Critical Load Research Articles

Interlayer design for strong adhesion in the double-layer flexible copper clad laminate via HiPIMS deposition

By designing different interlayers (Al, Si/SixNy and Cr interlayer) and oxygen plasma pretreatment of the substrate, strong adhesion was realized for the double-layer flexible copper clad laminate on polyimide (PI) substrate via high power impulse magnetron sputtering (HiPIMS) technology. The microstructures and properties of Cu films on PI substrate were characterized by an X-ray powder diffractometer (XRD), X-ray photoelectron spectroscope (XPS), atom force microscopy (AFM), scanning electron microscope (SEM), nano-scratch test, scotch tape test and four-probe detector. With the introduction of interlayer and oxygen plasma pretreatment, the critical load of Cu film (300 nm thick) peaked at 43.5 mN and the sheet resistance ranged from 124 to 227 mΩ/sq. The oxygen plasma pretreatment resulted in the drastic oxidation to generate functional groups on the PI substrate surface, which contributed to the improvement of adhesion strength by chemical interaction in terms of the film with Si/SixNy or Cr interlayer. Besides, for the Cu film with Si/SixNy interlayer, the resistance against copper diffusion by the SixNy layer can also promote the enhancement of adhesion strength.

Analyzing Solar PV Integrated UPQC Performance in Micro Grid Systems

The presented work proposes a methodology for the automated transition of a solar PV array and battery integrated unified power quality conditioner (PV-B-UPQC) between standalone and grid-connected modes of operation. The system consists of a shunt and series active filters connected back-to-back with a common DC link, addressing the challenge of integrating power quality improvement with clean energy generation. The automated transition ensures continuous power supply to critical loads, even during grid unavailability. Key innovations include implementing this automated transition in the PV-B-UPQC system with minimal disturbance to local loads. The system's performance is validated through experimental evaluation under various dynamic conditions, such as automated transition, supply voltage variations, grid unavailability, changes in solar power generation, and load variations - scenarios commonly encountered in modern distribution networks. The results are verified using MATLAB/Simulink simulations. Index Terms—Power Quality, shunt compensator, series compensator, UPQC, Solar PV, MPPT.

A micromagnetic-mechanically coupled phase-field model for fracture and fatigue of magnetostrictive alloys

Magnetostrictive alloys are usually brittle materials with micromagnetic structures. Their structural reliability and durability depend on the complex micromagnetic-mechanical coupling at smaller length scales encompassing the evolution of micromagnetic structures. Herein we propose a micromagnetic-mechanically coupled phase-field model for fracture and fatigue behavior of magnetostrictive alloys with evolution of the micromagnetic structure. The thermodynamically-consistent model is derived from microforce theory, laws of thermodynamics, and Coleman–Noll analysis. The evolution of crack phase-field and magnetization-vector order parameters that are fully coupled is governed by history field dependent Allen–Cahn and Landau–Lifshitz–Gilbert equations, respectively. The model is extended to fatigue by introducing a degradation prefactor for the fracture energy as a function of positive elastic energy. One-dimensional analyses are then presented to anatomize the crack driving forces in terms of fully coupled micromagnetic-mechanical and pure mechanical driving force. We demonstrate the model capabilities by finite-element numerical studies on the micromagnetic domain evolution during the crack propagation and the influence of external magnetic field for type-I, type-II, and three-point bending fracture, as well as for the fracture of a single-edge notched specimen with an elliptical inclusion. The simulation result shows that depending on how micromagnetic domains are switched under micromagnetic-mechanical coupling, the magnetic field can enhance or decrease the critical load. In the presence of inclusion with larger fracture toughness, a crack is found to nucleate in the tri-junction of multi-domain micromagnetic structure owing to the high elastic strain around the tri-junction point. It is further found that a suitable magnetic field promoting magnetization-vector rotation around the crack tip could remarkably improve the fracturing load and fatigue life. The results demonstrate the model promising for the study of micromagnetic-mechanically coupled fracture and fatigue in magnetostrictive alloys.

