Continuous Boundary Research Articles

Improvement of the Mechanical Properties of TC17 Alloy by Different Heat Treatments through Directed Energy Deposition

The microstructure evolution of TC17 alloy fabricated by directed energy deposition (DED) under different heat treatments was investigated, and its effects on tribological and mechanical properties were analyzed. The results indicated that the deposited TC17 alloy consisted of acicular α' martensite and residual β phase. Annealing at 840 ℃ and solution treatment at 800 ℃ promoted the precipitation and growth of lath and plate-like primary α phase (αP), as well as continuous and discontinuous grain boundary α phase (αGB). A phase free zone (PFZ) was observed adjacent to the continuous αGB. Aging induced the preferential precipitation of secondary α phase (αS) around the grain boundaries, but it did not fully occupy the PFZ region. As the aging temperature increased, both the αP and αS underwent coarsening. Heat treatment effectively enhanced the wear resistance of the TC17 alloy, with a wear rate of only 0.0343mg/m after aging at 580 ℃. The deposited TC17 alloy exhibited average tensile strength of 1224MPa and average elongation of 1.2%. Compared to the deposited samples, the average tensile strengths of the aging treatments at 580 ℃, 630 ℃, and 680 ℃ decreased by approximately 12.66%, 15.28%, and 18.06%, respectively; while the average elongation increased by 475%, 691.67%, and 600%, respectively.

Theoretical and experimental study on the consolidation of soil with continuous drainage boundary under electroosmosis–surcharge preloading

Electroosmosis and surcharge preloading represent two effective soil consolidation methodologies. Their combined application has been proven to be effective in shortening the consolidation period and mitigating the degradation of electroosmotic consolidation performance due to crack generation. In this study, an axisymmetric free-strain consolidation analytical model incorporating a continuous drainage top boundary was established. A semi-analytical solution was then derived utilizing Laplace–Hankel transform and boundary condition homogenization. The validity of the proposed solution was confirmed by comparing it with three cases documented in the existing literature. Additionally, a comparison with indoor model box test results demonstrated the rationality of setting the top boundary as a continuous drainage boundary. Parameter analysis revealed several key insights: firstly, under the free strain assumption, the spatiotemporal distribution of excess pore water pressure aptly captured the coupled effects of the radial electric field. Secondly, the combination of electro-osmosis and preloading technology significantly improved consolidation efficiency, with this effect becoming more pronounced as the applied voltage increased. Lastly, the general solution based on the continuous drainage boundary proved to be suitable for addressing the consolidation of soft soils enhanced by vertical drainage, applicable to real foundation consolidation problems with top boundaries exhibiting different permeabilities.

An Analytical Solution for the Steady Seepage of Localized Line Leakage in Tunnels

This paper proposes an analytical solution for the seepage field when a localized line leakage occurs in a tunnel by accurately considering the boundary conditions at the leakage site, which overcomes the problem of current methods, such as the equivalent method or methods improving on the existing analytical solution for fully drained tunnels, being unable to give an accurate analytical solution. First, the semi-infinite seepage region is converted into a rectangular seepage region using two conformal transformations. Subsequently, in order to accurately consider the boundary conditions at the leakage site, the rectangular seepage region with a discontinuous boundary is divided into three subregions with continuous boundaries, and the water head solution for each subregion is given by using the separated variable method. Finally, the principle of orthogonality of trigonometric functions is specially adopted to construct a non-homogeneous system of equations to solve the unknowns in the analytical solution, and through the inverse transformation of the conformal transformation, an analytical solution for the steady-state seepage field when localized line leakage occurs in a tunnel is obtained. The solution proposed is verified by its satisfactory agreement with the numerical simulation results and existing experimental results, and is much more accurate than the existing analytical solution. In addition, the proposed analytical solution is much less computationally demanding compared to numerical simulations. Finally, the capability of the proposed analytical solution is demonstrated by a parametric analysis of the tunnel burial depth, leakage location, and leakage width, and some meaningful conclusions are drawn.

