Symmetric Notches Research Articles

Recent Advances in the Analytical Stress Field Solutions for Radiused Notches in Orthotropic Solids.

The main aim of this work is to provide a brief overview of the analytical solutions available to describe the in-plane and out-of-plane stress fields in orthotropic solids with radiused notches. To this end, initially, a brief summary on the bases of complex potentials for orthotropic elasticity is presented, with reference to plane stress or strain and antiplane shear problems. Subsequently, the attention is moved to the relevant expressions for the notch stress fields, considering elliptical holes, symmetric hyperbolic notches, parabolic notches (blunt cracks), and radiused V-notches. Eventually, examples of applications are presented, comparing the presented analytical solutions with the results from numerical analyses carried out on relevant cases.

Estimating ductile crack initiation in structural steel under combined tension and shear stress using a modified void growth model

Ductile fracture initiation is one of the important issues in recent research on structural steels. Many models have been established to simulate the mechanism of ductile fracture and predict the ductile crack initiation in different loading conditions. The void growth model is one of the most successful micro-models that is originally developed to estimate ductile crack initiation in the first mode of fracture under monotonic loading. However, one of the main shortcomings of these types of uncoupled void growth models is the incapability of them in capturing the behavior of steels under shear stress and the effect of it on the resulting voids and the process of ductile fracture in low and moderate-stress triaxialities. A newly proposed modified void growth model represented in this article is able to overcome this issue by introducing normalized maximum shear stress. A series of scanning electron microscopy examinations and experimental and numerical monotonic tensile examinations have been carried out on the notched round bar and flat groove plate specimens with different notch radii to calibrate the represented fracture model. Steel-holed plates with symmetric notches around the hole and notched shear plates have been tested and analyzed to demonstrate the application and validation of the represented void growth model in predicting the initiation of ductile fracture in various combinations of tension and shear under monotonic loading. Different angles of notches were used in the specimens to achieve diverse stress states to examine the application of the represented micro-model in non-uniform stress state fields. Finally, the role of the characteristic length, as the representative of the density of the inclusions in the material, on the accuracy of the model has been discussed in this article.

In situ high-resolution ultrasonic visualization of damage evolution in the volume of quasi-isotropic CFRP laminates under tension

The work is devoted to novel experimental equipment for in situ visualization of damage development in the volume of CFRP under tensile. The acoustic microscope with long-focus probe beam of high-frequency ultrasound (50–100 MHz) was combined with mechanical testing machine. The experimental equipment provides visualization in dynamics of the processes of appearance, growth and transformation of microstructural damages in the volume of the specimen under mechanical loading. The method was validated by 4- and 7-ply quasi-isotropic CFRP laminates with symmetrical round notches. We explore the possibilities of ultrasound imaging for detection of matrix crack opening, and the mechanism of delamination formation with various combination of fiber orientation. According to the ultrasound imaging of the volumetric microstructure, we depicted several mechanisms of damage appearance and evolution under tension. For calculating the level of local deformation in the region with round notches, we applied the digital image correlation (DIC) of ultrasonic scans obtained during the experiment. The DIC data provides more correct values of deformations occurring in the specimen zone with round notches. It was shown that the values in the central area differ significantly from the deformation calculation along the whole length of the specimen, especially under loads close to the critical ones.

Ductile Fracture Investigation of High-Strength Steel SM570 under Low Stress Triaxiality

A comprehensive understanding of the fracture behavior of high-strength steel is of great significance for its structural application. In this study, experiments were conducted to investigate the ductile fracture mechanism of high-strength steel SM570, one type of conventional structural steel. Two types of shear specimens, one with symmetrical notches and the other with asymmetrical notches, were designed, and by changing the notch angles, a wide range of low-stress triaxiality could be obtained. Based on the discussion of the experimental results, crack initiation, and its propagation up to fracture failure were clarified. Compared with the fracture behavior of SM490 (one type of conventional normal-strength structural steel), the SM570 with higher yield stress has relatively severe stress concentration, the crack initiation appears earlier, and the brittle fracture is more likely to occur. Numerical simulations based on the finite element method (FEM) were performed with ABAQUS to obtain the stress triaxialities and equivalent plastic strain of the symmetrical and asymmetrical specimens. A modified N-VG model with a fracture criterion at a negative and low-stress triaxiality range from −0.6 to 1/3 was proposed for evaluating the fracture behavior of steel SM570.

