Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations

We present molecular dynamics simulations of [1 1 0]-oriented Si nanowires (NWs) under a constant strain rate in tension until failure, using the modified embedded-atom-method (MEAM) potential. The fracture behavior of the NWs depends on both temperature and NW diameter. For NWs of diameter larger than 4 nm, cleavage fracture on the transverse (1 1 0) plane are predominantly observed at temperatures below 1000 K. At higher temperatures, the same NWs shear extensively on inclined {1 1 1} planes prior to fracture, analogous to the brittle-to-ductile transition (BDT) in bulk Si. Surprisingly, NWs with diameter less than 4 nm fail by shear regardless of temperature. Detailed analysis reveals that cleavage fracture is initiated by the nucleation of a crack, while shear failure is initiated by the nucleation of a dislocation, both from the surface. While dislocation mobility is believed to be the controlling factor of BDT in bulk Si, our analysis showed that the change of failure mechanism in Si NWs with decreasing diameters is nucleation controlled. Our results are compared with a recent in situ tensile experiment of Si NWs showing ductile failure at room temperature.     

In-situ Strain Field Measurement and Mechano-electro-chemical Analysis of Graphite Electrodes Via Fluorescence Digital Image Correlation

Background

Mechano-electro-chemical coupling during the ion diffusion process is a core factor to determine the electrochemical performance of electrodes. However, relationship between the mechanics and the electrochemistry has not been clarified by experiments.

Objective

In this work, we conduct an in situ, visual, comprehensive characterization of strain field and Li concentration distribution to further explore the mechano-electro-chemical relationship.

Methods

The digital image correlation characterized by fluorescent speckle and active optical imaging is developed. Combined with electrochromic-based Li concentration detection, the spatiotemporal evolution of in-plane strain and Li concentration of a graphite electrode during the lithiation and delithiation processes are measured and displayed visually via a dual optical path acquisition system.

Results

The visual results show that in-plane strain and Li concentration possess a spatially non-uniform gradient distribution along the radial direction (i.e., diffusion path) with large values outside and small values inside, and that both present obvious temporal segmentation. And mechano-electro-chemical coupling analysis reveals that the in-plane strain is not always linearly related to the concentration and infers that a high strain limits the diffusion and lithiation. The strain–concentration evolution exhibits obvious asymmetric differences between lithiation and delithiation, wherein three equations are fitted to approximately represent the evolution process between in-plane strain and concentration during the lithiation and delithiation processes

Conclusions

This work overcomes the difficulties of fine strain measurements and collaborative concentration characterization during the electrochemical process, and provides an effective experimental method and data support for further exploration of mechano-electro-chemical coupling.

     

Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires

Previous atomistic simulations and experiments have shown an increased Young's modulus and yield strength of fivefold twinned (FT) face-centered cubic metal nanowires (NWs) when compared to single crystalline (SC) NWs of the same orientation. Here we report the results of atomistic simulations of SC and FT Ag, Al, Au, Cu and Ni NWs with diameters between 2 and 50 nm under tension and compression. The simulations show that the differences in Young's modulus between SC and FT NWs are correlated with the elastic anisotropy of the metal, with Al showing a decreased Young's modulus. We develop a simple analytical model based on disclination theory and constraint anisotropic elasticity to explain the trend in the difference of Young's modulus between SC and FT NWs. Taking into account the role of surface stresses and the elastic properties of twin boundaries allows to account for the observed size effect in Young's modulus. The model furthermore explains the different relative yield strengths in tension and compression as well as the material and loading dependent failure mechanisms in FTNWs.     

