Boundary Plane Research Articles

Evanescent Acoustic Waves

A theoretical study of “geometric” SP-evanescent (head) waves propagating in an isotropic homogeneous half-space or half-plane with a free boundary shows that these waves can satisfy the condition of absence of effort on the boundary plane if and only if the Lamé parameter λ is vanishingly small, which makes the existence of head waves of this type practically impossible. The analysis is based on the Helmholtz representation for the displacement field in combination with the decomposition of the stress and strain tensor into spherical and deviatoric parts. The obtained result about the non-existence of this type of evanescent waves can find application in theoretical geophysics in the study of seismic wave fields in the vicinity of earthquake epicenters, as well as in non-destructive acoustic diagnostic methods.

Data-Guided Low-Reynolds-Number Corrections for Two-Equation Models

Abstract The baseline Launder–Spalding k−ε model cannot be integrated to the wall. This paper seeks to incorporate the entire law of the wall into the model while preserving the original k−ε framework structure. Our approach involves modifying the unclosed dissipation terms in the k and ε equations specifically within the wall layer according to direct numerical simulation (DNS) data. The resulting model effectively captures the mean flow characteristics in both the buffer layer and the logarithmic layer, resulting in robust predictions of skin friction for zero-pressure-gradient (ZPG) flat-plate boundary layers and plane channels. To further validate our formulation, we apply our model to boundary layers under varying pressure gradients, channels experiencing sudden deceleration, and flow over periodic hills, with highly favorable results. Although not the focus of this study, the methodology here applies equally to the k–ω formulation and yields improved predictions of the mean flow in the viscous sublayer and buffer layer.

Misorientations across interfaces in spark plasma–sintered WC–Co cemented carbides

AbstractThis interdisciplinary work concerns misorientations across various interfaces in spark plasma–sintered (SPSed) WC–Co cemented carbides, as well as how these misorientations affect the intergranular fracture. The whole boundaries in cemented carbides were divided according to the phases on the two sides of the boundary plane, and carbide/carbide grain boundaries were further divided according to the misorientation across the boundary plane. Stereological statistics and five‐parameter analysis were comprehensively performed on the concerned boundary types. For Σ2 carbide/carbide boundaries, multiple boundary structures are observed. How Σ2 twist inhibits intergranular fracture and how such boundary structure is formed are analyzed. For random carbide/carbide boundaries, the habit planes that they are terminated by are calibrated, and their responses to intergranular fracture are examined according to their energy anisotropy. For WC/α‐cobalt and WC/β‐cobalt phase boundaries, misorientations across these boundary planes and the corresponding crack propagation routines are illustrated. On these bases, approaches to improve the fracture strength of SPSed cemented carbides are suggested.

Sink strength of grain boundaries for point defects in irradiated ferritic/martensitic steel

Dislocation-free ferritic/martensitic steel: F82H was prepared by heat-treatment in the appropriate condition in order to investigate the sink strength of grain boundaries for point defects. The size and the areal density of irradiation-induced secondary defects, such as dislocation loops and voids, were investigated in electron-irradiated F82H. The in-situ irradiation experiment resulted in the formation of a defect free zone and the gradient distribution of loop and cavity as a function of distance from boundaries, especially around prior austenite grain boundaries. The atomic density ratio of grain boundary planes is a key parameter in determining the width of defect free zone; a grain boundary with a higher atomic density ratio typically exhibits a wider defect free zone compared to one with a lower ratio. These results clearly indicate that the distribution of irradiation-induced secondary defects in ferritic/martensitic steels is not uniform and is likely controlled by the sink strength, as characterized by the atomic density ratio of grain boundary planes.

The adverse effect of grain refinement on hydrogen embrittlement in a high Mn austenitic steel

This study presents a novel observation wherein the reduction in grain size (GS) from 20 μm to 1 μm in austenitic steel adversely affects hydrogen embrittlement (HE). The findings indicate an increase in total absorbed hydrogen with grain refinement when subjected to cathodic hydrogen charging. The results demonstrate that even with grain refinement to 1 μm, the primary mode of hydrogen damage remains intergranular, with a significant increase in relative elongation loss (REL%). This phenomenon is attributed to the early nucleation of intergranular hydrogen-induced cracks (HICs) and the accelerated propagation rates of HICs, leading to local stress increments and rapid alloy failure. The accelerated development of HICs is ascribed to the impact of grain refinement on intensified normal stress exerted on grain boundary planes, as well as the suppression of ε-martensite and its positive effect on crack arresting. Besides the enhanced degradation rate of the hydrogen-affected area (HAA) due to grain refinement, the higher ratio of HAA to the entire cross-sectional area was identified as a crucial factor contributing to rapid failure and the inverse effect of grain refinement on HE resistance.

