Symmetric Boundary Research Articles

Characterization and visualization of grain boundary disconnections

We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional grain boundary phase nucleus in a symmetric tilt grain boundary in tungsten. This method can be applied to both bulk dislocations and grain boundary disconnections, which makes it ideal for studying the interactions and reactions of bulk dislocations with grain boundaries, and grain boundary disconnections.

Dynamic mixing models and analysis of the mixing processes for an oxidation ditch and an aeration tank.

A one-dimensional longitudinal mixing model for an oxidation ditch with a moving symmetrical boundary and a series model for a symmetric aeration mixing unit of an aeration tank were developed in this study to analyze their mixing processes. The analysis of these models showed that the mixing process in the oxidation ditch tended to that of a continuous stirred tank reactor (CSTR) in a mode of circulation flow and dispersion; however, the mixing in the aeration tank tended to that of a CSTR in a mode of dispersion. The tracer output patterns and complete mixing times of the oxidation ditch and aeration tank with treatment capacities of 1000-50,000 m3 /d and hydraulic retention time 12.0h were evaluated. The complete mixing time increased from 7.5min to 128.5min for the aeration tank with an increase in volume; and the oxidation ditch with same complete mixing time as that of the aeration tank was obtained. The complete mixing time for the oxidation ditch can be changed in a wider range, for matching the time scale of biochemical degradation of organic pollutants. PRACTITIONER POINTS: Mixing model of an oxidation ditch and an aeration tank were built. Mixing in oxidation ditch tends to that of CSTR in a mode of circulation flow and dispersion. Mixing in an aeration tank is in accordance with advection diffusion and tends to that of CSTR as its Peclet number is large. Complete mixing time for an oxidation ditch can be changed in a wider range.

O. A. Ladyzhenskaya’s System of Equations of Symmetric Boundary Layer of Modified Fluid

In this paper, we study the system of equations of a boundary layer for a nonlinearly viscous, electrically conductive liquid described by a rheological law proposed by O. A. Ladyzhenskaya for incompressible media. The boundary-layer equations for the Ladyzhenskaya model were first obtained from Prandtl’s axioms. By the Mises transform, the system of boundary-layer equations can be reduced to a single quasilinear equation. The main method used in this paper is the Crocco transform, which turns the system of boundary-layer equations into a quasilinear degenerate parabolic equation. In contrast to the Mises variables, the Crocco substitution allows one to study both stationary and nonstationary equations.

Effect of Symmetric Tilt and Twist Grain Boundaries on the Void Nucleation, Growth and Spall in polycrystalline Al : Multiscale modelling

Multiscale modelling using molecular dynamics (MD) and hydrodynamics (HD) in sequence is carried out to obtain the dynamic spall strength of aluminum (Al). Specifically, we simulate the effect of symmetric tilt and twist grain boundaries (GB) on the void nucleation and growth in Al using MD and transfer the information to HD simulations of plate impact. MD is used to create bi-crystals mimicking 11 tilt and 12 twist grain boundaries (GB) along <100>, with orientation angles spanning 0° to 90° using an NPT ensemble. The grain boundary energy (GBE) is validated with published results. MD simulations of the tri-axial tensile deformation of the Al bi-crystals show that the voids nucleate at the grain boundaries and then grow and coalesce. The time history of the bulk pressure and void volume fraction are recorded for calculating the material specific parameters of a void nucleation and growth (NAG) fracture model. 1-D Hydrodynamic flyer plate impact simulations are performed using these NAG parameters to obtain the free surface velocity vs time curve. The spall strength and spall thickness of Al, estimated from the free surface velocity profile, show a good match with published experimental values of the dynamic spall strength (relative error of 2.2%–6%) and spall thickness (relative error of 2.4%–4%) for three impact velocities viz. 518, 1588, and 2275 m/s respectively.

Evaluation of structural and mechanical strength of symmetric tilt interface in W/Fe composite laminate using molecular dynamics

In this work, a tungsten (W)/iron (Fe) composite laminate is constructed by joining two constituents W and Fe according to the symmetric tilt interface relationship. The performance of the newly built W/Fe symmetric tilt interfaces is evaluated by interface energy, tensile stress–strain relationship, and strength and then compared with semi-coherent W/Fe boundaries and W and Fe symmetric tilt grain boundaries. The results show that even though most W/Fe symmetric tilt interfaces have very high interface energy, some have interface energy comparable to those of semi-coherent W/Fe boundaries and W and Fe symmetric tilt grain boundaries, and thus should be considered for W/Fe composites. The mechanical properties for tensile deformation parallel to the interface of these stable W/Fe symmetric tilt interfaces outperform the estimated values from composite theory and even those of semi-coherent W/Fe boundaries. Our findings suggest that the symmetric tilt interfaces not only play an important role in the interface strength of W/Fe composite laminate, but also should be incorporated into future designs of W/Fe or other composites to circumvent the lattice, thermal, and mechanical mismatches between heterogeneous constituents.

Stabilization and Self-Passivation of Grain Boundaries in Halide Perovskite by Rigid Body Translation.

The physical properties of grain boundaries in halide perovskites, especially their atomic structure, have not been fully understood yet. We report that Σ5 [130] symmetrical tilt grain boundaries can be stabilized by rigid body translation which is moving one side of the grain parallel with respect to the adjacent grain. Such reconstruction passivates grain boundaries by removing Pb-Pb and I-I interactions that introduce shallow defect states in the band gap. Rigid body translation also stabilizes the [110] antiphase boundary as well in both CsPbI3 and CsPbBr3.

Numerical calculation of rock deformation during mining operations

The paper analyzes the classical definition of the stress field of an intact rock mass and proposes a new one. The definition of the daytime surface is generalized in the case of a work-out that goes to the border. The process of transition to the additional task of calculating elastic stresses and displacements near mutually influencing workings, independent of the own weight of the removed rocks, is described. A two-dimensional version of an array of rocks is considered. The presence of a recess, workings presupposes the removal of rocks in an appropriate volume, which only causes displacements and stresses. Models from elastic to elastic-plastic do not take into account the own weight of rocks and other irreversible processes, but consider weightless areas of counting. If the area of the rock deformation account near the mine contains an infinitely distant point, then, according to the general theory of equations of mathematical physics, the stresses and displacements found tend to zero when moving away from the cavity, a well-known fact in practice. The results obtained are significant when the transition from open to underground mining of minerals takes into account the sequence of workings, without which there is no mining. It is proved that the calculation of deformation in the vicinity of any weakening is carried out only through an additional task, formulating symmetric boundary conditions on the contour due to the refusal to take into account the weight of rocks.

Dean instability and vortex-induced mixing for two miscible fluids in T-micromixers

Based on the theory of Dean instability, the mixing process of two miscible fluids in a T-micromixer was investigated under symmetric and asymmetric inlet boundary conditions. The secondary vortex structures at selected cross-sections along the micromixer were obtained by CFD simulation and presented with different vortex identification methods. The mixing characteristics under the influences of vortices were qualitatively and quantitatively analyzed. The results demonstrate that four types of secondary vortex structures could be formed and developed in the micromixer, depending on the Dean number. For the symmetric inlet boundary condition, stable secondary vortex structures will increase the species contact areas, thus the engulfment Dean vortices provide much stronger mass transfer in the transversal direction compared with the asymmetric one. This study can provide an insight into the underlying vortex phenomena behind the mixing in a T-micromixer.

