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Vladislav Pakhomov
Vladislav Pakhomov

Crack [BEST] Fritz 18 Crack [BEST]


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CRACK Fritz 18 crack


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Fritz could freeze the "ranking list" at least to be on the safe side. In case he shouldn't crack the top 10 after all. Or as a motivational boost for how beautiful a single number in the ranking looks.


Another study, published in a 1998 issue of the journal Arthritis and Rheumatology, was done by a single doctor who experimented on his own hands. (Talk about dedicating your life to science.) Over his lifetime, he cracked the knuckles of one hand, but not the other. After decades of this behavior, he took X-rays and found that both hands had the exact same incidence of arthritis.


There has been some research indicating that longtime knuckle crackers may experience hand swelling and a reduced hand grip over time, but there is still no evidence that cracking your knuckles causes arthritis.


Silicon-based anodes are one of the promising candidates for the next generation high-power/energy density lithium ion batteries (LIBs). However, a major drawback limiting the practical application of the Si anode is that Si experiences a significant volume change during lithiation/delithiation, which induces high stresses causing degradation and pulverization of the anode. This study focuses on crack initiation within a Si anode during the delithiation process. A multi-physics-based finite element (FE) model is built to simulate the electrochemical process and crack generation during delithiation. On top of that, a Gaussian process (GP)-based surrogate model is developed to assist the exploration of the crack patterns within the anode design space. It is found that the thickness of the Si coating layer, TSi, the yield strength of the Si material, σFc, the cohesive strength between Si and the substrate, σFs, and the curvature of the substrate, ρ, have large impacts on the cracking behavior of Si. This coupled FE simulation-GP surrogate model framework is also applicable to other types of LIB electrodes and provides fundamental insights as building blocks to investigate more complex internal geometries.


In this study, a multi-physics-based FE model is built to investigate the crack pattern of Si anode and the critical design parameters, including thickness of the Si layer TSi, the cohesive strength between the Si layer and the substrate, and the curvature of the substrate. Subsequently, a GP-based surrogate model is developed with the simulated results as training data to predict the cracking behavior of the anodes within the anode design space. The GP surrogate model results are then used to analyze the general trends of the Si anode performance.


A multi-physics-based 3D FE model is established via comsol multiphysics to simulate the crack patterns of Si anodes with complex structures during the delithiation process. The model consists of two sub-models. In the first part, the electrochemical dynamics of the Si anode during delithiation, a lithium diffusion process, is simulated; subsequently, the lithium concentration profile is acquired and used to evaluate the crack pattern based on a standard cohesive zone modeling (CZM) technique. Finally, a GP-based surrogate model with adaptive fidelity enhancement is implemented to analyze the influences of the design parameters of the Si anode structure, such as the Si layer thickness, the curvature of the substrate, etc.


The CZM technique is utilized to investigate the crack initiation of Si during volume shrinkage. Recently, CZM methods have been widely used to analyze the crack initiation and growth in metals [22,23] and polymers [24,25]. In the following, the basic features of the model are outlined.


The governing equations are then implemented in the 3D FE model software (comsol multiphysics). The multi-physics simulation model consists of two sub-modules, the electrochemical (lithium battery) model and the mechanical (crack initiation) model, which are solved sequentially. The electrochemical model is used to calculate the lithium concentration, c, with respect to the delithiation process. Then, c is extracted from the simulation results and passed to the crack initiation model. The model simulates the Si half-cell battery, with pure lithium metal and Si as the two electrodes. One molar lithium hexafluorophosphate (LiPF6) in 1:1 ethylene carbonate:diethyl carbonate, one of the most commonly used liquid electrolytes, is used in the model. The lithiation-induced expansion is simulated analogously to the thermal expansion process with lithium concentration, c, as a substitute for temperature in the model to acquire stresses and deformations of the anode. Table 1 lists the electrochemical and mechanical parameters used in the simulation. The lithium diffusion coefficients in electrolyte and silicon are kept constant. Silicon active material has a maximum capacity cmax of 3.367 105 mol/m3 based on the theoretical specific capacity 3579 mA h/g of Li3.75Si [28], which is considered as the fully lithiated state in this study. The open circuit voltage of Si versus lithium is measured as a function of the state of charge (SoC) from slow rate discharging of half cells.