Machine learning-based prediction of FeNi nanoparticle magnetization

This work proposes a computationally efficient approach for estimating the magnetization of Fe0.7Ni0.3 body-centered cubic (bcc) nanoparticles (NPs) at room temperature using machine-learning algorithms, in terms of the average magnetic moment per atom, ⟨μ⟩. The magnetization data of isolated NPs were generated using atomistic spin dynamics (ASD) simulations for various nanoparticle shapes (cubes, spheres, octahedra, cones, cylinders, ellipsoids, flakes, and pyramids, with or without nanovoids) and FeNi distributions (random, core-shell, onion, sandwich, and Janus with different boundary planes). More than 1600 NPs were created and split into training and testing sets (70%-30% split), with features including the number of Ni/Fe surface and core atoms, potential energy distributions, pair correlation functions, and coordination distributions. Several machine-learning algorithms, including Random Forest (RF), Elastic Net, Support Vector Regression (SVR), and Gradient Boosting Regression (CatBoost), were applied to predict the average magnetic moment per atom of these NPs. The best-performing models, CatBoost and RF, achieved R2 scores of up to 0.86, demonstrating their accuracy in predicting NP magnetization. Feature analysis highlighted the significance of the interface between Fe and Ni clusters, Fe-Fe interactions, and the presence of Fe on the surface as critical contributors to overall magnetization. Random alloy spherical NPs without porosity exhibited the highest ⟨μ⟩ ∼ 1.6μB due to reduced Ni-Ni interactions. Applying machine-learning methods significantly reduces computational time and memory requirements compared to traditional ASD simulations. This allows for rapid prediction of NPs with desired magnetic properties, making them suitable for various technological applications.

Mathematical framework for the plastic flow of fine-grained solids, from yield to fracture

A newly proposed mathematical approach to plastic flow, holding from yield to fracture, of a fine-grained polycrystal with no voids or cracks is reviewed and applied to commercial steels. The formalism models the polycrystal by a continuum array of random deformable polyhedra leaving no voids between them, which can slide past each other along the shared faces when the shear stress resolved in the face plane exceeds a finite threshold. Grain reshaping for preserving matter continuity induces local forces assumed much weaker than those causing sliding. The relative velocity of adjacent sliding grains is taken as proportional to the local shear stress resolved in the common boundary plane. Explicit equations are derived for the plastic deformation, from yield to fracture. The analysis of mechanical tests of two commercial stainless steels is shown to illustrate how well the theory agrees with practice.

Determination of five-parameter grain boundary characteristics in nanocrystalline Ni-W by scanning precession electron diffraction tomography

Determining the full five-parameter grain boundary characteristics from experiments is essential for understanding grain boundaries impact on material properties, improving related models, and designing advanced alloys. However, achieving this is generally challenging, in particular at nanoscale, due to their 3D nature. In our study, we successfully determined the grain boundary characteristics of an annealed nickel-tungsten alloy (NiW) nanocrystalline needle-shaped specimen (tip) containing twins using Scanning Precession Electron Diffraction (SPED) Tomography. The presence of annealing twins in this face-centered cubic (fcc) material gives rise to common reflections in the SPED diffraction patterns, which challenges the reconstruction of orientation-specific virtual dark field (VDF) images required for tomographic reconstruction of the 3D grain shapes. To address this, an automated post-processing step identifies and deselects these shared reflections prior to the reconstruction of the VDF images. Combined with appropriate intensity normalization and projection alignment procedures, this approach enables high-fidelity 3D reconstruction of the individual grains contained in the needle-shaped sample volume. To probe the accuracy of the resulting boundary characteristics, the twin boundary surface normal directions were extracted from the 3D voxelated grain boundary map using a 3D Hough transform. For the sub-set of coherent Σ3 boundaries, the expected {111} grain boundary plane normals were obtained with an angular error of <3° for boundary sizes down to 400 nm². This work advances our ability to precisely characterize and understand the complex grain boundaries that govern material properties.

