Symmetric Boundary Research Articles

Development of computational methodology in simulating thermal responses of spent fuel in deep geological disposal

Deep geological repository with multiple barriers has been recognized as the safety management of nuclear wastes in the world. The decay heat from the spent fuel can elevate the temperature values of canisters, buffers, backfills, and host rock, which may challenge repository integrity. It is crucial to investigate the thermal response of in order to maintain the performance and the integrity of repository system. A gap of millimeter order in general exists between the canister/buffer interface. This gap effect would strongly influence the temperature distribution in the buffer and its peak temperature. A large amount of mesh size and computing power is needed to realistically model this small gap for numerically simulating the temperature responses in the entire disposal site. A simplified computational methodology with the effective conductivity of buffer (λeff) is proposed in this paper, which can reasonably predict the peak buffer temperature with dramatic reduction in the mesh size and numerical computation. In addition, under the uniform heat source distribution in the whole repository system, a geometric simplified model with 1/4 deposited hole + 4-side symmetric boundary conditions can also precisely capture the peak buffer temperature that is close to the value predicted using the entire disposal-site simulation. In the engineering point of view, the λeff model and the geometric simplified model can be applied in the numerical simulation of temperature responses for the whole repository system.

B-Spline Surface-Based Reduced-Order Modeling of Nonplanar Crack Growth in Structural Digital Twins

Nonplanar crack growth holds a critical role in aeronautical structures, necessitating effective analysis under mixed fatigue loading to assess structural integrity. This study introduces a reduced-order modeling (ROM) method for predicting nonplanar crack growth in structural digital twins. The method’s advantage lies in its representation of the entire crack surface morphology using a B-spline surface, which better captures its impact on crack growth. The symmetric Galerkin boundary element method–finite element method coupling method is adopted as a full-order method to generate the crack database. Isoparametric coordinates of the crack surface and stress intensity factor serve as input and output, respectively, for training the ROM, which integrates -means clustering, principal component analysis, and Gaussian process regression. The proposed approach is demonstrated using a rotorcraft-mast-like component. Results reveal superior fracture mechanics parameter prediction compared to the crack-front-based ROM. Furthermore, the method boasts three orders of magnitude greater efficiency than full-order simulation, enabling its coupling with approaches like Monte Carlo for probabilistic crack growth analysis. Future work entails integrating our method into the probabilistic framework of digital twins.

First-principles study of oxygen segregation and its effect on the embrittlement of molybdenum symmetrical tilt grain boundaries

Elemental segregation can pronouncedly affect the cohesion of grain boundary (GB), which shows tremendous potential in altering the thermal stability and mechanical properties of metals. In this work, we systematically investigate the segregation behavior of oxygen (O) atoms at a series of GBs in molybdenum (Mo), using first principles calculations, to reveal the effect of O segregation on the embrittlement of Mo GBs. It is found that O atoms energetically prefer to segregate at sites in both the GB core and the vicinity of the GB plane. The strengthening energy is strongly associated with the GB structure, and it linearly decreases with the continuous deformation of the GB. O segregation can lead to an increase in the volume of polyhedron sites and a decrease in the charge density among adjacent Mo atoms across the GB plane. The weakened Mo-Mo bonds are believed to disrupt the GB cohesion, thereby increasing the intergranular cleavage tendency of Mo. Interestingly, O segregation does not always trigger GB embrittlement. The Σ5(310)[001] symmetric tilt grain boundary (STGB) with an O atom doped at the cap trigonal prism (CTP) site possesses a strength as strong as the clean GB. O segregation promotes the generation of Mo-O bonds across the GB plane, which counteracts the adverse effect of weakened Mo-Mo bonds. This work deepens the understanding of the possible effect of O segregation on GB cohesion of Mo from the atomic and electronic scales, providing guidance for enhancing the mechanical properties of Mo via GB structure optimization.

STUDY OF THE TEMPERATURE DEPENDENCE OF THE SYMMETRICAL GRAIN BOUNDARY ENERGIES ON THE PLANE (110) IN ALUMINUM

In this work the energy of symmetric tilt and twist grain boundaries in the range of grain misorientation angles from 0 to 180◦ and temperatures from 100 to 700 K in pure aluminum is investigated. The bicrystal systems with different grain tilt/twist angles are maintained at constant temperatures of 100, 400, or 700 K by molecular dynamic method and the energy of each grain boundary is calculated. The results show that the minimum grain boundary energy decreases as the temperature increases from 100 to 400 K; but the energy may decrease, remain practically unchanged, or even increase with further heating to 700 K. The average grain boundary energy obtained by averaging the energies of the resulting grain boundary structure variations at constant temperature grows with increasing temperature from 100 to 700 K for random boundaries with initially high energies. In the case of special grain boundaries with small Σ values, the average energy will be practically unchanged. To describe the continuous energy dependence of symmetric tilt and twist boundaries on temperature, an approximation by an forward propagation of artificial neural network is proposed. The neural network is trained and tested on atomistic simulation data and shows high predictive ability on test data and to describe the boundary energy in the temperature range from 100 to 700 K.

Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method

The Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-linear acoustics, and other areas. A general methodology is proposed in this work to solve the mentioned equation or coupled systems formed by it using the network simulation method. Additionally, the implementation of the most common possible boundary conditions in different engineering problems is indicated, including the Neumann condition that enables symmetry to be applied to the problem, reducing computation times. The method consists mainly of establishing an analogy between the variables of the differential equations and the electrical voltage at a central node. The methodology is also explained in detail, facilitating its implementation to similar engineering problems, since the equivalence, for example, between the different types of spatial and time derivatives and its correspondence with the electrical device is detailed. As an example, several cases of both the equation and a coupled system are solved by varying the boundary conditions on one side and applying symmetry on the other.

Influence of Sintering Conditions on Anisotropy of Grain Boundary Networks and Microstructure Topology in Yttria-Stabilized Zirconia

The paper presents original data of 3D EBSD orientation maps collected for 13 Yttria-Stabilized Zirconia (YSG) samples, sintered at different temperatures for different times. The largest map contains 18,833 grains and 64,506 grain boundaries. These data allowed for the analysis of grain boundary networks, based on all 5 macroscopic parameters and some topological studies of microstructures. Grain boundaries having the (001) and (111) boundary planes are favored and disfavored respectfully in all YSZ samples. The anisotropy appears to be stronger if grains are larger. However, large grains themselves do not imply strong anisotropy. Symmetric boundaries are slightly more frequent in YSZ compared to random boundaries, but despite some premises, the evidence for over-representation of 180 deg-tilt boundaries is still too weak. Distributions of the number of faces per grain and mean number of faces per grain are similar to those reported for metals, and there is a close-to-linear correlation between the number of faces and grain size.Graphical

Revealing the influence of solute segregation on the stability and strength of Cu Σ11 [110](113) symmetrical tilt grain boundary via first-principles investigation

The stability and strength of the grain boundary (GB) structure are critical for the practical application of nanocrystals. This study systematically calculates the impact of the segregation of 26 transitional alloy elements on Cu Σ11 [110](113) GB using the first-principle theoretical calculation method. The research findings demonstrate that there is a parabolic connection between atomic number and segregation energy of TM elements in the same period. In addition to Fe, Co, and Ni, all other 23 elements have the potential to segregate to Cu GB, with Zr exhibiting the strongest segregation tendency. The difference in atomic radius and electronegativity between solute atoms and copper atoms strongly affects the segregation tendency, the greater the difference, the greater the tendency for segregation. The segregation energy of solute segregation has strong linear correlation with its GB energy, and the stronger the segregation ability, the more stable the GB. Except for Zn, Ag, Cd, and Au, other 19 alloying elements can increase the strength of GB. Electronic analysis indicates that the strengthening and embrittlement of solutes are primarily related to the accumulation and consumption of electrons near GB and the bonding between atoms.

Density functional study of atomic arrangements in CrMnFeCoNi high-entropy alloy and their impact on vacancy formation energy and segregation

Using the density functional theory-coupled Monte Carlo approach, we explored the chemical short-range order (SRO) and element segregation in equimolar CrMnFeCoNi alloy. We found that state-of-the-art approximation of random element distribution is only applicable at > 1100 K close to the melting temperature, while the Cr-Cr repulsion driving the system stabilization and accompanying the formation of cubic Cr sublattice, and mild Ni-Ni attraction are the most prominent pair interactions at lower temperatures. Chemical potential and vacancy formation energy calculations indicate that Cr is most sensitive to the local chemical environment, making Cr atoms most stabilized when the preferred SRO is introduced. While the vacancy formation is predicted equally probable among five constituting elements in the random solid solution, Cr and Ni atoms show the lowest vacancy formation energies in the structure with SRO. Furthermore, distinct element segregation was predicted in the vicinity of planar defects, including symmetric tilt grain boundary and stacking fault, which we correlated to the site- and chemistry-dependent atomic volume and bond lengths. It suggests that the local mechanical strain and bond energy induce the SRO development and element segregation: Namely, the system takes advantage of segregation of Ni atoms having large atomic volume or Cr-Cr pairs having elongated bond lengths to fill in the excess volume at defects that relaxes the mechanical strain field and optimizes bond energy distribution. The correlation between the SRO and properties of CrMnFeCoNi alloy needs further investigations, which is expected to greatly help understand and control the properties of high-entropy alloys.

