Rounded Corners Research Articles

Microstructural evolution and stress rupture behaviour of a Ni-Based wrought superalloy during thermal exposure

The microstructural evolution of a wrought Ni-based superalloy GH742 during long-term thermal exposure at 1023 K for durations up to 10,000 h was investigated. The influence of the microstructure degradation on the stress rupture properties at 923 K/823 MPa and 1023 K/510 MPa was systematically analysed. Scanning electron microscopy and electron probe microanalysis were utilised to study the material microstructures before and after the thermal exposure. The results show that small flower-like secondary γ′ precipitates changed their morphology from flower-like to cubic with rounded corners, while large flower-like secondary γ′ precipitates started to split. Tertiary spherical γ′ precipitates in the fine-equiaxed-grain region dissolved into the γ matrix. However, coarsening of tertiary γ′ precipitates occurred in large-fibrous-grain regions. The coarsening kinetics appeared to well conform to the Lifshitz–Slyozov–Wagner theory. Stress rupture tests at 923 K/823 MPa and 1023 K/510 MPa showed a sharp decrease in time to failure within the first 1,000 h of prior thermal exposure, which was then almost constant for the next 9,000 h of thermal exposure. This was attributed to the evolution of γ′ precipitates.

A comparative study on energy absorption of flat sides and corner elements in CFRP square tube under axial compression

The cross-sectional configuration is one of the factors influencing the energy absorption performance of composite tubes under axial compression. Flat sides and corners are basic elements for the configuration. However, their contributions to the energy absorption have not been systematically compared. This paper presents a “press and cut” approach which allows to investigate the energy absorption of flat side and corner elements in a condition closely resembling axial crushing of a tube. Using this method, the crushing responses and energy absorption behaviors of flat side and corner elements in carbon fiber reinforced plastics (CFRP) square tube under axial quasi-static compression were investigated experimentally. The results showed that the corner elements had higher specific energy absorption (SEA) values than the flat side elements. The higher SEA value is attributed to the additional axial tearing fracture of the fronds developed at the corner and the suppression to delamination by the hoop tension force in the round corner. A modified analytical model based on Hussein’s analytical model was established to predict the mean crushing force of the flat side and corner elements. Finally, axial crushing experiments were performed for CFRP tubes with a cross section consisting 12 corners. The 12-corner tubes exhibited an about 18% higher SEA value than the square tubes while maintaining a similar peak force.

Numerical simulations for studying the influence of friction in forging

ABSTRACT The modelling and simulation of forging has reached a matured stage, but the friction and friction models got only scant attention; this work intends to fill up that gap. Here, arbitrary Lagrangian-Eulerian (ALE) finite element method (FEM)-based numerical simulations are carried out for the forging of aluminium workpiece by considering two friction models – Coulomb-Siebel and Tresca. A relation between Coulomb’s coefficient of friction and friction factor has been established based on the slab method. The forging load is obtained by calculating the reaction force on the die as well as from energy method. Energy method provides more accurate and consistent results. Forging load and bulge increase with the friction, but at high friction, the effect is minimal. Bulge is found to be more sensitive to friction than the forging load. The distribution of normal stress is quite different on the die-workpiece interface compared to that on a parallel plane in the interior. The phenomenon of fold-over observed at high friction and high reduction observed in a Lagrangian formulation is absent in ALE formulation. The fold-over phenomenon occurs due to mesh distortion. It is not observed in a workpiece with round corners, even while using Lagrangian formulation.

Flow around square-like cylinders with corner and side modifications

Shape modification effectively reduces the wind loading and wind-induced vibrations of slender structures. Large-eddy simulation is used to investigate the flow around multiple square-like cylinders at a Reynolds number of 22,000. Based on a standard square cylinder, six square-like cylinders are simulated with sharp/rounded corners and straight/concave/convex sides. The combination of rounded corners and convex sides enables the best aerodynamic performance. Furthermore, a parametric study on the round-convex cylinder is conducted considering a fixed corner radius and various side curvatures B/K (B: nominal side length; K: side radius). The results show that both the aerodynamic characteristics of and the flow features around the cylinder change considerably with varying B/K and that three distinct flow regimes are observed. In Stage I (0 ≤ B/K ≤ 0.71), the flow separates at the front corners, and the aerodynamic forces decrease gradually. In Stage II (0.71 < B/K < 1.00), the shear layer separating at the front corner-side region reattaches to the lateral sides. The fluctuating coefficients rise at B/K = 0.74; thereafter, the aerodynamic forces drop and are minimized at B/K = 1.00. In Stage III (1.00 ≤ B/K ≤ 1.77), flow separates at the lateral sides, and the aerodynamic forces recover gradually.