A new understanding of hydrogen-assisted cracking of coarse-grained heat-affected zone in X65 pipeline steel through {110} lath bainite boundary texture

The susceptibility of subzones of the coarse-grained heat-affected zone (CGHAZ) in X65 pipeline steel to hydrogen embrittlement was studied through an in situ crack-tip opening displacement test in an H2S-containing environment. The intercritically reheated CGHAZ (IC-CGHAZ) exhibited the highest embrittlement factor of 89.4%, compared to 64.0% for the sub-critically reheated CGHAZ (SC-CGHAZ). Hydrogen transportation by dislocations to massive-slender martensite/austenite (M/A) constituents initiated cracks in IC-CGHAZ. Deterioration of lath bainite (LB) boundaries, with separation of M/A-ferrite interface, accelerated crack propagation across prior austenite grains and promoted hydrogen-assisted degradation of fracture toughness. Reheated CGHAZ at a peak temperature of 620 °C led to an increased intensity of the {110} LB boundary texture by up to 52% in SC-CGHAZ. This enhanced texture facilitated dislocation slipping along {110} LB boundary planes, thereby promoting deformation compatibility and preventing the deterioration of LB boundaries in the presence of hydrogen.

Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

Molecular Dynamics Study on the Mechanical Behaviors of Nanotwinned Titanium

Titanium and titanium alloys have been widely applied in the manufacture of aircraft engines and aircraft skins, the mechanical properties of which have a crucial influence on the safety and lifespan of aircrafts. Based on nanotwinned titanium models with different twin boundary spacings, the impacts of different loadings and twin boundary spacings on the plastic deformation of titanium were studied in this paper. It was found that due to the different contained twin boundaries, the different types of nanotwinned titanium possessed different dislocation nucleation abilities on the twin boundaries, different types of dislocation–twin interactions occurred, and significant differences were observed in the mechanical properties and plastic deformation mechanisms. For the {101-2} twin, basal plane dislocations were likely to nucleate on the twin boundary. The plastic deformation mechanism of the material under tensile loading was dominated by partial dislocation slip on the basal plane and face-centered cubic phase transitions, and the yield strength of the titanium increased with decreasing twin boundary spacing. However, under compression loading, the plastic deformation mechanism of the material was dominated by a combination of partial dislocation slip on the basal plane and twin boundary migration. For the {101-1} twin under tensile loading, the plastic deformation mechanism of the material was dominated by partial dislocation slip on the basal plane and crack nucleation and propagation, while under compression loading, the plastic deformation mechanism of the material was dominated by partial dislocation slip on the basal plane and twin boundary migration. For the {1124} twin, the interaction of its twin boundary and dislocation could produce secondary twins. Under tensile loading, the plastic deformation mechanism of the material was dominated by dislocation–twin and twin–twin interactions, while under compression loading, the plastic deformation mechanism of the material was dominated by partial dislocation slip on the basal plane, and the product of the dislocation–twin interactions was basal dislocation. All these results are of guiding value for the optimal design of microstructures in titanium, which should be helpful for achieving strong and tough metallic materials for aircraft manufacturing.

Semi-analytical solutions of kinked edge cracks

A surface crack may advance either by further penetrating inward or by kinking out in response to possible variations in driving force or material properties. This paper provides a general approach to solve the planar elastic boundary value problem (BVP) of a kinked edge crack in a half-space. Semi-analytical solutions to BVPs with far-field uniform tension and concentrated loads on the free surface are given. The solution enable us to derive related information for reliability analysis, including stress fields, stress intensity factors (SIFs), and crack opening displacement (COD). An extension to the Cotterell–Rice formula (Cotterell and Rice, 1980) on SIFs for infinitesimal kinks is supplied, which is applicable to cracks with kinked segments of arbitrary length. Zooming in on a broadly concerned BVP of a cross-coating crack in a coating–substrate with a kink in the interface, we show the SIFs of the kink tip following an empirical formula K∗=αexp(−βah)+K∞∗ as a/h>0.2, where a is the length of the interface segment and h the coating thickness, and K∞∗ is the asymptotic solution by Thouless et al. (1987, 1989). The formula is in accord with existing solutions on the two asymptotic limits of the kinked part.

