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Zirconium alloys are used in the nuclear industry due to their low neutron capture cross-section and resistance to corrosion, irradiation and creep. The microstructure of the nuclear fuel components evolves during the manufacturing route and can impact the subsequent processes or the final properties. Thus, numerical modeling of thermo-mechanical manufacturing processes is of interest to understand and master these microstructure evolutions.Numerical modeling of thermo-mechanical manufacturing processes with FORGE® NxT software is applied. These models provide the thermo-mechanical history of the material at each integration point of the finite element (FE) mesh, which can be used to assess locally the continuous dynamic and post-dynamic recrystallization during hot extrusion.Mean-field models were developed in Python and integrated into FORGE® NxT software, to quantify the microstructure evolution at the macro-scale of the component. Full-field models (DIGIMU® software1) were also developed for considering microstructural heterogeneities and the influence of initial microstructure at the mesoscopic scale while improving the mean-field equations by homogenization.After validation based on experimental results, these two recrystallization models provide complementary information to optimize the process parameters at the macro-scale and to better understand mesoscopic scale phenomena, such as:• At the macro-scale: influence of hot extrusion parameters on the continuous dynamic and post-dynamic recrystallization of Zircaloy-4.• At the meso-scale: influence of the initial microstructure on the recrystallization phenomena with improved precision. Indeed, the topology of the microstructure is predicted and not only the mean values/distributions of the state variables.

International audience; Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats the single boundary simplification of the anisotropic grain growth problem. By applying the first principles of thermodynamics and mechanics, an expression for the velocity field of a migrating grain boundary with an inclination-dependent energy density is expressed. This result is used to generate the first, to the authors’ knowledge, space-time analytical solution to the anisotropic grain growth problem. This new anisotropic benchmark is simulated in order to explore the convergence properties of the proposed level-set finite element numerical model. Convergence of the method being illustrated, another configuration, using a more general grain boundary energy density, is investigated in order to show the added value of the new formulation.

The thermal conductivity of granular planetary regolith is strongly dependent on the porosity, or packing density, of the regolith particles. However, existing models for regolith thermal conductivity predict different dependencies on porosity. Here, we use a full-field model of planetary regolith to study the relationship between regolith radiative thermal conductivity, porosity, and the particle non-isothermality. The model approximates regolith as regular and random packings of spherical particles in a 3D finite element mesh framework. Our model results, which are in good agreement with previous numerical and experimental datasets, show that random packings have a consistently higher radiative thermal conductivity than ordered packings. From our random packing results, we present a new empirical model relating regolith thermal conductivity, porosity, temperature, particle size, and the thermal conductivity of individual particles. This model shows that regolith particle size predictions from thermal inertia are largely independent of assumptions of regolith porosity, except for when the non-isothermality effect is large, as is the case when the regolith is particularly coarse and/or is composed of low thermal conductivity material.Plain Language SummaryThe temperature of a planetary surface is strongly controlled by the thermal inertia of the surface materials. Specifically, if the surface is covered in a granular regolith, then the size, thermal conductivity, and packing density of the regolith particles strongly affects the surface thermal inertia, which in turn controls surface temperatures. In this work, we use 3D numerical simulations of heat transfer through beds of spherical particles, representing a planetary regolith, to investigate how thermal conductivity and thermal inertia are controlled by the packing density and thermal conductivity of the spheres. Our results are presented in the form of a new empirical model, which could be used to calculate regolith thermal conductivity from knowledge of particle size, composition, and packing density. The use of this model is demonstrated in the typical reverse fashion, where an observed planetary thermal inertia is converted into a predicted regolith particle size. Our model shows that the predicted particle size is largely independent of regolith particle packing density, in contrast to other common regolith models.

Two finite element level-set (FE-LS) formulations are compared for the modeling of grain growth of 316L stainless steel in terms of grain size, mean values, and histograms. Two kinds of microstructures are considered: some are generated statistically from EBSD maps, and the others are generated by the immersion of EBSD data in the FE formulation. Grain boundary (GB) mobility is heterogeneously defined as a function of the GB disorientation. On the other hand, GB energy is considered as heterogeneous or anisotropic, which are, respectively, defined as a function of the disorientation and both the GB misorientation and the GB inclination. In terms of mean grain size value and grain size distribution (GSD), both formulations provide similar responses. However, the anisotropic formulation better respects the experimental disorientation distribution function (DDF) and predicts more realistic grain morphologies. It was also found that the heterogeneous GB mobility described with a sigmoidal function only affects the DDF and the morphology of grains. Thus, a slower evolution of twin boundaries (TBs) is perceived.

