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AbstractThis paper provides detailed investigations on void growth and crack-void interaction ahead of a moving crack-tip for a mode I crack in plastically compressible solid. A finite strain elastic-viscoplastic material model with hardening-hardening and hardening-softening-hardening hardness functions is used in the finite element simulation. The plastic compressibility leads to an increased crack opening displacement. The plastic compressibility together with material softening considerably increase stress triaxiality and decrease the void and crack growth. For plastically compressible solids, void growth is more in normal direction to the crack plane and increase in initial void size is accompanied by decrease in the crack and void growth. [ABSTRACT FROM AUTHOR]

Highlights One of the main issues in epoxy‐based composite manufacturing is the formation of porosity derived from moisture absorption during storage and layup due to the high hydrophilicity of epoxy matrices. During the curing process, the presence of moisture and other volatile compounds can initiate the nucleation and growth of voids. In this study, the effect of both the initial water content absorbed in the uncured resin and the pressure on the porosity development in an epoxy resin was investigated. In particular, Kardos' and Ledru's models, aimed at predicting void formation in polymers, were applied to study the effect of different hydrostatic pressures in an epoxy resin during curing up to the gel point, after conditioning it at two different relative humidity levels, 50% and 95%. Subsequently, the porosity of the cured resin samples was quantified through density measurements. Comparative analysis of the microscopy images of cured samples and the predictions of both models revealed an overestimation of the final void sizes by both models, with the Kardos' model exhibiting a higher deviation. Additionally, a finite element model was employed to investigate the conditions leading to void formation, aiming to understand the factors influencing the porosity development and properly set the process parameters during composite manufacturing. Evaluation of the conditions leading to void growth in epoxy resin during curing Moisture sorption in uncured epoxy resin Effect of curing pressure on pore development Finite element analysis for void growth during resin curing [ABSTRACT FROM AUTHOR]

Sheet metals subjected to biaxial plane stress loading typically fail due to localized necking in the thickness direction. Classical plasticity models using a smooth yield surface and the normality flow rule cannot predict localized necking at realistic strain levels when both the in-plane principal strains are tensile. In this paper, a recently developed multi-surface model for porous metal plasticity is used to show that the development of vertices on the yield surface at finite strains due to microscopic void growth, and the resulting deviations from plastic flow normality, can result in realistic predictions for the limit strains under biaxial tensile loadings. The shapes of the forming limit curves predicted using an instability analysis are in qualitative agreement with experiments. The effect of constitutive features such as strain hardening and void nucleation on the predicted ductility are discussed. [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]

Dual phase (DP) steels are amongst the most widely used structural steels for automotive applications. It is essential to understand the damage initiation and damage growth in these high strength steels and further shed light on improving mechanical properties. In this work, two DP800 dual phase grades are investigated, which exhibit identical ultimate tensile stress but significantly different elongation in the uniaxial tensile test. To explain the difference in ductility, particularly described by uniform elongation, we investigate the damage initiation and growth mechanisms by analyzing microstructural changes upon deformation, such as voids, dislocation structures and the grain morphology. Furthermore, ferrite micropillars in pre-strained samples are tested in situ to capture the strain hardening capability of ferrite. We found that the DP steel with harder martensite and softer ferrite exhibits more damage initiation sites after deforming to an identical strain. However, void growth is much slower compared to the DP steel grade with fewer initiation sites. We explain the suppressed void growth by significant strain-hardening of ferrite surrounding the voids, which is observed in the micropillar compression experiments. The improved strain hardening of ferrite originates primarily from the difference in chromium content considering the negligible influence of dispersed particles.

The size dependence of central nanovoid embedded in either monocrystalline or polycrystalline high-entropy-alloy (HEA) films under biaxial tension is investigated in this study. Regarding monocrystalline samples, our attention is paid to the proportional increase in the embedded nanovoid with invariant void volume fraction (VVF). The critical stresses in concerned materials at which dislocations start to emit from void under biaxial tension, in an ascending order, are CoCrFeCuNi < CoCrFeMnNi < metal Ni. Lattice distortion appears to facilitate dislocation emission from the void surface in HEAs, which lowers the critical stress compared with the theoretical model. Regarding polycrystalline samples, the size of both the film and embedded nanovoid is kept invariant, whereas grain size of either periodic hexagonal ones or randomly generated ones is allowed to vary. Apart from the random polycrystalline CoCrFeCuNi, the peak stresses of rest polycrystalline samples obey the reverse Hall–Petch effect. Both monocrystalline and polycrystalline CoCrFeMnNi samples fail due to the coalescence with nucleated secondary voids. For the latter, grain boundaries act as primary sites for secondary void nucleation. Unlike HEAs, polycrystalline Ni samples fail due to intergranular cracking instead of void growth and coalescence. [ABSTRACT FROM AUTHOR]

