Discontinuous Boundary Research Articles

Influence of heat treatment on metallurgical and mechanical properties of aluminium Al6061 hybrid metal matrix composites

Abstract The current investigation explores the metallurgical and mechanical properties of hybrid metal matrix composites (HMMC) with aluminum 6061 as the base material, reinforced with ceramic of tungsten carbide (WC) nanoparticles, graphite (as a solid lubricant) and redmud (RM). Four different composites with tungsten carbide nanoparticles (1.5 wt.%) and graphite (2 wt.%) with a varying proportions of redmud (0, 1, 3 and 5 wt.%) are fabricated by stir casting. Microscopic analysis reveals grain boundary with segregations, some of which dissolve to form discontinuous grain boundaries after heat treatment. FESEM examination shows the formation of intermetallic, some of which dissolve on heat treatment to form precipitate that are distributed evenly along the grain boundary and also inside grains. EDX mapping further validated the uniform distribution of reinforcements without any agglomeration. The addition of reinforcements and heat treatment (T6) resulted in substantial improvements in hardness, ultimate tensile strength, yield strength, and compressive strength compared to unreinforced Al6061 and untreated HMMC, respectively. Fractographic analysis of tensile tested samples reveals the presence of dimples, tearing edges and small voids, indicating ductile fracture.

Effects of multiple reflected P waves on crack-tip stress and crack propagation in directional fracturing blasting

Directional fracturing blasting is effective for rock engineering, but it is inevitably disturbed by multiple reflected waves from different directions in natural rock mass due to discontinuous boundaries. Reflected waves affect both crack-tip stress and crack propagation, hence affect the results of directional fracturing blasting. In this paper, with the aid of high-speed photography, an optical caustics method is used to study effects of multiple reflected P waves on a directional blast-induced crack in a polymethyl methacrylate (PMMA) plate, specifically on crack path, crack fracturing mode, crack-tip stress and crack velocity. Crack-tip stress field is indicated by the shape of caustics pattern. Before the loading of reflected P waves, the mode I directional crack driven by blast-induced gases propagates in a straight path; crack-tip stress field is K-dominated, and crack-tip caustics pattern is consistent with classical caustics theory. On the contrary, under the loading of reflected P waves, the directional crack changes to be mixed-mode I + II and propagates in a curved path; Crack-tip stress field is non-K-dominated due to transient stress superposition of reflected P waves, and crack-tip caustics pattern is consistent with modified caustics theory. Transient stress superposition is not obvious for reflected P waves with a longer reflection distance. The tension loading of reflected P waves plays a more important role than the compression loading, which increases crack-tip stress intensity factors and crack velocity. This study provides a comprehensive understanding of effects of multiple reflected P waves from different directions on directional fracturing blasting.

Enhancing mechanical property and corrosion resistance of Al0.3CoCrFeNi1.5 high entropy alloy via grain boundary engineering

In the present study, to improve the performances of Al0.3CoCrFeNi1.5 high entropy alloys (HEAs), grain boundary character distribution (GBCD) of Al0.3CoCrFeNi1.5 HEA has been optimized by an appropriate thermo-mechanical processing. The experiment results showed that the fraction of low-Σ coincidence site lattice (CSL) boundaries could reach approximately 80 % through cold rolling with deformation of 8 % and subsequent annealing at 1050 °C for 5 min. The reason for GBCD optimization could be attributed to sufficient strain-induced boundary migration (SIBM) or grain growth after recrystallization. While recrystallization is not favorable for optimizing GBCD. The mechanical properties and corrosion resistance have been enhanced, with a more pronounced improvement observed in the corrosion resistance. The corrosion current density icorr of the GBEM specimen stands at 0.23 μA∙cm−2, representing a reduction of 66 % in comparison to the BM specimen (0.68 μA∙cm−2). The improvement of corrosion resistance of Al0.3CoCrFeNi1.5 HEA resulted from the discontinuous random grain boundaries (RGBs) broken by the high fraction of low-ΣCSL boundaries, especially Σ3 boundaries suppressed the propagation of corrosion crack.