One-dimensional consolidation analysis of layered foundations with continuous drainage boundaries considering soil structure and physical properties

IntroductionMany theories of consolidation for soils have been proposed in the past, but most of them have ignored the structural characteristics of clay, yet the natural layered soils are widely distributed around the world.MethodsA theoretical model is established to analyze the one-dimensional consolidation behavior of layered soils, in which a time-dependent drainage boundary and the structural characteristics of the soil are taken into account. Using the integral transform and characteristic function methods, the analytical solution is derived, the effectiveness of which is evaluated against the degradation of solutions and the numerical results calculated using the finite element method.Results and discussionFinally, the influences of interface parameter, soil permeability coefficient and soil compressibility on consolidation behaviors are discussed. Results show that in structured soils, early dissipation of excess pore water pressure and consolidation rates are predominantly influenced by interface parameters, permeability, and volume compression coefficients. Higher values of these parameters accelerate early stages of consolidation, which is especially evident in the upper soil layers. Over time, the distinct effects of interface and permeability coefficients on consolidation diminish. Higher volume compression coefficients, while initially beneficial, eventually slow down the consolidation process, indicating an interaction with the ongoing soil structural changes.

Exploiting the positive effect of REFe2 (RE=rare earth) phase on coercivity in Nd-Ce-Fe-B sintered magnets

The REFe2 phase is inherent in high Ce content Nd-Ce-Fe-B magnets, and how to harness its existence and exert its beneficial effects on magnetic properties is an essential topic in the development of these magnets. In this work, we reveal the positive impact of the REFe2 phase on coercivity enhancement by designing the RE-rich B-lean composition in the Nd-Ce-Fe-B sintered magnet with 30 wt. % Ce replacing Nd. The coercivity in the as-sintered state attains 14.07 kOe and slightly increases to 14.54 kOe upon post-sinter annealing. Phase composition and microstructure analysis indicate that the Fe-storage effect of the REFe2 phase immobilizes a large amount of Fe elements in the triple junctions, resulting in the development of a continuous Fe-lean non-ferromagnetic grain boundary phase with thickness exceeding the exchange length. In addition, the magnetization and demagnetization behaviors were analyzed by the recoil loops to reveal the coercivity mechanisms. This work demonstrates that, in addition to improving wettability, the Fe-storage effect of the REFe2 phase positively influences coercivity.

Investigation of the microstructural characteristics of laser-cladded Ti6Al4V titanium alloy and its corrosion behavior in simulated body fluid

Laser cladding technology has a wide range of potential industrial applications in the surface strengthening, repair and reuse of orthopedic implants. By employing this technique to conduct same-material surface restoration and enhancement on titanium alloys, it demonstrates significant developmental potential. However, the microstructure of laser additively manufactured titanium alloy differs significantly from that of traditional titanium alloys, which affects its corrosion resistance in human body fluids. To compare the corrosion resistance differences between the cladding layer and the substrate, this study investigates the microstructure of multi-pass laser cladding Ti6Al4V (TC4) titanium alloy and analyzes the corrosion morphology and corrosion products of the cladding layer in simulated body fluids (SBF). By comparing the electrochemical corrosion behavior of laser cladding with that of traditionally manufactured TC4, this research reveals the differences in corrosion resistance between the two titanium alloys. The research demonstrates that the microstructure of cladding primarily consists of prior-β grains and continuous grain boundary α phase, along with a complex basketweave structure composed of fine acicular α phase and lamellar α phase. Additionally, due to the complex thermal cycling process, the acicular α' colonies within the prior-β grains. These features enhance the cladding layer’s resistance to plastic deformation and increase microhardness, though with some uneven distribution. Interestingly, the TC4 cladding layer forms a porous passivation layer after corrosion, primarily composed of a TiO2 passivation film and deposits of hydroxyapatite and other phosphates. Due to the lower β-phase content, finer grains with higher energy states, and a greater proportion of high-angle grain boundaries (HAGBs) in the cladding layer, it exhibits higher electrochemical activity. As a result of these microstructural differences, the corrosion resistance of the TC4 cladding layer in SBF is inferior to that of TC4 manufactured using traditional techniques.

Geometry of large normal fault growth and linkage with temporal constraints: a case study on the Lanliao fault in Dongpu Sag, Bohai Bay basin, NE China

