Void Evolution Research Articles

In situ study on heavy ion irradiation induced microstructure evolution in single crystal Cu with nanovoids at elevated temperature

Understanding the response of nanovoids to irradiation damage advances our capability to design radiation tolerant materials. Recent in situ studies reveal the shrinkage of hexagon-shaped nanovoids in (110) textured Cu. However, the evolution of voids with irregular geometries under irradiation is less well understood. Here, in situ Kr ion irradiation was performed at 100 °C on single-crystal Cu (112) that possesses nanovoids with high aspect ratio. In situ studies show these elongated voids fragment into smaller voids and shrink gradually with increasing dose. Phase field simulations confirm that fragmentation of the void is governed by the competing kinetics between atoms diffusing toward and away from the elongated nanovoid. Post irradiation analysis reveals the formation of high-density defect clusters.

Experimental Study on the Evolution Law of Coal Mine Underground Reservoir Water Storage Space under the Disturbance and Water—Rock Interaction Effect

The void of the cracked rock mass of the goaf is the main water storage space of underground reservoirs, which is in a time-space dynamic evolution process. Before the formation of the underground reservoir, the water storage space was primarily affected by disturbances. After the safe operation of the coal mine underground reservoir, the water level of the mine rises and falls repeatedly and the water storage space is affected by the water-rock interaction. To study the void evolution law of a cracked rock mass under mining disturbance and the compaction and void deformation characteristics of caving gangue under the effect of the water-rock interaction, a simulation test of a coal mine underground reservoir is conducted. Furthermore, the rupture motion law and movement deformation characteristics of the overburden during coal mining are analyzed. The digital image method and fractal theory are introduced to describe the fractal characteristics of the rock mass void of the caving zone, fracture zone, and entire goaf during the mining process. Five prototype gangue samples with different immersion times are prepared with the same grain size grading as the similar model caving gangue. The influence of the immersion times on the compaction characteristics and evolution law of the void rate of the gangue are also studied. Based on the parameter fitting method, the stress–strain relationship equation of the gangue sample and void rate-stress relationship equation of the cylindrical gangue sample, considering the influence of the immersion times, are constructed. The results show that the overburden of the model is of a “two zone” structure and the entire structure moves and sinks asymmetrically in a “∩” shape. As the advancing distance of the working face increased, the fractal dimensions of the rock mass void of the caving zone and entire goaf increased logarithmically, and the fractal dimension of the rock mass void of the fracture zone first increased rapidly (60–80 cm) and then decreased linearly (80–200 cm). As the immersion time increased, the saturated moisture content and density of the gangue samples increased logarithmically and exponentially, respectively. Under the same stress, the strain of the gangue sample increased gradually, and the void rate decreased gradually (except for the initial loading).

The void formation behaviors in working solid-state Li metal batteries.

The fundamental understanding of the elusive evolution behavior of the buried solid-solid interfaces is the major barrier to exploring solid-state electrochemical devices. Here, we uncover the interfacial void evolution principles in solid-state batteries, build a solid-state void nucleation and growth model, and make an analogy with the bubble formation in liquid phases. In solid-state lithium metal batteries, the lithium stripping-induced interfacial void formation determines the morphological instabilities that result in battery failure. The void-induced contact loss processes are quantified in a phase diagram under wide current densities ranging from 1.0 to 10.0 milliamperes per square centimeter by rational electrochemistry calculations. The in situ-visualized morphological evolutions reveal the microscopic features of void defects under different stripping circumstances. The electrochemical-morphological relationship helps to elucidate the current density- and areal capacity-dependent void nucleation and growth mechanisms, which affords fresh insights on understanding and designing solid-solid interfaces for advanced solid-state batteries.

Evolution of Cosmic Voids in the Schrödinger-Poisson Formalism

We investigate the evolution of cosmic voids in the Schrodinger Poisson formalism, finding wave mechanical solutions for the dynamics in a standard cosmological background with appropriate boundary conditions. We compare the results in this model to those obtained using the Zel'dovich approximation. We discuss the advantages of studying voids in general and the advantages of the Schrodinger Poisson description over other approaches. In particular, emphasizing the utility of the free particle approximation. We also discuss a dimensionless number, similar to the Reynolds number, for this system which allows our void solutions to be scaled to systems of different physical dimensions.

