress triaxiality variation, and intervoid ligament structure. For the first time, fracture toughness is linked to multiscale microstructures in a realistic large 3D model.     

Instability and failure of internally pressurized ductile metal cylinders

Forlong, ductile, thick-walled tubes under internal pressure instabilities and final failure modes are studied experimentally and theoretically. The test specimens are closed-end cylinders made of an aluminum alloy and of pure copper and the experiments have been carried out for a number of different initial external radius to internal radius ratios. The experiments show necking on one side of the tubes at a stage somewhat beyond the maximum internal pressure. All tubes, except for one aluminum alloy tube, failed by shear fracture under decreasing pressure. The aluminum alloy tubes exhibited localized shear deformations in the neck region prior to fracture and also occasionally surface wave instabilities. The numerical investigation is based on an elastic-plastic material model for a solid that develops a vertex on the yield surface, using representations of the uniaxial stress-strain curves found experimentally. In contrast to the simplest flow theory of plasticity this material model predicts shear band instabilities at a realistic level of strain. A rather sharp vertex is used in the material model for the aluminum alloy, while a more blunt vertex is used to characterize copper. The theoretically predicted bifurcation into a necking mode, the cross-sectional shape of the neck, and finally the initiation and growth of shear bands from the highly strained internal surface in the neck region are in good agreement with the experimental observations.     

Site of ductile fracture initiation in cold forging: A finite element model

Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. In this study a new ductile fracture condition that based on the microscopic phenomena of void nucleation, growth and coalescence was proposed. Using this condition and combining with finite element model to predict the fracture locations in bulk metal forming, the results show that it is in close accordance with observations of some experimental specimens. However, in order to obtaining the high trustiness many experiments have to be carried out.