A full-field numerical framework using the level-set method has been developed to simulate diffusive solid-solid phase transformation at the mesoscopic scale in the context of austenite decomposi- tion. A pseudo-1D test case with a planar interface is considered as a first case to demonstrate coherency in the results in terms of the expected steady states achieved. The ability of the numerical framework to model other diffusive solid state phenomena such as Ostwald ripening is successfully illustrated with a suitable test case.

International audience; In this study, four different finite element level-set (FE-LS) formulations are compared for the modeling of grain growth in the context of polycrystalline structures and, moreover, two of them are presented for the first time using anisotropic grain boundary (GB) energy and mobility. Mean values and distributions are compared using the four formulations. First, we present the strong and weak formulations for the different models and the crystallographic parameters used at the mesoscopic scale. Second, some Grim Reaper analytical cases are presented and compared with the simulation results, and the evolutions of individual multiple junctions are followed. Additionally, large-scale simulations are presented. Anisotropic GB energy and mobility are respectively defined as functions of the mis-orientation/inclination and disorientation. The evolution of the disorientation distribution function (DDF) is computed, and its evolution is in accordance with prior works. We found that the formulation called “Anisotropic” is the more physical one, but it could be replaced at the mesoscopic scale by an isotropic formulation for simple microstructures presenting an initial Mackenzie-type DDF.

An implementation of smoothing splines is proposed to reduce orientation noise in electron backscatter diffraction (EBSD) data, and subsequently estimate more accurate geometrically necessary dislocation (GND) densities. The local linear adaptation of smoothing splines (LLASS) filter has two advantages over classical implementations of smoothing splines: (1) it allows for an intuitive calibration of the fitting versus smoothing trade-off and (2) it can be applied directly and in the same manner to both square and hexagonal grids, and to 2D as well as to 3D EBSD data sets. Furthermore, the LLASS filter calculates the filtered orientation gradient, which is actually at the core of the method and which is subsequently used to calculate the GND density. The LLASS filter is applied on a simulated low-misorientation-angle boundary corrupted by artificial orientation noise (on a square grid), and on experimental EBSD data of a compressed Ni-base superalloy (acquired on a square grid) and of a dual austenitic/martensitic steel (acquired on an hexagonal grid). The LLASS filter leads to lower GND density values as compared to raw EBSD data sets, as a result of orientation noise being reduced, while preserving true GND structures. In addition, the results are compared with those of filters available in theMTEXtoolbox.

International audience; The influence of image segmentation on micromechanical simulations of ductile damage in nodular graphite cast iron coupled with 3D imaging is explored for two tensile specimens. Three different approaches are used to segment the microstructures from laminography data. These microstructures are immersed in a finite element mesh and simulations with experimental boundary conditions are carried out for each of the three segmentation techniques. The sensitivity of local and global mechanical quantities is assessed based on the results of these simulations. The comparison between the employed techniques is then used to estimate the uncertainty associated with the image segmentation stage.

International audience; The main purpose of this study is to better understand the relationship between the microstructure of foamed polymer and mechanical properties. X-Ray tomography was performed on polypropylene foam specimens machined from injected plates. These plates were obtained for different thicknesses and exhibit different microstructure morphologies. The tomography scans were first digitalized and meshed. Then, numerical simulations were performed on representative volume elements (RVEs) to get homogeneous mechanical property of the material using a parallel C++ library Cimlib developed at CEMEF. Numerical methods described in this study focused on immerged or body-fitted strategy (FE context - level set framework - meshing adaptation) for exact and statistical RVEs generation. The numerical results were compared to experimental testing performed under tension and compression at different strain rates using image correlation. Good agreement was observed between simulations performed at the mesoscale and experimental tests carried out at the macroscale for both real and statistical RVEs. This methodology opens a way for the development of digital materials designed for specific mechanical properties.