Unraveling the plasticity performance and melting in single crystal tantalum damaged by shock compression

In this work, non-equilibrium molecular dynamics simulations are conducted to investigate the melting and void evolution behind a shock-wave front in body-centered cubic (BCC)-based tantalum under hyper-velocity impact loading. The calculated radial distribution function combined with Simon melting curve are employed to determine the melting behavior. It is discovered that the classical spallation occurs when the particle velocity (Up) is less than 1.7 km/s, while the material is completely melted at Up ≥ 2.0 km/s. In other cases, the material is partially melted with a solid-liquid mixed state. Also, the dislocation and phase transformation are studied to demonstrate the role of plasticity on ductile damage. Interestingly, it is found that there is a strong sensitivity of plasticity performance to melting during cavitation. In the classical spallation, the degradation of dislocation survival space is attributed to void growth and coalescence, thereby leading to dislocation annihilation. For the micro-spallation, several dislocation lines are absorbed by surrounding voids and the remaining dislocation lines are blocked on void surfaces. In contrast, the void nucleation promotes the phase transition from BCC to face-centered cubic (FCC) crystal structure just for the classical spallation. Furthermore, the BCC phase is eventually restored in this case, but there is no similar phenomenon observed when the material is melted.

Fatigue damage evolution in asphalt mixture based on X-ray CT images

The fatigue damage of asphalt pavement occurs and develops under repeated vehicle loads, and its macro manifestation is the deterioration of mechanical properties and serviceability. In order to explore the internal cause of fatigue damage of asphalt mixtures, this paper proposed a method to obtain the internal section images of asphalt mixtures in different fatigue damage stages based on the X-ray CT (Computed Tomography) scanning technique and indirect tensile fatigue test. The fatigue damage evolutions in two different gradation types of AC and OGFC asphalt mixture were studied. The results show that the difference in gradation type causes different initial air void shapes, size and distribution, which result in different formation modes of the main cracks and fatigue damage resistance of asphalt mixture. The evolution of air voids during fatigue loading can be divided into three stages: compression, steady growth and rapid expansion. The macro fatigue damage presents an excellent linear relation (R-values > 0.98) with the internal structural damage.

(Invited) Computational Modeling of Void Formation Mechanism at the Lithium/Solid-Electrolyte Interface

Stabilization of the lithium deposition by the introduction of solid electrolytes was attempted in the past with partial success. However, electrochemical dissolution of lithium from the metal electrode to the solid electrolyte introduces unique challenges, such as, formation of micron sized voids at the electrode/electrolyte interface. These interfacial pores form due to stripping of lithium at a rate higher than they can actually be replenished from the bulk. Presence of these porous domains will minimize the electrochemically active surface area, dramatically increase the interfacial resistance, and effectively render the cell unusable. In the present research, a phase field based computational framework is developed that can capture the evolution of these micron sized voids at the lithium/solid-electrolyte interface during the electrochemical dissolution of lithium. Importance of lithium surface diffusion in determining the pore morphology is introduced for the first time. Impact of applied current density, external pressure, and operating temperature on the dynamics of void evolution is investigated in detail. Figure 1

Molecular dynamics simulations of tensile response for FeNiCrCoCu high-entropy alloy with voids

While preparing and using high entropy alloys (HEAs), many defects such as voids are inevitably formed. The effects of voids on the mechanical properties of FeNiCrCoCu HEAs are investigated using molecular dynamics simulations. The evolution of voids is examined by using models with one or two voids considering different void sizes, applied strain rates, and temperatures. The results demonstrate that the existence of the voids does influence the mechanical properties of HEAs. The tensile strength of the single-void model is higher than that of double-void model. The stress–strain curves demonstrate that a larger initial void size could reduce the tensile strength. During the tensile deformation, all dislocation emission occurs initially from the surface of the void. However, it occurs between the two voids in double-void models, which causes the deformation of the voids. With temperature increases, the tensile strength decreases. Under various strain rates, the tensile strength slightly rises at strain rates ranging from 108to 109 s−1. However, it significantly increases at a strain rate of 109 to 1010 s−1.