Indentation of an elastic half-space by the cylindrical flat punch with a rounded edge under non-monotonic loading

The paper presents a novel approach to solving the contact problem for interaction with friction between a rigid cylindrical flat punch with rounded corners and a linearly elastic half-space. Increasing and decreasing normal loads act on the punch sequentially. Coulomb’s law is used to account for friction. The contact problem is reduced to nonlinear operator equations that must be solved at each step of the discrete loading process. The numerical method is applied. This method includes regularization of the equation, discretization of the regularized equations and the usage of an iterative process to obtain the approximate solution. The calculations were performed for different values of the relative radius of the flat area of the punch base. Distributions of contact traction and configuration of the stick and slip zones are studied at each monotonic stage of the loading process.

Wind induced response of corner modified 'U' plan shaped tall building

In the present study, the well-adopted practice of minor aerodynamic modifications (chamfered corner and rounded corner) has been introduced on widely used irregular U plan shaped tall building to minimize the wind induced responses and also to give a good aesthetics. The necessary design inputs for a wind resistance design such as force coefficient and pressure coefficients have been well explored and illustrated graphically to provide a complete guideline to the designer. The randomness of wind directionality has a significant impact on tall structures, which is generally not detailed in existing design codes, is incorporated by considering wind directions ranging from 0° to 180° at an interval of 15°. Computational fluid dynamics (CFD) has been utilized to simulate wind flow using two turbulence models, i.e., k-epsilon and Shear Stress Transport. The model has been validated by comparing the results of a published research article on a U-shaped building without corner modification. The grid independence study has been done to check the reliability and accuracy of the analysis results. Since such study of wind directionality on corner modified U-shaped building is not observed in the existing literature, it constitutes the uniqueness of the present study. A significant reduction in force coefficient has been achieved by implementing modification, but the faces of those updated corners mostly been attracted by excessive pressure. This indicates the necessity of proper cladding configurations. The rounded corner buildings are turning out to be more effective when compared to the chamfered corner for reducing wind load.

Optimization of Nonlinear Pressure-Flow Characteristics of a Spring-Loaded Pressure Relief Valve Based on Computational Fluid Dynamics Simulation

Abstract In this study, the nonlinear pressure-flow characteristics of a spring-loaded pressure relief valve (PRV), which is used in the automotive fuel supply system for pressure control is analyzed, and its characteristics are improved by means of geometrical modifications of the valve structure. Given the complexity of the coupling mechanism between the valve internal flow characteristics and spring system, a quasi-steady computational fluid dynamics (CFD) method is introduced to predict the nonlinear pressure-flow characteristic curve of the valve and the accuracy is validated by experimental data. The total hydraulic force on the valve spool and diaphragm are divided into three parts according to the loading position and the correlation between the internal flow characteristics, hydraulic force, and pressure-flow characteristics of the valve are explained by CFD analysis and visualization. The results show that the quasi-steady CFD method can accurately predict the trends of the valve nonlinear pressure-flow characteristic curve, which is mainly determined by the hydraulic force produced in the middle chamber of the valve. When the valve opening reaches a certain value, a main vortex would be formed in the middle chamber and lead to the sudden increase of hydraulic force which causes the fluctuation of the pressure-flow characteristic curve of the valve. It is also found that the toggle point for the flow regimes seen in the valve is affected by the geometric structure of the middle chamber and the pressure-flow characteristics can be improved by the round corner size modification.

Refined Mathematical Models for Across-Wind Loads of Rectangular Tall Buildings with Aerodynamic Modifications

This paper aims to systematically study the across-wind loads of rectangular-shaped tall buildings with aerodynamic modifications and propose refined mathematic models accordingly. This study takes the CAARC (Commonwealth Advisory Aeronautical Research Council) standard tall building as a benchmark model and conducts a series of pressure measurements on the benchmark model and four CAARC models with different round corner rates (5%, 10%, 15% and 20%) in a boundary layer wind tunnel to investigate the across-wind dynamic loads of the typical tall building with different corner modifications. Based on the experimental results of the five models, base moment coefficients, power spectral densities and vertical correlation coefficients of the across-wind loads are compared and discussed. The analyzed results shown that the across-wind aerodynamic performance of the tall buildings can be effectively improved as the rounded corner rate increases. Taking the corner round rate and terrain category as two basic variables, empirical formulas for estimating the across-wind dynamic loads of CAARC standard tall buildings with various rounded corners are proposed on the basis of the wind tunnel testing results. The accuracy and applicability of the proposed formulas are verified by comparisons between the empirical formulas and the experimental results.