Lithiation-enhanced charge transfer and sliding strength at the silicon-graphene interface:A first-principles study

The application of silicon as ultrahigh capacity electrodes in lithium-ion batteries has been limited by a number of mechanical degradation mechanisms including fracture, delamination and plastic ratcheting, as a result of its large volumetric change during lithiation and delithiation. Graphene coating is one feasible technique to mitigate the mechanical degradation of Si anode and improve its conductivity. In this paper, first-principles calculations are performed to study the atomic structure, charge transfer and sliding strength of the interface between lithiated silicon and graphene. Our results show that Li atoms segregate at the(lithiated) Si-graphene interface preferentially, donating electrons to graphene and enhancing the interfacial sliding resistance. Moreover, the interfacial cohesion and sliding strength can be further enhanced by introducing single-vacancy defects into graphene.These findings provide insights that can guide the design of stable and efficient anodes of silicon/graphene hybrids for energy storage applications.     

A micromechanics-based strain gradient damage model for fracture prediction of brittle materials – Part II: Damage modeling and numerical simulations

In this paper, we established a strain-gradient damage model based on microcrack analysis for brittle materials. In order to construct a damage-evolution law including the strain-gradient effect, we proposed a resistance curve for microcrack growth before damage localization. By introducing this resistance curve into the strain-gradient constitutive law established in the first part of this work (Li, 2011), we obtained an energy potential that is capable to describe the evolution of damage during the loading. This damage model was furthermore implemented into a finite element code. By using this numerical tool, we carried out detailed numerical simulations on different specimens in order to assess the fracture process in brittle materials. The numerical results were compared with previous experimental results. From these studies, we can conclude that the strain gradient plays an important role in predicting fractures due to singular or non-singular stress concentrations and in assessing the size effect observed in experimental studies. Moreover, the self-regularization characteristic of the present damage model makes the numerical simulations insensitive to finite-element meshing. We believe that it can be utilized in fracture predictions for brittle or quasi-brittle materials in engineering applications.     

Coupled Diffusion-Dissolution Around a Fracture Channel: The Solute Congestion Phenomenon

The paper studies the coupled diffusion-dissolution process in reactive porous media, separated by a fracture channel. An aggressive solute, corresponding for e.g., to a complete demineralization that dissolves the solid skeleton of the surrounding porous material, is prescribed at the inlet of the fracture. By means of asymptotic dimensional analysis it is shown that for large times the diffusion length in the fracture develops with the quadratic root of time. In comparison with the 1D-Stefan Problem, in which the dissolution front evolves with the square root of time, this indicates that the overall solute evacuation through the structure slows down in time. This phenomenon is referred to as a diffusive solute congestion in the fracture. This asymptotic behavior is confirmed by means of model-based simulation, and the relevant material parameters, related to only the chemical equilibrium condition, are identified. The obtained results suggest that the presence of a small crack does not significantly increase the propagation of the dissolution front in the porous bulk, and hence the overall chemical degradation of the porous material. The same applies to other diffusion induced demineralization, mineralization, sorption and melting processes, provided that the convective transport of the solute in the crack is small in comparison with the solute diffusion. The result is relevant for several problems in durability mechanics: calcium leaching of concrete in nuclear waste containment, mineralization and demineralization in bone remodeling, chloride penetration, etc.     

Uncertainty Analysis of Radionuclide Transport in a Fractured Coastal Aquifer with Geothermal Effects