Rayleigh-type wave in non-planar pre-stressed nearly incompressible elastic structure

The primary objective of the current work is to establish the impacts of planar boundary and non-planar boundary on the displacement components (DCs) of Rayleigh-type wave propagation in an elastic structure. The elastic structure, precisely, incorporates a pre-stressed nearly incompressible elastic material in the half-space along with the non-planar boundary at the free surface. The methodology applied features variable separable technique and Taylor’s series expansion along with substitution method to establish the expressions for DCs and frequency relation. The frequency relation of Rayleigh-type wave is obtained for the situation considering planar free surface, which is further reduced as a special case of the study and validated with the classical result present in the literature. The DCs of Rayleigh-type wave have been numerically computed, and their reliance on wave number have been exhibited graphically. In addition to this, the influences of affecting parameters viz., hydrostatic stress, principal Cauchy stress and curvature parameter on DCs have been traced out. The computational result also manifests the domain of existence of Rayleigh-type wave propagating in the considered model in the presence of planar free surface.

Analytical solution for acoustic radiation force and torque on a spheroid near a rigid or free planar boundary.

An analytical solution is developed for the acoustic radiation force and torque caused by an arbitrary sound field that is incident on a compressible spheroid of any size near a planar boundary that is either rigid or pressure release. The analysis is an extension of a recent solution for a compressible sphere near a planar boundary [Simon and Hamilton, J. Acoust. Soc. Am. 153, 627-642 (2023)]. Approximations that account for a boundary formed by a two-fluid interface may be incorporated as in the previous analysis for a sphere. The present solution is based on expansions of the total acoustic pressure field in spheroidal wave functions and the use of addition theorems. Verification of the solution is accomplished by comparison with a finite element model. Examples are presented for incident fields that are either plane or spherical waves. Effects resulting from the presence of the boundary are studied by comparing the full theory with a simplified model in which multiple scattering is neglected. Numerical implementation of the proposed solution is also discussed.

Structural evolution and mechanical response of multiple Al Σ5(210) grain boundaries with segregation of solute atoms: First-principles study

Grain boundary (GB) segregation of solute atoms is a key factor affecting the microstructure and macroscopic properties of materials. In this study, first-principles calculations were carried out to investigate the effect of solute atoms (Mg and Cu) segregation on the structural evolution and mechanical response of Al ground-state Σ5(210) GB (GB-Ⅰ) and metastable Σ5(210) GBs (GB-Ⅱ and GB-Ⅲ). The GB energy, segregation energy, and the theoretical tensile strength of the multiple Σ5(210) GBs were calculated. The results show that both Mg and Cu atoms tend to segregate in the boundary plane, thus reducing GB energy and improving GB stability. The segregation of Cu atoms reduced the GB energy more significantly than that of Mg atoms. The segregation of solute atoms can change the symmetric GB structure into an asymmetric one or induce GB phase transformation. The theoretical strength of GB-I is weaker than that of the metastable GB-II with higher GB energy, suggesting that grain boundaries with higher energy are not necessarily unstable. In addition, the effect of solute atom segregation on the GB strength depends not only on the type of element but also on the specific GB structure. The weakening effect of Mg segregation in GB-I and GB-II is due to the weak MgAl bond which enlarges the low charge density region of GB and increases the free volume of GB. The strengthening of GB-I and GB-II by Cu segregation mainly depends on the stronger AlCu bond than AlAl bond along the GB fracture path. The enhanced strength of GB-III with Mg and Cu segregation is attributed to the GB structural phase transformation caused by the segregation of solute atoms. The calculation results further elucidate the relationship between element segregation and grain boundary characteristics.

Building Facade Acquisition and Restoration Generation Method Based on Point Cloud Plane Boundary Extraction Algorithm

Building Facade Acquisition and Restoration Generation Method Based on Point Cloud Plane Boundary Extraction Algorithm

Thermal boundary conditions and rotation effects on the onset of casson fluid convection in a permeable layer produced by purely interior heating

In this work, we inspect the effect of thermal boundary conditions and rotation on the coming of Casson fluid convective motion generated by purely internal warming in a flat porous layer. Two types of thermal boundaries are utilized, namely, type (I) both boundary planes are isothermal and type (II) bottom boundary plane is insulated and top plane is isothermal. The altered Darcy model is used to characterize the rheological performance of Casson fluid movement in porous medium. The classical Horton–Rogers Lapwood stability examination is accomplished and the resultant eigenvalue problem is resolved numerically with the help of advanced-term Galerkin technique with the internal Rayleigh Darcy number as the eigenvalue. It is observed that the Taylor Darcy number has a stabilizing weight while the Casson parameter shows the dual influence on the system. The structure is more stable when both boundary planes are isothermal. The magnitude of the convection cells falls with increasing both the Taylor Darcy number and the Casson parameter. In the absence of Taylor Darcy number, the system’s stability decreases with the Casson parameter. Further, it is remarkable to observe that without rotation, the Casson parameter has no impression on the magnitude of convection cells.