Structural, morphological, and electrical properties of ZnSe nanostructures: Effects of Zn precursors

Synthesizing semiconductors at the nano level are progressing rapidly, with promising results thus opening up diversified applications across the scientific and industrial sectors. By a solvothermal technique integrating a subsequent calcination process, series of nano dimensional ZnSe samples with distinct crystallite sizes and morphologies are synthesized and characterized. The effects of using different Zn precursors on the ZnSe samples characteristics’ are scrutinized. The particle size, their morphologies, and electrical properties are significantly influenced amongst various characters. The crystallite size of the as-synthesized samples varied from 10 to 18 nm with change in Zn precursors and nanorods, rectangular shapes, cuboids with rounded corners and some mixed type morphologies are examined through field emission scanning electron microscopy (FESEM) analysis. The ZnSe samples which have the largest crystallite size manifest maximum electrical conductivity.

Preliminary Experimental and Numerical Study of Metal Element with Notches Reinforced by Composite Materials

The presented study is related to the application of the composite overlays used in order to decrease the effect of the stress concentrations around the cut-outs in structural metal elements. The proposed approach with the application of the digital image correlation extends the recently presented studies. Such structural elements with openings of various shapes have been accommodated for a wide range of industrial applications. These structures exhibit certain stress concentrations which decrease their durability and strength. To restore their strength, various reinforcing overlays can be used. In the present paper, the flat panel structure without and with the composite overlays made of HEXCEL TVR 380 M12/26%/R-glass/epoxy is under the experimental and the numerical study. Particular attention is paid to the investigation of the samples with the rectangular holes, which for smooth rounded corners offer a higher durability than the samples with the circular hole of the same size. The experimental results are obtained for the bare element and are reinforced with composite overlay samples. The experimental results are obtained with the use of the Digital Image Correlation method, while the numerical results are the product of the Finite Element Analysis. In the numerical analysis, the study of the shape, size and fiber orientation in applied overlays is done. The reduction of the stress concentration observed in opening notches has confirmed the effectiveness of the overlay application. In the investigated example, the application of the square composite overlay increased the structure strength even by 25%.

Single-Crystalline Mesoporous Palladium and Palladium-Copper Nanocubes for Highly Efficient Electrochemical CO 2 Reduction

Single-Crystalline Mesoporous Palladium and Palladium-Copper Nanocubes for Highly Efficient Electrochemical CO ₂ Reduction

C-Bant ve X-Bant Uygulamaları için İyileştirilmiş Kazanç ve Grup Gecikme Özelliklerine Sahip Çift Bantlı Yama Anteni

In this study, a dual-band patch antenna with improved gain and group delay characteristics is proposed for C-band and X-band applications in radar and satellite communications. In the study, conventional square patch antenna is modified by partially removing the ground plane and rounding the patch corners. The radius of the rounded patch corners is determined by parametric study to achieve the best antenna performance. According to this parametric study, the value of the radius is set to 2 mm. Antenna performance is analysed both in frequency and time domains. Return Loss, Voltage Standing Wave Ratio, gain, radiation pattern, and group delay are investigated via CST Microwave Studio program. Experimental study is also performed to verify the simulation results. The results show that the designed antenna with rounded patch corners and partial ground plane has dual band characteristic. The two resonance frequencies are 6.85 GHz and 9.1 GHz in the simulation results, and 6.56 GHz and 9.12 GHz in the measurement results. The antenna has maximum gain of 5.8 dB. Additionally, group delay variation is very small in the related frequency range. Thus, it is verified that, the proposed antenna has enhanced bandwidth, improved gain and more uniform group delay as compared to the conventional square patch antenna. The proposed dual-band antenna is a quite promising structure with its appropriate gain and uniform group delay characteristics for C-band and X-band applications in radar and satellite communications.

Asymptotic behaviour of the Oore-Burns integral for cracks with a corner and correction formulae for embedded convex defects

In this paper, the asymptotic behaviour of the stress intensity factor (SIF) near a corner of a crack is discussed. The weight function of Oore-Burns and FE analysis are used in order to explain the trend of the SIF. The analytical analysis shows that the SIF at the corner has a cusp behaviour as a function of the distance from the corner. This is a crucial mathematical property obtained from the Oore-Burns integral. Explicit formulae for the estimation of the SIF are obtained for square and equilateral triangular cracks. Then, the value of the SIF along the crack border is corrected (quantitative intervention) by means of a new simple formulation that is able to considerably increase the accuracy of the Oore-Burns integral. Finally, in the case of a crack with a rounded corner, a new simple correction formula is given and, in order to check the accuracy of the proposed equations, a comparison is carefully made with an FE analysis as well as with numerical results taken from the literature.