Stepwise Alternating Direction Implicit Method of the Three Dimensional Convective-Diffusion Equation

A stepwise alternating direction implicit method of the three dimensional convective-diffusion equation is considered in this paper. We constructed an implicit difference scheme and analyzes it's truncation error, convergence and stabilities. The theoretical and numerical analysis shows that the implicit difference scheme is unconditional stable. Then the Greedy Algorithm is proposed to solve the numerical solution on x,y and z axis separately by using implicit difference scheme and the numerical solution is convergent theoretically, however with no physical meaning. The Stepwise Alternating Direction Implicit Method (SADIM) is proposed, which uses the implicit difference scheme in this paper. Using Sauls scheme to pretreat the initial-boundary condition before iterating, thus eliminate the numerical oscillation caused by discontinuous initial boundary conditions. This SADIM is at least six ordered convergent, and is one of high ordered numerical methods for three dimensional problem. Our implicit difference scheme is more ideal than the standard Galerkin centered on finite difference scheme, quicker than SOR iteration method. The convergence of our implicit scheme is better than finite element method, characteristic line method, and mesh-less method. Our method eliminates the numerical oscillation caused by the convection dominant, resists the dispersion effectively and addresses dissipation caused by diffusion dominant.The implicit difference scheme has good theoretical and practical value.

Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure

This paper considers a heat conduction process for isotropic layered media with internal thermal heating. As a result of the heterogeneity of environments, significant temperature gradients arise as a result of the thermal load. In order to establish the temperature regimes for the effective operation of electronic devices, linear and non-linear mathematical models for determining the temperature field have been constructed, which would make it possible to further analyze the temperature regimes in these heat-active environments. The coefficient of thermal conductivity for the above structures was represented as a whole using asymmetric unit functions. As a result, the conditions of ideal thermal contact were automatically fulfilled on the surfaces of the conjugation of the layers. This leads to solving one heat conduction equation with discontinuous and singular coefficients and boundary conditions at the boundary surfaces of the medium. For linearization of nonlinear boundary value problems, linearizing functions were introduced. Analytical solutions to both linear and nonlinear boundary value problems were derived in a closed form. For heat-sensitive environments, as an example, the linear dependence of the coefficient of thermal conductivity of structural materials on temperature, which is often observed when solving many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in these environments were obtained. Based on this, a numerical experiment was performed, and it was geometrically represented depending on the spatial coordinates. This proves that the constructed linear and nonlinear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but also the entire structure

Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions

In this study, a fiber-reinforced composite (FRC) sandwich cylindrical shell with a functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) core is investigated, and the traveling wave vibration characteristics of this new sandwich cylindrical shell under discontinuous elastic boundary conditions are analyzed for the first time. The influences of centrifugal and Coriolis forces are introduced into the model. By employing the first-order shear deformation theory (FSDT) and the continuity assumption of the layerwise theory, the governing equations of the rotating sandwich shell are obtained. The artificial springs are implemented at the ends of the sandwich shell to represent the discontinuous elastic boundary conditions. The natural frequency of the shell is solved via the Rayleigh-Ritz method and the state space method. Then, the approach proposed is validated by comparing the present results with those reported in the literature and the finite element method. Finally, the effects of various parameters on the traveling wave frequency of the shell are evaluated. It was found that in practical engineering, the appropriate thickness of the FGP-GPLRC core should be selected according to the boundary conditions and other factors, and the ply angle should be adjusted to obtain more stability of vibration.

Elevating Detection Performance in Optical Remote Sensing Image Object Detection: A Dual Strategy with Spatially Adaptive Angle-Aware Networks and Edge-Aware Skewed Bounding Box Loss Function.