Heat Transport at Silicon Grain Boundaries

AbstractEngineering microstructural defects, like grain boundaries, offers superior control over transport properties in energy materials. However, technological advancement requires establishing microstructure‐property relations at the micron or finer scales, where most of these defects operate. Here, the first experimental evidence of thermal resistance for individual silicon grain boundaries, estimated with a Gibbs excess approach, is provided. Coincident site lattice boundaries exhibit uniform excess thermal resistance along the same boundary, but notable variations from one boundary to another. Boundaries associated with low interface energy generally exhibit lower resistances, aligning with theoretical expectations and previous simulations, but several exceptions are observed. Transmission electron microscopy reveals that factors like interface roughness and presence of nanotwinning can significantly alter the observed resistance, which ranges from ∼0 to up to ∼2.3 m2K/GW. In stark contrast, significantly larger and less uniform values ‐ from 5 to 30 m2K/GW ‐ are found for high‐angle boundaries in spark‐plasma‐sintered polycrystalline silicon. Further, finite element analysis suggests that boundary planes that strongly deviate from the sample vertical (beyond ∼45°) can show up to 3‐times larger excess resistance. Direct correlations of properties with individual defects enable the design of materials with superior thermal performance for applications in energy harvesting and heat management.

Phase-field simulation study on dendritic growth behavior during bilateral directional solidification

The directional solidification technique can uniform the crystal growth direction within the material, but does not remove the lateral side branches of the axial main arm during the growth process. The influence of such lateral side branches existing in the directionally solidified dendritic organisation on the mechanical properties of the material cannot be neglected. In this paper, based on the Kim-Kim-Suzuki (KKS) phase-field model, the competitive behaviour of lateral secondary dendrites between the two main arms under different boundary conditions and non-synchronous growth conditions is investigated for Fe-0.5 %C alloys. In addition, the diffusion and enrichment rules of solutes are analysed by the distribution of solutes. The results show that the molten pool is spherical without external force, and the size distribution of the molten pool is as follows: dendrite tip collision zone > dendrite root > dendrite wall, and the solute segregation rule is the same; The spacing of the main arms has little effect on the concentration values between the dendrites, and the solutes are very symmetrically over the entire computational region; The dendrite tip interface concentration during the stable phase of dendrite growth is 0.89 %. Without considering the initial liquid-phase concentration, the concentration in the collision zone at the dendrite tip is approximately twice the concentration at the tip of the dendrite in the stable period, which is 1.28 %, when the bilateral dendrites are encountered. Dendrites always collide preferentially on the centreline of the included angle under non-parallel conditions, and solute-enriched zones also occur on the centreline of the included angle; During the curved surface bilaterally directional solidification process, when the left and right sides have the same shape of surfaces, the solute enrichment at the end of solidification is on the centreline. For the case of a single planar boundary, the solute-enriched region is influenced by the curved surface and is similar to the initial curved surface profile.

Effect of grain boundary character on intergranular hydrides precipitation in zirconium

Grain boundary characteristics play a crucial role in the formation of intergranular hydrides, which may cause brittle fracture in zirconium alloys. However, the impact of grain boundary character on microscopic hydride precipitation remains unclear. Here, we investigate the nucleation and precipitation of intergranular hydrides in zirconium by using In-situ transmission electron microscopy observations and post-precipitation electron backscattered diffraction analysis. The nucleation of intergranular hydrides is highly dependent on the interacting angle (αGB-BP) between the grain boundary plane and the basal plane. For low-angle grain boundaries, hydrides prefer to grow into the grain interior when the αGB-BP is less than 60°, otherwise, no hydride precipitation occurs. For high-angle grain boundaries, hydrides nucleate along the grain boundary when the αGB-BP is less than 39°. As the αGB-BP increases, hydrides grow into the grain interior. A thermodynamic model is developed to analyze the nucleation of needle-shaped hydrides. The variation of the intergranular hydride as a function of the grain boundary energy and the αGB-BP is predicted. This finding provides new insight into utilizing grain boundary engineering to modulate intergranular hydride precipitation and offers a pathway to control hydrogen embrittlement in zirconium alloys.