A micromechanics-based yield criterion is developed to model void coalescence of three-dimensional voids under combined tension and shear. The analysis treats a cylindrical cell containing a coaxial cylindrical cavity, both having an elliptic cross section. Limit analysis is employed to first derive a criterion for homothetic cells. The model is then generalized to incorporate independent void spacing ratios (non-homothetic cells) The model predictions are assessed against finite-element based limit analysis on similar geometries. The effects of relative void spacing and void shape on effective yielding are investigated. In tension, the results indicate an increase in the coalescence stress with increasing in-plane anisotropy for both homothetic and non-homothetic cells. The new criterion is chiefly motivated by modeling shear failure. The extent to which the shear limit load reduces when shearing perpendicular to the largest transverse void dimension, as compared with shearing parallel to it, is discussed. • A yield criterion is developed for a material in a state of void coalescence under tension or shear. • The criterion is obtained using an elliptic cylindrical cell and a concentric elliptical void. • Finite-element based limit analysis is used to assess the new criterion. • The coalescence stress is found to increase with increasing cell distortion in tension. • It is found to decrease with increasing distortion in shear along the minor transverse void axis. [ABSTRACT FROM AUTHOR]

In 1969, Rice and Tracey proposed that the rate of void growth during ductile failure is a strong function of the hydrostatic stress state. Numerous in-situ x-ray computed tomography (XCT) studies demonstrated that the average rate of void growth is well-predicted by modified versions of the Rice-Tracey equation. However, recent in-situ XCT studies of void growth demonstrated that individual voids grow in highly heterogeneous manners in a way that is not predicted by Rice-Tracey or similar models. Model-based studies using crystal plasticity finite element (CP-FE) suggest that local effects of grain orientation play a strong role during void growth, but we lack experimental data to test this hypothesis. The present study leverages recent advances in laboratory-based diffraction contrast tomography (Lab-DCT) and in-situ XCT to systematically examine the effects of grain orientation on void growth experimentally in an Al-2219 alloy. CP-FE modeling was used to assess the local stress states associated with voids and their influence on void growth rates. These data indicate that void growth is not simply controlled by the local hydrostatic stress or stress triaxiality. Additionally, no clear relationship between void growth rates and grain orientation were observed. Instead, void growth rates were highly stochastic in ways that could not be directly linked to the local stress or strain states. The combination of experimental and modeling data suggests that our current assumptions regarding the mechanisms of void growth are flawed and that additional factors, which may include the local dislocation density, affect the rate of void growth. [Display omitted] [ABSTRACT FROM AUTHOR]

Poly-vinylidene fluoride (PVDF) is a semi-crystalline thermoplastic featuring a high chemical resistance, good thermal stability, and high pressure resistance, rendering it attractive for a wide range of engineering applications. This study assesses the influence of temperature, strain rate, and stress triaxiality on the large-strain response of a commercial PVDF copolymer containing poly-ethylene (PE) particles.The thermo-viscoplastic response of the material was investigated at six temperatures ranging between −20 °C and 100°C at a quasi-static strain rate ė of 0.005s−1, and three strain rates ė={0.005,0.1,1.0} s−1 at room temperature. To study the pressure sensitivity of the material, tensile tests using axisymmetric notched tensile specimens with three different notch radii as well as uniaxial compression tests were performed. The mechanical response was assessed in terms of net axial stress and volume strain vs. longitudinal strain, measured using digital image correlation (DIC). To gain insight into the interrelationship between the macroscopic volume strain and void morphology on the microscale, selected cross sections of deformed specimens were imaged employing scanning electron microscopy (SEM).The material exhibited a temperature- and strain-rate-dependent response as well as a pressure-sensitive flow stress. For ambient temperatures up to 60°C, pronounced plastic dilatancy was observed, promoted by increasing the stress triaxiality. The SEM study confirmed that the plastic dilatancy was a result of extensive void nucleation and growth on the microscale. Two sources of void nucleation were identified, namely particle–matrix interface separation as well as cavitation within the matrix material itself. In tests performed at ambient temperatures higher than 80°C, no plastic dilation was observed and no voids or PE particles were identified in the SEM images.Apart from an improved understanding of the material’s mechanical response, this study provides data and insights suitable for the development and calibration of constitutive models, aiding the design of robust and reliable structures using PVDF.