Removal Characteristics of Gas-Phase D-Limonene in Biotrickling Filter and Stoichiometric Analysis of Biological Reaction using Carbon Mass Balance

Volatile organic compounds (VOCs) pose significant risks to human health and environmental quality, prompting stringent regulations on their emissions from various industrial processes. Among VOCs, d-limonene stands out due to its low threshold and contribution to malodorous emissions. While biofiltration presents a promising approach for VOC removal, including d-limonene, a comprehensive understanding of its performance and kinetics is lacking. This study aims to comprehensively assess the performance of a lab-scale biotrickling filter in treating gas-phase d-limonene. The experimental results indicate that the biotrickling filter efficiently removed d-limonene, achieving a critical loading rate of 19.4 g m−3 h−1 and a maximum elimination capacity of 31.8 g m−3 h−1 (correspondingly, up to 85% removal) at the condition of 94.2 s of EBRT. Microbial activity played a significant role in biotrickling filter performance, with a strong linear correlation being observed between CO2 production and substrate consumption. The Michaelis–Menten model was employed to represent enzyme-catalyzed reactions, suggesting no inhibition during biotrickling filter operation.

A data-driven computational optimization framework for designing thin-walled lenticular deployable composite boom with optimal load-bearing and folding capabilities

The thin-walled lenticular deployable composite boom (LDCB) is promising for aerospace engineering applications due to its lightweight and compact nature, but its mechanical behaviors are the main challenges limiting its practical application. Here, the axial compression and folding behaviors of LDCB were numerically simulated and the simulation results were verified according to the experimental data in the literature. Then, a new double chains quantum genetic algorithm (DCQGA)-gaussian process regression (GPR) model and data-driven computational optimization framework were proposed and the new model was trained using a database with 400 simulation results, the superiority of which was demonstrated by prediction accuracy evaluation. Additionally, benchmarking five state-of-the-art algorithms found that the coupling technology of DCQGA-GPR-non-dominated sorting genetic algorithm III (NSGA-III) is an excellent optimization strategy to obtain a well-designed structure of LDCB that maximizes the effectiveness of the material while satisfying the lightweight. The optimized LDCB design exhibits a significant performance improvement, with a 26.3 % reduction in the folding moment, a 34.2 % reduction in the maximum Tsai-Hill failure index, a 43.6 % increase in the critical load, and an 11 % reduction in linear density of mass compared to the initial design.

Avalanche shapes in the fiber bundle model.

We study the temporal evolution of avalanches in the fiber bundle model of disordered solids, when the model is gradually driven towards the critical breakdown point. We use two types of loading protocols: (i) quasistatic loading and (ii) loading by a discrete amount. In the quasistatic loading, where the load is increased by the minimum amount needed to initiate an avalanche, the temporal shapes of avalanches are asymmetric away from the critical point and become symmetric as the critical point is approached. A measure of asymmetry (A) follows a universal form A∼(σ-σ_{c})^{θ}, with θ≈0.25, where σ is the load per fiber and σ_{c} is the critical load per fiber. This behavior is independent of the disorder present in the system in terms of the individual failure threshold values. Thus it is possible to use this asymmetry measure as a precursor to imminent failure. For the case of discrete loading, the load is always increased by a fixed amount. The dynamics of the model in this case can be solved in the mean field limit. It shows that the avalanche shapes always remain asymmetric. We also present a variable range load sharing version of this case, where the results remain qualitatively similar.