Failure process and characteristics of three-dimensional high-stress circular tunnel under saturated water content

True-triaxial compression tests were carried out on cubic granite samples with a circular through hole using a true-triaxial testing system to investigate the influence of saturated water content (SWC) on the failure process and characteristics of a circular tunnel of surrounding rocks. The spalling failure under SWC can be divided into four periods: calm period, buckling deformation period, period of rock fragment gradual buckling and exfoliation, and period of formation of symmetrical V-shaped notches. When the horizontal axial and vertical stresses were constant, the spalling failure severity was reduced with the increase in lateral stress. Under natural water content, a strong rockburst with dynamic failure characteristics occurred on the circular hole sidewall. Under SWC, the failure severity was reduced and the circular hole sidewall experienced spalling failure, exhibiting progressive static failure characteristics. Therefore, water can reduce the failure severity of surrounding rocks in deep underground engineering, which has a certain guiding significance for the prevention and control of rockbursts.

A Compact Dual-Band Dual-Circularly Polarized SIW Cavity-Backed Antenna Array for Millimeter-Wave Applications

A compact millimeter-wave (mm-Wave) dual-band dual-circularly polarized (CP) antenna based on substrate integrated waveguide (SIW) cavity-backed structure is proposed in this letter. By introducing the square aperture with two symmetric perturbation notches on the SIW cavity, right-hand CP (RHCP) can be generated at the low frequency band. On this basis, the dumbbell-shaped patch is placed inside the square aperture to generate left-hand CP (LHCP) at the high frequency band. To optimize the impedance matching and adjust resonant frequency, stacked parasitic patches are adopted. In addition, the two shorted vias are introduced to realize the independent tuning of high frequency band. The measured results show that the array achieves the impedance bandwidths of 7.3% and 7.5%, AR bandwidths of 2.8% and 2.6%, with gains of 18.2 and 18.5 dBic at 28 and 38 GHz, respectively. The proposed array will be a potential candidate component for 5G mm-Wave full-duplex wireless communication systems.

The Analysis of Small-Scale Notches on the Fatigue Performance of SLM Ti-6Al-4V; A Theory of Critical Distances Approach

Selective Laser Melting is an additive manufacturing practice that permits the production of metal alloy-based parts. While facilitating the design of complex geometry, SLM leads to the fabrication of a unique material structure that showcases distinct behavioural characteristics relative to their traditional methods of material manufacture. Defects that are innate to SLM inspire the presence of a compositional outlook that is inhomogeneous in nature and only serves to hinder part efficiency. Thus, the Theory of Critical Distances offers a refreshed proposal to evaluating notched Ti-6Al-4V material produced by additive manufacturing processes. Key principles of the theory’s working mechanisms are outlined. Subsequently, symmetrical notches of contrasting size are assessed. Findings reveal that the Theory of Critical Distances is adequately compatible with accurate fatigue prediction of SLM Ti-6Al-4V in its as-built state. Additionally, fracture surface analysis reveals that crack initiation is predominantly a surface-based phenomenon. Hereby, increased focus must be given to the quality of processed material that is located at the externalities of additively manufactured components, in order to enhance their service life capabilities. This will induce an increasingly uniform material structure that will allow for more predictable behavioural characteristics.

Lamb Wave Wireless Communication Through Healthy and Damaged Channels With Symmetrical and Asymmetrical Steps and Notches.

Data transmission through solid metallic channels is recommended in certain industries where no other options are proposed, such as nuclear, aerospace, and smart vehicles. In addition to the Faraday shielding effect of electromagnetic waves, another issue related to damage presence due to mechanical loads exists. Severe damage in the transmission channel leads to signal loss at the receiver. For this sake, ultrasonic guided waves, such as Lamb waves, maybe a good substitute since they can propagate through long distances in solid metallic structures. The scope of this work is to build a reliable, reproducible, and high data-rate wireless communication experimental platform, using ultrasonic guided waves, through healthy and damaged plates for industrial usage. The target is to compensate at first for the effect of dispersion, reverberation, scattering, and boundary reflections for the healthy plate. The novelty of this work falls within the performance analysis of the demodulation algorithm based on cross-correlation combined with binary phase-shift keying (BPSK), using a finite-element simulation through healthy and damaged plates with different depths of symmetrical and asymmetrical notches (SN and AN) and steps based on the bit error percentage (BEP). Furthermore, another contribution related to the impact of multiple reflections and mode conversions caused by symmetrical and asymmetrical steps and notches is taken into account. After this, numerical results are validated using an ultrasonic guided wave experimental platform. Results based on BEP analysis prove that the algorithm has successfully compensated for the effect of dispersion and boundary reflections for the healthy plate and multiple reflections and mode conversions for the damaged ones. A highly effective data rate of up to 350 kb/s can be reached even in the presence of severe damage in the transmission channel.