Ductile fracture consists of the nucleation, growth, and coalescence of microvoids observed as dimples on the fracture surface. Typical alloys contain diverse heterogeneities that are stochastically distributed, so that void nucleation is essentially heterogeneous and statistical. The scenarios of homogeneous vs. stochastic heterogeneous void nucleation are systematically compared under simple shear deformation in two limiting cases: (1) a uniform sheet that can be viewed as representing the initial stages of plastic deformation, and (2) the same sheet with an embedded central pore, the latter representing the prevailing situation for which large voids have already nucleated and grown. The homogeneous case provides a reference to which the statistically heterogeneous cases are compared. In the uniform sheet model, heterogeneous void nucleation decreases the porosity accumulation and the stress triaxiality. However, when embedding a geometrical pore at the center of the simulation cell, the averaged triaxiality increases irrespective of the void nucleation heterogeneity. The overall ductile failure process can be thought of as a gradual evolution from the initial stage (1) of a homogeneous sheet with heterogeneous void nucleation towards the final stage of a similar void-containing sheet (2), with the associated evolutions of the stress and porosity fields presented here. [ABSTRACT FROM AUTHOR]

The microvoid growth in an infinite medium under thermal shock was analyzed on the basis of the viscoelastoplastic theory. In the mathematical model of the problem, the stage of purely viscoelastic deformation was taken into account. The direct integration method is used to find the analytical expressions of displacement and stress. The moving interface between the viscoelastic and the viscoplastic zones was involved, and its location was determined by the nonlinear ordinary differential equation with initial condition. As an example, the evolution of void with time for the aluminum alloy material was investigated by numerical computation. The effects of the temperature variation, the heating rate, and the viscosity of material on the void growth were examined. The analysis indicated that the relationship between void growth and temperature load is nonlinear due to the appearance of moving interface. [ABSTRACT FROM AUTHOR]

Void growth plays a significant role in ductile fracture prediction of aluminum. This study proposes 2 deep learning models to address this issue. For voids that retain their ellipsoidal characteristics during growth, the ellipsoidal void Semiaxes Long Short-Term Memory (SLSTM) method is proposed, using the 3 principal features of the ellipsoid to represent the voids. For voids that undergo arbitrary shape changes during growth, an innovative deep learning method called Voronoi tessellation-assisted LSTM (VLSTM) is proposed. This method uses the Voronoi algorithm to standardize data features and employs Principal Component Analysis (PCA) to perform data compression before neural network training. This new method combines the Voronoi algorithm, LSTM neural networks, and PCA algorithms, and is termed as VLSTM-PCA. In this study the deep learning-based SLSTM surrogate models and VLSTM-PCA surrogate models run approximately 514 and 537 times faster than ABAQUS finite element simulations, significantly enhancing efficiency while maintaining high prediction accuracy. Finally, growth patterns of ellipsoidal voids under different stress triaxialities are analyzed. • An investigation of voids growth at different stress triaxialities. • The SLSTM surrogate model was proposed for ellipsoidal voids. • The VLSTM-PCA surrogate model was proposed for voids with arbitrary shape changes. • Surrogate models improve void growth analysis efficiency over ABAQUS finite element simulations. [ABSTRACT FROM AUTHOR]

Initiation, growth, and coalescence of microscopic voids are precursors to failure in amorphous glassy polymers. Hence, void growth analysis is important for understanding the failure in these polymers. Under quasi-static conditions, void growth in polymers is well understood; however, a similar analysis under dynamic conditions is not available in the literature. In the present work, we analyse the effect of loading rate on the void growth behaviour using large deformation finite element simulations. An axisymmetric unit cell model of a spherical void is considered for the analysis. The void is subjected to a range of strain rates (1 0 − 3 s − 1 to 1 0 5 s − 1 ). Remote triaxialities equivalent to uniaxial loading, biaxial loading, and higher triaxiality conditions are considered. Remote mean stresses, which are important from the perspective of void growth, have been characterized as a function of void size, strain rate, and triaxiality. Results show that the critical mean stresses required for unstable void growth increase with increasing triaxiality. Higher loading rates further amplify the critical mean stresses, and the amplification depends upon the material rate sensitivity of polymers. The void growth mechanism does not change because of material rate-sensitivity. During void growth, inertia effects are found to be significant after a strain rate of 1 0 3 s − 1 . It is found that inertia increases with increasing triaxiality and increasing void size. It stabilizes the void growth and makes them expand in a more spherical shape, even at low triaxialities. • Critical mean stresses are characterized w.r.t. strain rate, triaxiality, and void size • Critical mean stresses increase with increasing remote loading rate and triaxiality • Inertia becomes prominent for void growth at strain rates higher than 1 0 3 s − 1 • Inertia increases with increasing triaxiality and void size and stabilizes the growth • Modified constitutive model to capture the correct yield stresses at high strain rates [ABSTRACT FROM AUTHOR]