A phase field electro-chemo-mechanical formulation for predicting void evolution at the Li–electrolyte interface in all-solid-state batteries

We present a mechanistic theory for predicting void evolution in the Li metal electrode during the charge and discharge of all-solid-state battery cells. A phase field formulation is developed to model vacancy annihilation and nucleation, and to enable the tracking of the void-Li metal interface. This is coupled with a viscoplastic description of Li deformation, to capture creep effects, and a mass transfer formulation accounting for substitutional (bulk and surface) Li diffusion and current-driven flux. Moreover, we incorporate the interaction between the electrode and the solid electrolyte, resolving the coupled electro-chemical-mechanical problem in both domains. This enables predicting the electrolyte current distribution and thus the emergence of local current 'hot spots', which act as precursors for dendrite formation and cell death. The theoretical framework is numerically implemented, and single and multiple void case studies are carried out to predict the evolution of voids and current hot spots as a function of the applied pressure, material properties and charge (magnitude and cycle history). For both plating and stripping, insight is gained into the interplay between bulk diffusion, Li dissolution and deposition, creep, and the nucleation and annihilation of vacancies. The model is shown to capture the main experimental observations, including not only key features of electrolyte current and void morphology but also the sensitivity to the applied current, the role of pressure in increasing the electrode-electrolyte contact area, and the dominance of creep over vacancy diffusion.

Phase field microelasticity accommodating large deformation and modeling of voids evolution under creep

The phase-field microelasticity theory of Khachaturyan has been widely applied in materials science that is based on the small strain assumption. Here we develop an incremental realization of inelastic deformation (IRID) algorithm to deal with finite/large deformation with yet small elastic strain. A large deformation process is decomposed into a sequence of small deformation processes with intervals. At each interval the grids are stretched to accommodate the average inelastic deformation and advection/rotation operations are performed to account for the heterogeneous inelastic deformation. It is shown that Kachaturyan’s Fourier-transform based solutions can be adapted to the stretched grids. The IRID algorithm is compared against literature results regarding growth of a single void under remote stress of different triaxialities. Based on the IRID algorithm a phase-field model is developed that incorporates material microstructure, plasticity, multicomponent diffusion, and surface and grain boundary diffusion. The void growth kinetics and morphology evolution under coupling of diffusion and plasticity under creep are studied and the results show that coupling of the two mechanisms can significantly accelerate growth and coalescence of multiple voids at grain boundaries.

Molecular dynamics study on spallation fracture in single crystal and nanocrystalline tin

Spallation fracture in ductile metals with low melting points is an important scientific concern of dynamic fracture. Classical spallation and micro-spallation simulations of single crystal (SC) and nanocrystalline (NC) tin were carried out using non-equilibrium molecular dynamics at shock pressures of 13.5–61.0 GPa. The shock wave velocity had no effect on the waveform evolution in the SC Sn but not in the NC Sn. The front width of the stress wave in the classical spallation of the NC Sn was predominantly affected by grain boundary sliding. The atomic trajectory technique was first introduced to reproduce the evolutionary processes of void growth and coalescence quite effectively. In the classical spallation, the differences in void evolution behavior of SC and NC Sn were mainly reflected in nucleation position, spatial distribution, and growth zone, while their evolutionary behaviors were shared in the micro-spallation. In the NC model, for the classic spallation, voids mostly nucleated at grain boundaries and grew along grain boundaries, resulting in intergranular fractures; for the micro-spallation, voids nucleated at the grain boundary and inside the grain, resulting in intergranular, intragranular, and transgranular fractures. Furthermore, the void volume fraction followed the bilinear rise at the early nucleation and growth stages, and the critical transition point fundamentally signified the initiation of void nucleation to growth.

Evolution of interfacial voids in Cu-to-Cu joints

In this study, the Cu joints were fabricated by Cu pads with the highly (111)-oriented nano-twinned structure at 250 °C. We reported a new characterization approach by plan-view images of focused ion beam (FIB) to observe the evolution of interfacial voids in the Cu joints under annealing. The distribution function of interfacial voids and the kinetics of void evolution were then studied and analyzed. The evolution of interfacial voids was proposed to occur at different stages, which were dominant by plastic deformation, creep deformation, and void ripening caused by grain boundary and lattice diffusion. Significant void ripening was observed at early stage of bonding attributed to fast grain boundary diffusion. However, after the bonding interface was eliminated, the void sizes did not change due to slow lattice diffusion.

A micromechanics-based damage constitutive model considering microstructure for aluminum alloys