Performance Improvement of the Hybrid Switch Reluctance Motor by Notching Method

Hybrid switch reluctance motors are the family of switch reluctance motors (SRMs) that attenuate the magnetic saturation and increase the air gap magnetic flux by exploiting permanent magnets. The permanent magnet auxiliary air gap flux can affect the average torque and ripple. Commonly, the torque ripples reduction comes with the average torque drop. In this paper, the torque ripple reduction and average torque improvement are achieved for a 6/10 pole hybrid switch reluctance motor by inserting two symmetrical notches on its rotor. Also, the lengths of magnet and rectangular notches are optimized by the finite element method and sensitivity analysis. The comparison of the optimized design with the initial one carried out by finite element proves the efficiency of the proposed model.

Quantifying the Shape of the Greater Sciatic Notch Using Elliptical Fourier Analysis

The greater sciatic notch is a well-established, sexually dimorphic feature in humans. The traditional anthropological perspective describes females as having wide and shallow notches, while the male notch is described as being narrow and deep. However, the size and shape of the notch can vary between populations, which can complicate the use of this feature as a sex determinant in forensic analyses. The current study investigates the relative contributions of sex, ancestry, and age at death to the shape of the greater sciatic notch using a morphometric approach called elliptical Fourier analysis (EFA). The study sample includes 975 dry bone specimens obtained from three skeletal collections, including three ancestral groups. The results indicate that the notch varies systematically with each of the aforementioned variables, with sex having the greatest contribution. While classical anthropological descriptions of notch shape differences between the sexes arepartially confirmed, the relationship between sex and notch shape is more complex than previously assumed. Females tend to displayshallow and symmetrical notches, while those of males are deep, asymmetrical, and tend to demonstrate a piriform tubercle. A smallerproportion of the variation in notch shape is attributable to the other variables. The results for ancestry indicate that African Americanstend to have short and narrow notches, while European Americans tend to exhibit short and wide notches. Chilean notches tend to be tall and wide. When considering age at death, the notch appears to deepen and widen with increasing age, suggesting that the changes are resorptive rather than depositional.

Design of dual-polarized triple-band concentric annular-ring microstrip patch antenna for GPS applications

AbstractA triple-frequency operated concentric annular ring microstrip antenna which is single fed is presented. The proposed antenna with three concentric annular rings and two symmetrical notches on its outer ring and having a cross slot in its ground surface shows triple band at resonance frequency 1.22760, 1.57542, and 2.18 GHz, respectively. At the first two bands (GPS L2 and GPS L1), circular polarization characteristic is observed and the third band observes linear polarization finding its application in Universal Mobile Telecommunication System (UMTS). The complete dimension of the antenna designed and fabricated is only 51.6 × 51.6 × 1.6 mm3. Experimental results depict the proposed antenna gain of 3.31, 3.55, and 3.50 dBi in three bands, respectively, and closely matches with the theoretical results.

Stress distributions in orthotropic solids with blunt notches under in-plane shear loadings

The present work is devoted to the analysis of the stress distributions in orthotropic solids weakened by blunt notches and loaded under in-plane shear. In particular, using Lekhnitskii's approach, new closed form equations are derived for the stress components, explicitly accounting for the notch geometrical features, namely the notch radius and the opening angle, in conjunction with the elastic material properties.Three main geometries are considered, described using proper conformal mappings: lateral symmetric hyperbolic notches, parabolic notches and hyperbola-like notches in plates loaded under in-plane shear. Appropriate complex potential functions are introduced in the analytical formulation and analytical expressions for the whole stress fields are derived, taking advantage of free-of-stress boundary conditions along the notch edge.Eventually, the very good accuracy of the new solutions is proved against numerical results, as obtained from a number of two-dimensional finite element analyses carried out on plates with rounded notches under shear, also discussing the main features of the mode II stress fields in notched plates.