This paper aims to study the effect of initial void shape on void growth of structural steels, which is a critical stage for ductile fracture of steel. Typical void shapes of structural steels were characterized by an in situ high-resolution micro X-ray computed tomography (μXCT) technique, including spherical, elliptical, and cylindrical voids. Then, a micromechanical representative volume element (RVE) model containing a single void was established with periodic boundary conditions. On this basis, impacts of the void shape on void growth were analyzed through Python-based parametric modeling in ABAQUS with respect to the stress triaxiality, aspect ratio, orientation, and initial void volume fraction, respectively. The results indicate a significant effect of the void shape on void growth under low stress triaxialities, and the effect tends to decrease with the increase of the stress triaxiality. Under low stress triaxialities (e.g., 0.33), there is a remarkable void growth difference between cylindrical and elliptical voids with the same initial aspect ratio, and this difference tends to disappear when the stress triaxiality increases to a high value, e.g., 0.8. Compared with the void orientation aligned in a coordinate axis, the off-axis one presents a smaller void growth difference induced by the void shape when the stress triaxiality is low, but reverse under high stress triaxialities. Finally, accurate and simplified formulas were proposed to consider the effects of void shape on void growth at the mesoscale. [ABSTRACT FROM AUTHOR]

A study has been performed using a crystal plasticity based finite element method to understand the effect of various stress states and crystal orientations with respect to loading direction for FCC single crystals in both hydrogenated and nonhydrogenated environment. Simulations have been performed for a variety of stress triaxilaities, Lode parameters, crystal orientations and hydrogen concentrations. It has been observed that crystal orientation has a varied effect on the influence of hydrogen on plastic deformation and void growth. Hydrogen in trap distribution at various stages of the deformation process was also found to be influenced by crystal orientation. From analyses performed, an analytical relationship between normalised void fraction and equivalent strain has been derived. [ABSTRACT FROM AUTHOR]

The modeling of ductile damage in engineering metallic materials is an essential step in a design process. In this paper, a mixed finite element formulation is developed to predict ductile damage in thermoviscoplastic porous metals. The novel aspect of the model is the enhancement of Gurson's plasticity formulation with a void shearing mechanism capable describing thermoviscoplastic flow stress and thermal diffusion. Thus, the model accounts for void growth, nucleation and coalescence; strain and strain-rate hardening; thermal softening; heating by plastic work; thermal diffusion; localized shear banding; and material strength degradation. Associative plasticity and small strains are assumed. Both strong and weak forms describing the material complex behavior are presented. Time discretization by means of backward Euler and Newmark- β schemes is employed together with Galerkin finite element approximations, leading to a fully discrete set of nonlinear coupled algebraic equations. Two dynamic fracture problems involving ductile failure of plates under a plane strain assumption are numerically analyzed. The effects of the strain rate, thermal diffusion and void shearing mechanism are investigated in detail and shown to be significant. Results show that the present approach can reproduce plastically induced damage, localized shear banding, heating, porosity-induced stress degradation and crack-type damage evolution. The numerical performance is also reported in order to illustrate the convergence of the method. [ABSTRACT FROM AUTHOR]