Groundwater flow and radionuclide transport at the Milrow underground nuclear test site on Amchitka Island are modeled using two-dimensional numerical simulations. A multi-parameter uncertainty analysis is adapted and used to address the effects of uncertainties associated with the definition of the modeled processes and the values of the parameters governing these processes. In particular, we focus on the effects on radioactive transport of uncertainties associated with conduction and convection of heat relative to the uncertainties associated with other flow and transport parameters. These include recharge, hydraulic conductivity, fracture porosity, dispersivity and strength of matrix diffusion. The flow model is conceptualized to address the problem of density-driven flow under conditions of variable salinity and geothermal gradient. The conceptual transport model simulates the advection–dispersion process, the diffusion process from the high-velocity fractures into the porous matrix blocks, and radioactive decay.For this case study, the uncertainty of the recharge-conductivity ratio contributes the most to the output uncertainty (standard deviation of mass flux across the seafloor). The location of the freshwater–saltwater transition zone changes dramatically as this ratio changes with the thickness of the freshwater lens and the location of the seepage face changing as well. In the context of radionuclide transport from the nuclear test cavity that is located in the area where the transition zone is uncertain, travel times of radionuclide mass from the cavity to the seepage face along the seafloor are significantly impacted. The variation in transition zone location changes the velocity magnitude at the cavity location by a large factor (probably an order of magnitude). When this effect is combined with porosity and matrix diffusion uncertainty, the uncertainty of transport results becomes large. Although thermal parameters have an effect on the solution of the flow problem and also on travel times of radionuclides, the effect is relatively small compared to other flow and transport parameters.     

Application of Fractional Differential Equations for Modeling the Anomalous Diffusion of Contaminant from Fracture into Porous Rock Matrix with Bordering Alteration Zone

Solute diffusion from a fracture into a porous rock with an altered zone bordering the fracture is modeled by a system of two diffusion equations (one for the altered zone and another for the intact porous matrix) with different coefficients of effective diffusivity. Since experimental studies of diffusion into rock samples with altered zones indicate that mathematical models of diffusion based on Fick’s law do not adequately describe the concentration field in a sample, fractional order diffusion equations are chosen in this study for modeling the anomalous mass transport in the rocks. In the case of significantly higher porosity of the altered zone (e.g., this is typical for carbonates) the effective diffusivity here can be much higher than the effective diffusivity of non-altered rocks. By introducing a small parameter that is the ratio of effective diffusivities in the non-altered and altered regions and applying the technique of perturbations, approximate analytical solutions for concentrations in the altered zone bordering the fracture and in the intact surrounding rocks are obtained. Based on these solutions, different regimes of diffusion into the rocks with different physical properties are modeled and analyzed. It is shown that, using experimentally obtained data, the orders of the fractional derivatives in the differential equations can be readily calibrated for the every specific rock.     

Fracture-Flow-Enhanced Matrix Diffusion in Solute Transport Through Fractured Porous Media

Over the past few decades, significant progress of assessing chemical transport in fractured rocks has been made in laboratory and field investigations as well as in mathematic modeling. In most of these studies, however, matrix diffusion on fracture–matrix surfaces is considered as a process of molecular diffusion only. Mathematical modeling based on this traditional concept often had problems in explaining or predicting tracer transport in fractured rock. In this article, we propose a new conceptual model of fracture-flow-enhanced matrix diffusion, which correlates with fracture-flow velocity. The proposed model incorporates an additional matrix-diffusion process, induced by rapid fluid flow along fractures. According to the boundary-layer theory, fracture-flow-enhanced matrix diffusion may dominate mass-transfer processes at fracture–matrix interfaces, where rapid flow occurs through fractures. The new conceptual model can be easily integrated with analytical solutions, as demonstrated in this article, and numerical models, as we foresee. The new conceptual model is preliminarily validated using laboratory experimental results from a series of tracer breakthrough tests with different velocities in a simple fracture system. Validating of the new model with field experiments in complicated fracture systems and numerical modeling will be explored in future research.     

Convection induced by composition gradients in miscible systemsConvection induite par des gradients de composition dans les systèmes miscibles

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, a large concentration (and density) gradient exists, which relaxes through diffusion. With a mathematical model based on the Korteweg stress, we show that convection can occur which is analogous to surface-tension induced convection (STIC) or Marangoni convection. Specifically, we show that with realistic parameters significant flows can occur with plane interfaces and that drops of miscible fluids can act like their immiscible counterparts. Regarding plane interfaces, an experimental confirmation of this phenomenon is planned for the International Space Station. To cite this article: V.A. Volpert et al., C. R. Mecanique 330 (2002) 353–358.     

