Double Notch Research Articles

Phase field numerical strategies for positive volumetric strain energy fractures

AbstractA reasonable crack driving force is the key to preventing compression cracks and eliminating unrealistic crack propagation in phase field fracture analysis. Thus, examining the roles of volumetric strain energy (VSE) and deviatoric strain energy (DSE) in influencing crack propagation is necessary. This paper presents a comprehensive analysis of the following four different approaches to energy decomposition‐driven crack propagation: the positive volumetric strain energy method (VSEM), deviatoric strain energy method (DSEM), volumetric‐deviatoric strain energy method (VDSEM), and no decomposition method (NM). All of the strain energy is involved in the development of the crack propagation. The following four examples are investigated: two benchmark single‐side notched examples, a complex crack containing a hole example, and a crack coalescence in an asymmetric double notch example. The VSEM's numerical findings align with literature and experimental observations, confirming that positive VSE rather than DSE promotes crack propagation.

Investigating the impact of notch shapes on oxide–oxide ceramic matrix composites strength: A computational approach

AbstractThis study utilizes finite element analysis (FEA) to explore the effect of standardized notch shapes—triangular, circular, and rectangular on the tensile behavior of oxide–oxide (O–O) ceramic matrix composites (CMCs) across various temperature ranges. Findings reveal that unnotched samples exhibited a superior equivalent stress of ∼425 MPa, closely aligning with experimental values. However, under elevated temperatures of 1000°C and 1200°C, degradation occurs, reaching up to 54% decrease at 1200°C. Notched samples demonstrate similar behavior, with all notches acting as stress concentrators. Analysis of single and double notches highlights that circular notches have the most significant stress concentrators due to their smooth surfaces and lack of sharp edges, in contrast to rectangular and triangular notches. Although all notch types influence stress concentration, the absence of non‐sharp corners in circular notches limit stress dissipation, resulting in higher stress concentrations. This trend persists under high temperature as well. The study emphasizes the critical need for a thorough assessment of notch effects, considering their position, orientation, shape, and size, as they significantly affect the mechanical properties of O–O CMCs.

Syndiotactic chiral metastructure with local resonance for low-frequency vibration isolation

Isolating low-frequency vibrations is a challenge in engineering due to their long wavelength. The bandgap within inertial amplification metastructures has proven to be an effective solution for isolating low-frequency vibrations. In this study, a chiral local resonator is proposed and integrated into a syndiotactic chiral inertial amplification metastructure (SCM) to create a low-frequency bandgap. Under equal mass and stiffness conditions, SCM-CR exhibits a bandgap starting frequency 32.3 % lower than that of traditional metastructures with traditional local resonators (TM-TR), and the normalized width of the bandgap is 31.7 % wider than TM-TR. The low-frequency bandgap is attributed to the presence of chiral local resonators. The inertial amplification effect induced by the chiral structure results in a resonance frequency lower than that of local resonators with equivalent mass and stiffness. Within the low-frequency bandgap, the transmission of the SCM-CR proposed in this study exhibits double attenuation notches over a specific number of periods, leading to the normalized width of the deep attenuation region 45.8 % broader than that of traditional metastructures with chiral local resonators (TM-CR). The tunability of the bandgap has also been investigated. Experimental results verified the double attenuation notches and the tunability of the bandgap. This work provides a promising solution for low-frequency vibration isolation.

Bioinspired soft-hard interfaces fabricated by multi-material additive manufacturing: A fracture mechanics investigation using essential work of fracture

This study employs the Essential Work of Fracture (EWF) concept to evaluate the interfacial fracture toughness of bioinspired interfaces between soft and hard polymer phases. The experimental framework utilizes a model material system with Polylactic Acid (PLA) as the hard phase and Thermoplastic Polyurethane (TPU) as the soft phase. Employing the Fused Filament Fabrication (FFF) technique, bioinspired sutural interfaces are created, characterized by interpenetrating soft and hard protrusions. The modulation of a critical parameter in the FFF process enables the variation of interpenetration length of protrusions at the interface, thereby achieving a spectrum of interfacial strength and toughness. The determination of essential work of fracture from double edge notch tension samples, with varied ligament sizes, allows for the specific EWF measurement. This specific EWF is found to align with the initiation value of plane strain interfacial fracture toughness obtained through the Double Cantilever Beam (DCB) test. Therefore, the proposed approach asserts the elimination of the need for complex interfacial fracture tests, such as DCB. A noteworthy discovery is the establishment of a correlation between specific plastic energy dissipation and protrusion length. This correlation suggests an increased plastic dissipation with longer protrusions within the investigated bioinspired interface. Due to this heightened plastic energy dissipation, the shape of the interfacial nominal stress-displacement curves demonstrates substantial dependence on interface morphology, shifting from a triangular to a trapezoidal shape as protrusion length increases. These findings offer valuable insights into the mechanics of bioinspired interfaces, presenting a more efficient and nuanced approach to characterizing their fracture properties.

Computed Tomography Evaluation of Frontal Sinus Volume in Migraine Patients.

This study aimed to assess the frontal sinus volume (FSV) on computed tomography (CT) scans in migraine patients. Cranial and paranasal CT images from 75 migraine patients (mean age: 39.14±13.63y) and 23 control cases (mean age: 38.78±13.32y) were analyzed retrospectively. Three-dimensionally reconstructed images of frontal sinuses were generated. Total FSV, anterolateral, and transverse diameters of the head were measured. The presence/absence and nature of supraorbital foramen and notches were evaluated. The total FSV was 8.02±5.97cm 3 in the migraine group and 8.38±4.83cm 3 in the control group, with no significant differences between them. Mean FSV values showed no statistically significant difference between females (7.79±5.85cm 3 ) and males (9.12±6.66cm 3 ) within and between the groups. Single notch was the most observed structure in both groups, with bilateral presence being the most common. Double foramen and notch were observed only in the migraine group, and the coexistence of both structures was higher in the migraine patients than in controls. There was no statistical difference in FSV between migraine and control groups, nor based on sex. Overall, the frontal region anatomy, particularly the exit locations of the supraorbital or supratrochlear foramen/notches, may be influenced by hyperplasia/hypoplasia of FSV. Therefore, assessing FSV using CT may be crucial for surgical planning in migraine patients undergoing open or endoscopic approaches to the frontal region.

Fracture load in double keyhole notch PLA-Cu2O nanocomposites manufactured via compression molding and 3D printing: An experimental and numerical study

Polylactic acid (PLA) polymer has garnered significant attention due to its biocompatibility. The incorporation of copper oxide (Cu2O) nanoparticles into this polymer is expected to enhance its antibacterial, electrical, and thermal properties. This modification can potentially improve the performance of PLA in the fields of prosthetics manufacturing or printed circuit fabrication. However, the current research is rather focused on the mechanical properties of the PLA-Cu2O nanocomposites. This research is thus aimed to analyze PLA-Cu2O (97-3 wt%) nanocomposites with a double keyhole notch configuration both experimentally and numerically. Scanning electron microscopy (SEM), X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), X-ray mapping of elemental distribution(X-map), and thermogravimetric analysis (TGA) were employed to explore the morphology, crystallinity, homogeneity, purity, and thermal stability of the nanocomposite. The specimens were fabricated through two different processes: the classical method of compression molding and the innovative method of 3D printing. The results revealed the superior mechanical performance of the 3D-printed nanocomposite at a 0° raster angle, while the mechanical properties gradually decreased for raster angles of 45° and 90°. The experimental test also indicated a decline in the maximum fracture load of specimens with a double keyhole notch and constant notch inclination angle by raising the notch radius. This behavior was also observed by increasing the notch inclination angle at constant notch radius. The numerical results were similar to the experimental findings. Moreover, the nanocomposite manufactured through the classical method exhibited higher critical fracture load compared to their 3D-printed counterparts with the same geometry.

Tunable double notch filter on a thin-film lithium niobate platform.

Tunable optical filters at the chip scale play a crucial role in fulfilling the need for reconfigurability in channel routing, optical switching, and wavelength division multiplexing systems. In this Letter, we propose a tunable double notch filter on thin-film lithium niobate using dual microring architecture. This unique integrated filter is essential for complex photonic integrated circuits, along with multiple channels and various frequency spacing. With only one loaded voltage, the device demonstrates a wide frequency spacing tunability from 16.1 to 89.9 GHz by reversely tuning the resonances of the two microrings while the center wavelength between the two resonances remains unaltered. Moreover, by utilizing the pronounced electro-optic properties of lithium niobate associated with the tight light confined nanophotonic waveguides, the device demonstrates a spacing tunability of 0.82 GHz/V and a contrast of 10-16 dB. In addition, the device has an ultracompact footprint of 0.0248 mm2.

Fatigue Life and Residual Stress of Flat Stainless Steel Specimens Laser-Cladded with a Cobalt-Based Alloy and Postprocessed with Laser Shock Peening

Laser cladding (LC) is a versatile additive manufacturing process where strands of metallic material are deposited and melted by a laser. However, there are some limitations associated with this process that may affect the performance of the final manufactured parts. In the present work, the influence of laser shock peening (LSP) on the fatigue life of 304 stainless steel flat specimens with a cobalt-based alloy (Stellite 6) coating applied by LC was investigated. The analysis was carried out both experimentally and numerically. In the LSP simulation, the ABAQUS/Explicit code was used to determine the residual stress distribution of specimens with double central notches with a radius of curvature of 5, 10, 15, and 20 mm. From the numerical results, an improvement was found regarding fatigue life up to 48% in samples with LSP. Experimentally, 14% in fatigue life enhancement was observed. The residual stress, determined by the contour method, showed good agreement with the LSP simulation. The SEM images revealed that the fatigue failure started at the Stellite 6 coating and propagated towards the center of the specimen. LSP has been shown to be a suitable postprocessing alternative for laser-cladded parts that will be subjected to fatigue loading since it led to fatigue improvement through the introduction of compressive residual stresses on clad coatings.

Fracture behavior of double edge notch AlSi10Mg alloy fabricated by laser powder bed fusion

In the present study, the fracture behavior of additively manufactured (AM) metal parts has been investigated. To this aim, double edge notch tension (DENT) specimens have been printed using AlSi10Mg alloy based on the laser powder bed fusion (PBF) technique. Particularly, DENT specimens have been fabricated with three different ligament lengths and three different printing directions for each ligament length. In this study, we used the concept of essential work of fracture to describe the fracture behavior AMed parts. According to a series of tests under static loading conditions, influences of the ligament length and printing direction on the structural integrity of the DENT specimens have been determined. According to the experimental practices, levels of ductility and size of plastic zone in the ligament region have been documented. Here, we utilized digital image correlation technique to measure strain fields on the surface of the examined samples. Moreover, numerical simulations have been conducted to simulate the stress distribution from DENT specimens. In addition, visual inspection of the fracture surfaces has been conducted using a free-angle observation system. The outcome of this study can be used for future designs of PBF printed parts with a better structural performance.

Effects of carbon/glass nonwoven interleaving veils and their areal density on opening and shearing mode interlaminar fracture toughness of glass epoxy composites

The study explores the impact of Carbon and Glass nonwoven interleaving veils with varying areal density on delamination resistance in unidirectional (UD) Glass epoxy composites under Opening (Mode-I) and Shearing (Mode-II) mode loadings. Commercially available non-woven Carbon and Glass interleaves with areal densities of 15, 20, 25, and 30 g/m2 were used to manufacture the interleaved Glass epoxy laminates. Double Cantilever Beam (DCB) and End Notch Flexural (ENF) specimens were used to determine the mode-I and mode-II fracture energies. The results reveal that, during mode-I initiation, interleaved laminates exhibit a lower interlaminar fracture toughness (IFT) except for the Carbon fiber interleaved laminates of areal density 30 g/m2. However, during propagation, all veils interleaved laminates presented significant improvement in IFT ranging from 5 to 25 % accompanied by substantial fiber bridging. In case of mode-II test, the laminates with Carbon and Glass veils exhibit enhanced IFT (60–182 %) with increasing areal density compared with the non-interleaved Glass laminates. Optical and scanning electron micrographs (SEM) provide evidence of fracture mechanisms involved in the interleaved and non-interleaved composite laminates.

Fracture assessment of inclined double keyhole notches in polylactic acid specimens fabricated by fused deposition modeling and traditional method

AbstractThe fracture behavior of specimens made of polylactic acid and weakened by inclined double keyhole notches is investigated by both experimental and numerical methods. The test specimens are fabricated by two different methods; fused deposition modeling and traditional methods. The mechanical behavior of specimens was investigated under mixed‐mode loading with different notch inclination angles, various notch tip radius, and multiple raster angles. An experimental program was performed, and 72 new experimental data were provided. A fracture criterion based on the strain energy density is used to assess the critical fracture loads of the tested specimens. Good agreement is found between experimental and numerical data. The results showed that increasing the notch inclination angle and notch tip radius led to a decrease in the fracture load of the specimens. Also, fracture loads of the classical specimens are higher than the 3D‐printed specimens. In the 3D‐printed specimens, fracture loads for the samples with raster angles of 0°, 45°, and 90° have the highest value, respectively.Highlights Fracture assessment of polylactic acid specimens Specimens were weakened by using an eccentric inclined double keyhole notch Specimens manufactured by fused deposition modeling and traditional method Investigation of different notch inclination angles and notch tip radius Evaluation of specimens using experimental and numerical analysis methods

A Double Band Notch Antenna with Flexible Frequency Tuning for Ultra Wideband Applications

A Double Band Notch Antenna with Flexible Frequency Tuning for Ultra Wideband Applications

Influence of co-deposition modification on mode I and II interlaminar toughness of epoxy laminates interleaved with waste textiles using experimental measurement and finite element technique

Interlaminar delamination has been a persistent problem that restricts the ability of fiber reinforced laminated composites under applied load. The influence of polyethyleneimine-catechol (PEI-CCh) co-deposition modification on the mode I (GIC) and II interlaminar fracture toughness (GIIC) of plain glass fiber fabric reinforced epoxy composites (PGFRECs) were discussed using double cantilever beam (DCB) and end notch flexural (ENF) tests. It was found that interfacial properties of PET/epoxy and PET/cotton/epoxy interfaces were substantially improved after co-deposited modification, which laid a solid foundation for enhancing the resistance to interlaminar delamination. GIC and GIIC in platform of crack propagation greatly increased with the introduction of co-deposition layer. The fracture surfaces of delaminated failure specimens were observed by scanning electron microscope. The higher propagation fracture toughness for co-deposition modified PGFRECs is due to the anchoring effect of functional layer combining waste fabrics with epoxy matrix to provide favorable stress transfer channel prior to macroscopic crack formation. In regard to the delamination crack, new crack generation and bridge fiber failure mainly dominated the mode I crack extension process, while zigzag sections were particularly common for mode II fracture specimens.

Brewing sustainability and strength: Biocomposite development through tea waste incorporation in polylactic acid

This study aims to enhance the mechanical properties of polylactic acid by incorporating black tea waste as an economical and sustainable additive capable of being recycled. The black tea waste, after the hot water color removal process, is milled to a fine and uniform powder size. The combination of these particles with polylactic acid is carried out using a twin-screw extruder. Specimens of pure polylactic acid and biocomposites containing 3 and 5 wt% black tea waste are manufactured using a hot press machine at a temperature of 200 °C. The filaments are also successfully extruded for three-dimensional printing purposes. Scanning electron microscopy images reveal that in the polylactic acid–3% tea biocomposite, the tea particles are appropriately dispersed within the polylactic acid matrix. The tensile test results indicate that biocomposite polylactic acid-3% tea has the highest mechanical properties, with a tensile strength of 67 MPa, demonstrating a 34% increase compared to polylactic acid. Furthermore, the biocomposite of polylactic acid–3% tea waste exhibits the best performance with a fracture energy of 2.5 kJ/m2 in the impact test. Hence, polylactic acid–3% tea biocomposite can be recommended as a suitable sustainable substitute. Finally, numerical simulations are performed on biocomposites containing double keyhole notches. This analysis is conducted to observe the behavior of biocomposite models with double keyhole notch under mixed-mode loading. The critical fracture load of the models is calculated using the strain energy density criterion. It is observed that an increase in the notch inclination angle and notch radius leads to a decrease in the fracture load in the models.

Fatigue and Fracture Evaluations in Ti-10V-2Fe-3Al (Ti 10-2-3)

A mechanical assessment was conducted to characterise the near β titanium alloy Ti-10V-2Fe-3Al (Ti 10-2-3), which was heat-treated to provide two strength variants. Low cycle fatigue and crack propagation tests were performed under standard laboratory air plus a salt fog environment. The differences in static strength were also demonstrated under fatigue conditions utilising plain specimens. However, the alloy was essentially insensitive to the test environment when comparing LCF performance in air and salt fog. Salt fog also provided no effect on crack growth behaviour. A double edge notch specimen geometry was employed to measure free initiation and the growth of cracks from a stress-raising feature. The current data now supplement previous studies aimed at expanding the mechanical database for Ti 10-2-3 component design and in-service life predictions.

Enhancing the fracture toughness of laminated composites through loop warp yarns

The delamination tendency is a key factor affecting the practical use of laminated composites. How to improve the interlaminar strength and interlaminar fracture toughness of laminated composite is a focus of research on composite materials. A three-dimensional (3D) weaving technique is employed to weave loop warp yarns (loops) with 3D fiber bundles instead of warp yarns on the basis of plain fabrics. The contribution of loops to the interlayer performance is revealed by double cantilever beam (DCB) tests, end-notch flexure (ENF) tests, flexural tests, and double notch shear (DNS) tests. Test results show that the mode I and mode II interlaminar fracture toughness values of the single-sided-loop two-dimensional (2D) woven laminated composite (SWLC) are 77% and 58.2% higher than the interlaminar fracture toughness values of the general 2D woven laminated composite (GWLC). As companied with the ones of GWLC, flexural strength and modulus of SWLC increase by 73% and 69.1%, and the interlaminar shear strength of SWLC increases by 45.7%. The loop yarns act as a link between the interlaminar matrix and the reinforcing fiber fabric and thus improve the poor interlaminar performance of GWLC. The reported information may provide a reference for the application of the SWLC in practice.

Evaluation of the level of damage to thermoplastic flat sheets of acrylonitrile butadiene styrene (ABS) subjected to static tensile tests using static and unified damage and estimation of service life

In this study, we are interested in the characterization of a flat plate in polymeric ABS under the uniaxial solicitation. We ran a series of tests on smooth rectangular specimens (defect-free) by ASTM 882-02 standards to characterize the material and provide a scale of comparison, as well as to investigate the combined defect effect on the mechanical behavior of ABS. Another panoply of tests was performed on rectangular test pieces with holes with a single notch and holes with a double notch. Then, we experimentally identify the propagation of their damage. The calculation of the damage, using models of experimental damage, led to determining the three stages of the evolution of the damage, which are the initiation, propagation, and complete deterioration of the material. Therefore, the approach of reliability (R) is a statical parameter, used to designate the critical life fraction concerning the notch depth (βc) of a modeled defect as a combined defect on an ABS specimen. In addition, the unified theory was developed in this context, on the one hand, to define the damage parameter, which is the internal variable that describes the state of damage of the structure in terms of the life fraction, and on the other hand for the theoretical re-evaluation of the level of damage. These techniques have the advantage of quickly assessing the performance and stability of the studied polymer and deciding whether to have an anticipatory maintenance strategy and an awareness of the safety requirements policy regarding the damage-reliability behavior of the studied specimens. From the latter, the discussion of the curves allowed us to maintain the limits of the ABS materials’ mechanical behavior and confirmed that the theoretical and experimental results show good agreement and correlation.

Micromechanics-Based Modeling of SiC/SiC Ceramic Matrix Composites and Structures

The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses. Finally, to demonstrate the multiscale analysis framework, a CMC gas turbine engine vane structure is analyzed involving a progressive damage model.

On the use of the Combined Loading Compression fixture to estimate the intralaminar compressive fracture toughness of composites

This study reassesses the constraint effect provided by a Combined Loading Compression (CLC) fixture on notched specimens used to measure the compressive intralaminar fracture toughness of composite materials. An experimental campaign is carried out to determine whether a variation in the specimen gauge section length would result in a significant change in the nominal strength of Double Edge Notch CLC specimens. Following the testing of six sets of different specimen geometries for both a uni-directional thermoplastic and a bi-directional woven thermoset composite, the effect of the gauge length is analysed using the size-effect method. Results show that nominal notched strength variation is minimal, suggesting that the CLC clamp does not effectively constrain the gripped sections against in-plane deformations. This assessment proves that the correction factor used in the determination of the R-curve needs to be computed considering the entire specimen geometry, including the gripped regions. Furthermore, the results reveal that previous characterisation campaigns conducted using end-loaded Double Edge Notch Compression specimens could have led to a significant underestimation of the steady-state fracture toughness.

Cloverleaf filtenna with reconfigurable quintuple rejection bands using defected microstrip structure

This paper presents a quintuple-notched Filtenna based on a cloverleaf ultra-wideband (UWB) antenna and an inverted L-shaped bandstop filter (BSF). This filtenna rejects frequencies of Bluetooth (2.4 GHz), Wi-Max (3.5 GHz), Wi-Fi (5.2 GHz), ISM (5.8 GHz), and satellite communications (7.8 GHz). Using the defected microstrip structure (DMS) technique, all notches are obtained. The UWB antenna resonates over a frequency range from 2.1 to 13.6 GHz with double notches at 2.4 and 5.8 GHz, generated by etching two C-shaped DMSs on the patch. Two switches are connected to these two C- shaped slits. Controlling the ON/OFF states of these switches enables notch reconfiguration. The inverted L-shaped BSF suppresses triple notch rejections at 3.5, 5.2, and 7.8 GHz using three DMSs. Similarly, by controlling the ON/OFF states of three switches, frequency reconfiguration is observed. Simulation and measurement confirm that the UWB antenna, the BSF and the filtenna can operate in four states, eight states, and 20 states, respectively. The filtenna has good efficiency (79–95 %) and presents low radiation efficiency at rejection bands. It obtains stable gain (2–5.5 dBi) except at notches where the gain registers negative values. Additionally, this filtenna can freely switch between ultra-wideband mode and any notch-band mode.