Experimental Investigation of Spalling Failure of D-Shaped Tunnel Under Three-Dimensional High-Stress Conditions in Hard Rock

The D-shaped cross section is a commonly used tunnel cross section in underground engineering. To simulate the failure process of a D-shaped hole under deep three-dimensional (3D) high-stress conditions, true-triaxial tests were conducted on cubic granite specimens with a through D-shaped hole, and the failure process of the hole sidewall was recorded in real time. Results show that the spalling failure process of the D-shaped hole sidewall can be divided into four periods: calm, fine particle ejection, crack generation and propagation, and rock slab gradually buckling and spalling. Afterwards, symmetrical V-shaped notches were formed on both sidewalls between the corner and arch springing. The spalling failure shows tensile failure characteristics. Under high vertical stress and constant horizontal axial stress, increasing the lateral stress reduces the severity of the spalling failure and the depth of the V-shaped notch. The initial failure vertical stress of the D-shaped hole sidewall is higher than that of circular hole sidewall, and the failure of D-shaped hole sidewall is mainly characterized by static failure. The failure of the circular hole sidewall is a more severe dynamic failure. When the vertical applied stress is the maximum principal stress, the position of the V-shaped notch tip is 0.20–0.25 h (h is the height of the D-shaped tunnel) from the tunnel floor, whereas that in the circular tunnel is 0.5 d (d is the diameter of the circular tunnel) from the tunnel floor. Specific support schemes should therefore be designed for tunnels with different cross sections according to the damage location, depth of failure zone, and severity of failure.

Mechanical Performance of Zr-Containing 354-Type Al-Si-Cu-Mg Cast Alloy: Role of Geometrical Discontinuities

The main objective of this study was to evaluate the performance of 354-type Al-Si-Cu-Mg cast alloys at both ambient (25 °C) and elevated temperatures (250 °C) through the addition of zirconium (Zr), nickel (Ni) and manganese (Mn). The motive behind these additions was to develop thermally stable alloys capable of resisting softening instigated by prolonged exposure at elevated temperatures and hence preserve acceptable mechanical properties. Another parameter affecting performance is geometry. Four different notch geometries were employed: two hole-type geometries and two types of V-notches (symmetric and asymmetric for each). The results reveal that the presence of asymmetric notches in the tensile test bars proved to be more deleterious than symmetric notches to the notch tensile strength and percentage elongation to fracture at both 25 °C and at 250 °C. The softening that took place during tensile testing at 250 °C rendered the alloys some ductility (in particular, the M1S (354 + 0.3 wt.% Zr), M2S (354 + 0.3 wt.% Zr + 2 wt.% Ni) and M3S alloys (354 + 0.3 wt.% Zr +0.75 wt.% Mn)), as a result, the notched tensile bars with asymmetric holes exhibited high strength values for these alloys compared to the tensile strength of unnotched bars subjected to similar heat treatment conditions owing to the presence of notches. The notch sensitivity ratios vary between 0.78 and 0.95 for asymmetric holes versus 0.7 and 0.85 for asymmetric V-notches at room temperature and 0.9 and 1.07 for asymmetric holes versus 0.7 and 0.92 for asymmetric V-notches at 250 °C.

Universal equations for the mode I stress distribution in finite size orthotropic plates with blunt notches and holes

In this work a new universal formula suitable for accurately describing the maximum normal stress distribution along the entire ligament of orthotropic plates weakened by central holes or symmetric lateral notches is provided.To this end, a recent analytical solution proposed to describe the local stress distributions in the close neighbourhood of U- and V-shaped notches is significantly improved using an asymptotic matching approach which explicitly introduces in the analytical formulation two new parameters able to account for the global size of the notched component.The comparison with a large bulk of numerical results reveals that the new solution proposed is very accurate for many geometrical variations, from lateral notches and central holes. Accordingly, it represents a useful engineering tool to calculate the normal stress field ahead of several geometrical variations in orthotropic plates under tension.

Design of a Compact Microstrip Patch Antenna with Dual Notched Characteristics

The paper presents a microstrip patch antenna with dual band-notched characteristics. The proposed antenna is fed by a thin microstrip patch and provides band-notched characteristics by etching 2 symmetric C-shaped notches and one hollow cylindrical arc-shaped notch and notched partial ground. The antenna size was 30×19 mm2, covering a range from 2.8-12.3 GHz. The UWB covers a large band of frequencies including WLAN band (4.75-5 GHz) and the X-Band (7.75-8.35 GHz). To prevent interference with the operation of our antenna and devices operating in these bands, the frequencies are rejected through notches in the antenna. The simulated results show that the VSWR of the antenna is <-10 in the radiating bandwidth. This can be used in wireless applications.

