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ABSTRACT Ductile fracture of modified 9Cr–1Mo steel was investigated using smooth and notched bar tension tests. Round and flat notched specimens with varying notch acuity ratio were used to investigate the influence of stress state on the fracture strain. Simulations of the experiments were performed using the extended finite element method, together with an instability‐based crack initiation criterion based on the micromechanics of void coalescence. The parameters in the plasticity model were determined using smooth bar tension tests, whereas the void nucleation parameters were calibrated from experiments on a shallow‐notched specimen. Subsequently, the load–deflection responses and strain to crack initiation have been predicted for round and flat notched specimens with various notch acuities, and central notched specimens with notches oriented at various angles to the loading axis. Using a single set of parameters, the model was able to quantitatively predict fracture in different specimen geometries encompassing a range of stress states. [ABSTRACT FROM AUTHOR]

A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution (rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.

A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution (rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations. [ABSTRACT FROM AUTHOR]

Adiabatic shear bands (ASBs) are known to be the dominant damage mechanisms in structural materials under high strain rate loading such as magnesium (Mg) alloys. Therefore, to tailor the mechanical performance of Mg alloys for structural applications, there is a need to understand their susceptibility to strain localization and formation of ASBs, including the mechanism of crack initiation and propagation. In this study, as-fabricated (extruded) and heat-treated (annealed at 400 °C) AZ31B Mg alloys were subjected to high strain rate loading using the direct impact Hopkinson pressure bar (DIHPB) under different strain rates (834–2435 s−1) at room temperature. The impact specimens failed through the occurrence of strain localization, formation of diffused ASBs, and initiation/propagation of micro-cracks along the path of evolved ASBs. Thus, strain localization results in crack initiation and propagation despite the inherent brittle nature of the Mg alloys. Furthermore, in regions with evolved shear bands, there was a low occurrence of twin/micro-twins. This observation suggests that shear band formation dominates over the micro-twinning effect in Mg alloys. Also, the presence of fractured second-phase particles dispersed within voids and along shear band path suggests particle fragmentation and refinement due to the strain localization. Second-phase particle fragmentation also played a role in void nucleation, growth, and coalescence during the deformation. In addition, there seems to be a threshold strain rate (~>2225 s−1) beyond which the specimen fractures regardless of the initial microstructure of the Mg alloys. [ABSTRACT FROM AUTHOR]

The harshness of the submarine environment represents a serious threat for immersed high voltage power cables, extensively used for offshore wind farms, which in turn are supposed to last for at least 20 years for their total investment to be economically viable. The Crosslinked Polyethylene (XLPE) used for the insulating layer of the cables may suffer different degradation phenomena, leading to unexpected breakdowns and rises in costs. In this work, numerical simulations have been developed to study the mechanisms by which micrometric pores inside XLPE can enlarge and coalesce (namely, water treeing) when the insulation is subjected to the intense electric field generated by hi-voltage wires. The study aim is to predict material plasticization next to voids, which is supposed to represent the onset of coalescence of neighboring pores. A microscale-level finite element coupled electro-mechanics model has been developed to describe the interactions between the intense electric fields and the subsequent Maxwell stresses in a dielectric. The roles of different influencing parameters such as distance, relative volumes, and the shape of two neighboring voids in a representative unit volume are considered. Finally, the behavior of a generic microstructure characterized by randomly distributed voids immersed in an electric field is simulated. [ABSTRACT FROM AUTHOR]

The formation of void damage and spalling failure in ductile metallic materials under strong impact is a well-established phenomenon. In aerospace and defense technology engineering design, understanding the spalling failure process and related mechanisms is of utmost importance. This paper develops an explicit Gurson-type phase-field model that can simulate the void evolution and spalling damage of three-dimensional ductile metallic materials under high-velocity impacts based on the study of Aldakheel et al.. The model incorporates the Gurson-type void evolution equation and the phase-field approach while taking into account the pressure-dependent bulk modulus and inertia effects. This model is used to study the main processes and mechanisms of impacted layer cracking of metals in different dimensions. Meanwhile based on the study of complex spallation cracking processes in metals in two and three dimensions, observing and proposing the formation mechanism of complex spallation cracking modes in materials due to lateral and edge (base angle) rarefied effects. • An explicit Gurson-type phase-field model is developed to simulate the void evolution and spalling process in ductile metallic materials. • The model considers the pressure-dependent bulk modulus, inertia effects, heat generation and diffusion during large plastic deformation. • The processes of different impact spallation cracking problems in 1, 2, and 3 dimensions are verified and studied. • The 2D flat plate non-parallel spallation cracking mechanism and the spallation cracking cut-off mechanism are investigated; the mechanisms of different damage regions of the 3D conical spallation cracking process are given. [ABSTRACT FROM AUTHOR]

The harshness of the submarine environment represents a serious threat for immersed high voltage power cables, extensively used for offshore wind farms, which in turn are supposed to last for at least 20 years for their total investment to be economically viable. The Crosslinked Polyethylene (XLPE) used for the insulating layer of the cables may suffer different degradation phenomena, leading to unexpected breakdowns and rises in costs. In this work, numerical simulations have been developed to study the mechanisms by which micrometric pores inside XLPE can enlarge and coalesce (namely, water treeing) when the insulation is subjected to the intense electric field generated by hi-voltage wires. The study aim is to predict material plasticization next to voids, which is supposed to represent the onset of coalescence of neighboring pores. A microscale-level finite element coupled electro-mechanics model has been developed to describe the interactions between the intense electric fields and the subsequent Maxwell stresses in a dielectric. The roles of different influencing parameters such as distance, relative volumes, and the shape of two neighboring voids in a representative unit volume are considered. Finally, the behavior of a generic microstructure characterized by randomly distributed voids immersed in an electric field is simulated.

The geometric and distributive properties of voids significantly influence anisotropic coalescence behaviour. However, this problem has received little attention owing to the complexity of considering all the properties in the current analytical framework of limit analysis. To address this issue, this study proposes an analytical framework based on an elliptic coordinate system, including the determination of the ligament zone, characterization of plastic flow, and derivation of the void coalescence criterion, for porous materials with various geometric and distributive properties, including size, shape, spacing, and orientation. This framework is motivated by our observations that the evolution of the void geometry and surrounding plastic flow can be well characterized by the grid of the elliptic coordinate system. Subsequently, an analytical function is proposed to determine the ligament zone and coalescence direction with various void properties. A hollow nonaxisymmetric cylindrical unit cell is proposed to describe this ligament zone, and the corresponding trial velocity field is derived by extending the previous Gurson-like velocity field into the elliptic cylindrical coordinate system. The rationality of the field is validated by comparing its equivalent strain rate field with numerical simulations. Finally, a coalescence criterion is derived via the limit analysis of the proposed unit cell undergoing internal necking. Two heuristic adjustments are formulated for the overflow phenomenon in the rigid zone and outer ligament zones. Numerical assessments with various void properties confirm the accuracy of the analytical model. The coalescence criterion can predict the independent and coupling effects of geometric and distributive properties on anisotropic void coalescence. This study provides possible solutions to future plasticity problems of ellipsoidal inclusions. [Display omitted] • The anisotropic coalescence behaviours are described in elliptic coordinate system. • An analytical function is proposed to determine the intervoids ligament zone. • The Gurson-like trial velocity field is extended into the proposed coordinate system. • The coalescence criterion agrees with the numerical assessments on void properties. • The effects of void properties on anisotropic coalescence are identified. [ABSTRACT FROM AUTHOR]

A reliable determination of the onset of void coalescence is critical to the modelling of ductile fracture. Numerical models have been developed but rely mostly on analyses on single defect cells, thus underestimating the interaction between voids. This study aims to provide the first extensive analysis of the response of microstructures with random distributions of voids to various loading conditions and to characterize the dispersion of the results as a consequence of the randomness of the void distribution. Cells embedding a random distribution of identical spherical voids are generated within an elastoplastic matrix and subjected to a macroscopic loading with constant stress triaxiality and Lode parameter under periodic boundary conditions in finite element simulations. The failure of the cell is determined by a new indicator based on the loss of full rankedness of the average deformation gradient rate. It is shown that the strain field developing in random microstructures and the one in unit cells feature different dependencies on the Lode parameter L owing to different failure modes. Depending on L, the cell may fail in extension (coalescence) or in shear. Moreover the random void populations lead to a significant dispersion of failure strain, which is present even in simulations with high numbers of voids. [ABSTRACT FROM AUTHOR]

A new ductile fracture criterion is proposed based on three stages of ductile fracture: void nucleation, growth and coalescence from the microscopic viewpoint. Based on the observation of SEM fracture surfaces of AA2024-T351 aluminum alloy sheet and bar samples under different stress states, it is assumed that the void aggregation is controlled by shear or shear-tension fracture mechanism according to the stress state. And the stress triaxiality is deemed as the only influence factor for controlling the void growth. The new ductile fracture criterion applied to a wide range of stress triaxiality is built. By fitting the available testing data of AA2024-T351 aluminum alloy and AISI 1045 steel, the fracture loci in the stress triaxiality, Lode parameter and equivalent fracture strain space (η , L , ε ¯ f ) built by the new criterion are compared with those by DF2014, Hu criterion, modified Mohr-Coulomb criterion (MMC) and Hosford- Coulomb (H-C) criterion. The fitting results prove better prediction accuracy for the new criterion. To further compare the stability of these criteria, the fracture loci in the space of (η , L , ε ¯ f ) for AA2024-T351 alloy are established by only fitting five tests. The new criterion can still well predict the equivalent fracture strain ( ε ¯ f ). Compared with DF2014, Hu criterion, MMC and H-C criterion, the average errors of the new criterion are reduced by 26.72%, 20.07%, 31.78% and 34.62%, respectively. Furthermore, the maximum errors are reduced by 49.62%, 27.31%, 33.76% and 29.91%, separately. Therefore, the new fracture criterion has higher prediction accuracy and better prediction stability. Last but certainly not least, the new criterion can predict more accurately under high stress triaxiality conditions. [ABSTRACT FROM AUTHOR]

Single point incremental forming process is a most economical Die-less forming process. The major constraint of it is that it is a time consuming process. In this work, a new attempt was made in incremental forming process using Multipoint tool for SS430 sheets to increase the formability and to reduce forming time. Fractography analysis was made to study the size of voids that were formed during fracture. The forming limit diagrams were drawn and compared for single point incremental forming and the multipoint incremental forming of SS430 sheet. It was proved that the formability of SS430 sheet in the multipoint forming was better than the formability of that in single point forming and the time consumed was reduced. The strain distribution in both processes had also been studied along with surface roughness.

Intergranular ductile fracture is a failure mode that may arise in many metallic alloys used in industrial applications. It manifests as the successive nucleation, growth, and coalescence of cavities at grain boundaries. Thus, simulation of intergranular ductile fracture in polycrystals requires modeling those three different stages at the scale of grain boundaries, i.e. at the interface between two different crystals. In this study, a yield criterion for the coalescence of cavities at the interface between two isotropic materials obeying Mises plasticity is first developed by limit analysis in order to provide some insights into that phenomenon. This criterion is checked against numerical limit analysis under combined tension and shear and is found to agree with unit-cell simulations quantitatively. The model is then extended to crystals so as to account for the complex coupling between loading state, crystallographic orientations, and void microstructure in intergranular coalescence. This second criterion is also assessed through comparisons to numerical limit analysis for an FCC crystal lattice. The agreement is very good in the case of coalescence by internal necking and the trends displayed by coalescence under combined tension and shear are captured correctly. Some implications of the model on the competition between transgranular and intergranular ductile fracture are discussed. Finally, by combining this model with an existing criterion for void growth at grain boundaries, a multi-surface yield function relevant to intergranular ductile fracture is obtained and compared to unit-cell simulations. • Yield criteria are obtained for both porous Mises bimaterial and porous bicrystal. • Coalescence by internal necking and shear-assisted coalescence are accounted for. • Evidence of two modes of coalescence: in the softer material or in both materials. • Complete yield surface for intergranular ductile fracture unprecedently predicted. • Results confirmed by corresponding porous unit-cell small-strain computations. [ABSTRACT FROM AUTHOR]

The competition between ductile rupture mechanisms in high-purity Cu and other metals is sensitive to the material composition and loading conditions, and subtle changes in the metal purity can lead to failure either by void coalescence or Orowan Alternating Slip (OAS). In situ X-ray computed tomography tensile tests on 99.999% purity Cu wires have revealed that the rupture process involves a sequence of damage events including shear localization; growth of micron-sized voids; and coalescence of microvoids into a central cavity prior to the catastrophic enlargement of the coalesced void via OAS. This analysis has shown that failure occurs in a collaborative rather than strictly competitive manner. In particular, strain localization along the shear band enhanced void nucleation and drove the primary coalescence event, and the size of the resulting cavity and consumption of voids ensured a transition to the OAS mechanism rather than continued void coalescence. Additionally, the tomograms identified examples of void coalescence and OAS growth of individual voids at all stages of the failure process, suggesting that the transition between the different mechanisms was sensitive to local damage features, and could be swayed by collaboration with other damage mechanisms. The competition between the different damage mechanisms is discussed in context of the material composition, the local damage history, and collaboration between the mechanisms. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Void growth and void coalescence in Cu-Ta metallic glasses (Cu 50 Ta 50) under the tensioning process at room temperature and a strain rate of 108 s−1. • The tensile strength of two-void specimen is higher than one-void specimen, however, it is faster destroyed. • The tensile strength decreases as the increasing size scale. • The tensile strength and g(r) value decrease as the increasing temperature. • The tensile strength significantly increases at a strain rate of 5 × 109 s−1 compared to 108 and 109 s−1. • Cu 20 Ta 80 MGs specimen seems to be relatively more crunchy and harder than other cases. In this study, molecular dynamics (MD) simulations were executed to investigate the deformation mechanisms and mechanical properties of Cu-Ta metallic glasses (MGs) nanofilms with one- and two-void defect under the tensioning process. The deformation behavior is evaluated through the void growth and void coalescence mechanisms of specimens. The influences of the specimen size scale, temperature, strain rate and component concentration in Cu x Ta 100−x MGs are assessed by stress-strain response and radial distribution function (g(r)) diagram. The results indicate that with the Cu 50 Ta 50 MGs specimens that possess the same number of atoms, the tensile strength of two-void specimen is higher than one-void specimen, however, it is faster destroyed. The tensile strength decreases as the increasing size scale and the tensile strength of one-void specimen is lower than the tensile strength of two-void specimen. As the increasing temperature, the tensile strength and g(r) value decrease. In the case of various strain rates, the tensile strength values slightly rise up at strain rates in the range from 108 to 109 s−1, however, it significantly increases at a strain rate of 5 × 109 s−1. The Cu 80 Ta 20 MGs specimen seems to be relatively softer and more flexible, while the Cu 20 Ta 80 MGs specimen seems to be relatively more crunchy and harder. [ABSTRACT FROM AUTHOR]

An analytical micromechanics-based yield criterion is developed to describe both void growth and coalescence under combined tension and shear, with smooth transition between growth and coalescence, thus its name unified. The model is obtained by limit analysis over a cylindrical elementary cell embedding a coaxial cylindrical void of finite height. The velocity field employed is an extended counterpart of the discontinuous, yet kinematically admissible trial field utilized in a recent work. Plasticity in the deformable matrix is modeled using rate-independent J 2 flow theory, and the effective dissipation function is calculated by exact as well as approximate integration techniques, the latter generating a simpler flow potential. The model is aimed to predict void growth as well as coalescence by internal necking or shearing. The complete yield surface, being function of normal as well as shear stresses, exhibits curved and planar parts signifying void coalescence. The transition between the curved and planar parts is cornerless. The analytical predictions are compared to results of FEM single-step cell-model calculations of limit analysis executed on an identical geometry exposed to quasi-periodic boundary conditions. • A closed-form yield criterion was developed for void growth and coalescence under combined tension and shear through a unified perspective. • The model was derived on the basis of limit analysis over a cylindrical elementary cell embedding a coaxial cylindrical void.. • Upon the primitive inequality of limit analysis, the surface comprised straight and curved portions with transitions of the C 1 continuity. • Yield surfaces were compared to FEM counterparts over identical cell geometry, and satisfactory agreement was envisaged. • A comprehensive parametric study was presented based on various microstructural parameters as well as varied shear stresses. [ABSTRACT FROM AUTHOR]

Abstract The loading path dependence of ductile failure by void growth to coalescence is studied using a unit cell model of a porous material, containing a periodic distribution of voids in an elasto-plastic power law hardening matrix. The unit cell is subjected to triaxial proportional loading paths, and predictions for the strains to failure, defined as the onset of void coalescence by plastic strain localization in the inter-void ligaments, are obtained as a function of the loading path parameters, the stress triaxiality and the Lode parameter. Analogous simulations of a macroscopic material element subjected to proportional loading are performed using a multi-surface plasticity model, which accounts for void growth by diffuse plastic flow and void coalescence by the localization of plastic strains inside a micro-scale representative volume element. A phenomenological hardening law that approximately accounts for the physics of strain hardening during both pre- and post-coalescence deformation is proposed. The strains to failure in the continuum simulations are determined as the equivalent strains to the onset of void coalescence at the micro-scale of the voids. It is shown that the multi-surface plasticity model quantitatively predicts the loading path dependence of the strains to failure obtained from the cell model simulations over a wide range of values of the Lode parameter, from axisymmetric to shear dominated states, and moderate to large values of the stress triaxiality. Quantitative agreement with cell model simulations is obtained for two representative values of the strain hardening exponent, and in the absence of heuristic adjustable parameters in the model. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Specimens with various geometries to achieve multiaxial stress states. • The twins and stress-states play a key role in the voids nucleation and deformation. • The twins provide more sites for void nucleation and constrain void shape change. • The voids can coalesce to reach large size under the low stress-triaxiality. Abstract In situ scanning electron microscope (SEM) investigation is carried out on high-entropy alloy (HEA) specimen with various geometries to realize the multi-axial stress states. The dimple structure on the fracture surface is quantified and the nucleation of void is examined. The deformation twins can provide more sites for void nucleation and constrain shape change of the voids. Even under the low stress-triaxiality, the void can coalesce to reach large size accompanying twinning. The evolution of void size and density deduced from the fractograph is important to quantify ductile fracture of HEA. [ABSTRACT FROM AUTHOR]

Abstract A model of coalescence by internal necking of primary voids is developed which accounts for the presence of a second population of cavities. The derivation is based on a limit-analysis of a cylindrical cell containing a mesoscopic void and subjected to boundary conditions describing the kinematics of coalescence. The second population is accounted locally in the matrix surrounding the mesoscopic void through the microscopic potential of Michel and Suquet (1992) for spherical voids. The macroscopic criterion obtained is assessed through comparison of its predictions with the results of micromechanical finite element simulations on the same cell. A good agreement between model predictions and numerical results is found on the limit-load promoting coalescence. [ABSTRACT FROM AUTHOR]

Single point incremental forming process is a most economical Die-less forming process. The major constraint of it is that it is a time consuming process. In this work, a new attempt was made in incremental forming process using Multipoint tool for SS430 sheets to increase the formability and to reduce forming time. Fractography analysis was made to study the size of voids that were formed during fracture. The forming limit diagrams were drawn and compared for single point incremental forming and the multipoint incremental forming of SS430 sheet. It was proved that the formability of SS430 sheet in the multipoint forming was better than the formability of that in single point forming and the time consumed was reduced. The strain distribution in both processes had also been studied along with surface roughness. [ABSTRACT FROM AUTHOR]

More precise modeling on ductile fracture of metals at the scale from micron to meter is still urgently needed in many engineering applications. Due to the variety of metal and its alloys, a lack of understanding on the mechanisms and quantitative experimental data impede building and assessing mechanics models for ductile fracture at different length scales. In this paper, in situ tensile tests are carried out in Transmission Electronic Microscope (TEM) on copper, high entropy alloy and aluminium alloy. We examine the full process of void growth and coalescence of neighboring voids under the view of the TEM. Nanotwins on the ligament between neighboring voids lead to a new coalescence mechanism for copper and high entropy alloy. Necking and shearing coalescence of aluminium alloys are clearly illustrated, which are demonstrated by the samples with manually drilled hole before by SEM (Scanning Electronic Microscope). The quantitative data on the evolution of void geometry are recorded, and are then used to verify the existing coalescence models in the literature. It is found that the McClintock model for void coalescence provides a better prediction than the Brown-Embury model (including the modified Brown-Embury model). A multiscale homogenization framework for in situ experiments can be further used to extract the stress state around the voids, and explaining the importance of stress-state on cavitation/nucleation, growth and coalescence of voids. [ABSTRACT FROM AUTHOR]

Highlights • Micromechanical analyses are performed on a cubic unit cell with a centrally embedded spherical void. • Combined effects of stress triaxiality, Lode parameter and shear stress on the void growth and coalescence are investigated. • At a given triaxiality and Lode parameter, shear stress influences the load carrying capacity of the unit cell, rotation and elongation of the void. • Shear stress promotes the process of void growth and coalescence at a wide range of triaxialities. • Internal shearing dominates the onset of void coalescence at low triaxialities. Abstract Shear stress has been recognized as an important parameter, in addition to stress triaxiality and Lode parameter, that characterizes the stress state and influences the ductile fracture process. Micromechanical analyses are performed on a cubic unit cell with a centrally embedded spherical void in this paper. An effective method for controlling triaxiality, Lode parameter and shear stress component throughout the loading history is provided. The combined normal and shear stress is applied to investigate the effects of shear stress as well as the triaxiality and Lode parameter on the void growth and coalescence as well as material response. The results show that increasing triaxiality, shear stress and Lode parameter decrease the loading carrying capacity of the ductile solid and the rate of void growth at high and intermediate triaxialities. The unit cell model is then used to analyze two different void coalescence mechanisms, including internal necking at high and intermediate triaxialities and shearing at low triaxialities. The increasing weight of shear stress component facilitates the internal necking at high and intermediate triaxialities. At low triaxialities, the shear stress benefits to the void rotation, elongation, coalescence and reducing the distance of ligament between adjacent voids. Comparison of the state variables at the onset of void coalescence between the numerical modeling and the analytical criteria is performed. The results indicate that improvement to the current criteria is needed to obtain more accurate predictions of the onset of void coalescence under combined normal and shear stress over a wide range of triaxialities. [ABSTRACT FROM AUTHOR]

The rolling of an Al-3Mg-0.25Sc alloy at room and cryogenic temperature to 50% and 75% reduction in thickness resulted in the formation of a bimodal microstructure. The grain size distribution based on electron backscattered diffraction (EBSD) analyses showed an enhanced fraction of ultra-fine grains with nearly 100 nm in cryorolled samples whereas; room temperature rolled samples exhibited sub-micron grains with 300 nm. The transmission electron microscopy (TEM) studies revealed the dense dislocation cell structures for cryorolled samples due to the restriction of dynamic recovery. The better forming and fracture limit strains were noted for cryorolled samples compared to room temperature rolled ones in the forming and fracture limit diagrams. A good correlation of formability with void coalescence parameters based on larger void size, lower ligament thickness and lower d -factor were obtained. This indicated better accumulation of plastic deformation and improved formability of cryorolled samples. Further, the reduced aspect ratio (L/W) of void signified delayed fracture behaviour of cryorolled samples compared to room temperature rolled samples and showed better fracture resistance. The improved fracture limit strain in combined forming and fracture limit diagram exhibited by cryorolled samples was consistent with the void coalescence parameters. [ABSTRACT FROM AUTHOR]

A micromorphic single crystal plasticity model is formulated at finite deformations as an extension of Mandel’s classical theory based on a multiplicative decomposition of the deformation gradient. It involves a single microslip degree of freedom in addition to the usual displacement components. Two main variants of the constitutive equations are proposed. The first one relies on a Lagrangian microslip gradient and leads to a Laplace term in the isotropic hardening law. In contrast, the second formulation, based on a generalized strain measure defined with respect to the intermediate configuration, is shown to induce both isotropic and kinematic enhanced hardening. The first formulation is implemented in a 3D finite element code. The model is applied first to strain localization phenomena in a single crystal in tension undergoing single slip. The regularization power of the model is illustrated by mesh-independent simulations of the competition between kink and slip bands. The model is then used to investigate void growth and coalescence in FCC single crystals. Cylindrical and spherical voids are considered successively. The simulations show, for the first time in the case of spherical voids embedded in a single crystal matrix, that smaller voids grow slower than bigger ones, and that the onset of void coalescence is delayed for smaller voids. These results are related to the fact that the field of plastic slip is found to be more diffuse around smaller voids. [ABSTRACT FROM AUTHOR]

A finite element analysis of large 3D microstructures of randomly distributed particles is proposed to investigate the influence of particle debonding and fragmentation on void coalescence. This analysis is possible thanks to recent developments in parallel automatic remeshing techniques tailored for simulations of microstructures undergoing large deformations. These techniques are extended herein to model void nucleation by particle debonding and fragmentation. Micromechanical simulations of a model material with 20% particle volume fraction show that void nucleation leads to an early plastic strain localization micromechanism that favors void coalescence and reduces ductility significantly. [ABSTRACT FROM AUTHOR]

Ductile fracture of metals at room temperature has been studied extensively. Since localization of plastic flow is often viewed as a precursor to ductile fracture, several computational studies analyzing the influence of stress triaxiality and the Lode parameter on the critical strain for onset of localization have been reported. The implications of strain localization in materials containing randomly distributed voids for the mode of failure, that is, internal necking or shear banding have also been discussed. Apart from the influence of stress state, it is also of interest to model the effect of fine-scale microstructural attributes on the mode of failure and, hence, on material's ductility. Therefore, in the present work, the mechanism of ductile fracture of an elastic–plastic solid containing two populations of pre-existing voids is modeled numerically. In the undeformed state, all the voids belonging to each family are assumed to have identical shape and size. Two different periodic spatial arrangements of primary voids are considered such that, in the absence of secondary voids, one of the configurations leads to internal necking whereas the other one exhibits a tendency for shear localization as the mode of coalescence for the larger voids. Small size secondary voids are then introduced explicitly and the role of shape and distribution of these sub-microscopic voids in the mechanism of coalescence and final failure is illustrated under plane strain as well as axisymmetric tension with a superposed hydrostatic stress. Depending on the microstructural attributes of the secondary voids, the mode of primary void coalescence is observed to shift from internal necking to void-sheeting and vice-versa. The implications of this shift in the mode of void coalescence on mesoscopic ductility is examined and a comparison of numerical predictions is made with the available experimental results. • The role of small secondary voids in the mechanism of coalescence is illustrated. • Initial shape and distribution of small voids may shift the mode of coalescence. • The influence of mode of void coalescence on mesoscopic ductility is examined. • A comparison of numerical predictions is made with available experimental results. [ABSTRACT FROM AUTHOR]

Aluminum lithium alloy was rolled at two different temperatures, viz., 28 °C (301 K) and −196 °C (77 K). The thickness of the alloy was reduced by 75 % from its initial thickness (6 mm) in each condition. X-ray diffraction analysis was carried out on all samples to determine the grain size and dislocation density. The cryorolled sample exhibited a finer grain size with higher dislocation density, which was evidenced from micrographs obtained with transmission electron microscopy. Electron backscattered diffraction images revealed the presence of bimodal grain distribution in the rolled samples, in which the cryorolled sample exhibited a larger amount of ultrafine grains. Both tensile and hardness tests were performed on rolled samples. Cryorolled samples showed superior properties when comparing with room temperature rolled sample. Scanning electron microscopic images of fractured samples were used to analyze the void coalescence behavior. The various void coalescence parameters like void size, void area, length to width ratio of void, and ligament thickness were analyzed, and these results were correlated with microstructure, mechanical properties, crystallite size, and dislocation density in all conditions. [ABSTRACT FROM AUTHOR]

Void growth and coalescence, known as main mechanisms of ductile fracture, are investigated for irradiated FCC single crystals. Finite element simulations of voided unit cells are performed with a single crystal plasticity model accounting for strain hardening and softening associated with irradiation-induced defects. The simulations predict a rather brittle overall behavior for the voided irradiated single crystal at high stress triaxiality, with a large amount of local plastic deformation, which is consistent with experimental observations reported in the literature for stainless steels irradiated in fast reactors. Compared with unirradiated single crystals, irradiated crystals exhibit a higher void growth rate leading to an earlier void coalescence, which is caused by a stronger plastic slip localization in the region near the voids. [ABSTRACT FROM AUTHOR]

An accurate prediction of blow-out preventer (BOP) drill pipe shearing is of critical importance in the applications of offshore drilling equipment. To simulate the shear process, a ductile failure criterion is clearly needed. In this paper, we employ an extended Mohr-Coulomb (EMC) criterion, which makes validated predictions for shear fracture by including the stress triaxiality T and Lode parameter L . This criterion has six parameters to be calibrated either by experimental tests or by numerical simulations. Here, we present a micromechanics model to calibrate the undetermined parameters via a void coalescence mechanism, and predict the forces for pipe shearing by finite element analyses. The shear force profile for the case where the EMC criterion parameters are micromechanically determined agrees with that for the case where the parameters are experimentally determined. This paper demonstrates the predictive capability of a micromechanics-based ductile fracture model in conjunction with the EMC criteria for BOP drill pipe shearing. [ABSTRACT FROM AUTHOR]

• In-situ micro-CT experiments were performed on a mild steel sample using X-ray microscopy. • Void evolution behaviors were quantitatively analyzed. • Two stages of void coalescence, local and global, were observed. • Micro ductile fracture mechanism of mild steel based on realistic observation was elucidated. In this paper, in-situ micro-computed tomography (micro-CT) experiments were performed on mild steel samples under monotonic tension using X-ray microscopy. A three-dimensional (3D) visualization model was reconstructed and the characteristics of void evolution under different strain states, such as void distribution, void shape, void growth and void coalescence, were quantitatively analyzed from a 3D perspective. It is found that void growth mainly depends on the stress state, while void coalescence is controlled by the stress state and intervoid spacing. The critical intervoid spacing for void coalescence occurring at the post-necking stage was given. Two stages of void coalescence, local coalescence and global coalescence, were found during void evolution. Local void coalescence was first observed at a strain of 10.02%, well before necking, but has a negligible effect on the overall void evolution. Global void coalescence was developed after the formation of a strain localization band dominated by large coalesced voids in the necking region. The propagation of fine cracks between voids along the strain localization band leads to the formation of macroscopic ductile cracks. Overall, the micro ductile fracture of mild steel is triggered by the combined effects of multiple damage mechanisms rather than independent competition. [ABSTRACT FROM AUTHOR]

• The studied anisotropic effects are induced by combination of crystallographic orientations and void shapes. • Combined anisotropic effects on competition between void coalescence and plastic strain localization are studied. • Plastic strain localization is predicted by bifurcation theory at homogenized scale. • Combined anisotropic effects play an important role in ductile failure initiation. Ductile failure reveals to be an anisotropic phenomenon, for which the proper mechanism has not been clearly addressed yet in the literature. In this paper, the effects of some key anisotropy factors on ductile failure initiation, detected by void coalescence and plastic strain localization, are investigated using unit-cell computations based on crystal plasticity finite element method. The studied anisotropic effects are induced by the combination of initial crystallographic orientations and void shapes. Therefore, single crystals with three different initial orientations and polycrystalline aggregates with three different initial crystallographic textures are respectively considered. A single void with either spherical, prolate or oblate shape is assumed to be preexisting at the center of each unit cell. By contrast to previous analyses in the literature, plastic strain localization is predicted in the present study on the basis of bifurcation theory. To cover a wide range of stress states, the simulations are performed under two macroscopic loading configurations: proportional triaxial stressing, characterized by constant stress triaxiality and Lode parameter, and proportional in-plane straining, specified by constant strain-path ratio. The obtained results show that the combined anisotropic effects play an important role in the occurrence of void coalescence and plastic strain localization, as well as in the competition between them. [ABSTRACT FROM AUTHOR]

The influence of cryorolling on the tensile properties, fracture behaviour (void coalescence) and its limit with respect to strain traixaility (ε m /ε eff ) was investigated on a commercial pure Al (CP-Al), an Al-Mg alloy (AA5083) and an Al-Mg-Si alloy (AA6061). The above sheets were rolled at both room temperature and liquid nitrogen temperatures up to 50% and 75% rolling reductions. The rolled sheets were formed on a double action hydraulic press up to fracture and the fracture strains were measured and correlated with respect to strain triaxiality. The work hardening behaviour and the relative slip distance were also evaluated for the three alloys in all conditions. The work hardening rate was high for AA 5083 due to the effect of solute drag mechanism, which resulted better strain hardening along with strain hardening due to rolling. The void coalescence analysis on fractured samples supported the enhanced fracture resistance tendency of AA5083, based on void size and other void coalescence parameters. However, the AA 6061 and CP-Al showed inferior response to fracture resistance, but AA 6061 was better in fracture resistance compared to CP-Al. In accordance with void coalescence analysis, the AA 5083 showed better fracture limit with respect to strain triaxiality compared to AA 6061 and CP-Al. [ABSTRACT FROM AUTHOR]

The fracture behavior of twin roll cast AZ31B magnesium has been studied in tension. Explored ranges of temperature and strain rate were wide enough to encompass noticeable transitions in fracture characteristics at both macroscopic and microscopic scales. Overall properties include strain rate sensitivity, thermal softening, strain to failure, failure mode, plastic anisotropy and work of fracture. The micromechanisms of damage initiation and accumulation were inferred from tests interrupted at incipient macrocrack formation for key test conditions. The competing roles of voids nucleated on aligned inclusion clusters and at presumed contraction double twins are discussed. [ABSTRACT FROM AUTHOR]

We present a numerical implementation of a model for void coalescence and fracture in nonlinear elasticity. The model is similar to the Ambrosio–Tortorelli regularization of the standard free-discontinuity variational model for quasistatic brittle fracture. The main change is the introduction of a nonlinear polyconvex energy that allows for cavitation. This change requires new analytic and numerical techniques. We propose a numerical method based on alternating directional minimization and a stabilized Crouzeix–Raviart finite element discretization. The method is used in several experiments, including void coalescence, void creation under tensile stress, failure in perfect materials and in materials with hard inclusions. The experimental results show the ability of the model and the numerical method to study different failure mechanisms in rubber-like materials. [ABSTRACT FROM AUTHOR]