In numerous polycrystalline materials, grain size is controlled by second phase particles (SPPs) that hinder the grain boundaries (GBs) by pinning mechanisms. The Smith–Zener pinning (SZP) model describes the physical interaction between SPPs and GBs. Both of them can evolve when applying a heat treatment to the material. As industrial forging processes involve hot deformation steps near the solvus temperature, it is thus of prime importance to characterize the evolution of the SPPs due to their impact on the final microstructure, notably on the grain size. The level set (LS) method is classically used to describe the influence of SPPs on grain growth (GG) by considering the simulated particles as inert and represented by static holes in the used finite element (FE) mesh. A new formalism to model GG mechanism under the influence of the SZP phenomenon, able to take into account evolving particles is proposed. It involves the representation of SPPs by a LS function and a particular numerical treatment around the grain interfaces encountering SPP, making possible the modelling of SPPs evolution without altering the undergoing pinning pressure. Validation and comparison of the new method regarding previous FE-LS formulation in 2D and 3D simulations and an application on GG under the influence of dissolving particles are described.

A new method for the simulation of evolving multi-domains problems has been introduced in previous works and further developed in parallel in the context of isotropic grain growth (GG) with no consideration for the effects of the stored energy (SE) due to dislocations. The methodology consists in a new front-tracking approach where one of the originality is that not only interfaces between grains are discretized but their bulks are also meshed and topological changes of the domains are driven by selective local remeshing operations performed on the finite element (FE) mesh. In this article, further developments and studies of the model will be presented, mainly on the development of a model taking into account grain boundary migration (GBM) by SE. Further developments for the nucleation of new grains will be presented, allowing to model dynamic recrystallization (DRX) and post-dynamic recrystallization (PDRX) phenomena. The accuracy and the performance of the numerical algorithms have been proven to be very promising in Florez et al (2020). Here the results for multiple test cases will be given in order to validate the accuracy of the model taking into account GG and SE. The computational performance will be evaluated for the DRX and PDRX mechanisms and compared to a classical FE framework using a level-set formulation.

International audience; In this work we present a simple and convenient method for handling tensors within computational mechanics frameworks based on the Kelvin decomposition. This methodology was set up within a crystal plasticity framework which permits, using the Kelvin base related to the crystal symmetries, to account for elastic anisotropy. The classical mixed velocity pressure finite element formulation has been modified in order to account for the elastic anisotropic behavior introduced into the crystal plasticity model. Moreover this modification of the mixed formulations allows to account for volume/pressure variations that can stream from constitutive models that could allow present compressible plasticity. Using this numerical framework, we explore the influence of elastic anisotropy onto the mechanical behavior of olivine. Our results suggest that at the polycrystal scale, the elastic anisotropy is not of first order importance. However the local changes on the stress state can be important for some physical phenomena such as recrystallization and damage.

International audience; The movement of grain boundaries in pure metals and alloys with a low concentration of dislocations has been historically proved to follow curvature flow behavior. This mechanism is typically known as grain growth (GG). However, recent 3D in-situ experimental results tend to question this global picture concerning the influence of the curvature on the kinetics of interface migration. This article explains, thanks to 2D anisotropic full-field simulations, how the torque effects can complicate these discussions. It is then illustrated that neglecting torque effects in full-field formulations can have a significant effect on the overall rate of GG, the shape of grains and grain boundaries as well as their local kinetics. The apparent reduced mobility can be much more complex than expected without necessarily questioning the influence of the curvature on the local kinetic equation.

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In this work the recently proposed full field approach to model dynamic recrystallization [1] is applied to model 304L steel. The framework couples a CPFEM (crystal plasticity finite element method) model with a LS-FE (level-set finite element method) for grain boundary migration and phenomenological laws. 304L steel samples are subjected to thermomechanical tests and their flow behaviour is characterized, additionally Electron Back Scattered Diffraction (EBSD) is used to study microstructure evolutions. Part of the experimental data is used to calibrate the model parameters and describe their evolution as a function of the thermomechanical conditions. The calibrated model is used to predict the microstructural evolution of 304L steel, the results are compared with the remaining experimental measurements. The comparison shows that the model correctly predicts the flow behaviour and recrystallization fraction evolution. However the results also show that the use of classical phenomenological models limit the model capability to predict grain size evolution. Different approaches to improve the model grain size prediction are presented and compared, the results show significant improvements when compared with experimental data.

Thermophysical analyses of planetary bodies such as the Moon, Mars, and numerous asteroids have allowed for remote estimates of regolith physical properties, such as particle size and packing density, as well as the relative spatial abundance of boulders. Here we define “regolith” as a particulate assemblage where most particles are comparable to or smaller than the length scale of the diurnal skin depth (the e-folding depth of the diurnal thermal wave). Until recently, regolith and boulders were believed to be thermally quite distinct; regolith on the Moon, Mars, and most asteroids was usually known or suspected to be fine (i.e., ranging from fine dust to sand), meaning that it was known or assumed to have a thermal inertia much lower than that of boulders and bedrock. Upon the arrival of NASA OSIRIS-REx at asteroid Bennu and JAXA Hayabusa2 at asteroid Ryugu and the subsequent thermophysical analyses of the respective asteroid surfaces, this preconceived notion of thermophysically distinct regolith and boulders/bedrock was found to be flawed (DellaGiustina and Emery et al., 2019; Sugita et al., 2019). Boulders cover the vast majority of both asteroids’ surfaces, yet the thermal inertia values determined for these boulder-rich surfaces fall within a range that was previously believed to exclusively represent coarse, sand-to-pebble–sized regolith. Recent work has been devoted to the analysis of the boulders’ thermal inertia and the physical interpretation thereof (Grott et al., 2019; Rozitis et al., in revision); the general conclusion so far is that the boulders have very low thermal conductivity and density owing to the presence of numerous pores and fractures, more so than most (or perhaps all) carbonaceous chondrite meteorites in Earth’s collections. As such, these boulders are likely to be structurally distinct from all known meteorite specimens. Although fine-particulate regolith is rare on the surface of Bennu, it is present in some locations. It is still of great interest to probe the physical properties of this regolith by means of thermal analysis so as to make predictions about the properties of the samples that will be returned by OSIRIS-REx and to learn about the evolution of the asteroid surface and the mechanisms by which regolith is produced and lost or destroyed. There remains the enigmatic question: although we suspect that the boulders on Bennu are distinct from the meteorite collection, will the returned samples of particulate material share these distinct properties? At what scales can we define the physical thermally relevant properties of boulders and regolith particles on Bennu? In other words, if the boulders are indeed highly fractured and porous, are the regolith particles also fractured and porous or are their dimensions below the relevant length scales? It is very challenging to estimate the physical properties of the regolith on Bennu using thermal data, even in regions where it appears to be abundant, due to the coarseness of the regolith. Commonly used planetary thermophysical models rely on the assumption that the material on the surface, be it regolith or rock, can be approximated as a continuous, non-discretized material with physical properties that are either constant with depth or are allowed to vary with depth in some well-defined way (e.g. an exponential density increase, or up to a few layers of physically distinct material, such as regolith on bedrock or dust coatings). This assumption of material continuity is valid when regolith particles are smaller, or perhaps even much smaller, than the diurnal skin depth of the thermal wave. However, high-resolution images of the Nightingale Crater on Bennu, which is the OSIRIS-REx mission’s primary sample collection site, revealed a particle size frequency distribution (SFD) that crosses this threshold; i.e., there are particles present that are smaller than, comparable to, and larger than the diurnal skin depth (~1­–5 cm) present within a single, meters-wide observation footprint. The thermophysical behavior of such a regolith configuration has never been comprehensively studied and likely cannot be properly approximated with standard 1D thermal modeling methods. We will present preliminary results using a 3D regolith model where we render hundreds of regolith particles and rocks, approximated as spheres, in a finite element mesh framework. The model is heated diurnally with a solar source to study the thermal response of such skin depth–crossing SFDs under Bennu surface-like conditions. The SFD of the particles is informed by particle size counts in Nightingale Crater from high-resolution visible images. With the SFD partially constrained, we are able to focus our efforts on exploring the material property parameter space, namely to estimate the thermal conductivity and density of individual regolith particles. Given the coarseness of the regolith on Bennu, we find that the model is more sensitive than one might expect to the thermal conductivity of the individual regolith particles owing to the effects of particle non-isothermality (Ryan et al., 2020). Although this present modeling work is focused on analyzing thermal emission data of Bennu obtained by the OSIRIS-REx Thermal Emission Spectrometer (OTES, Christensen et al., 2018), we aim to expand our efforts to study the more general thermal behavior of coarse regoliths and regoliths with wide SFDs under a range of solar heating conditions. Acknowledgements This material is based upon work supported by NASA under Contract NNM10AA11C issued through the New Frontiers Program. We are grateful to the entire OSIRIS-REx Team for making the encounter with Bennu possible. References: Christensen, P.R. et al. (2018). The OSIRIS-REx Thermal Emission Spectrometer (OTES) Instrument. Space Science Reviews 214, 87. DellaGiustina, D.N., Emery, J.P., et al. (2019) Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis, Nature Astronomy, DOI:10.1038/s41550-019-0731-1. Grott, M., Knollenberg, J., et al. (2019) Low thermal conductivity boulder with high porosity identified on C-type asteroid (162173) Ryugu, Nature Astronomy, DOI:10.1038/s41550-019-0832-x. Rozitis, B., Ryan, A.J., Emery, J.P., et al. (in revision) Asteroid (101955) Bennu’s Weak Boulders and Thermally Anomalous Equator, Science Advances, submitted March 2020. Ryan, A., Pino Muñoz, D., Bernacki, M., Delbo, M. (2020) Full-Field Modeling of Heat Transfer in Asteroid Regolith: Radiative Thermal Conductivity of Polydisperse Particulates, JGR:Planets. DOI:10.1029/2019JE006100. Sugita, S., Honda, R., et al. (2019) The geomorphology, color, and thermal properties of Ryugu: Implications for parent-body processes, Science. DOI:10.1126/science.aaw0422