Fracture process zone analysis of concrete using moiré interferometry

The fracture process zone (FPZ) ahead of a crack tip in concrete and mortar beams subjected to threepoint bending was studied using moiré interferometry. A large FPZ can occur in concrete before the external load reaches its maximum value. Comparing the experimental results between concrete and mortar suggests that the aggregate contributes to the formation of the large FPZ in concrete. The formation of this large FPZ makes concrete less brittle than mortar. The effect of the FPZ on the fracture property, such as stress intensity factor, is investigated by combining moiré interferometry measured displacements with the smoothing FEM method. The study shows that a large FPZ significantly affects the value of the stress intensity factor.     

EBSD Study of Delamination Fracture in Al–Li Alloy 2090

Aluminum–lithium (Al–Li) alloys offer attractive combinations of high strength and low density for aerospace structural applications. However, a tendency for delamination fracture has limited their use. Identification of the metallurgical mechanisms controlling delamination may suggest processing modifications to minimize the occurrence of this mode of fracture. In the current study of Al–Li alloy 2090 plate, high quality electron backscattered diffraction (EBSD) information has been used to evaluate grain boundary types exhibiting delamination fracture and characterize microtexture variations between surrounding grains. Delamination was frequently observed to occur between variants of the brass texture component, along near-Σ3, incoherent twin boundaries. EBSD analyses indicated a tendency for intense deformation along one side of the fractured boundary. A through-thickness plot of grain-specific Taylor factors showed that delaminations occurred along boundaries with the greatest difference in Taylor factors. Together, these suggest a lack of slip accommodation across the boundary, which promotes significantly higher deformation in one grain, and stress concentrations that result in delamination fracture.     

Evidence of Multi-Process Matrix Diffusion in a Single Fracture from a Field Tracer Test

Compared to values inferred from laboratory tests on matrix cores, many field tracer tests in fractured rock have shown enhanced matrix diffusion coefficient values (obtained using a single-process matrix-diffusion model with a homogeneous matrix diffusion coefficient). To investigate this phenomenon, a conceptual model of multi-process matrix diffusion in a single-fracture system was developed. In this model, three matrix diffusion processes of different diffusion rates were assumed to coexist: (1) diffusion into stagnant water and infilling materials within fractures, (2) diffusion into a degraded matrix zone, and (3) further diffusion into an intact matrix zone. The validity of the conceptual model was then demonstrated by analyzing a unique tracer test conducted using a long-time constant-concentration injection. The tracer-test analysis was conducted using a numerical model capable of tracking the multiple matrix-diffusion processes. The analysis showed that in the degraded zone, a diffusion process with an enhanced diffusion rate controlled the steep rising limb and decay-like falling limb in the observed breakthrough curve, whereas in the intact matrix zone, a process involving a lower diffusion rate affected the long-term middle platform of slowly increasing tracer concentration. The different matrix-diffusion-coefficient values revealed from the field tracer test are consistent with the variability of matrix diffusion coefficient measured for rock cores with different degrees of fracture coating at the same site. By comparing to the matrix diffusion coefficient calibrated using single-process matrix diffusion, we demonstrated that this multi-process matrix diffusion may contribute to the enhanced matrix-diffusion-coefficient values for single-fracture systems at the field scale.     

Fatigue damage evolution in silicon films for micromechanical applications

In this paper we examine the conditions for surface topography evolution and crack growth/fracture during the cyclic actuation of polysilicon microelectromechanical systems (MEMS) structures. The surface topography evolution that occurs during cyclic fatigue is shown to be stressassisted and may be predicted by linear perturbation analyses. The conditions for crack growth (due to pre-existing or nucleated cracks) are also examined within the framework of linear elastic fracture mechanics. Within this framework, we consider pre-existing cracks in the topical SiO₂ layer that forms on the Si substrate in the absence of passivation. The thickening of the SiO₂ that is normally observed during cyclic actuation of Si MEMS structures is shown to increase the possibility of stable crack growth by stress corrosion cracking prior to the onset of unstable crack growth in the SiO₂ and Si layers. Finally, the implications of the results are discussed for the prediction of fatigue damage in silicon MEMS structures.     