Accurate 3D reconstruction of complex defects based on combined method of MFL and MFDs

The two-step strategy for 3D reconstruction of complex defects was updated by combining the magnetic field disturbance (MFD) with magnetic flux leakage (MFL) measurement methods. Firstly, the plane-scanned MFD imaging was employed to achieve high-accuracy reconstruction of the opening outlines of complex defects. Secondly, the finite element simulation model of the defect with the recognized opening outline was established as the forward model for depth profile inversion with the particle swarm optimization algorithm. The performances of the conventional MFL-based and updated strategies were carefully compared through finite element simulation. The results proved that the updated method combining MFD signals with MFL signals had the better performance in accurate 3D reconstruction of complex defects than the conventional MFL-based inversion strategy, displaying smaller errors in opening outline, peak depth and the profile. Experimental results confirmed that the updated strategy could accurately reconstruct the 3D shape of 8-shaped defect and rectangular defect with rounded corners.

Constrained shell finite element method of modal buckling analysis for thin-walled members with curved cross-sections

The objective of this study is to develop a constrained shell finite element method (cFEM) for curved cross-sections based on a force-based approach and to enrich the elastic buckling analysis of these thin-walled members for a potentially broader engineering application. These curved thin-walled sections, with significant material efficiency, can experience very complex buckling behaviors that commonly exist for thin-walled members, namely global (G), local (L), and distortional (D) buckling. Given the limitations of the current constrained finite strip method (cFSM) and constrained finite element method for handling curved cross-sections, the cFEM method developed in this study provides a constrained approach to enable buckling mode separation for curved sections. This is a unified method not only applicable to curved sections, but also for straight wall sections. In this study, four criteria utilizing the displacement and force characteristics of modes are defined to separate these mode classes (i.e., G, D, and L). Constraint matrices of G, D, and L mode classes were then constructed and implemented based on the shell element formulations in ANSYS. Numerical examples are presented to demonstrate how the method’s capability in modal decomposition and identification can be applied to the stability analysis of thin-walled structural members, such as circular cylindrical tubes, elliptical cylindrical tubes, and open-branch lipped channel sections with and without rounded corners. All these numerical examples demonstrate the potential of the developed cFEM in advancing structural mechanics to provide an enriched structural analysis capability that can aid the design and enable broad applications of these members.

Solution for square notch problem with small round corners in plane elasticity under remote loading (technical note)

In the paper, the solution for square notch problem with small round corners in plane elasticity under remote loading is studied. Based on the two obtained particular solutions and the extrapolation technique, the general relation between the stress concentration and the small radius at the corner point is obtainable. It is emphasized here that this relation can be used to the arbitrary small radius case.

SREC‐RT: A Structure for Ray Tracing Rounded Edges and Corners

AbstractMan‐made objects commonly exhibit rounded edges and corners generated through their manufacturing processes. The variation of surface normals at these confined locations produces shading details that are visually essential to the realism of synthetic scenes. The more specular the surface, the finer and more prominent its highlights. However, most geometric modellers represent rounded edges and corners with dense polygonal meshes that are limited in terms of smoothness, while tremendously increasing scene complexity. This paper proposes a non‐invasive method (i.e. that does not modify the original geometry) for the modelling and rendering of smooth edges and corners from any input polygonal geometry defined with infinitely sharp edges. At the heart of our contribution is a geometric structure that automatically and accurately defines the geometry of edge and corner rounded areas, as well as the topological relationships at edges and vertices. This structure, called SREC‐RT, is integrated in a ray‐tracing‐based acceleration structure in order to determine the region of interest of each rounded edge and corner. It allows systematic rounding of all edges and vertices without increasing the 3D scene geometric complexity. While the underlying rounded geometry can be of any type, we propose a practical ray‐edge and ray‐corner intersection based on parametric surfaces. We analyse comparisons generated with existing methods. Our results present the advantages of our method, including extreme close‐up views of surfaces with a much higher quality for very little additional memory, and reasonable computation time overhead.