In optical remote sensing image object detection, discontinuous boundaries often limit detection accuracy, particularly at high Intersection over Union (IoU) thresholds. This paper addresses this issue by proposing the Spatial Adaptive Angle-Aware (SA3) Network. The SA3 Network employs a hierarchical refinement approach, consisting of coarse regression, fine regression, and precise tuning, to optimize the angle parameters of rotated bounding boxes. It adapts to specific task scenarios using either class-aware or class-agnostic strategies. Experimental results demonstrate its effectiveness in significantly improving detection accuracy at high IoU thresholds. Additionally, we introduce a Gaussian transform-based IoU factor during angle regression loss calculation, leading to the development of Edge-aware Skewed Bounding Box Loss (EAS Loss). The EAS loss enhances the loss gradient at the final stage of angle regression for bounding boxes, addressing the challenge of further learning when the predicted box angle closely aligns with the real target box angle. This results in increased training efficiency and better alignment between training and evaluation metrics. Experimental results show that the proposed method substantially enhances the detection accuracy of ReDet and ReBiDet models. The SA3 Network and EAS loss not only elevate the mAP of the ReBiDet model on DOTA-v1.5 to 78.85% but also effectively improve the model's mAP under high IoU threshold conditions.

Geodesic conformal gradient device based on a torus.

In recent years, optical fields on non-Euclidean geometry have become a hot topic. The geodesic conformal transformation theory, linking curved surfaces with planar gradient refractive indices, holds unique advantages in controlling curved optical fields. However, this theory has not yet addressed surfaces with non-trivial topology with a certain genus. In this work, we design a gradient planar device based on the geodesic conformal transformation theory for toroidal surfaces, which can achieve Gaussian beam focusing. Unlike traditional angle-preserving geodesic theories, the non-zero genus results in the one-to-two discontinuous boundaries in the device, and we utilize inversion transformations to rectify this drawback.

Closed-form expressions for some of the integrals related to the method of Kobayashi potential

Closed-form solutions are derived for some improper integrals used in the Kobayashi Potential (KP) method, using the calculus of residues. These integrals are categorized as waveguiding and radiating, which are single-valued and double-valued, respectively. Both classifications are considered for interior and exterior regions, with respect to the discontinuous boundary. Fourier functional space is used to facilitate contour integration for interior problems. It has been demonstrated that radiating integrals are a limiting case of waveguiding integrals. Therefore, the same strategy can be applied to both types of integrals.

Evolution of microstructure and mechanical properties of Ti65 high-temperature titanium alloy after additive manufacturing and annealing

Ti65 was prepared by Laser Direct Energy Deposition (LDED) and subjected to Annealing Heat Treatment (AHT). The microstructure and mechanical properties of different specimens were evaluated. The results indicated that the prior β columnar crystals had a strong [0001] texture along the grain growth direction. The coarsening or spheroidization of α lath was attributed to the splitting of lamellar α, subsequent non-directional growth, element migration, and Ostwald ripening. The isotropy of the specimen annealed at 950 °C was caused by trimodal microstructure, discontinuous grain boundary α (αGB), precipitates dissolution, and low-angle grain boundary. A mathematical model was established to predict yield strength (YS) and microhardness based on the α lath thickness. The microhardness-strength correlation of LDED Ti65 followed an empirically derived model (Tabor's relationship). Improvements to the original models of the microhardness-strength relationship for Ti65, in conjunction with the strain-hardening effect and α orientation, made it possible to use these models to predict the strength of LDED Ti65 parts and improve the accuracy of the predicted values. Simultaneously, the model can provide data support for the industrial application of Ti65 or, where appropriate, provide a reference for other technical production (material applications).

Surface defect visualisation using scanning electromagnetic induction thermography

ABSTRACT Scanning electromagnetic induction thermography (SEIT) has great potential for industrial applications, such as rapid visualising of surface cracks. This dynamic non-destructive testing method has improved detection efficiency but has led to blurred or discontinuous defect boundaries at varying scanning speeds. To alleviate this problem, we explore the use of the patch-based sparse decomposition (PSD) technique. This technique improves dynamic imaging by retaining only the information associated with sparse regression and introducing a locally adaptive threshold. Besides, this method offers a potential thermal image preconditioned scheme for follow-up artificial intelligence detection. Experimental results show that PSD can correct blurred images caused by relative motion, thus improving defect detection accuracy. Moreover, it is suitable for both translational and rotational detection systems. Images reconstructed through the deblurring process demonstrate the ability to visualise holes with a radius of 0.5 mm at velocities up to 150 mm/s, while cracks with a defect width of 0.2 mm on a railroad wheel can be detected at speeds ranging from 25 mm/s to 75 mm/s.