ATOMIZATION OF A LIQUID DROP BY PULSATION

ＡＴＯＭＩＺＡＴＩＯＮＯＦＡＬＩＱＵＩＤＤＲＯＰＢＹＰＵＬＳＡＴＩＯＮ￥(林松飘，周哲玮)Ｓ．Ｐ．Ｌｉｎ；（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃａｌａｎｄＡｅｒｏｎａｕｔｉｃａｌＥｎｇｉｎｅｅｒｉｎｇＣｌａｒｋｓｏｎＵｎｉｖｅｒｓｉｔｙ，Ｐｏｔｓｄ...     

Influence of large eddies on the suspension of solid particles

The phenomena of solid particles suspensions, in a turbulent flow, can more conveniently be described by stochastic models than by diffusion models, particularly in the case of relatively coarse particles.

The fundamental difficulties of using such models are principally due to the difficulty of performing direct measurements of probabilities, because the number of observations (or tests) necessary to obtain physically representative values is important (theoretically infinite).

We have used such a model to describe the movement of spheres in an inclinable pipe.

To do so, we have identified the movement through a Markov process which permits us to show that we can characterize it by the limit distribution for passage probabilities in a cross section. We have used a special system of close-circuit television to measure it, doing a sufficiently large number of observations for the measurements to be significant.

In the case of a vertical pipe, the phenomena is one-dimensional. By using the model stochastic displacement, we obtain a differential equation which it is possible to integrate by assuming an obviously constant radial dispersion. The interpretation of limit distributions for passage probabilities and visual observations of particles movement in the pipe have caused us to conclude that the mean displacment is due, on one hand, to a radial acceleration bounded to a stochastic rotation of the flow and, on the other hand, to the effect of the mean velocity gradient. The experimental results show that the radial dispersion is a function of the relative dimension of particles with respect to the macroscale of the turbulence.

In the case of an inclined pipe, a two-dimensional stochastic model of the displacement is possible, but the integration of the equation is quite complicated and may be done numerically. We have prefered a two-dimensional simulation model. The results of the simulations permit us to obtain a limit repartition of passage probabilities, the moments of which we have compared with those that we have measured. These comparisons show that the model obviously represents the phenomena when the pipe is horizontal or very slightly inclined but differs in the near vertical case. This is due to the simplicity of the model in which we neglect the radial acceleration we have considered previously and the effect of which is negligible in comparison with gravity when the pipe is inclined.

The interpretation of the measurements by comparison of moments with the two-dimensional model shows that the angular dispersion of solid particles is essentially due to big eddies and that the particle diameters are not essential parameters in this case.

By associating this conclusion with that obtained previously concerning the radial dispersion, it seems that the eddies bigger than the macroscale of turbulence may be of capital importance in the dispersion of solid particles and that it will be of practical interest to characterize them as a function of a mean parameter of the flow.

The study of the movement of sufficiently large particles seems to be a method which is able to give this result.     

材料参数对韧性材料高应变率拉伸碎裂过程的影响

Grady-Kipp将一个与断裂能量相关的内聚断裂模型引入Mott[1]的刚性卸载波分析,导出一个预测韧性材料在高速拉伸碎裂过程中产生碎片的平均尺度的计算公式[2]。为定量评估Grady-Kipp公式的适用程度,采用数值方法模拟了具有不同材料参数的一维弹塑性杆在高应变率拉伸过程中的碎裂现象。通过改变材料的断裂能 、密度 和应变率敏感系数c,模拟了杆在不同应变率 下的碎裂过程,研究了材料参数对碎裂时的碎片尺度、表观断裂应变和断口温升等的影响。通过对应变率和碎片尺寸进行无量纲化,证实Grady-Kipp公式在广泛的材料参数范围内能较好地预测碎裂过程中发生的碎片平均尺寸。     