Global smoothing of short line segment toolpaths by control-point-assigning-based geometric smoothing and FIR filtering-based motion smoothing

The toolpaths for curved surfaces generated by most existing computer-aided-manufacturing applications are always consisted by short line segments. Due to the first-order discontinuity of the short line segment toolpath, the precise following of them must result in frequent acceleration/decelerations, which is easy to excite structural vibration of the machine tools, thus degrading the machining quality. To solve this problem, local corner rounding approaches are widely researched, however, most areas on the toolpath after corner rounding remains linear segments, unlike the global smoothing method who replaces all short line segments to spline curves thus obtaining smoother feed motion. Compared with the local corner rounding method, the global smoothing always requires iterative computes to satisfy the accuracy requirement, which makes it so time consuming that can hardly be utilized in CNC systems. To deal with above problem, this paper proposes a highly stable global smoothing method which does not need iterative computations. This is realized by a control-point-assigning-based global geometric smoothing algorithm and a FIR (Finite Impulse Response) filtering-based global motion smoothing algorithm. During global geometric smoothing, the short line segment toolpath is replaced by piecewise B-spline curve segments whose control points are directly assigned under the error tolerance constraint. During the global motion smoothing, a fast spline interpolation method based on FIR filtering is provided to generate smooth axial position references of the piecewise B-spline curve segments under the axial drive constraint. The whole global smoothing approach does not require pre-processing or iterative computation, which makes it easy to be applied. Extensive illustrations including numerical tests and experimental verification/comparison tests demonstrate the favorable effects of the proposed method in real-time capability and motion smoothing performance. Comparing with typical local corner rounding approach, the proposed global smoothing approach results in shorter motion time and better smoothness. Comparing with typical existing global smoothing method, the proposed method performs better in no required pre-processing and high-order motion smoothness.

Monazite Microstructures and Their Interpretation in Petrochronology

The phosphate mineral monazite (LREE,Y,Th,Ca,Si)PO4 occurs as an accessory phase in peraluminous granites and Ca-poor meta-psammopelites. Due to negligible common Pb and very low Pb diffusion rates at high temperatures, monazite has received increasing attention in geochronology. As the monazite grain sizes are mostly below 100 μm in upper greenschist to amphibolite facies meta-psammopelites, and rarely exceed 250 μm in granulite facies gneisses and in migmatites, microstructural observation and mineral chemical analysis need the investigation by scanning electron microscope and electron probe microanalyzer, with related routines of automated mineralogy. Not only the microstructural positions, sizes and contours of the grains, but also their internal structures in backscattered electron imaging gray tones, mainly controlled by the Th contents, can be assessed by this approach. Monazite crystallizes mostly euhedral to anhedral with more or less rounded crystal corners. There are transitions from elliptical over amoeboid to strongly emarginated grain shapes. The internal structures of the grains range from single to complex concentric over systematic oszillatory zonations to turbulent and cloudy, all with low to high contrast in backscattered electron imaging gray tones. Fluid-mediated partial alteration and coupled dissolution-reprecipitation can lead to Th-poor and Th-rich rim zones with sharp concave boundaries extending to the interior. Of particular interest is the corona structure with monazite surrounded by apatite and allanite, which is interpreted to result from a replacement during retrogression. The satellite structure with an atoll-like arrangement of small monazites may indicate re-heating after retrogression. Cluster structures with numerous small monazite grains, various aggregation structures and coating suggest nucleation and growth along heating or/and enhanced fluid activity. Microstructures of monazite fluid-mediated alteration, decomposition and replacement are strongly sutured grain boundaries and sponge-like porosity and intergrowth with apatite. Garnet-bearing assemblages allow an independent reconstruction of the pressure-temperature evolution in monazite-bearing meta-psammopelites. This provides additional potential for evaluation of the monazite microstructures, mineral chemistry and Th-U-Pb ages in terms of clockwise and counterclockwise pressure-temperature-time-deformation paths of anatectic melting, metamorphism and polymetamorphism. That way, monazite microstructures serve as unique indicators of tectonic and geodynamic scenarios.

Numerical Investigation of Newtonian Fluid Flow around Sharp &amp; Rounded Corner Rectangular Obstruction

In the present study, very stable and converging Least Square finite element method (LSFEM) is employed to calculate the approximate solution of steady state Navier – Stokes equation, consisting continuity and momentum equations in two dimensions. The 2D rectangular domain is considered to study the behavior of linear fluid passing two parallel rectangular obstructions in an open channel. The current numerical analysis is based on two instances, in the first one two rectangular obstructions possesses sharp corners set to face the entering flow while in the other case, obstructions having round corners are analyzed concerning to examine the enhancement in the size of vortex formed due to the flow blockage, intensity of vortex and the recirculation flow rate in the dead zone for Reynolds number from 250 to 2000. The stream line patterns are also presented to monitor the changes appears in the shape of vortex for different Re. The information gather through the analysis suggests the cutoff corner obstruction is congenial in restricting the vortex length and favorable for slow down the flow circulation rate in the lower stream of the channel. The acquired results are compared with established data in past literature which turn out to be in good agreement.