The channeling effect of symmetrical tilt grain boundaries on helium bubbles in tungsten

Helium atoms can migrate easily and aggregate at various crystal defects, such as grain boundaries, which promote the nucleation and growth of helium bubbles, ultimately causing severe radiation damage to nuclear materials. Structure characteristics of grain boundaries with low-angle symmetrical tilt of the [100] axle and their channeling effects on helium bubbles in tungsten were investigated by molecular dynamics simulations. The triaxial variation curves of the helium bubble size in each grain boundary model and the relationship of the helium diffusion coefficient of each grain boundary to their intrinsic crystal structures are analyzed. The results indicate that the helium bubbles grow into one-dimensional nanochannels at the selected grain boundaries, and there is a significant difference in the maximum number of helium bubbles these grain boundaries can accommodate before forming one-dimensional nanochannels. Furthermore, the existence of helium nanochannels along the 〈100〉 edge dislocation line in the low-angle symmetrical tilt grain boundaries is well verified by molecular dynamics simulation of the helium bubble growth and helium diffusion equations at the 〈100〉 edge dislocation line. This suggests that releasing helium outside of the tungsten matrix through the nanochannel structures of low-angle symmetrical tilt grain boundaries may be a potential strategy to address the root causes of bubble nucleation and swelling of tungsten material.

Viewpoint: Can symmetric tilt grain boundaries represent polycrystals?

Grain boundaries control a wide variety of bulk properties in polycrystalline materials, so simulation methods like density functional theory are routinely used to study their structure-property relationships. A standard practice for such simulations is to use compact, high-symmetry (coincident site lattice) boundaries as representatives of the much more complex polycrystalline grain boundaries. In this letter, we question this practice by quantitatively comparing the spectra of atomic sites and properties amongst grain boundaries. We show, using solute segregation as an example property, that highly symmetric tilt boundaries (with Σ values less than 10) will fail to capture polycrystalline grain boundary environments, and thus lead to incorrect quantitative and qualitative insights into their behavior.

Ab initio calculations and empirical potential assessments of the energy and structure of symmetric tilt grain boundaries in tungsten

Molecular statics/dynamics (MS/MD) based on empirical interatomic potentials (IAPs) is an effective means for conducting grain boundary (GB) related studies. The accuracy of these MS/MD simulations, however, can be greatly affected by the IAP used. Unfortunately, the large discrepancies between the ab-initio values make it difficult to evaluate, improve and further develop IAPs. Motivated by this issue, in the present work we perform a systematic investigation of 〈100〉 and 〈110〉 symmetric tilt GBs in tungsten (W) via atomistic simulations, including the stable structure, GB energy, work of separation, excess volume, and vacancy formation energy. We here use a two-step relaxation process, initially obtaining the candidate structures from MS and then performing DFT validation of these structures to determine the ground state structure, where six empirical IAPs and four exchange–correlation (xc) functionals are used. And the step-like feature is revealed that can be used to reduce the cost of time-consuming optimization processes. Taking the results yielded by PBEsol xc-functional as a benchmark, it is shown that for the same xc-functional, the relative errors of GB energy and work of separation are almost identical, independent of the GB character. The performance of six typical empirical IAPs considered for W is also evaluated by comparing it with the DFT data. The quantities chosen for the comparison include the structure and energetic properties of GBs, as mentioned before. We demonstrate that these empirical IAPs tend to better describe only part of the properties of GBs; for example, some IAPs can predict the energetic properties well, while others can better describe the structure. This suggests that a fully reliable description of GBs remains an elusive objective, requiring further efforts in the development and optimization of the IAP.