Diffusion-controlled melting and re-solidification of metal micro layers on a reactive substrate

The paper offers a theoretical approach to a prediction of residue formation inherent to melting and subsequent solidification of micro layers of molten aluminum alloys. The residue formation follows a reactive flow of a portion of the melt that is removed by a surface tension action. The residue portion solidifies in situ. The phenomenon studied is associated with materials’ processing during controlled atmosphere brazing of aluminum. The model assumes that diffusion of Silicon, present in an Al+Si clad of a brazing sheet, has a twofold role. First, a solid state Si diffusion prior to melting and across the clad–core interface of a composite brazing sheet takes place and modifies alloys’ composition on both sides of the interface. Subsequently, Si diffusion within clad controls the melting process. Both processes are essential for clad residue formation. The approach advocated in this paper leads to a prediction of the residue formation through a modeling of the non-equilibrium diffusion-controlled melting. A heuristic interpretation of physical mechanisms was discussed and a related mathematical model devised. The model was solved numerically in terms of Si concentration distributions for a moving boundary problem and corroborated with empirical data. Empirical data were gathered using an experimental controlled atmosphere brazing facility. The results of the modeling and their corroboration with the experimental data indicate a strong dependence of residue formations on the pre-melting state of the clad, in particular on the grain size within Al-clad matrix. A good agreement between numerically predicted residue mass and experimental findings is documented in detail.     

Fracture-mode map of brittle coatings: Theoretical development and experimental verification

Brittle coatings, upon sufficiently high indentation load, tend to fracture through either ring cracking or radial cracking. In this paper, we systematically study the factors determining the fracture modes of bilayer material under indentation. By analyzing the stress field developed in a coating/substrate bilayer under indentation in combination with the application of the maximum-tensile-stress fracture criterion, we show that the fracture mode of brittle coatings due to indentation is determined synergistically by two dimensionless parameters being functions of the mechanical properties of coating and substrate, coating thickness and indenter tip radius. Such dependence can be graphically depicted by a diagram called ‘fracture-mode map’, whereby the fracture modes can be directly predicated based on these two dimensionless parameters. Experimental verification of the fracture-mode map is carried out by examining the fracture modes of fused quartz/cement bilayer materials under indentation. The experimental observation exhibits good agreement with the prediction by the fracture-mode map. Our finding in this paper may not only shed light on the mechanics accounting for the fracture modes of brittle coatings in bilayer structures but also pave a new avenue to combating catastrophic damage through fracture mode control.     

Cracking mechanisms in lithiated silicon thin film electrodes

The massive cracking of silicon thin film electrodes in lithium ion batteries is associated with the colossal volume changes that occur during lithiation and delithiation cycles. However, the underlying cracking mechanism or even whether fracture initiates during lithiation or delithiation is still unknown. Here, we model the stress generation in amorphous silicon thin films during lithium insertion, fully accounting for the effects of finite strains, plastic flow, and pressure-gradients on the diffusion of lithium. Our finite element analyses demonstrate that the fracture of lithiated silicon films occurs by a sequential cracking mechanism which is distinct from fracture induced by residual tension in conventional thin films. During early-stage lithiation, the expansion of the lithium-silicon subsurface layer bends the film near the edges, and generates a high tensile stress zone at a critical distance away within the lithium-free silicon. Fracture initiates at this high tension zone and creates new film edges, which in turn bend and generate high tensile stresses a further critical distance away. Under repeated lithiation and delithiation cycles, this sequential cracking mechanism creates silicon islands of uniform diameter, which scales with the film thickness. The predicted island sizes, as well as the abrupt mitigation of fracture below a critical film thickness due to the diminishing tensile stress zone, is quantitatively in good agreement with experiments.