Theory of spontaneous grain boundary roughening in high entropy alloys

High Entropy Alloys (HEAs) are a new broad class of near-random solid solution alloys that can possess some impressive mechanical and physical properties including high stability against grain growth (i.e. low grain boundary (GB) mobility). Here, it is shown that an initially flat GB in an HEA can become spontaneously rough, driven by natural local compositional fluctuations. Roughening lowers the total GB energy and thus can inhibit migration. A parameter-free theoretical framework is developed to demonstrate the energetics and size scales of the roughening in terms of solute/GB interaction energies and GB disconnection energies. Above a critical level of solute/GB interactions, a planar GB is predicted to roughen down to the scale of the GB periodic unit. A similar theory for 1D GBs (minimum periodic length in one direction) is also developed since such geometries are common in atomistic simulations. Specific predictions are made for the [100] symmetric tilt boundaries Σ17[100](530) and Σ5[100](310) in a model CoCuFeNi alloy and atomistic simulations demonstrate roughening consistent with the theory. Analysis of the stresses needed to drive migration shows how migration can be inhibited or enhanced, rationalizing variations in mobility of GBs in HEAs.

Complexions and stoichiometry of the 60.8°//[100](011) symmetrical tilt grain boundary in Mg2SiO4 forsterite: A combined empirical potential and first-principles study

AbstractIn this work we explore the low-energy complexions of the symmetrical tilt grain boundary (GB) 60.8°//[100](011) in forsterite through molecular dynamics and first principles calculations. Using a conservative sampling, we find six stoichiometric complexions with energies ranging from 0.66 to 1.25 J/m2. We investigate the segregation of MgO vacancy pairs, and find that in most cases it is more favorable for the vacancies to lie within the GBs than in the surrounding crystals, leading to new atomic structures. From these results we infer that at finite temperature when vacancies are present in the system, GBs are likely to absorb them and to be non-stoichiometric. We find many GB complexions containing a free oxygen ion, which may have profound implications for geological processes.

Weakly-singular symmetric Galerkin boundary element method in thermoelasticity for the fracture analysis of three-dimensional solids

The Symmetric Galerkin Boundary Element Method has demonstrated significant advantages for the fracture mechanics analysis of three-dimensional solid structures. However, when dealing with structures in thermal environments, strongly-singular domain integrals resulting from the temperature field require meshing of the interior of the domain. In this paper, formulation and implementation of the weakly-singular SGBEM of three-dimensional thermoelastic intact and cracked solids are presented where temperature-induced domain integrals are transformed into boundary integrals. The strong singularity of these temperature-induced integrals is reduced to the weak singularity by exploring the feature of double-layer surface integrals in the SGBEM. Obtained temperature-induced boundary integrals affect only the right-hand-side vector of the SGBEM equation, and therefore the advantages of the SGBEM, such as the symmetry of the stiffness matrix, are retained. Several examples of three-dimensional solids with or without cracks subjected to thermal loadings are presented to validate the developed methods. Advantages and disadvantages of SGBEMs with different temperature-induced boundary integrals are also discussed.

Central mean temperature scaling in compressible turbulent channel flows with symmetric isothermal boundaries

Originating from the generalized Reynolds analogy theory, an empirical scaling for the central mean temperature in compressible turbulent channel flow with symmetric isothermal boundaries is proposed. The empirical scaling is quite accurate and most of the relative errors are below 1.5% as assessed by available direct numerical simulation data at various Reynolds and Mach numbers. The mean temperature profile can be quantitatively obtained through the mean velocity with empirical scaling.

Novel methods for measuring the thermal diffusivity and the thermal conductivity of a lithium-ion battery

Thermal conductivity is a fundamental parameter in every battery pack model. It allows for the calculation of internal temperature gradients which affect cell safety and cell degradation. The accuracy of the measurement for thermal conductivity is directly proportional to the accuracy of any thermal calculation. Currently the battery industry uses archaic methods for measuring this property which have errors up to 50 %. This includes the constituent material approach, the Searle’s bar method, laser/Xeon flash and the transient plane source method. In this paper we detail three novel methods for measuring both the thermal conductivity and the thermal diffusivity to within 5.6 %. These have been specifically designed for bodies like lithium-ion batteries which are encased in a thermally conductive material. The novelty in these methods comes from maintaining a symmetrical thermal boundary condition about the middle of the cell. By using symmetric boundary conditions, the thermal pathway around the cell casing can be significantly reduced, leading to improved measurement accuracy. These novel methods represent the future for thermal characterisation of lithium-ion batteries. Continuing to use flawed measurement methods will only diminish the performance of battery packs and slow the rate of decarbonisation in the transport sector.

Molecular Dynamics Study of Phosphorus Migration in Σ3(111) and Σ5(0-13) Grain Boundaries of α-Iron

Phosphorus atoms in steels accumulate at grain boundaries via thermal and irradiation effects and induce grain boundary embrittlement, which is experimentally confirmed by an increase in the ductile-brittle transition temperature. Quantitative prediction of phosphorus segregation at grain boundaries under various temperature and irradiation conditions is essential for preventing embrittlement. To develop a model of grain boundary phosphorus segregation in α-iron, we studied the migration of a phosphorus atom in two types of symmetrical tilt grain boundaries (Σ3[1-10](111) and Σ5[100](0-13) grain boundaries) using molecular dynamics simulations with an embedded atom method potential. The results revealed that, in the Σ3 grain boundary, phosphorus atoms migrate three-dimensionally mainly in the form of interstitial atoms, whereas in the Σ5 grain boundary, these atoms migrate one-dimensionally mainly via vacancy-atom exchanges. Moreover, de-trapping of phosphorus atoms and vacancies was investigated.

Co-segregation behavior and weakening effect of the major elements in Al-Zn-Mg-Cu series alloys on Al Σ3(111)[110] symmetrical tilt grain boundary: a first-principles study

This study comprehensively investigated the co-segregation behavior of Mg, Zn, and Cu atoms at the Al Σ3(111)[110] symmetrical tilt grain boundary (GB) and its strengthening effect on the GB strength by first-principles calculation. The atoms of the three elements had a strong tendency to segregate at the GB based on the calculation of the segregation energy. The order of their co-segregation was Mg, Zn, and Cu, respectively. The change of the bond lengths between atoms near the GB increased/decreased the charge density attributed to the different atomic radii of the elements. The separation energy and tensile strength of the Al Σ3(111)[110] GB decreased with the preferential segregation of Mg first, then continued decreasing with the co-segregation of Zn, and finally increased with the co-segregation of Cu, decreasing overall. These results suggest that the co-segregation behavior of Mg, Zn, and Cu atoms at the Al Σ3(111)[110] symmetrical tilt GB embrittles the GB and reduces the mechanical properties of the alloy. Besides, O and H atoms further reduce the strength of the GBs co-segregated by Zn, Mg, and Cu.

Highly Transparent and Polarization-Maintained Terahertz Plasmonic Metamaterials Based on Metal-Wire-Woven Hole Arrays: Fundamentals and Characterization of Transmission Spectral Peaks.

Metal-hole-supported terahertz (THz) waves through the structure of a metal-wire-woven hole array (MWW-HA) present high-frequency-passed transmittance spectra of one plasmonic metamaterial with artificial plasmonic frequencies, which are inversely proportional to metal-hole widths. For the transmitted THz waves of MWW-HA, transverse-electric (TE) and transverse-magnetic (TM) waveguide modes mix within a symmetric metal-hole boundary. THz resonance waves transversely crossing the holes of MWW-HA are experimentally characterized with spectral peaks in the frequency range of 0.1–2 THz that are correlated with aperture sizes, unit-cell-hole widths, metal-wire thicknesses, and wire-bending angles. The metal-hole-transported resonance waves of MWW-HA are dominated by TE waveguide modes instead of TM ones because a hole width of MWW-HA is approximate to the half wavelength of a resonance wave. The round metal edges of the woven metal wires can minimize the effective optical length of a thick metal hole to transmit THz resonance waves, thereby resulting the smallest rotation angle of linear polarization and high transmittance up to 0.94. An MWW-HA structure is therefore reliable for supporting metal-hole resonance waves with low resistance, whereas a metal-slab-perforated hole array cannot achieve the same result.