Influence of symmetric/asymmetric boundaries on axisymmetric convection in a cylindrical enclosure in the presence of a weak vertical throughflow

The linear and nonlinear stability of axisymmetric convection of a viscous fluid in a cylindrical enclosure heated from below is investigated for various radius to height ratios. A weak vertical throughflow is imposed in a gravity-aligned or a gravity-opposing manner. Symmetric and asymmetric boundaries of free-free, rigid-rigid and rigid-free types are considered for lower and upper boundaries with isothermal temperature boundary condition. The side-walls are assumed to be rigid and adiabatic. A convergent Maclaurin series representation is considered for the finding of axial trial eigenfunctions. In order to corroborate the results of the present study with those of a previous investigation, the critical Rayleigh number and the number of radial rolls manifesting for any given aspect ratio are determined in the case of no throughflow and an exact match is found. Further, the influence of boundaries and the effect of throughflow on chaotic and periodic regimes of motion are studied with the help of a time series solution and the largest Lyapunov exponent as indicators of chaos. The novelty of the present study is the use of a Maclaurin series representation for the eigenfunctions of the linear problem and using the same in determining the solution with the convective mode.

Defect sites on symmetric coupling two-channel boundaries

Defect sites on symmetric coupling two-channel boundaries

Effect of symmetrical and asymmetrical tilt grain boundaries with as the tilt axis on the shock response of bi-crystalline Ni

Aim of this article is to study the effect of tilt grain boundaries on the shock response of single and bi-crystalline nickel. Nickel is commonly used in many structural applications, but research on dynamic response is very limited or in an immature stage. In this article, molecular dynamics-based simulations were performed in conjunction with embedded atom method potential to quantify the response of shock in bi-crystalline Ni containing symmetrical or asymmetrical tilt grain boundaries. Simulations were performed under the influence of adiabatic conditions. Compressive ultra-shock pulse of width 2 ps was simulated in the simulation box; stress, particle velocity, dislocation emission and phase transformation were quantified for symmetrical and asymmetrical tilt grain boundaries in bi-crystalline Ni. It was concluded from the simulations that higher mis-orientation angle between the crystals of Ni help in retarding the shock front velocity and stress. The alternation in the shock front behavior was associated with the change in deformation governing mechanism. The emission of dislocations and formation of Lomer Cottrell lock governs deformation in symmetrical tilt grain boundary configurations under shock pulse loading. It was concluded from the set of simulations that plastic deformation blunts the shock front in bi-crystalline Ni, whereas the sharp shock front was observed in single crystal Ni. Radial distribution function in post shock atomistic configurations was performed to capture the stability of the crystal in post shock scenario. Asymmetrical tilt grain boundaries are not as efficient in restricting the shock front as symmetrical tilt grain boundary configurations.

Loading-unloading of spherical and cylindrical cavities in cohesive-frictional materials with arbitrary radially symmetric boundary conditions

Many scenarios in geotechnical engineering involve cavity unloading from a loaded state under different boundary conditions, especially for thick-walled cylinder tests in laboratory conditions. A novel analytical cavity expansion-contraction solution is proposed for modeling thick-walled cylinder tests during a complete loading-unloading process under arbitrary symmetric boundary conditions. The proposed solution has potential implication in investigating ambiguous boundary effects for problems involving cavity expansion-contraction. The mechanical model considers two concentric layers of materials around the cavity, where the inner layer is considered as cohesive-frictional and the circumambient infinite layer is assumed as elastic to simulate the arbitrary radially symmetric boundary condition, including two extreme scenarios with constant-pressure and zero-displacement boundaries. The derived solution provides the evolutions of cavity pressure and distributions of stresses and displacements in both layers during the loading-unloading process, which is then rigorously validated against finite element results. The effects of boundary conditions and size of the cohesive-frictional layer have been comprehensively investigated by analyzing the cavity pressure and the developments of plastic zones during expansion and contraction. The developed solution has been proved to be applicable in geotechnical engineering, with comparisons between analytical results and experimental data for pressuremeter tests in calibration chambers and pile installation tests in a rigid container. The proposed solution might also be helpful in the analysis of autofrettaged pressure vessels.

Electromagnetic analysis and detent force minimization of a linear vernier motor

This paper proposes a new dual-sided linear permanent magnet vernier motor (LPMVM). The advantages of high thrust density, low thrust ripple, positive force elimination and structural stability are introduced in detail. The double-sided structure and toroidal winding proved the novelty of the machine tool, which is suitable for high definition digital control machine tools. Firstly, the basic structure and working principle of the engine are introduced. Through theoretical analysis, the expressions of electromagnetic thrust and detent force are derived. Thirdly, basic characteristics of permanent magnetic magnet flux coupling, backless electromotive force, detent force and electromagnetic drive are analyzed by using a a simplified three-phase model with symmetric boundary in 3-D finite element analysis. Finally, the thrust density and the detent force of the designed motor are calculated and analyzed. The results show that the designed motor is superior to the linear permanent magnet synchronous motor.