The Dongpu Sag exhibits highly representative structural features of the Bohai Bay Basin. By utilizing time depth quantification (TDQ) technology, geological profiles were generated through the processing of seismic data with a velocity model. These profiles were integrated to investigate the linkage geometry and timing of the Lanliao fault, the eastern boundary fault of the Dongpu Sag. Structural analysis revealed at least five original fault segments of the Lanliao fault, each initiating independently during the early growth phase. The development of these isolated fault segments began in the early Eocene, which is concurrent with the deposition of the Es4 member. The southern fault segments were active earlier but became inactive later as the northern segments gained activity during the Es3 member. Transverse anticlines separate the northern and southern faults. By the time of the Es2 member, all segments had linked, forming a continuous boundary fault across the transverse anticlines. As the Dongpu Sag expanded, the depocenter relocated. The southern fault formed a graben, known as the Gegangji subsag, controlling the depocenter during the Es33 and Es32 members. The depocenter of the Es31 member shifted northward swiftly, developing into a half-graben depocenter called the Huzhuangji subsag. In the post-linkage development phase, the activity of the Lanliao fault decreased over time, with displacement becoming more concentrated on the Huanghe fault, an intrabasin fault. The Huanghe fault then dominated basin sedimentation, moving the depocenter to the Mengmangji subsag. This study demonstrates that the fault linkage is a significant event in basin evolution, exerting considerable control over sedimentation and the overall evolution of the basin.

Effect of precipitate evolution on galvanic corrosion behavior of friction stir welded AA6061-T6 joint after post-weld aging

The microstructural transformation of FSW AA6061-T6 joint after post-weld T6 and its effects on the mechanical properties and corrosion behavior was investigated through electrochemical tests, immersion experiments and transmission electron microscopy (TEM) observation. The research results show that the joint efficiency and strength can be enhanced by post-welding aging. The hardness of SZ is recovered to a level close to that of matrix due to the sufficient precipitation of the effective strengthening phase β''. The main β' precipitate in over-aged HAZ coarsens during post-weld aging and cannot effectively restore strength, resulting in the lowest hardness in HAZ and limited tensile strength of the joint. The presence of macro-galvanic effects in the whole joint was confirmed. In SZ, the highest level of aging characteristics is caused by the highest aging drive due to fully solidified atoms, and is confirmed by the continuous grain boundary precipitates (GBPs) and dense matrix precipitates, which lead to the most positive potentials. Whereas, in HAZ, discrete GBPs and coarsened matrix precipitates indicate over-aged features, which lead to the most negative potentials. The potential difference between SZ and HAZ results in a macro-galvanic effect in the joint, where SZ is protected as the cathode and HAZ is corroded faster as the anode.

Refinement of microstructure and improvement of mechanical properties of directed energy deposited titanium alloys by adding Fe

Elemental alloying is a validated strategy for enhancing the mechanical properties of directed energy deposited titanium alloys. However, it is still a challenge to obtain titanium alloys with both high strength and high ductility. In this work, to balance strength and ductility, the alloying element Fe was in-situ added to the TC4 melt pool during the directed energy deposited process and the effects of its content on the microstructure and mechanical performance of the TC4 alloy deposits were investigated. The results showed that the Fe additive ranging from 0.5 to 2.0 wt% were completely solid-solved in the retained β phase of TC4 alloys. Moreover, the primary β columnar grains were transformed into fully equiaxed grains. Meanwhile, the presence of Fe refined the α-laths, increased the proportion of the retained β phase, and the continuous grain boundary α (GB-α) became discontinuous. The tensile strength of the deposited alloys was continually improved with increasing Fe content, while the elongation had a peak value. When the Fe content was 1.0 wt%, the deposited alloy exhibited the best comprehensive performance, with an ultimate tensile strength of 1071 MPa and an elongation of 9.3 %. The enhancement of tensile strength was attributed to the solid solution strengthening and the refinement of α-laths and primary β grains. The increased proportion of retained β phase and the formation of discontinuous GB-α were beneficial for the alloy ductility. However, increased α/β interfaces inhibited dislocation movements, resulting in a decrease in ductility. The development of this alloy is important for aerospace and other fields that require high strength, high ductility and lightweight.

Calculation model for settlement of soft soil foundation with continuous drainage boundary considering the Hansbo’s flow law and the linear load

Calculation model for settlement of soft soil foundation with continuous drainage boundary considering the Hansbo’s flow law and the linear load

Statistical mechanics of the wave maps equation in dimension 1 + 1

We study wave maps with values in Sd, defined on the future light cone {|x|≤t}⊂R1+1, with prescribed data at the boundary {|x|=t}. Based on the work of Keel and Tao, we prove that the problem is well-posed for locally absolutely continuous boundary data. We design a discrete version of the problem and prove that for every absolutely continuous boundary data, the sequence of solutions of the discretised problem converges to the corresponding continuous wave map as the mesh size tends to 0.Next, we consider the boundary data given by the Sd-valued Brownian motion. We prove that the sequence of solutions of the discretised problems has a subsequence that converges in law in the topology of locally uniform convergence. We argue that the resulting random field can be interpreted as the wave-map evolution corresponding to the initial data given by the Gibbs distribution.

Effect of grain boundary ferrite morphologies on impact toughness of X80 girth weld

The X80 girth weld microstructure formed by high-strength acicular ferrite and low-strength grain boundary ferrite was studied to investigate the effect of grain boundary ferrite morphologies on impact toughness. The results show that due to the difference in direction of heat loss caused by the narrow groove, the grain boundary ferrite morphology of the weld metal center and the weld metal edge are continuous network structure and parallel layered structure, respectively. The continuous network structure grain boundary ferrite causes strain localization, resulting in the formation of a large number of secondary cracks in the crack propagation process, which seriously deteriorates the toughness.

An insight on local defect resonance based on modal decomposition analysis: A two-dimensional case

The resonance behaviors of defects, specifically local defect resonance (LDR), are useful for defect detection in structures. However, there is a lack of intuitive elucidation regarding the underlying mechanisms governing defect resonance. This study aims to analyze the LDR of a horizontal crack in a plate activated by Lamb waves using the modal decomposition method (MDM). The MDM involves an approximate decomposition of the wavefield into finite constituent Lamb wave modes, including propagating, non-propagating, and inhomogeneous modes. The amplitude of each mode is determined according to the continuous boundary conditions of displacement and stress between the damaged zone and the intact zone. Analytical results reveal specific frequencies at which the damaged zone exhibits significantly stronger vibrations than the intact zone, indicating the emergence of LDR. The corresponding wavefields exhibit various resonance patterns, encompassing both in-plane LDR and out-of-plane LDR types. In contrast to finite element simulations and experimental observations, the MDM unveils the dominant constituents of resonance patterns: out-of-plane LDR results from the combination of reflected and transmitted A0 and A1 modes within the damaged zone, while in-plane LDR is formed by the superposition of reflected and transmitted A0, A1, and S0 modes.

Orientation-related and temperature-dependent continuous grain boundary migration in multi-principal element alloys

Grain boundaries (GBs) significantly affect the mechanical properties of metals and alloys. In this study, we investigated using molecular dynamic simulations the migration behavior of Σ25 (710), Σ5 (310), and Σ37 (750) [001] symmetric tilt GBs in CoCrCuFeNi multi-principal element alloy (MPEA) and Cu samples subjected to shear deformation. In Cu, the migration of the GBs exhibits a coupled migration pattern, consistent with the Cahn model; while in MPEA, the migration pattern varies with GB angle and temperature. Both Σ25 (710) and Σ37 (750) GBs, along with higher temperatures, induce GB roughening and continuous migration in the MPEA samples. Further investigation to the effects of GB angle and temperature was conducted through microstructure evolution tracing and quantitative analysis. A model was developed to describe the temperature-dependent continuous GB migration and average flow stress in MPEA samples with Σ25 (710) or Σ37 (750) GBs. This work can help understand the mechanical behavior of GB in MPEA and provide valuable insights for the development of high-performance materials.

One‐dimensional consolidation analysis of layered soil with exponential flow under continuous drainage boundary

AbstractTo comprehensively consider the influence of boundary conditions, non‐Darcy flow, load forms, and soil stratification on soil consolidation, a one‐dimensional soil consolidation equation is established. By subdividing the soil layer and employing time discretization, the nonlinear consolidation equation is linearized, resulting in an analytical solution for layered soil foundation at any given time. Subsequently, an iterative approach for time solution is employed to obtain a semi‐analytical solution. The correctness of the solution is verified by comparison with solutions based on Darcy's flow and the semi‐analytical method under traditional drainage boundary conditions. Subsequently, the influence of interface parameters, loading conditions, flow index, and other factors on consolidation characteristics is analyzed. The results indicate that higher interface parameter values for continuous drainage boundaries correspond to faster average consolidation rates for stratified soil foundations, while these parameters have little effect on the time required for complete consolidation of the soil layers. Improved boundary drainage performance amplifies the influence of exponential flow on pore water pressure and average consolidation degree. Conversely, poor boundary drainage performance diminishes the impact of exponential flow on soil consolidation, rendering it negligible. Moreover, faster loading rates accentuate the influence of the flow index on the average consolidation degree defined by pore pressure.

Lowest-order nonstandard finite element methods for time-fractional biharmonic problem

In this work, we consider an initial-boundary value problem for a time-fractional biharmonic equation in a bounded polygonal domain with a Lipschitz continuous boundary in R2 with clamped boundary conditions. After stating the well-posedness, we focus on some regularity results of the solution with respect to the regularity of the problem data. The spatially semidiscrete scheme covers several popular lowest-order piecewise-quadratic finite element schemes, namely, Morley, discontinuous Galerkin, and C0 interior penalty methods, and includes both smooth and nonsmooth initial data. Optimal order error bounds with respect to the regularity assumptions on the data are proved for both homogeneous and nonhomogeneous problems. The numerical experiments validate the theoretical convergence rate results.

Constructing a three-dimensional continuous grain boundary with lithium ion conductivity and electron blocking property in LLZO to suppress lithium dendrites

Li7La3Zr2O12 (LLZO) stands out as a promising material for solid-state batteries due to its superior performance. However, the lithium dendrite growth in LLZO significantly affects battery performance due to high electronic conduction of LLZO. Herein, amorphous Li3BO3 (ALBO) is introduced into LLZO to construct a three-dimensional continuous grain boundary with lithium ion conductivity and electron-blocking property to suppress lithium dendrites. The symmetric cells of ALBO-LLZO achieved a high critical current density (CCD) of 1.1 mA·cm−2 and cycled stably for 2000 h at 0.3 mA·cm−2. The capacity retention of LFP/1 ALBO-LLZO/Li battery retains 84.6 % after 200 cycles at 0.2 C, room temperature. This research offers a potential solution to enhance the performance of the garnet electrolyte for ASSBs.

Screen printing Ag2Se/carbon nanocomposite films for flexible thermoelectric applications

Flexible thermoelectric generators offer the possibility of harvesting waste heat from the human body. However, intrinsic brittleness and the high production cost of bulk thermoelectric materials limit their applications in flexible thermoelectric generators. Herein, flexible Ag2Se/carbon nanocomposite films on polyimide substrates are prepared by scalable screen-printing followed by facial heat treatment. An optimal film shows a maximum power factor of 1617 μW m−1 K−2 at room temperature and good flexibility. The film consists of mainly Ag2Se grains with a preferred (00Ɩ)-orientation and a small amount of carbon. Microstructure observations reveal that the Ag2Se grains with sizes of nano to micrometers have coherent or continuous grain boundaries, and the carbon is mainly amorphous with slight graphitization. A flexible thermoelectric device assembled with the optimal film exhibits a power density of 29.1 W/m2 at a temperature gradient of 35.4 K. This work demonstrates a cost-effective route to high-performance flexible thermoelectric films.

Shape optimization of cast steel tubular joints based on subdivision surface and genetic algorithm

Cast steel tubular (CST) joints are extensively employed in steel structures for their excellent integrity and mechanical performance. However, the diverse configurations of CST joints result in the absence of standard verification formulas, leading to inefficient trial-and-error design approaches. To tackle this issue, this paper introduces a novel shape optimization method for CST joints that integrates subdivision surface techniques with genetic algorithms. The method comprises three key components: geometric modeling, structural analysis, and optimization algorithm, with shape optimization achieved through their collaborative operation. Applied to two types of CST joints, this approach resulted in significant reductions in joint volume by 39.2 % and structural stress by 49.0 %, respectively. The shape-optimized joints were compared with topology-optimized joints from published literatures, and demonstrated enhanced mechanical performance while presenting superior manufacturability. The proposed method offers considerable advantages over traditional trial-and-error approaches and topology optimization methods. It generates designs with continuous and smooth boundaries, better suited for the conventional casting process, and overcomes manufacturability issues of topology optimization. Additionally, the genetic algorithm allows for flexible selections of optimization objectives, addressing the restrictions of topology optimization methods. Furthermore, the methodʼs high level of automation is anticipated to expedite the joint design process, significantly reducing the requirement for manual intervention.

High Power Factor Flexible Ag2Te Film on Nylon by a Wet Chemical Method for Power Generator.

Herein, we develop a facile wet chemical method for the synthesis of Ag2Te powders at room temperature and flexible Ag2Te/nylon thermoelectric (TE) films are prepared by vacuum-assisted filtration of the synthesized Ag2Te powders and then hot pressing. Because of the good crystallinity of Ag2Te grains and continuous grain boundaries, an optimized film exhibits a power factor of 513 μW m-1 K-2 at 300 K, which stands among the highest values reported for Ag2Te-based films to date. In addition, the film also has good flexibility. A four-leg flexible TE device assembled with the film generates a power density of 5.46 W m-2 at a temperature gradient of 31.8 K. This work provides a facile and environmentally friendly method for preparing flexible Ag2Te films.