Large Amplitude Axisymmetric Free Vibration of a Closed Two-Dimensional Spherical Pressure Vessel with a Constrained Volume

The nonlinear axisymmetric vibrational modes of a closed two-dimensional spherical pressure vessel with a constrained volume are presented using the fundamental forms of surfaces. The strain energy of the spherical pressure vessel is derived as a quadratic function of the initial Eulerian, added, and total Lagrangian strains. Two-dimensional bilinear elements described in spherical polar coordinates with the symmetric boundary condition along both sides of the meridian line are used for investigating the nonlinear axisymmetric mode shapes of a spherical pressure vessel. Numerical results were obtained by a nonlinear finite element approach and verified in the case of an empty spherical shell for both lower and upper branches. This study showed that the spherical pressure vessel gave a higher nonlinear axisymmetric natural frequency than the empty spherical shell. The elastic modulus has a large effect on the nonlinear axisymmetric frequencies of both the lower and upper branches for the spherical pressure vessel. Changing the thickness and initial internal pressure significantly affects only the lower branch of the spherical pressure vessel at high mode numbers. The results also indicate that the ratios of the nonlinear natural frequencies of the lower to upper branches decrease when the vibrational modes increase.

Modelling of the fatigue cracking resistance of grid reinforced asphalt concrete by coupling fast BEM and FEM

We present a computational modelling approach aimed at investigating the effect of fibre grid reinforcement on crack opening displacement and fatigue crack propagation. Grid reinforcements are modelled using elastic membrane finite elements, while the cracked concrete is treated using a symmetric boundary element method (BEM), which in particular allows easy geometrical modelling and meshing of cracks. The BEM is accelerated by the fast multipole method, allowing the handling of potentially large BEM models entailed by three-dimensional configurations hosting multiple cracks. Fatigue crack growth is modelled using the Paris law. The proposed computational approach is first verified on a reinforced cracked beam, and then applied to a three-dimensional configuration featuring a grid-reinforced asphalt pavement.

Real-Time Prediction of Probabilistic Crack Growth with a Helicopter Component Digital Twin

To deploy the airframe digital twin or to conduct probabilistic evaluations of the remaining life of a structural component, a (near) real-time crack-growth simulation method is critical. In this paper, a reduced-order simulation approach is developed to achieve this goal by leveraging two methods. On the one hand, the symmetric Galerkin boundary element method–finite element method (SGBEM-FEM) coupling method is combined with parametric modeling to generate the database of computed stress intensity factors for cracks with various sizes/shapes in a complex structural component, by which hundreds of samples are automatically simulated within a day. On the other hand, machine learning methods are applied to establish the relation between crack sizes/shapes and crack-front stress intensity factors. By combining the reduced-order computational model with load inputs and fatigue growth laws, a real-time prediction of probabilistic crack growth in complex structures with minimum computational burden is realized. In an example of a round-robin helicopter component, even though the fatigue crack growth is simulated cycle by cycle, the simulation is faster than real-time (as compared with the physical test). The proposed approach is a key simulation technology toward realizing the digital twin of complex structures, which further requires fusion of model predictions with flight/inspection/monitoring data.

Exploiting symmetries in skyrmionic micromagnetic simulations: Cylindrical and radial meshes

Micromagnetic simulations are an essential tool in the theoretical study of magnetic skyrmions. When confined into nanometric samples, these structures can serve as bits of information among other possible applications. Accurate simulations are one of the major sources of theoretical results. In the case of confined skyrmions, it is known that the boundaries play a critical role in their stabilization. However, most of the micromagnetic simulations are done using a finite-difference method with quadrilateral meshes, that do not exactly fit the boundaries. The use of this mesh can introduce a significant numerical error that can completely change the results of the simulations. We present here two different finite-difference meshes to study skyrmions in confined disks, taking advantage of the symmetry of that geometry. A two-dimensional cylindrical mesh for non-symmetric scenarios but geometrically symmetric (boundary conditions) that reduces the propagation of the numerical error, and the particular case of a one dimensional mesh for axisymmetric scenarios where the computation time is hugely reduced.