Numerical Calculation of Thermal Radiative Boundary Layer Nanofluid Flow across an Extending Inclined Cylinder

This research presents the numerical analysis of the fluid flow containing the micro gyrotactic organism with heat and mass transfer. The flow is allowed to pass through an inclined stretching cylinder with the effects of heat generation/a heat source and activation energy subject to the symmetric boundary conditions at the cylinder walls. Similarity transformation is employed in the system of PDEs (partial differential equations) to transform them into non-dimensional ODEs (ordinary differential equations). The solution to the proposed problem is obtained by using the bvp4c (numerical scheme). The graphical results are plotted for various flow parameters in order to show their impact on the flow, mass, energy, and motile microorganism profiles. Moreover, the angle of inclination disturbs the flow within an inclined cylinder and slows down the fluid motion, while it elevates the energy of the fluid inside an inclined cylinder. Similarly, the curvature effect is also highlighted in the dynamics of fluid velocity, temperature, and the motile microorganism profile. From the obtained results, it is elucidated that growing values of the curvature factor accelerate the temperature, velocity, and motile microbes’ profiles. Finally, some engineering quantities are calculated in terms of skin friction, the Nusselt and Sherwood number, and the density of motile microbes. The acquired results are also displayed in tabular form.

Modeling of disc springs based on energy method considering asymmetric frictional boundary

Disc springs have excellent ability to absorb and dissipate energy, and are widely used as basic vibration isolation units in the design of vibration isolators for naval power systems. Focusing on the effect of friction on disc springs, a mechanical model of disc springs considering asymmetric frictional boundary is developed. The additional load to overcome the Coulomb friction damping is derived analytically by the energy method. Finite element analysis of disc springs is carried out and the results for large and small frictional conditions are compared with the theoretical results. Quasi-static experiments on disc springs are carried out and the proposed method is further validated. The results show that the analytical model based on energy method can describe the load–displacement characteristics of disc springs and their combinations under symmetric and asymmetric frictional boundaries accurately. Based on the analytical solution, the influence of the structural parameters of the disc springs on the damping effect is investigated. The stiffness and damping of disc springs are linearly related to the friction coefficient. In addition, the magnitude of the effect of asymmetry of the boundary friction on the mechanical properties of the disc springs varies with the structural parameters.

Numerical Simulation of Train-Induced Structural Vibration

Train-induced structural vibration caused more and more attentions nowadays, and the present paper developed a numerical approach of train-induced structural vibration simulation with ANSYS software. The finite element model is composed by buildings, rail, sleepers, ballast and several layers of soil, and the moving load is represented by wheel-rail coupling forces, and both solid element, shell element and beam element are used in the finite element model. Acceleration time history and vibration levels of the key point on the buildings are given, and effect of different wheel-rail coupling forces and the dynamic response of the building are also numerically investigated. Comparisons of free boundary, symmetric boundary, fixed boundary and transmitting boundary conditions on the dynamic responses are also illustrated. Numerical results show that, both boundary condition and load type could affect the dynamic response of the structures near the train tracks, and validation test should be performed firstly to determine the proper boundary condition and load amplitude and frequency. The proposed numerical method provides a powerful technic tool for numerically predicting the dynamic response of train-induce structural vibration, and could also be employed to evaluate the vibration control results of different approaches.

Nonmetallic trace elements induced rhenium co-segregation in nickel Σ5 [001](210) symmetrical tilt grain boundary

The thermally/mechanically-driven structural instability of nano- and coarse-grained polycrystalline metals originates from the unstable grain boundaries (GBs). GB segregation of solute elements could not only stabilize but also embrittle GBs. To improve GB stability and cohesion in parallel via solute segregations, in this work the segregation behavior of six non-metallic impurities X at the Σ5 [001](210) GB of nickel-based alloys, their co-segregations with Re element that has no GB segregation tendency, and segregation-induced changes in GB properties were investigated comprehensively from first-principles calculations. We discovered that these nonmetallic elements can segregate to the Ni GB and thus stabilize it, but they are GB embrittlers except B. Annealing temperature and bulk concentration have no effect on the S segregation. With the X pre-segregations, induced GB segregations of Re were observed, which lowers the excess energy and enhances the cohesive strength of all X-segregated GBs. The attractive interactions between C/N/B and Re atoms promote the Re segregation. The stabilizing and strengthening mechanisms of Re segregation were mainly attributed to the changes in Fermi level location and the increased interplanar bonding, respectively. Our findings may gain more insights into the atomic-scale GB co-segregations and stabilization of polycrystalline Ni-based alloys.