Optimizing Structural Integrity of Fighter Aircraft Wing Stations: a Finite Element Analysis Approach

Modern fighter aircraft are equipped with multiple stations on the fuselage and under the wings to accommodate various external stores, both jettisonable and non-jettisonable. Each configuration undergoes airworthiness certification, including structural analysis of individual stations within the carriage flight envelope. This study focuses on the structural analysis of a fighter aircraft wing station within this specified envelope. To perform this analysis, the wing station is extracted from the comprehensive global wing model, creating a sub-model with equivalent stiffness properties. Utilizing ANSYS Workbench®, Finite Element Analysis (FEA) is conducted for critical load cases to determine the Factor of Safety (FoS). The initial analysis reveals that the wing station has an FoS of 1.2 under the maximum design load. Prestressed modal and buckling analyses indicate a 10% increase in stiffness due to stress-stiffening effects. To further enhance load-carrying capacity, parametric design changes are introduced. Increasing the bolt diameter from 8 mm to 10 mm raises the FoS to 1.33, resulting in an 8% increase in the maximum load-carrying capacity of the wing station. This comprehensive approach, employing FEA, ensures the wing’s structural integrity under static load conditions within the carriage envelope. The study's findings support the wing station's enhanced performance and contribute to safer and more efficient aircraft operations.

Distribution Network Restoration Strategy Considering Mobile Energy Storage Systems

Abstract The increasing occurrence frequency of disruptive extreme weather events and the growing share of distributed resources further enhance the importance of restoration of distributed resource-assisted distribution networks. However, most distributed sources are not spatially flexible in scheduling, severely impacting the restoration performance of distribution networks. The emergence of mobile energy storage systems (MESS) provides temporally and spatially flexible resources. Based on the mobility of mobile energy storage, this paper proposes a distribution network restoration strategy considering MESS and prioritized restoration of critical loads. The restoration strategy is established aiming at maximizing weighted loads while satisfying multiple constraints. Specific operating characteristics of MESS are modeled and incorporated into the restoration model. The established restoration model is then reformulated into a mixed-integer second-order cone program. Case studies on a modified IEEE 33-node system verify the proposed restoration strategy.

Operational optimisation of a microgrid using non-stationary hybrid switched model predictive control with virtual storage-based demand management

Demand-shaping mechanisms are a key component of modern energy management systems, although not unproblematic. The degree of social acceptance of interference with demand or generation and the ease of integration of various types of non-critical loads depends on the method of their implementation. In addition, the critical load pool typically includes devices with different response times. The energy management systems currently in use often cannot meet user expectations. Especially when considering other vital aspects, such as energy market spread, storage wear, or connection to the utility grid and neighbouring microgrids. The authors adopted an approach of unifying demand side management and response in the form of virtual energy storage. Said store allows for the accommodation of loads operating under differing scheduling horizons. Such a new concept allows management not only in terms of quantity but also in terms of time. The storage is the focal point of a comprehensive energy management system based on switched model predictive control. The receding horizon algorithm relies on a non-stationary hybrid microgrid model. The study compares the operating costs of microgrids with virtual storage, allowing only demand postponement, preponement or bidirectional operation. The energy management system is also examined for sensitivity to changes in the weight matrices of the cost function, horizon length and forecast inaccuracy. Introducing virtual energy storage reduces microgrid operating costs by up to 16%. The decrease in control performance is proportional to the prediction accuracy, and the sensitivity allows for customisation.

Multi-Functional Device Based on Superconducting Magnetic Energy Storage

Presently, there exists a multitude of applications reliant on superconducting magnetic energy storage (SMES), categorized into two groups. The first pertains to power quality enhancement, while the second focuses on improving power system stability. Nonetheless, the integration of these dual functionalities into a singular apparatus poses a persistent challenge. Considering this, this paper proposes a multi-functional device based on SMES, encompassing both power quality enhancement and power system stability improvement capabilities. It incorporates power quality enhancement features such as current harmonic filtering, active power smoothing, reactive power compensation, and critical load protection, while also furnishing virtual inertia to bolster grid frequency. Simulation results validate the effectiveness of the proposed methodologies.

Neural networks for critical load factors of unstiffened plates according to the reduced stresses method of EN 1993-1-5

The critical load factor resulting from the complete stress field is the main input parameter for the verification against plate buckling according to the reduced stresses method (RSM) from Eurocode EN 1993-1-5. Currently, the code provides just a simple and often conservative interaction formula with a limited application range. Realistic values can only be obtained by numerical methods, like the FEM, which is tedious for many load cases. To enhance the ease of use of the RSM, simple-to-use but accurate methods are needed, which can be automated and implemented into EN 1993-1-5. The current research deals with this problem by applying artificial neural networks (ANN) to predict the critical load factors of unstiffened plates under longitudinal, shear, and patch loading stresses, including their interaction behaviour. ANNs were used because approximated solutions with polynomials (as actual in the standard) are not suitable due to the complexity of the problem. The developed ANNs are highly accurate (as shown by an independent verification), can be implemented into the Eurocode, and can easily be used, even without in-depth programming skills. Moreover, a simple Python code is provided to demonstrate the ease of use. Still, the code can also be implemented into other software packages (like Excel), as only basic matrix operations are needed. The interaction surfaces are visualized, gaining a deeper understanding of plates under multiaxial loading situations. Finally, recommendations are given for generating ANNs for plate buckling problems.

Nonlinear bending and buckling analysis of 3D-printed meta-sandwich curved beam with auxetic honeycomb core

The present study investigates the static responses of a 3D-printed polymeric meta-sandwich curved beam with an auxetic honeycomb core, including buckling and nonlinear bending behavior. After extracting the mechanical properties of the core material, the nonlinear governing equations for the curved beam under two types of loading, namely uniform transverse and axial mechanical loads, are derived based on the first-order shear deformation theory and von-Kármán nonlinearity. After examining the convergence of the static responses and validating them by using the Ritz method, the influence of various geometrical parameters of the 3D-printed meta-sandwich structure on the results of buckling and nonlinear bending behavior as well as their optimization using the response surface methodology (RSM) are studied. The results indicate that by increasing the thickness-to-length ratio of the inclined wall, the critical load of the auxetic sandwich beam is enhanced due to improved stiffness, and its lateral displacement declines. The amount of buckling load increase from m = 0.005 to m = 0.1 is 1.92% in the clamped-clamped boundary conditions, 1.56% in the clamped-simply supported conditions, and 1.2% in the simply supported-simply supported edge conditions. Therefore, by selecting appropriate geometrical parameters for the core cells, the occurrence of instability can be delayed, leading to enhanced buckling resistance of the structure. Furthermore, optimizing the results by using the RSM showed that the highest critical load value and the lowest transverse deflection value of the meta-sandwich curved beam are obtained when θc = 15, n = 1, m = 0.1, 2θ0= 30, b = 0.07, λ= 1.1, h/h2= 1.2, and the edge conditions are of the clamped-clamped type.

Probing the Atomic Erosion Wear Characteristics of TiC-Coated Fe in Oil and Gas Drilling Environments.

The titanium carbide (TiC) coating is considered one of the key coating materials to resist erosion wear in oil and gas drilling environments due to its excellent impact and wear resistance. Based on molecular dynamics, the erosion wear resistance of TiC coatings and the pure Fe system in the simulation of nanoindentation, scratch, and particle impact was studied at the microscale. The results indicate that TiC coatings can effectively enhance the load-bearing capacity of the Fe substrate within the critical load range and exhibit low friction characteristics and erosion resistance. However, the protection is lost after the TiC coating cracks, leading to an increase in the tangential force. In addition, when TiC coatings and pure Fe systems exhibit typical erosion characteristics of brittle materials, the TiC coating will significantly reduce the erosion wear of the substrate.

Experimental studies of the explosion resistance of steel plate with an energy-absorbing layers

The aim of this paper is to examine explosion resistance of a composite structure which consists of the steel plate and energy-absorbing layers. With this end, an experimental study of the deformation of 2-3 mm thick steel plates containing different protective layers, namely, an aluminum honeycomb plate, an aluminum sheet, tubular core, polyurethane foam, or an aramid fabrics layer, subjected to explosion generated air shock wave load, has been carried out. At the initial stage of testing, absorbing properties of various composites were examined under relatively low intensity dynamic loads (820 kPa). The dynamic response was assessed by applying bending attenuation and plate center acceleration attenuation factors. This was followed by testing sandwich structures under critical load conditions, when the plate was demolished or subjected to a substantial residual deformation. The study has shown that the composite containing an aluminum honeycomb plate has higher explosion resistance as compared to other tested composites. The proposed design ensures retention of explosion resistance under relatively high dynamic impacts at a reduced distance W = 0.46 m/kg1/3.

Analytical and numerical analysis on local and global buckling of sandwich panels with strut-based lattice cores

Additive manufacturing (AM) offers new possibilities to fabricate and design lightweight lattice materials. Due to the superior mechanical properties of these lattice structures, they have the potential to replace honeycombs as cores in sandwich panels. In addition to the advantage of the integral fabrication thanks to AM, additively manufactured lattice core sandwich panels may be also used as heat exchangers, enabling a multifunctional use of the core. To ensure a reliable and safe structure, the mechanical response of lattice core sandwich panels under given load conditions must be predictable. In conventional sandwich panels subjected to compressive loads, the sandwich’s global buckling and the face sheets’ local buckling are the dominant failure modes. In constrast, core strut buckling may be the critical failure mode in lattice core sandwich panels. Therefore, an analytical 2D model to predict the local buckling of lattice core struts is considered in this study. Furthermore, the critical load for global buckling is obtained based on the first-order shear deformation theory. Thus, the transition from local buckling to global buckling depending on the length-to-thickness ratio is captured by the presented model. The comparison with finite element modeling of the sandwich model with truss cores has proved the accuracy of the derived model.

On nonlinear dynamic analysis of hyperbolic tangent FG-GPL-reinforced shallow spherical cap under supersonic flow

Shallow spherical caps are commonly encountered in the design of spacecraft components, such as fuel tanks or structural elements. Understanding the dynamic behavior can contribute to the identification of potential failure modes. The modulus of elasticity of the augmented composite upper layer is obtained using the model Halpin–Tsai, and this layer is augmented with graphene platelets (GPLs). Also, GPLs’ volume fraction from the top layer is considered for different cases of GPLs. The bottom layer is assumed functionally graded (FG) with two kinds, type A: FG layers and homogeneous core, and type B: FG core and homogeneous layers. To approximate the displacement field, the new hyperbolic tangent shear deformation theory (HTSDT) has been used which is no need for shear modification coefficients. By adopting Hamilton’s principle, the equations of motion are obtained and are solved by the discrete differential quadrature method (DQM) as well as Newmark's time marching scheme by implementing the famous Newton–Raphson iterative technique. When the FG index is infinite, it is observed that the point of maximum displacement decreases by 12.5%, and critical load increases by about 23% compared to the case where it is zero.

Critical behavior of thick rubber bearings under compression and shear

Thick rubber bearings (TRBs) are used for seismic isolation as well as for subway-induced vertical vibration mitigation. Under earthquake ground shaking, TRBs typically undergo large horizontal displacements that lead to a reduction of their vertical bearing capacity, which should be carefully evaluated during design. This study investigates the performance of TRBs under compression and compression-shear loading. Eight full-scale TRB specimens were designed and tested. The test results show that increasing the axial load increases the compressive stiffness of TRBs. During compression-shear loading, TRBs under design level axial loads failed due to rubber rupture at shear strain γ > 350 %, while under higher axial loads, they failed because of instability at γ ＜ 300 %. In addition, in cyclic shear deformation under axial loads larger than twice the design level axial load, the TRBs exhibited negative stiffness at the unloading branch of the F-u loop. The effective damping ratio significantly increased with increased axial load. Then, the test data were used to validate existing mechanical models for the prediction of the compression-shear behavior of elastomeric bearings. Existing analytical models were modified by accounting for the compressive stiffness change due to increased axial loads, leading to more accurate prediction. Finally, models for the critical load of TRBs under zero and lateral displacement were examined and improved.

Investigation of the nano and micromechanical performance of β-Ga2O3 epitaxial films on sapphire using nanoindentation

Beta-phase gallium oxide (β-Ga2O3) has attracted considerable attention because of its excellent properties as one of the emerging semiconductor materials. However, not only the fabrication of high quality β-Ga2O3 thin films on heterogeneous substrates is challenging, but there is also a lack of research pertaining to their mechanical properties. In this work, the mechanical properties of β-Ga2O3 epitaxial films of varying thicknesses on c-plane sapphire substrates fabricated via plasma enhanced chemical vapor deposition were investigated through nanoindentation and nano-scratch experiments. The β-Ga2O3 hetero-epitaxial thin films exhibit preferential orientation growth along the (−201) plane when deposited on the c-plane sapphire substrate. The elastic modulus, hardness, and fracture toughness of β-Ga2O3 films grown on sapphire substrates are 249.1 ± 14.1 GPa, 18.7 ± 0.9 GPa, and 1.822 MPa m1/2, respectively. The elastic-plastic behavior of β-Ga2O3 thin films with varying thicknesses is consistent. The critical loads for the elastic-plastic and plastic-brittle transitions are 9.4 ± 1.8 mN and 50.7 ± 2.7 mN respectively, while the scratch depths for the same are 91.8 ± 7.8 nm and 216.4 ± 10.1 nm, respectively. The critical adhesion and adhesive energy for the desquamation of the β-Ga2O3 film from the substrate are dependent on the thickness of the film. These results establish an experimental basis for understanding the mechanical behavior in the preparation and application of β-Ga2O3 thin films grown on sapphire substrates.

Kinetostatic Modeling of an Asymmetrical Double-Stepped Beam for Displacement Amplification

Abstract A kinetostatic model of an asymmetrical double-stepped beam under axial loading is developed. The beam is composed of two thick segments and three thin segments where a thick segment is between two thin segments, and the longitudinal axis of the thick segment is not colinear with that of the thin segment. The kinetostatic model based on the beam constraint model (BCM) is capable of predicting accurate bending and near-buckling behaviors of the beam. A virtual rigid link neighboring the noncolinear segments is introduced in the BCM to broaden the applicability of the BCM. An analytical formula to represent the critical load of a symmetrical double-stepped beam under axial loading is derived and the value calculated by the formula agrees with the limit load of the asymmetrical double-stepped beam within the elastic range. The investigated beam has potential applications in displacement amplifiers and robotic grippers.

Effect of laser-assisted heat treatment on material removal behavior of sapphire in indentation and scratching

Sapphire is widely used in aerospace, microelectronics and defense applications. Due to its high hardness and low fracture toughness, it is difficult to achieve high efficiency and low damage machining. Laser-assisted machining is an effective method for machining hard and brittle materials and has been explored in many experimental and theoretical studies. In this paper, the mechanical property of sapphire and the variation of the coefficient of friction assisted by different laser powers are investigated in detail. Meanwhile, Raman spectroscopy was employed to reveal the residual stress characteristics in the deformation zone of the scratch grooves, and to analyse the changes in the depth of plastic-brittle transition of sapphire after heat treatment with different laser powers. Comparing the material removal behavior of sapphire in indentation and scratching experiments with and without laser-assisted heat treatment (LAHT), and exploring their material removal mechanisms. Experimental results show that LAHT can improve the ductility and workability of sapphire by reducing the hardness and improving the fracture behavior of the material. Hardness and elasticity modulus decrease with increasing power, and the distribution of residual stress changes from compressive to tensile with increasing power. Laser treated surface was found to possess shorter crack length, no significant localized chipping and spalling in indentation, and its scratch grooves were deeper with no radial cracks observed, the scratching force ratio was higher, the critical load for brittle-plastic transition became larger, and plastic flow lines and lumpy spalling debris appeared in the scratch areas. Nearly zero cracks were observed in material subsurface under the LAHT. With LAHT, the material is removed at a higher rate and in a more plastic way, fracture behavior of the material is improved, surface and subsurface damage is reduced, and the machining efficiency is enhanced. This study has important implications and benefits for the machining of sapphire in ensuring surface quality and achieving high efficiency.