Aluminum alloys undergoing deformation exhibit complex multi-type-void damage evolution driven by microscale heterogeneous deformation; in return, the accumulated damage evolution would affect the microscale heterogeneous deformation. Meanwhile, the above interaction depends significantly on the microstructure characteristics and determines the macroscale flow and ductile fracture behaviors. These make it difficult to model the deformation response and ductile fracture of aluminum alloys with various microstructures. Aiming at this issue, a micromechanics-based damage constitutive model considering the mutual effects between microstructure, micro/macro-scale deformation, and damage and fracture was developed in this study for deformation of aluminum alloys under tension-dominated loading conditions. During the modeling, the damage was characterized in terms of the evolutions of coexisting multi-type voids. The multiple-type voids were modeled separately as functions of the local micro-strain/stress of their respective phases and microstructure characteristics according to the micromechanical mechanisms. Furthermore, a self-consistent method was employed to calculate the heterogeneous micro-strain/stress of phases and the overall macroscale flow behavior of the multiphase aggregate. In particular, the constitutive behavior of each phase in the self-consistent method was modeled by coupling the softening effect of void evolution and microstructure characteristics, thus the interaction between microscale heterogeneous deformation and damage evolution was captured. The model parameters were determined by matching the calculated and experimental evolutions of the multi-type voids measured via in-situ synchrotron radiation X-ray computed tomography and load-displacement curves during deformation. Applied to the 2219 aluminum alloy, this model accurately predicts the flow stress, damage evolution and fracture behavior under various microstructures and those of tailor-welded blanks with a gradient microstructure. Furthermore, the model clarifies the mutual effects between the microstructure, damage evolution and deformation behavior of aluminum alloys. The developed model can also be generalized to other multiphase metals containing a distribution of hard-brittle particles. And it is thus believed to be with a well general prediction for the deformation response and ductile fracture of this kind of multiphase metals with various microstructures or gradient microstructures, and further facilitates the understanding of their complex damage evolution and flow behavior.

TEM characterization of irradiation-induced dislocation loops and voids in ion-irradiated pure chromium

Chromium (Cr) based coatings have been proposed for Zircaloy fuel rods to enhance the accident tolerance in water-cooled reactors. However, the response of Cr to irradiation has received limited attention in prior studies. To get a better understanding of radiation damage in Cr for future nuclear applications, in the present study, the irradiation-induced microstructure evolution of dislocation loops and voids was studied in pure Cr subjected to 2.8 MeV iron ions irradiation at 550 °C (belonging to stage III, intermediate-temperature). TEM observation results show that the distribution of dislocation loops extends the SRIM simulated irradiation depth to 3.5 µm, while voids were only formed in the irradiated region up to a depth of 1.3 µm. A rigorous method with combined consideration of edge-on view and inside-outside analysis was proposed to determine the habit plane. With this method, what has normally considered as an unsafe zone becomes a favored zone for determining the nature of dislocation loops. The nature of dislocation loops was determined including both interstitial and vacancy types with ½<111> Burgers vector in all regions. Within the irradiation region, the loops are approaching half interstitial and half vacancy, while beyond the irradiated region interstitial loops became dominant. The irradiation-induced swelling was quantified by the void size and density. The swellings are mostly corresponding well with the irradiation dose distribution which is simulated by SRIM. The swelling rate close to the peak region is around 0.3%/dpa. Results demonstrate that Cr tends to experience some similarities in irradiation loop evolution to W-based, Mo-based materials, as they are in the same group in the periodic table, despite the discrepancy in the characteristic of loops such as the irradiation temperature-dependent dislocation loop formation was observed as well. The present study is significant not only for supplementing the fundamental knowledge of irradiation damage in Cr but also for the application of Cr coating to the accident tolerant fuel claddings or other nuclear structure materials.

Atomistically-informed modeling of point defect clustering and evolution in irradiated ThO2

A cluster dynamics (CD) model has been developed to investigate the nucleation and growth of point defect clusters, i.e., interstitial prismatic loops and nanoscale and sub-nanoscale voids, in ThO2 during irradiation by energetic particles. The model considers cluster off-stoichiometry due to the asymmetry of point defect generation on the O and Th sublattices under irradiation, as well as the point defect diffusivities and the defect binding energies to clusters. The energies were established using detailed molecular dynamics simulations considering the statistical variability of cluster configuration. A high-order adaptive time-integration has been used to solve the model. The predicted loop density and their average size is in good agreement with reported experimental observations for proton irradiated ThO2 at 600°C. The model did not predict void evolution due to the sluggish kinetics of cation vacancies, explaining the absence of voids in proton irradiated ThO2 (and other oxides) at relatively low temperatures.

New approach for filling simulations of dual-scale preforms used in the manufacturing of composites materials.