The present study deals with a numerical design strategy of a novel class of three-dimensional random Voronoi-type geometries, called M-Voronoi. These materials comprise random, non-quadratic convex void shapes and non-uniform intervoid ligament thicknesses, and can span high-to-low relative densities. The starting point for their generation is a random adsorption algorithm (RSA) construction with spherical voids embedded in an incompressible, nonlinear elastic matrix phase. The initial RSA geometry is subjected to large elastic volume changes by prescribing Dirichlet boundary conditions. Due to the incompressibility of the matrix phase, the externally imposed volume changes lead to significant void growth. The numerical growth process may be stopped at any desired porosity. The proposed M-Voronoi process is general and allows the formation of isotropic (or anisotropic) designs. As a byproduct of the developed approach, we also present a novel remeshing technique allowing to read arbitrary geometries of one or multiple phases. The elasto-plastic properties of the M-Voronoi porous materials are numerically investigated at small strains as well as large compressive and shear loads. Their response is assessed by comparison with other well-known random and periodic porous geometries such as polydisperse porous materials with spherical voids (RSA), classical TPMS Gyroid geometries and random Spinodoid topologies. The results show that M-Voronoi and RSA (with spherical voids) geometries exhibit the stiffest elastic and highest flow stress response compared to the other two geometries. This study shows unambiguously that randomness may or may not lead to enhanced mechanical response such as higher stiffness or flow stress. • 3D mechanically grown M-Voronoi geometries. • Extreme void growth using nonlinear incompressible elasticity. • Enhanced elasto-plastic response via random void shape and intervoid ligament size. • Closed-cell geometries generated seamlessly using mechanical loads. [ABSTRACT FROM AUTHOR]

Randomness in the void distribution within a ductile metal complicates quantitative modeling of damage following the void growth to coalescence failure process. Though the sequence of micro-mechanisms leading to ductile failure is known from unit cell models, often based on assumptions of a regular distribution of voids, the effect of randomness remains a challenge. In the present work, mesoscale unit cell models, each containing an ensemble of four voids of equal size that are randomly distributed, are used to find statistical effects on the yield surface of the homogenized material. A yield locus is found based on a mean yield surface and a standard deviation of yield points obtained from 15 realizations of the four-void unit cells. It is found that the classical GTN model very closely agrees with the mean of the yield points extracted from the unit cell calculations with random void distributions, while the standard deviation S varies with the imposed stress state. It is shown that the standard deviation is nearly zero for stress triaxialities T ≤ 1 / 3 , while it rapidly increases for triaxialities above T ≈ 1 , reaching maximum values of about S / σ 0 ≈ 0. 1 at T ≈ 4. At even higher triaxialities it decreases slightly. The results indicate that the dependence of the standard deviation on the stress state follows from variations in the deformation mechanism since a well-correlated variation is found for the volume fraction of the unit cell that deforms plastically at yield. Thus, the random void distribution activates different complex localization mechanisms at high stress triaxialities that differ from the ligament thinning mechanism forming the basis for the classical GTN model. A method for introducing the effect of randomness into the GTN continuum model is presented, and an excellent comparison to the unit cell yield locus is achieved. • Mesoscale unit cells are studied to find statistical effects on macroscopic properties. • 15 realizations of random unit cells with four equally sized voids are investigated. • A mean yield surface and a standard deviation of yield points are obtained. • The standard deviation varies with the imposed stress triaxiality. • A method for including statistical effects in the GTN continuum model is presented. [ABSTRACT FROM AUTHOR]

The micromechanics of ductile failure is revisited using the voided cell model. Emphasis is laid on comparing shearing stress states with axisymmetric states. The unit cell is subjected to proportional loading and fully periodic boundary conditions. The progression of elastic unloading in the unit cell is analyzed, leading to a definition of unhomogeneous yielding. Overall strain localization is determined by evaluating "on the fly" the tangent operator using a perturbation method. The connection between unhomogeneous yielding and strain localization is thus thoroughly investigated. Other potentially critical strain measures are introduced and their relevance to failure by void coalescence or strain localization is discussed. The effects of initial porosity and strain hardening in modulating the relative ductility under tension versus shear are further examined. • Voided unit cell calculations are carried out under fully periodic boundary conditions. • Unhomogeneous yielding is defined based on the percolation of elastically unloaded domains. • Strain localization is analyzed using a perturbation method. • In all cases, strain localization is found to occur after the onset of unhomogeneous yielding. • The common trend that axisymmetric stress states are "more ductile" than shearing states is found to break down. [ABSTRACT FROM AUTHOR]

High-throughput (several thousand) calculations have been carried out to investigate the yield behavior of porous materials with randomly distributed pores, porosity levels over four orders of magnitude and up to a hundred pores per simulation box. To this end, a Galerkin based fast Fourier transform (FFT) formulation was enhanced to deal with high phase contrast materials. In addition, GPU parallelization was employed in solving the governing equation for strain fluctuations using a Krylov iterative solver. Emphasis is laid on the conditions under which percolation of plastically non-deforming zones through the porous network emerge, a regime termed unhomogeneous yielding. By way of contrast, the regime where the plastic strain fluctuations (associated with the heterogeneous void-matrix aggregate) fall below the percolation threshold is defined as homogeneous yielding. We find that nonuniform pore distributions only affect unhomogeneous yielding and have a universal softening effect. The extent of this distribution softening is analyzed as a function of porosity, cell size and number of realizations. Whether the uncovered universal distribution softening has direct implications on failure resistance of porous materials is discussed. [ABSTRACT FROM AUTHOR]

[Display omitted] • The dual phase steel initiating more damage sites exhibits longer uniform elongation, as the damage evolution is suppressed. • The suppression of damage growth primarily benefits from higher strain hardening capacity of ferrite in this steel grade. • The improved strain hardening of ferrite originates from alloy elements Cr and Ti. • Strain hardening capacity of ferrite is key to tailor the tradeoff of strength and ductility in dual phase steels. Dual phase (DP) steels are amongst the most widely used structural steels for automotive applications. It is essential to understand the damage initiation and damage growth in these high strength steels and further shed light on improving mechanical properties. In this work, two DP800 dual phase grades are investigated, which exhibit identical ultimate tensile stress but significantly different elongation in the uniaxial tensile test. To explain the difference in ductility, particularly described by uniform elongation, we investigate the damage initiation and growth mechanisms by analyzing microstructural changes upon deformation, such as voids, dislocation structures and the grain morphology. Furthermore, ferrite micropillars in pre-strained samples are tested in situ to capture the strain hardening capability of ferrite. We found that the DP steel with harder martensite and softer ferrite exhibits more damage initiation sites after deforming to an identical strain. However, void growth is much slower compared to the DP steel grade with fewer initiation sites. We explain the suppressed void growth by significant strain-hardening of ferrite surrounding the voids, which is observed in the micropillar compression experiments. The improved strain hardening of ferrite originates primarily from the difference in chromium content considering the negligible influence of dispersed particles. [ABSTRACT FROM AUTHOR]

Temperature- and irradiation-assisted failure mechanisms in miscible phase boundaries are clarified via atomistic calculations. We first establish the temperature-dependent brittle-to-ductile transition in U–Zr miscible phase boundaries. Our results confirm that these boundaries are mostly brittle at low temperatures and ductile at elevated temperatures. We then investigate the changes induced by irradiation on the fracture mechanisms in such phase boundaries. The irradiation-induced defect accumulation follows a multi-stage process that starts with the accumulation of isolated small dislocation loops before transitioning to the saturation and growth of larger dislocation loops and end up with a reorganization into forest dislocations. The accumulation of loops is the primary feature to participate in the delineation between brittle and ductile interfacial fracture in irradiated phase boundaries. At low damage levels, radiation defect interactions with the crack tip are limited and U–Zr miscible boundaries fail through the emission of dislocations ahead of the crack tip followed by brittle cleavage in agreement with the classical Griffith's criterion for crack stability. At higher damage levels, the failure mode transitions from brittle crack growth to ductile void growth. In this case, the microcrack tip is blunted by the high density of pre-existing, radiation-induced defects in the vicinity of the crack. This interaction leads to the development and growth of a cavity at the interface as opposed to interfacial cleavage. [ABSTRACT FROM AUTHOR]

Void growth and morphology evolution are studied using a 3D representative volume element with a spherical void embedded in an FCC single crystal. The plastic flow contours are studied to determine the scenarios leading to fully plastic flow and plastic flow with elastic region. Further, the effect of anisotropy on void growth is studied through three initial crystallographic orientations (ICOs) [100], [110], & [111] with respect to loading direction. Void growth and macroscopic stress variations with applied strain are obtained from our simulations. It is observed that the peak stress corresponds to rapid void growth initiation. The peak stress is found to be dependent on void volume fraction and ICO. Furthermore, an additional geometrical parameter, diagonal distortions (D d i) is introduced to classify the non-spheroidal void shapes observed in deformed anisotropic crystal. [ABSTRACT FROM AUTHOR]

Void growth and morphology evolution in fcc bi-crystals are investigated using crystal plasticity finite element method. For that purpose, representative volume element of bi-crystals with a void at the grain boundary are considered in the analysis. Grain boundary is assumed initially perpendicular/coaxial with the straight sides of the cell. Fully periodic boundary conditions are prescribed in the representative volume element and macroscopic stress triaxiality and Lode parameter are kept constant during the whole deformation process. Three different pairs of crystal orientations characterized as hard-hard, soft-soft and soft-hard have been employed for modelling the mechanical response of the bi-crystal. Simulations are performed to study the implications of triaxiality, Lode parameter and crystallographic orientation on slip mechanism, hardening and hence void evolution. The impact of void presence and its growth on the heterogeneity of lattice rotation and resulting grain fragmentation in neighbouring areas is also analysed and discussed. [ABSTRACT FROM AUTHOR]

This work presents a damage evolution framework including liquid-assisted healing. The model incorporates contributions from void size, void pressure, surface tension and liquid pressure. Experimental motivation for the damage-healing model is provided with in-situ melting experiments, where the evolution of the void distribution under monotonic tension is illustrated. The damage evolution is based on nucleation and growth of voids, which are modeled in a unified creep and plasticity framework. The proposed damage formulation introduces a void collective, which computes the void distribution in the material and allows to describe void collapse using the Rayleigh-Plesset equation. The necessary conditions for healing are discussed with use of model results. Particularly, the role of external load during healing, the dependence on liquid viscosity and surface tension are investigated. [ABSTRACT FROM AUTHOR]

Under shock loading, the spall strength of nanocrystals exhibits intricate grain-size effects due to the presence of abundant grain boundary and dislocation activities. However, the influence of size on spall toughness and void evolution has been largely overlooked. This study employs molecular dynamics simulations to investigate the damage accumulation characteristics of nanocrystalline aluminum across various grain sizes. Unlike the trade-off observed in quasi-static loading conditions, our study reveals a consistency in which grain size governs both nanovoid nucleation and coalescence, yielding a novel spall strength-toughness synergy. These insights highlight grain sizes that are particularly susceptible to spall fracture, offering a crucial understanding of nanocrystal failure mechanisms in extreme environments.

A crystal plasticity-based finite element study is performed to understand hydrogen effects on void growth in single crystals of austenitic stainless steel. The model assumes plastic deformation is driven primarily by dislocation motion and captures the influence of hydrogen. Hydrogen effects are incorporated by assuming agreement with the hydrogen enhanced localised plasticity (HELP) mechanism. Despite experimental evidence, hydrogen effect on face centred cubic (FCC) crystals has hitherto not been considered in a numerical void growth model for a wide range of stress states. For the first time, the influence of hydrogen on void growth for different Lode parameters at single crystalline levels is investigated for a range of stress triaxialities in FCC crystals. Hydrogen was found to increase equivalent stresses and hardening responses for various stress triaxialities and Lode parameters. Hydrogen also induces higher void growth response at different stress states, and this was more pronounced at high stress triaxialities. Image 1 • Crystal plasticity study of hydrogen effect on face centred cubic crystals. • Model is based on the hydrogen enhanced localised plasticity theory. • Model accounts for slow diffusion of hydrogen in face centred cubic crystals. • Hydrogen initially inhibits void growth but this changes with void shape. • Hydrogen influence is affected by void shape and strain localisation. [ABSTRACT FROM AUTHOR]

Analyses in the present study focus on understanding the evolution of the tungsten microstructure under He/D irradiation. A fractal dimension analysis was utilized to characterize the structural pattern of the microstructure irradiated by both low (10–80 eV) and high (8–30 keV) irradiation energy. All examined W microstructures show a direct correlation between the fractal dimension and irradiation energy. Analyses establish an empirical relation expressing a change in the microstructure as a function of the irradiation energy based on the changes in the fractal dimension of the microstructures. The proposed relation was implemented in the phase-field model formulation with an account of the interfacial energy induced by the crystallographic mismatch between grains under irradiation. The current phase-field model captures the evolution of the void under irradiation, including nucleation and the growth of voids, and sink efficiency for vacancy annihilation in the vicinity of grain boundaries.

Ductile rupture of 13% Cr-4% Ni martensitic stainless steels was examined during tension testing in order to better understand the role of second phase particles in these materials. SEM fracture surface examinations revealed that micro-voids were initiated from inclusions, and these inclusions were characterized from metallographic polished sections. Effect of stress triaxiality on the growth and impingement of the micro-voids were examined using a modified model of Rice and Tracey. In the case of the cast and wrought versions, the true fracture strains predicted for the measured stress triaxiality values were in a good agreement with the measured ones. For the weld metals, only the contribution of the micro-void growth cannot explain the experimental results, and it shows that the matrix properties such as austenite content and hardness of martensite play a significant contribution. The magnitude of the final stress triaxiality ratio measured after rupture was also related to the inclusion characteristics. [ABSTRACT FROM AUTHOR]

Electromigration (EM) causes intermetallic and void growth that decreases the reliability and lifetime of solder joints. As a diffusion-controlled process, EM is highly dependent on the fastest diffusion pathways in a structure. In anisotropic β-tetragonal Sn those pathways are along high angle grain boundaries and along the c-axis of the Sn grains. A bicrystal sample with two major grain orientations and two major grain boundary types was EM tested for 100 h. EM was interrupted at intervals for x-ray microtomography to reveal the 3D evolution of intermetallic compounds (IMCs) and voids within the joint. Quantitative IMC growth along high angle grain boundaries and twins was captured for the first time and related to the effective Cu diffusivity of multiple grains. Using a correlative approach that combined scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) mapping, IMC growth and morphology were linked to the evolution of the Sn grain structure. Unusual void shrinkage and void splitting behavior were connected to uneven cathode interface consumption and thermal compression. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Ductile rupture or tearing usually involves structural degradation from the nucleation and growth of voids and their coalescence into cracks. Although some materials contain preexisting pores, the first step in failure is often the formation of voids. Because this step can govern both the failure strain and the fracture mechanism, it is critical to understand the mechanisms of void nucleation and the enabling microstructural configurations which give rise to nucleation. To understand the role of dislocations during void nucleation, the present study presents ex-situ cross-sectional observations of interrupted deformation experiments revealing incipient, subsurface voids in a copper material containing copper oxide inclusions. The local microstructural state was evaluated using electron backscatter diffraction (EBSD), electron channeling contrast (ECC), transmission electron microscopy (TEM), and transmission kikuchi diffraction (TKD). Surprisingly, before substantial growth and coalescence had occurred, the deformation process had resulted in the nucleation of a high density of nanoscale (≈50 nm) voids in the deeply deformed neck region where strains were on the order of 1.5. Such a proliferation of nucleation sites immediately suggests that the rupture process is limited by void growth, not nucleation. With regard to void growth, analysis of more than 20 microscale voids suggests that dislocation boundaries facilitate the growth process. The present observations call into question prior assumptions on the role of dislocation pile-ups and provide new context for the formulation of revised ductile rupture models. While the focus of this study is on damage accumulation in a highly ductile metal containing small, well-dispersed particles, these results are also applicable to understanding void nucleation in engineering alloys. Image, graphical abstract [ABSTRACT FROM AUTHOR]

High strength titanium alloys are generally used in widespread applications ranging over, but not limited to biomedical, aerospace, automotive, marine, oil and gas, and energy. Besides other manufacturing processes, forming is one of the common manufacturing process used to produce components out of these alloys. Forming processes generally involve significant plastic deformation of material under complex multiaxial loading conditions. Titanium alloys undergo considerable plastic deformation before failure while later is governed by the mechanisms of void nucleation, growth and coalescence. A number of titanium alloys used for high strength applications are multiphase alloys having α and β phases. It has been reported in the past that the voids tend to nucleate on the phase boundaries. This study is focused on understanding the growth of the nucleated voids at two selected locations in a dual phase titanium alloy (Ti-10V-2Fe-3Al); globular α phase (hexagonal closed pack, HCP) and at the interface of lamellar α and β phases (α - HCP and β – body centred cubic, BCC). This is one of the very few 3D representative volume element (RVE) study of void growth in single crystal titanium (HCP), carried out using crystal plasticity finite element modelling (CPFEM) at higher triaxialities (ranging 1/3-3) and the first one on the interface of bicrystals with different crystal symmetry. The effects of initial porosity, crystal orientation and the Lode parameter on void growth in single crystal (α -HCP) has been studied and it is found that they affects void growth considerably. An effort has been made to explain the physics behind it. In the second part, growth in a void at the interface of two distinct single crystals (α - HCP and β –BCC) was studied. The effects of Burgers orientation relationship (BOR) variant of the two phases, initial porosity, and phase boundary inclination (PBI) on void growth is investigated. It is found that the PBI has a very strong impact on the void growth. The effect of initial porosity is similar to the void growth in single crystals. Choice of BOR variant affected the void growth in moderate triaxialities. • A 3D CPFEM RVE void growth study in a dual phase Ti alloy is presented. • Two cases of nucleated voids in α-β Ti alloys are studied; α and α-β phase boundary. • A very first void growth study at interface of dissimilar α-β crystals is presented. • Initial porosity, loading & crystal orientation have strong effect on void growth. • Phase boundary inclination was found to greatly influence void growth in bicrystal. [ABSTRACT FROM AUTHOR]