Figure 6 illustrates the representative simulation results of crack patterns (top and perspective view) in Si layers with different thicknesses coated on a flat substrate after delithiation/volume shrinkage. The red-dash-circled regions in Figs. 6(a) and 6(b) are the Si islands separated by cracks. Although, due to the modeling assumptions, the Si islands all have square shapes which are not realistically accurate comparing with experiments, the model can still capture the general trends of crack initiation behaviors and thus be used to analyze the impacts of critical design parameters. It is observed that, with the increase of the Si layer thickness, the area of the Si island also increases. The changes of the areas of the Si island are crucial to the reliability performances of Si anode: smaller Si island area indicates more cracks in the Si layer, which could introduce more sites for the formation of solid electrolyte interphase (SEI) and more intensive degradation of the anode.


The GP-based surrogate model is used to predict the Si island area within the design space. FEA-based simulation results with different Si anode design parameters, i.e., fracture ratio, k, Si layer thickness, TSi, and curvature of the substrate, ρ, are used as training data to develop the surrogate model. Additionally, the CCL [32] is adopted to qualify the accuracy and reliability of the surrogate model. In order to have a clear comparison, the Si cracking performance is analyzed using two performance surfaces as illustrated in Figs. 12 and 13. Figure 12 shows the predicted cracking areas of the Si layer on a flat substrate (curvature ρ = 0) with respect to TSi and ratio k. Within the whole parameter space, a monotonically increasing surface is generated from the point at (20 nm, 0.1) to the (600 nm, 2.0) corner. The performance surface is not linear with respect to the two variables: at the (400 nm, 1.5) point, a small concave region is observed. This is due to the non-linear relationships between the Si island area and the design variables, as illustrated in Figs. 8 and 9. Similarly, as illustrated in Fig. 13, a relatively smooth performance surface is observed. By increasing TSi or curvature ρ, the Si island area also increases.


The GP surrogate modeling can be particularly useful to investigate the Si anodes with complex structures. Recently, with emerging electrode fabrication technologies, various complicated designs of the Si anode have been proposed, such as nanowires [37,38], porous inverse opal structures [12], etc. It is challenging and time consuming to study the Si cracking phenomenon in these sophisticated designs and find the optimal design through experimental approaches or physics-based numerical simulation methods. The GP-based surrogate model, therefore, is an effective alternative method to evaluate the crack generations in those Si anodes. First, researchers may acquire the statistical distributions of the critical geometric features of the Si anode through experimental measurements, such as the thickness of the Si layer, the curvature of the substrate, etc. Then, one can refer to the GP surrogate model results as lookup tables to quickly predict the Si island area distribution and the crack generation in the anodes. Through this approach, enormous experimental efforts and computational costs can be saved, which will largely benefit the design of the novel Si anode. In the future work, we will use the GP surrogate model results to investigate the Si cracking in the novel inverse opal structured Si anode.


Cracking sounds emitted from human synovial joints have been attributed historically to the sudden collapse of a cavitation bubble formed as articular surfaces are separated. Unfortunately, bubble collapse as the source of joint cracking is inconsistent with many physical phenomena that define the joint cracking phenomenon. Here we present direct evidence from real-time magnetic resonance imaging that the mechanism of joint cracking is related to cavity formation rather than bubble collapse. In this study, ten metacarpophalangeal joints were studied by inserting the finger of interest into a flexible tube tightened around a length of cable used to provide long-axis traction. Before and after traction, static 3D T1-weighted magnetic resonance images were acquired. During traction, rapid cine magnetic resonance images were obtained from the joint midline at a rate of 3.2 frames per second until the cracking event occurred. As traction forces increased, real-time cine magnetic resonance imaging demonstrated rapid cavity inception at the time of joint separation and sound production after which the resulting cavity remained visible. Our results offer direct experimental evidence that joint cracking is associated with cavity inception rather than collapse of a pre-existing bubble. These observations are consistent with tribonucleation, a known process where opposing surfaces resist separation until a critical point where they then separate rapidly creating sustained gas cavities. Observed previously in vitro, this is the first in-vivo macroscopic demonstration of tribonucleation and as such, provides a new theoretical framework to investigate health outcomes associated with joint cracking.


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