Some fibrous reinforcements used in the manufacturing of parts by Liquid Composite Molding (LCM) have a dual-scale nature, which supposes flow imbalances between the tows and channels at mesoscopic scale, which in turn, cause uncontrolled defects (voids, dry points, among others) and could considerably affect the global flow behavior during the filling of cavities at macroscopic scale. In the present work, a new approach to conduct filling simulations of dual-scale fibrous reinforcements at mesoscopic scale is proposed. This consists of prescribing a pressure gradient along the Representative Unitary Cell, and imposing Stokes-Darcy matching conditions between the tows and the channel sub-domains to determine the filling of the former ones. Contrarily to the traditional approach, where a uniform pressure is assumed for the channels and only the porous media fluid is modeled, the present one allows considering the fluid pressure gradient at channels (fluid motion), air compressibility and dissolution, flow-direction dependent capillary pressure, and vacuum pressure, as well as capturing several phenomena involved in the dynamic evolution of intra-tow voids, namely, compression, mobilization at constant volume and migration from tows towards channel. The velocity vectors and streamlines in the tows and channel subdomains, when these phenomena take place, are analyzed as well.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model formulation

A model for plasticity and damage, developed in the context of continuum damage mechanics and consistent with micromechanisms of void nucleation, growth, and coalescence, is presented. The damage dissipation potential has been formulated specifically to account for different damage contributions due to intervoid necking, shearing, and sheeting under arbitrary stress states. The existence of a cut-off for the negative stress triaxiality was questioned and unilateral conditions for ductile damage have been reformulated accordingly, considering the combination of stress triaxiality and Lode parameter. The model allows the derivation, although in implicit form, of the fracture locus for the whole range of stress triaxiality. An example application to Al2024-T351 and Al6061-T6 is presented. The proposed formulation represents an attempt to reconcile CDM theoretical framework with the ductile fracture specific mechanisms and their sequential progression under general loading conditions, making advantages of micromechanical modeling to establish correlations between void evolution and continuum scale physical quantities. Finite element model implementation and plasticity model formulation will be discussed in a forthcoming companion paper.

Multi-scale analysis of void evolution in large-section plastic mold steel during multi-directional forging

Multi-scale analysis of void evolution in large-section plastic mold steel during multi-directional forging

A unified model for yield strength and plastic behavior of nanovoid evolution in tungsten based on molecular dynamics simulations

Void evolution is closely related to the damage and failure of materials under dynamic conditions, such as high strain rate. The rearrangement of atoms on the entire void surface results in microscopic plastic behaviors like dislocation emission and twinning on the surface and further macroscopic plastic flow nearby. In this work, molecular dynamics simulations are conducted to study the compression flow stress and the corresponding plastic behavior of nanovoid inside monocrystal tungsten as a function of crystallographic orientation, void size, and strain rate. Colorful plastic deformation mechanisms, like shear loops, prismatic dislocation loop, twinning, amorphization, etc., are observed at different strain rates and for compression along various crystallographic orientations. A Kelvin tetrakaidecahedron, formed before yielding, is utilized to determine the critical shear stress for initiation of plastic deformation on void surface within the framework of yield criterion and facture mechanics. A unified model is thus proposed based on the macroscopic hardening effect raised by plastic strain and strain rate, and the microscopic plastic behavior of dislocation emission related to the crystallographic orientation and nanovoid size. The newly proposed unified equation gives a good recount on the yield strength and plastic behaviors obtained from molecular dynamics simulations, but also shed lights on the future works of crack members, inclusions, voids, and porous materials at extremely high strain rate.

Novel Correlations Between Process Forces and Void Morphology for Effective Detection and Minimization of Voids During Friction Stir Welding

Abstract Sub-surface voids and material heterogeneities resulting from the friction stir welding (FSW) process often necessitate post-weld inspection to ensure the quality of weld obtained from this solid-state welding process. In this context, in-process void detection techniques can potentially help in optimizing the process conditions and thereby reduce expensive and time-consuming post-process inspection of welds. Current in-process void detection techniques rely on approaches that try to directly correlate the part-scale welding quality to void formation, without a fundamental understanding of the underlying mechanics and materials physics that modulate void evolution. In this work, we demonstrate an effective in-process numerical technique that uses process force signals to detect volumetric void formation and connect the variations in the force signals to interactions between the tool probe and the underlying material voids. Our approach relies on a high-fidelity finite element analysis simulation of the FSW process and on correlation of numerically obtained process force signals with the corresponding void structures. This correlation is obtained in the phase-space relating in-plane reaction forces on the tool to the tool rotation angle. We focus on the interactions of the tool geometry and tool motion with the surrounding material undergoing plastic deformation and deduce novel insights into various correlations of tool motion and void formation. Through this approach, we can identify tool-related process conditions that can be optimized to minimize void formation and demonstrate a potential in situ force-based void monitoring method that links to the underlying plastic flow and void structures during the FSW process.