New anatomical information on Dsungaripterus weii Young, 1964 with focus on the palatal region.

Pterosaur specimens with complete and well-preserved palatal region are rare. Here we describe new and previously collected specimens of the pterodactyloid pterosaur Dsungaripterus weii that are three-dimensionally preserved and provide new anatomical information for this species. Among the unique features is a lateral process of the pterygoid divided into two parts: an anterior thin, parabolic arc shaped element that separates the secondary subtemporal and the subtemporal fenestrae, followed by a dorsoventrally flattened portion that is directed inside the subtemporal fenestrae. The interpterygoid fenestrae join forming an irregular oval shape with two symmetrical posterior notches and a smooth anterior margin. Among all pterosaurs where the palate is known, the posterior configuration of the palate of D. weii is similar to some azhdarchoids, which is consistent with the suggested phylogenetic position of the Dsungaripteridae as closely related to the Azhdarchoidea. Furthermore, we identify symmetrical grooves on the lateral surface of the upper and lower jaws, that likely represent the impression of the edge of a keratinous sheath that would cover the upturned toothless rostrum during foraging activity, most likely consisting of hard elements, as has been previously assumed. Wear facets on the teeth also support this feeding mode.

One example of image digital processing of experimental data obtained by the method of photoelasticity

The article is devoted to the digital processing interferograms (isochromatic fringe patterns) obtained by the photoelasticity method. The application to interpretate the isochromatic fringe patterns allows us to automate image processing, gets to avoid the routine and time-consuming work. The features of the developed software package are described in detail by means the problem of stretching plate with two symmetrical edge notches. The application’s algorithm includes following main steps: image pre-processing, localization interference fringe, fringe tracing. The application creates a text file containing all the necessary data to further determine the stress-strain state (isochromatic fringe’s number and locus of fringes).

Notch Effect on Plastic Deformation of Metallic Glass: A Numerical Study by Revised Free‐Volume Theory

By means of a revised free‐volume theory, the notch effect on metallic glass was systematically investigated by the numerical method. Simulations on specimens without notches demonstrated that the parameters being determined in this work could reasonably describe the strength asymmetry of tension and compression. Moreover, four samples with different notches were used to numerically investigate the notch effect on global strength and plasticity. A better agreement could also be achieved between current simulations with existing experimental results, compared with another free‐volume model. Combined with the free‐volume distribution during deformation process, it was proven that the intersection of two major shear bands is the cause for the strength and plasticity enhancement found in sample with two symmetric notches. Besides, strength asymmetry between tension and compression was also found for notched samples. Compressive strengths are accordingly higher than tensile ones. Moreover, with the augment of the aspect ratio, the plasticity for specimens with two symmetric notches was found to increase firstly and then decrease afterwards.

An Equilateral Arm Inverted U-Slot and Notch Loaded UWB-CPMA with Rendered Ground Plane

In this paper, a microstrip fed modified circular patch monopole antenna (CPMA) with the rendered ground surface is presented for bandwidth enhancement. In order to extend the bandwidth of a demonstrated antenna, symmetrical slots and equilateral arms inverted U-slot are loaded on the partial ground and patch individually. For additional enhancement in the secured bandwidth, symmetrical notches are truncated from the bottom of the patch. The antenna has a dimension of 30x40x1.6 mm3, which is erected on low cost, FR-4 substrate with relative permittivity , permeability and loss tangent of . The proposed design is analyzed and simulated using high frequency structure simulator (HFSS). The analyzed results are validated through experimented results. The proposed antenna offers a bandwidth of 140.2 % with a maximum radiation efficiency of 94 % over the frequency scope of 2.54 GHz to 14.47 GHz. The crosspolarization levels are also found to be 20-30 dB and 12-23 dB smaller than the co-polarized level for E-plane and H-plane respectively. For better execution and assessment of proposed antenna, a parametric study has been done to analyze the performance of antenna with variations in the length of a partial ground conductor beside the other parameters. The exhibited antenna is suitable for various applications incorporating WiMAX, WLAN, UWB, C-band, X-band and UWB.