This work presents an analytical mean field model of agglomeration (equivalent agglomeration model, EAM) by contact between growing precipitates. The principle of the EAM is to add a 2-steps task to existing precipitation models: at each time-step, (1) calculate the number of agglomerations per unit volume, then (2) use it to update the numbers and radii of classes in order to take agglomeration into account. The first step is validated by full-field simulations of growing spheres randomly placed in a cube. The EAM can be added as extension to existing precipitation models and be applied to the mean radius, multi-class Lagrangian and multi-class Eulerian representations of the precipitate population. The EAM is incorporated to a mean field precipitation model based on the classical nucleation theory and Zener’s law for size evolution, and catches the rarefaction of γ″ precipitates agglomerating as they grow during an isothermal annealing in a nickel-based superalloy.

Characterizing the surface material of an asteroid is important for understanding its geology and for informing mission decisions, such as the selection of a sample site. Diurnal surface temperatur...

International audience; The Level-set (LS) method has been shown to be a powerful approach to model dynamic interfaces in the context of large deformations. The LS method has been applied to the simulation of microstructural evolutions as Grain Growth (GG) and Recrystallization (ReX) at the mesoscale Maire et al. (2017). Interfaces between grains are implicitly described in an Eulerian framework, as the zero-isovalue of the LS fields and their evolution is governed by convective-diffusive partial differential equations (PDEs). The LS approach circumvents the notoriously difficult problem of generating interface-conforming meshes for geometries subjected to large displacements and to changes in the topology of the domains.Generally, in order to maintain high accuracy when using the LS method, moving interfaces are generally captured by a locally refined FE mesh with the help of mesh adaptation techniques. In a microstructural problem, the large number of interfaces and the fine mesh required in their vicinity make the mesh adaptation process very costly in terms of CPU-time, particularly in 3D Scholtes (2016).In this work, a different adaptation strategy is used. It maintains the benefits of the classical Eulerian LS framework, while enforcing at all times the conformity of the FE mesh to implicit interfaces by means of local remeshing operations, special treatments for vacuum regions have been adopted and will be presented within the generalization of a previous adaptation algorithm presented in Shakoor et al. (2015). Source of errors will be presented and compared for different test cases. Finally, we will illustrate how the new method decreases the requirement in mesh density while maintaining the accuracy at the interfaces, hence reducing the computational cost of the simulations.

International audience; In a previous article (Fausty et al., 2018) a new level-set finite element formulation for pure grain growth with heterogeneous grain boundary energies (i.e. one energy per grain interface) was developed and validated for simple configurations. In this work, the authors apply this new tool to the simulation of two dimensional grain growth of polycrystals using different disorientation dependent grain boundary energy functions. The results of these full-field calculations are assessed using the time dependent evolution of the following criteria: grain size, grain number, total interface energy, grain boundary disorientation distribution, grain boundary energy distribution and number of neighboring grains distribution. Of particular interest is the relationship between the grain boundary energy function and the evolution of the grain boundary network in the sense of both its morphology and its constitution. Some notable results are that the disorientation distribution evolution is inversely correlated to the grain boundary energy function itself and that the kinetics of grain growth are heavily effected by the heterogeneity of the system.

International audience; We present a full field framework based on the level‐set (LS) approach, which enables to simulate grain growth in a multiphase material. Our formalism permits to take into account different types of second phases, which can be static or dynamic (i.e. evolving also by grain growth) and reproduce both transient (evolving relative grain sizes) and steady‐state structures. We use previously published annealing experiments of porous olivine or olivine and enstatite mixtures to constrain the parameters of the full field model, and then analyse the results of a peridotite‐like annealing simulation. The experimental grain growth kinetics is very well reproduced while the simulated microstructure morphologies show some differences with experimental ones. We then propose a mean field model calibrated thanks to the full field simulations, which allow us to predict the mean grain size evolution depending on the simplified peridotite composition (e.g. second phase mean grain sizes, fractions).

The mechanical properties of nickel-based superalloys depend strongly on their microstructure, namely the grain size and the state of precipitation. Main design criteria in aeronautical turbine disks are the resistance to disk burst and low cycle fatigue in the bore, but also to creep in the rim part due to higher temperatures. The chosen microstructures result from a compromise between these contradictory requirements. Indeed, creep durability is improved using a coarse grain microstructure while the increase of static and fatigue strength requires a fine grain microstructure. Moreover, the volume fraction and the size distribution of γ′ precipitates are the predominant parameters controlling mechanical properties at lower temperatures. A spatial optimization of the microstructure is reachable using specific technologies, e.g. dual-microstructure heat treatment. The development of microstructure-sensitive models is thus a major concern for the optimal design of these components including gradient of grain size and/ or precipitate size. Full-field finite element simulations may be employed to predict the macroscopic behavior of polycrystalline aggregates using crystal plasticity constitutive equations whose parameters depend explicitly on the microstructural attributes. In this framework, the present study is devoted to the evaluation of the yield stress of polycrystalline AD730TM nickel-based superalloy, chosen as a model material. This work includes microstructural characterization and mechanical tests carried out on single crystals and polycrystalline specimens with well-controlled microstructures. Predictions of the macroscopic yield stress are provided by preliminary simulations carried out in the elastic regime combined with a specific post-processing.

Characterizing the surface material of an asteroid is important for understanding its geology and for informing mission decisions, such as the selection of a sample site. Diurnal surface temperature amplitudes are directly related to the thermal properties of the materials on the surface. We describe a numerical model for studying the thermal conductivity of particulate regolith in vacuum. Heat diffusion and surface-to-surface radiation calculations are performed using the finite element (FE) method in three-dimensional meshed geometries of randomly packed spherical particles. We validate the model for test cases where the total solid and radiative conductivity values of particulates with monodisperse particle size frequency distributions (SFDs) are determined at steady-state thermal conditions. Then, we use the model to study the bulk radiative thermal conductivity of particulates with polydisperse, cumulative power-law particle SFDs. We show that for each polydisperse particulate geometry tested, there is a corresponding monodisperse geometry with some effective particle diameter that has an identical radiative thermal conductivity. These effective diameters are found to correspond very well to the Sauter mean particle diameter, which is essentially the surface-area-weighted mean. Next, we show that the thermal conductivity of the particle material can have an important effect on the radiative component of the thermal conductivity of particulates, especially if the particle material conductivity is very low or the spheres are relatively large, owing to non-isothermality in each particle. We provide an empirical correlation to predict the effects of non-isothermality on radiative thermal conductivity in both monodisperse and polydisperse particulates., Comment: Accepted by Journal of Geophysical Research: Planets

International audience; This paper is a state-of-the-art review of computational damage and fracture mechanics methods applied to model ductile fracture at the microscale. An emphasis is made on robust and stable methods that can handle heterogeneous structures, large deformations , and cracks initiation and coalescence. Duc-tile materials' microstructures feature brittle and duc-tile components whose heterogeneous behavior can give raise to cracks initiation due to stress concentration. Due to large deformations, cracks initiated by brittle components failure transform into large voids. These major voids interact and coalesce by plastic localiza-tion within ductile components and lead to final failure. This process can involve minor voids nucleated directly within ductile components at sub-micron scales. State-of-the-art discontinuous approaches can be applied to discretize accurately brittle components and model their failure, given that large deformations can be handled. For ductile components, continuous approaches are discussed in this review as they can model the homogenized influence of minor voids, hence alleviating the burden and computational cost overhead that an explicit discretization of those voids would require. Close to final failure, when major voids are coalesc-ing, and the influence of minor voids becomes comparable to that of major voids, the transition from a continuous damage process within ductile components to the initiation and propagation of discontinuous cracks within these components has to be modeled. This review ends with a discussion on computational methods that have successfully been applied to model the continuous-discontinuous transition, and that could be coupled to discontinuous approaches in order to model ductile fracture at the microscale in its full three-dimensional complexity. Keywords ductile fracture; heterogeneous structure; microstructure; computational fracture mechanics; computational damage mechanics Nomenclature 2D Two-Dimensional 3D