A dual attentional skip connection based Swin‐UNet for real‐time cloud segmentation

AbstractDeveloping real‐time cloud segmentation technology is urgent for many remote sensing based applications such as weather forecasting. Existing deep learning based cloud segmentation methods involve two shortcomings. (a): They tend to produce discontinuous boundaries and fail to capture less salient feature, which corresponds to thin cloud pixels; (b): they are unrobust towards different scenarios. Those issues are circumvented by integrating U‐Net and the swin transformer together, with an efficiently designed dual attention mechanism based skip connection. Typically, a swin transformer based encoder‐decoder network, by incorporating a dual attentional skip connection with Swin‐UNet (DASUNet) is proposed. DASUNet captures the global relationship of image patches based on its window attention mechanism, which fits the real‐time requirement. Moreover, DASUNet characterizes the less salient features by equipping with token dual attention modules among the skip connection, which compensates the ignorance of less salient features incurred from traditional attention mechanism during the stacking of transformer layers. Experiments on ground‐based images (SWINySeg) and remote sensing images (HRC‐WHU, 38‐Cloud) show that, DASUNet achieves the state‐of‐the‐art or competitive results for cloud segmentation (six top‐1 positions of six metrics among 11 methods on SWINySeg, two top‐1 positions of five metrics among 10 methods on HRC‐WHU, two top‐1 positions of four metrics among 12 methods with ParaNum on 38‐Cloud), with 100FPS implementation speed averagely for each image.

Semi-analytical modeling and analysis on traveling wave vibration characteristics of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions

Semi-analytical modeling and analysis on traveling wave vibration characteristics of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions

Effects of real gas models on the wave dynamics and refrigeration of gas wave rotor

The gas wave rotor was usually designed and performed on the ideal gas model. However, the real gas effect could not be ignored anymore under high-pressure ratio conditions. In this study, for the first time, a two-dimensional computational model of a double-opening gas wave refrigerator (GWR) using a multi-parameter Benedict–Webb–Rubin equation of state is established and the influence of the real gas effect on gas wave dynamics and energy transfer processes in the GWR with discontinuous boundary conditions is thoroughly investigated. The numerical results show that the wave dynamics of the ideal gas and the real gas are similar under different operating conditions, but compression waves and expansion waves in real gas obviously lag behind the ideal gas. In addition, the low-temperature real gas is completely discharged earlier than the ideal gas and the difference between them gradually increases as the pressure ratio gets higher, which benefits the GWR compact structure design and cost reduction. At the same time, the temperature of the real gas being discharged is lower than that of the ideal gas. Therefore, the refrigeration efficiency of the isentropic expansion of the real gas will be improved compared with the operation in ideal gas. The research results on the real gas effect reveal the mechanism of wave dynamics and energy transfer, providing support for the optimization design of GWR.

Hydrodynamics for Asymmetric Simple Exclusion on a Finite Segment with Glauber-Type Source

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a source term. Different from the usual boundary conditions introduced in Bardos et al (Commun Partial Differ Equ 4(9):1017–1034, https://doi.org/10.1080/03605307908820117, 1979) and Otto (C R Acad Sci Paris 322(1):729–734, 1996), discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme.

Adaptive sliding mode boundary control of a perturbed diffusion process

SummaryThis paper proposes a sliding‐mode‐based adaptive boundary control law for stabilizing a class of uncertain diffusion processes affected by a matched disturbance. The matched disturbance is assumed to be uniformly bounded along with its time derivative, whereas the corresponding upper bounding constants are not known. This motivates the use of adaptive control strategies. In addition, the spatially‐varying diffusion coefficient is also uncertain. To achieve asymptotic stability of the plant origin in the ‐sense in the presence of the disturbance, a discontinuous boundary feedback law is proposed where the gain of the discontinuous control term is adjusted according to a gradient‐based adaptation law. A constructive Lyapunov analysis supports the stability properties of the considered closed‐loop system, yielding sufficient convergence conditions in terms of suitable inequalities involving the controllers' tuning parameters. Simulation results are presented to corroborate the theoretical findings.

Achieving enhanced tensile strength-ductility synergy through phase modulation in additively manufactured titanium alloys

The quest for titanium alloys with an optimal combination of tensile strength and ductility is paramount for their application in critical industries. Additive manufacturing (AM) offers a unique avenue to control the alloy's microstructure, thereby modulating its mechanical properties. This study presents a comprehensive investigation into the phase modulation strategies in AM-processed titanium alloys to achieve a synergistic improvement in tensile strength and ductility. The advancements in this work have enabled the progressive evolution of titanium alloy microstructures with addition of β stable elements, transitioning from near α-Ti alloys to α+β alloys, and finally to near β-Ti alloys. This approach has led to a significant enhancement in the tensile strength of as-prepared titanium alloys, complemented by a moderate retention of ductility. The primary contributors to this mechanical property improvement are identified as solid solution strengthening, grain refining strengthening, and grain boundary strengthening, all of which are facilitated by strategic phase modulation. Moreover, the generation of refined α lamellas, equiaxed α phases, and discontinuous grain boundary α phases has been shown to be instrumental in promoting coordinated deformation within the alloy, thus enhancing the overall ductility. Varying fracture modes demonstrated the potential of microstructure tailoring via multi-eutectoid elements alloying, facilitating the in-depth understanding of crack initiation, propagation, and strain-to-failure, shedding the lights on the enhancement of strength-ductility synergy.

Ultrasonic peening-waterjet composite surface modification of 7075-T6 aluminum alloy for residual stress release and transformation mechanism

The release and transformation mechanism of residual stress contributes to the improvement of metal materials' processing and performance, enhancing their structural stability, surface integrity, and fracture resistance. This paper focuses on the Ultrasonic Impact Treatment-Solid Particle Entrainment by Waterjet (UIT-SPEWJ) composite surface modification of 7075-T6 aluminum alloy, investigating the effects of UIT-SPEWJ process parameters (jet pressure and target distance) on the alloy's surface quality, roughness, microhardness, residual stress, and the evolution mechanism of microstructure. The results indicate that the 7075-T6 aluminum alloy modified by UIT-SPEWJ mainly exhibits a "meteorite crater" effect, accompanied by significant smearing and ploughing phenomena. Surface roughness shows a trend of first decreasing and then increasing with the rise of jet pressure and target distance. The minimum surface roughness, 0.852 μm, is achieved at a jet pressure of 25 MPa and a target distance of 7.5 mm. The microhardness of the samples modified by UIT-SPEWJ gradually decreases from the surface to the substrate with increasing depth. The hardened layer depths of the samples UIT-SPEWJ-1–6 after modification are approximately 174 μm, 226 μm, 200 μm, 196 μm, 176 μm, and 172 μm, respectively. After UIT, SPEWJ, and UIT-SPEWJ surface modifications, the surface of 7075-T6 aluminum alloy mainly exhibits compressive residual stress (CRS). The surface residual stress σ_srs of samples modified by UIT and SPEWJ are approximately 195.161 and 215.752 MPa, respectively. The surface residual stresses of UIT-SPEWJ-1–6 samples are significantly improved to 277.089, 529.499, 393.615, 459.261, 368.084, and 220.635 MPa, respectively, with UIT-SPEWJ-2 sample having the highest surface residual stress, which is 2.7 and 2.4 times that of UIT and SPEWJ modified surfaces. Samples modified by UIT-SPEWJ present significant dislocation phenomena, and the precipitated phases mainly include the needle-like metastable phase η', as well as the equilibrium phase η (MgZn2) with a rod-like structure. At lower jet pressures and larger target distances, the 7075-T6 aluminum alloy exhibits a continuous PFZ with a size of approximately 12–23 nm. As jet pressure increases and target distance decreases, discontinuous grain boundary precipitate bands appear, sized around 8–17 nm. Moreover, when the jet pressure is 25 MPa and the target distance is 7.5 mm, the grain boundary precipitated phases are more dispersed.

Structural Shape Optimization Based on Multi-Patch Weakly Singular IGABEM and Particle Swarm Optimization Algorithm in Two-Dimensional Elastostatics

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective.

A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions

A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions