Surface Cracks Research Articles

Performance and failure modes of thermal barrier coatings deposited by EB-PVD on blades under real service conditions in gas turbine

Thermal barrier coatings (TBCs) with a double columnar crystal structure of CoCrAlY/YSZ, prepared using electron beam physical vapor deposition (EB-PVD), were applied to turbine blades and tested in real gas turbine conditions. This study investigates their failure mechanisms under both actual operating conditions and simulated external loads, using three-point bending tests. The performance of full-sized, TBC-coated blades was analyzed through finite element modeling, while the thermomechanical and mechanical properties of the coatings after service were measured to support the simulation and provide insights into the failure processes. A new degradation mode, characterized by penetration cracking, was observed in the EB-PVD coatings. This behavior is linked to the columnar grain structure of YSZ and CoCrAlY, lower operational temperatures, and the reduced thickness of the YSZ layer. Surface cracks in the YSZ coating primarily occurred in regions with large curvature, where stress concentrations are higher. This study offers new insights into the failure modes of TBCs under real gas turbine operating conditions.

Quantifying Seismic Damage in RC Walls with Image Analysis

ABSTRACT This study presents an image-assisted method for seismic damage evaluation of RC walls, integrating image processing, feature ranking, and machine learning. The method utilizes features from surface crack images, such as crack patterns and ratios, combined with design parameters, to predict damage levels and states. Seismic damage evaluation tools based on damage state, strength degradation, and drift ratio are introduced as indicators for quantifying structural damage. The approach is tested using 450 crack images, and feature selection was applied to identify the most important predictors. The results demonstrate high accuracy with an R-squared of 0.87 and an RMSE of 0.28.

Experimental study on damage of steel fiber reinforced concrete- and wood-filled GFRP tubes under axial compression

In order to reduce the self-weight of concrete structures and improve its corrosion resistance, it is an effective way to fill GFRP tubes with wood columns instead of part of concrete. However, concrete structures are prone to cracks, which will reduce the bearing capacity of the structure and affect the safety and applicability of the structure. Incorporating the steel fibers (SF) in concrete seems to be an excellent solution to limit crack propagation and improve the ductility of concrete structures. Based on the premise, in this paper, a new type of structure composite material of steel fiber reinforced concrete- and wood-filled GFRP tubes was developed. The mechanical properties, damage evolution process and crack fractal characteristics of steel fiber reinforced concrete- and wood-filled GFRP tubes under axial compression with different SF volume fractions (0 %, 1 %, 1.5 % and 2 %) were studied by acoustic emission (AE) technology. The finite element method (FEM) was established to simulate the test work and expand the analysis. The results showed that the bearing capacity and ductility of the specimens increased first and then decrease with the increase of SF content, and the specimens with 1.5 % volume fraction of SF showed the best mechanical properties. According to the characteristics of AE ringing counts, the damage process of the specimen was described by three marker events, which were concrete cracking, wood cracking and GFRP tube fracture. The incorporation of SF increased the intensity of AE signal and the proportion of shear cracks, and reduced the damage scale. The fractal dimension of concrete surface cracks had a good correlation with the degree of local damage and the complexity of crack propagation. The damage evolution model based on AE cumulative events and stress obeyed the two-parameter Weibull distribution. The incorporation of SF reduced the degree of damage, and the parameter m had a negative correlation with brittleness. In addition, the damage process of the specimens revealed by the FEM matched well with the experimental results. Additionally, the incorporation of SF made the stress distribution of each part of the specimen more uniform and avoided the phenomenon of stress concentration.

Influence of water vapor partial pressure on self-healing and oxidation of SiC-dispersed yttrium silicate composites

The self-healing and oxidation behavior of SiC-dispersed Y2Si2O7-Y2SiO5 composites were elucidated under various water vapor partial pressures PH2O. Samples were exposed in a furnace for self-healing experiments at 1100–1300°C and for high-temperature oxidation at 1200–1400°C, both for 1–24 h, under PH2O ranging from 2×104 to 5×104 Pa, while keeping PO2constant at 2×104 Pa. Water vapor promoted the self-healing effectiveness of the composites. A mechanism contributing to the closure of surface cracks was consistent with volume expansion derived from the oxidative conversion of SiC into SiO2 and the outward diffusion of yttrium cations. The formation of the internally oxidized zone signifies oxidation behavior, resulting from the inward diffusion of oxygen ions. Growth of the internally oxidized zone obeys the parabolic pattern. The influence of PH2O on the high-temperature oxidation of SiC/Y2Si2O7-Y2SiO5 is discussed in this study.

New insights into fracture and cracking simulation of quasi-brittle materials based on the NMMD model

The simulation of crack-induced failure is of vital importance for the safety and integrity assessment of solids and structures but still challenging. Being the foremost approach, fracture mechanics is plagued by the logical inconsistency in dealing with crack and non-cracked region, and to make matters worse, it has been contradicted by the ongoing experiments that the fracture energy is not a material constant irrelevant to geometry even for the unsophisticated situations. In this paper, based on the recently proposed nonlocal macro-meso-scale consistent damage (NMMD) model, it is demonstrated that the logical consistency of governing equations either on crack-tip or off crack-tip plays a crucial role in the complete solution of cracking problems. To this end, the central themes of fracture mechanics, including the definition of an idealized crack, the separated equilibrium laws and the cracking criteria attached to crack-tip, are firstly revisited. Then, after a concise description of NMMD model with emphasis on the geometrical transmission form micro- to macro-scale and the physical–mechanical translation from geometry to energy, it is theoretically proved that the geometry-based damage zone reproduces idealized crack as a limit when the nonlocal characteristic length, i.e., the influence radius in NMMD model, tends to zero. As a result, the separated equilibrium laws of fracture mechanics can be covered by NMMD model with a unified set of governing equations that does not distinguish between points at crack surface and at non-cracked region. This advantage permits NMMD model to be well-suited to analyze both crack-induced failure problems with and without pre-existing cracks in the absence of additional cracking criteria. In contrast, owing to its macro-meso-scale consistent feature, a new criterion for kinking angle of crack, the maximum stress intensity factor (SIF) of mode-I, can be derived from NMMD model. Some representative numerical examples are also presented to further confirm the above intrinsic link to fracture mechanics. In particular, the superiority of the NMMD model is demonstrated by capturing not only the non-constant fracture parameters (especially the fracture energy) but also the cracking initiation not from the pre-existing crack-tips, which are revealed by experimental results but contradict fracture mechanics. These investigations imply that the NMMD model could provide a potential avenue to understand when and how cracks nucleate and propagate based on a two-scale perspective.

Exploiting the synergy of SARIMA and XGBoost for spatiotemporal earthquake time series forecasting

AbstractEarthquakes are vibrations that occur on the surface of earth, generating fires, ground shaking, tsunamis, landslides and cracks. These incidents can cause severe damage and loss of life. Accurate earthquake forecasts are critical for anticipating and mitigating these hazards, which can avoid damage to buildings and infrastructure and save lives. To address the challenges given by earthquakes probabilistic nature, this paper presents a hybrid SARIMA–XGBoost approach to earthquake magnitude prediction. The suggested technique consists of a two‐step process: an exploration phase that uses exploratory data analysis, which includes descriptive statistics and data visualisation, and a prediction phase that focusses on forecasting future earthquakes. Using a large significant earthquake dataset spanning 1965–2023, the study intends to gain insights and lessons for more effective earthquake prediction methods. Further, in a comparison analysis, the results of SARIMA‐XGBoost model are compared to those of traditional ARIMA and SARIMA models. The results highlight the superior performance of the hybrid SARIMA–XGBoost model, showcasing a mean absolute error (MAE) of 0.038, a mean squared error (MSE) of 0.0040, and a root mean squared error (RMSE) of 0.068. These metrics collectively underscore the model's enhanced accuracy in forecasting earthquake magnitudes. The notably low values of MAE, MSE and RMSE indicate that our hybrid approach significantly improves prediction accuracy compared to alternative models. By integrating SARIMA's time series (TS) analysis with XGBoost's machine learning (ML) capabilities, the hybrid model reduces forecasting errors more effectively, demonstrating its clear advantage in precision.

Changes in physical and chemical properties of microplastics by ozonation

This study evaluated the altered properties of microplastics during the ozonation process in water matrices. The selected polymers include low-density polyethylene, high-density polyethylene, polypropylene, polystyrene, polyethylene terephthalate, and polyvinyl chloride. The morphology, contact angle, and chemical composition of the pristine and altered microplastics were characterized using field-emission scanning electron microscopy-energy dispersive spectrometry, contact angle analysis, Fourier-transform infrared spectroscopy, and X-ray photoelectron spectroscopy (XPS). Microplastic oxidation can lead to surface abrasion, cracking, and fragmentation. XPS analysis indicated that a C=O double bond (carbonyl group) and carboxylic acid/ester bond (O−C=O) were generated in the ozone process. In addition, all the carbonyl index values increased, implying that the number of oxygen functional groups on the surface of the microplastics increased. The contact angle also decreased, indicating that the hydrophilic portion of the microplastics increased due to oxidation. Microplastics, whose surfaces are roughened owing to oxidation or reduced in size owing to fragmentation, pose a fatal threat to aquatic life. In addition, microplastics with increased oxygen functional groups and hydrophilicity due to oxidation treatment have different adsorption properties. Relatively hydrophilic microplastics adsorb heavy metal cations that can adversely affect ecosystems by acting as heavy metal transport mediators.

Micromechanical properties of reaction-bonded silicon carbide using atomic force microscopy and nanoindentation

Reaction-bonded silicon carbide (RB-SiC) ceramics have been produced using advanced technology for the production of space mirrors. Changing the volume content of SiC (from 78 to 93 %) in the ceramic's composition allows for improved the mechanical properties, which is achieved by a combination of the SiC and Si phases properties. In this work, a thorough study of the structure and micromechanical properties of individual SiC and Si phases for RB-SiC ceramics (with a SiC content of 78–93 vol%) was carried out at the micro- and nanolevel using atomic force microscopy and nanoindentation. The studies have shown the crack resistance limit each phase (an important factor for RB-SiC space mirrors) under mechanical loads, after which microcracks appear (sources of further degradation and destruction). The surface morphology, deformation area and crack propagation in each phase after exposure to mechanical load during indentation were studied using atomic force microscopy. Nanomechanical mapping of elastic modulus and microhardness on the surface, analysis of boundaries between phases (SiC and Si), assessment of mutual influence of phases and determination of micromechanical properties were carried out using the nanoindentation method. The fracture toughness KIC was determined using an improved indentation method with visualization of the deformation areas using atomic force microscopy. The highest values of microhardness H, elastic modulus E and fracture toughness KIC on the SiC and Si phases were obtained on a ceramic sample with 93 vol % SiC: for the SiC phase – E=486 GPa, H=35.6 GPa, KIC=5.03 MPa m1/2, for the Si phase – E=205 GPa, H=12.2 GPa, KIC=2.73 MPa m1/2. This study demonstrated the efficiency and possibility of using the atomic force microscopy and nanoindentation to determine the micromechanical properties of ceramics at the micro- and nanolevel.

Nanotechnology enabled casting of aluminum alloy 7075 turbines

Aluminum alloy 7075 is well-known for its high-performance structural systems due to its lightweight and excellent mechanical properties. However, its susceptibility to hot cracking and limited fluidity hinder its casting suitability, posing challenges in manufacturing near-net-shaped structures economically, especially for thin and intricate aerospace components. This paper presents experimental results based on nano-treating, an emerging nanotechnology-enabled manufacturing method by incorporating a low fraction of nanoparticles in liquid aluminum, to allow the casting of complex aluminum alloy 7075 parts. Vacuum fluidity tests demonstrated that nano-treating of aluminum alloy 7075 with only 0.5 vol% TiC nanoparticles increased the fluidity of aluminum alloy 7075 by more than 20%, effectively eliminating hot cracking and enhancing surface quality. Through the Rapid Investment Casting process, nano-treated aluminum alloy 7075 can be successfully cast into turbines with 0.5 mm thick blades. In contrast, aluminum alloy 7075 without nano-treating failed to produce good casting quality due to poor filling and severe cracks. The manufacturing trials highlight the significant improvement in castability achieved through nano-treating, opening a novel pathway for the cost-effective production of complex aluminum alloy 7075 structures for numerous applications.

Elimination of OISF in large-size Si substrate for low warpage and crack-free GaN epitaxial wafer

The oxygen induced stacking fault (OISF) in heavy boron-doping Si substrates causes severe warpage and surface cracks of GaN epitaxial wafers, which will lower the production yield of GaN-based power devices. In this work, high-quality 8-inch Si substrates were fabricated by using rapid thermal annealing (RTA) to eliminate OISF. RTA at 1200 °C effectively eliminated OISF, then surface cracks of 8-inch epitaxial wafers were removed fully and its bow value was decreased markedly from 45.7 μm to 14.3 μm. Consequently, the yields of high electron mobility transistors based on GaN wafers were improved up to 97 %.

Interplay between deformation and fracture mechanism in gradient nanostructured austenitic stainless steel

The plastic deformation parameters are crucial for the grain size of gradient nanostructured (GNS) materials, and the multiscale grain structure within the GNS layer has a significant impact on fracture behavior. In this study, the detailed depth-dependent microstructures of GNS310S stainless steel fabricated by surface mechanical rolling treatment (SMRT) were investigated, and the relationship between the geometrically necessary dislocation (GND) density and the strain gradient was established through the local misorientation obtained by electron backscatter diffraction. The critical deformation parameters (strain gradient, shear strain, and strain rate) of SMRT-induced grain refinement at different scales were quantitatively evaluated. The tensile results show the yield strength and tensile strength of GNS310S are improved by 103 % and 23.1 % respectively compared to CG310S. Additionally, we elucidate the underlying tensile fracture mechanism of GNS310S stainless steel through detailed microstructural analysis. Due to the poor ductility of the near-equiaxed nanograins, cracking occurred on the surface of the SMRT specimen at low strain during the tensile testing. These cracks evolved into competitive shear offsets and multi-cracks with increased strain on the specimen surface, eventually leading to a hybrid fracture mode. In contrast, the subsurface nanotwinned lamellae layer displayed good ductility during tension, which can accommodate the deformation through lamellae widening and forming secondary twinning. This nanotwinned lamellae layer can suppress the inward propagation of surface cracks when the strain was not large. This work provides new insights into the fabricating parameters of the GNS stainless steel, as well as the deformation and fracture mechanisms.

Repair of heat load damaged plasma–facing material using the wire-based laser metal deposition process

Due to its unique properties tungsten is a promising candidate as plasma-facing-material (PFM) in future nuclear fusion reactors. Tungsten features an exceptionally high melting point, high thermal conductivity, low tritium inventory and comparatively low erosion rate under plasma loading [1]. But given the extreme loads on the PFM during operation of a fusion reactor, the lifetime of plasma-facing components (PFC)s is limited. Currently, it is planned to replace damaged PFCs when they reach the end of their service life. However, the lifetime of PFCs could be increased by in situ repair using additive manufacturing technology (AM) in the form of direct-energy-deposition (DED). The wire–based laser metal deposition process (LMD-w) meets several necessary conditions for operation in the vessel and could be used for performing such in situ repairs.It was investigated if the LMD-w process is able to heal thermal induced surface cracks and roughening by remelting the substrate during deposition of tungsten. For this purpose, tungsten samples of 12 × 12 × 5mm3, which later served as substrate plates for the LMD-w experiments, were treated with combined steady-state and transient thermal loads in the electron beam facility JUDITH 2. These samples were brazed to a copper cooling structure and exposed to 105 thermal shocks of 0.5 ms duration and an intensity of Labs = 0.55 GW m−2 (FHF = 12 MW s0,5 m−2) at a base temperature of Tbase = 700 °C. This way, edge localized mode (ELM) like thermal load damage was induced on the tungsten samples. On these samples, different LMD-w and laser remelting process strategies were performed. Subsequently, these samples were analyzed, and it was examined that the healing of the pre-damaged substrate material was successful. In parallel, the laser remelting process was modeled in a thermal transient finite element method(FEM) simulation in order to gain an insight into the temperatures prevailing in the material during the process.

Experimental study on the rock breaking effect of different tooth shapes of inserted teeth in a hobbing-cone hybrid PDC bit under complex stress environment

The hobbing-cone hybrid PDC bit has emerged with the increasing exploitation of deep oil and gas resources. As an important component of new bits, studying the mechanism of toothed fracturing of deep rocks is crucial for improving rock-breaking efficiency. In this paper, the spherical teeth and conical teeth were used to intrude sandstone under different confining pressures, and the brittleness index (BIm), specific energy (SE), and average fragment size (dm) were used to analyze the rock-breaking effect. The 3D contour scanner quantitatively analyzed the crushing pit area. Finally, the in-situ CT scanning and discrete element numerical simulation were used to summarize the crack propagation law. The results show that with the increase of confining pressure, the BIm of inserted teeth increases continuously, and the growth rate of conical teeth increases, while that of spherical teeth decreases. The SE and dm exhibit a symmetrical distribution with a confining pressure of 10MPa as the axis of symmetry. When the difference in principal stress is 5MPa, the SE is the lowest point, the rock-breaking efficiency is the highest, and the corresponding dm is at the highest point, but the curve trend is the opposite. When the stress difference is 5MPa, it is conducive to propagating surface cracks, thus forming a larger crushing area and the highest rock-breaking efficiency. Based on CT results, the dense particle core is formed near the inserted teeth, and that of the spherical teeth is located below. In contrast, that of the conical teeth is located on the side, which is also the reason for the difference in crack propagation between different tooth shapes.

Durability improvement of electrochromic WO3 thin films by deposition of an ultra-thin Al2O3 layer via atomic layer deposition

Introduction of an ultra-thin Al2O3 protective layer via atomic layer deposition (ALD) significantly enhances the durability and performance of amorphous tungsten trioxide (a-WO3) thin films for electrochromic devices. The Al2O3 layer, despite being less than 4 nm thick, effectively suppresses the dissolution of WO3 that typically occurs through hydration reactions forming WO3·H2O and tungstic acid (H2WO4). XRD and XPS analyses confirmed the presence of Al2O3 and its minimal impact on the amorphous structure of WO3 thin films. Optical transmittance measurements showed that the Al2O3-protected a-WO3 thin films maintained a higher transmittance modulation (ΔT) compared to bare a-WO3 thin films, with the ALD30 sample retaining 87.9 % of its initial transmittance modulation after 1000 cycles, in contrast to the rapid degradation observed in unprotected films. Microstructural analysis revealed significantly fewer surface cracks and reduced thickness loss in Al2O3-coated films after 100 cycles. Additionally, ICP-MS analysis indicated a much lower W concentration in the electrolyte for Al2O3-protected samples, confirming reduced dissolution.

Synergistic Effects of Ternary Microbial Self-Healing Agent Comprising Bacillus pasteurii, Saccharomyces cerevisiae, and Bacillus mucilaginosus on Self-Healing Performance in Mortar

In order to prevent structural damage or high repair costs caused by concrete crack propagation, the use of microbial-induced CaCO3 precipitation to repair concrete cracks has been a hot topic in recent years. However, due to environmental constraints such as oxygen concentration, the width and depth of repaired cracks are seriously insufficient, which affects the further development of microbial self-healing agents. In this paper, a ternary microbial self-healing agent composed of different proportions of Bacillus pasteurii, Saccharomyces cerevisiae, and Bacillus mucilaginosus was designed, and its crack repair ability was evaluated. When the mixing ratio was 7:1:2, the cell concentration was the highest, the precipitation amount of CaCO3 was the highest, and the crystallinity of calcite crystal was the highest. Compared to the single microorganism, the mortar specimens with ternary microorganisms had the largest repair area (up to 100%) and the deepest repair depth (CaCO3 presents at 9–12 mm from the crack surface). This is because when the concrete breaks, all three microorganisms are activated by water, O2, and CO2. Saccharomyces cerevisiae and Bacillus mucilaginosus accelerated the growth of Bacillus pasteurii and more mineralized products; CaCO3 was rapidly formed and quickly filled on the crack surface. When CaCO3 seals the surface of the crack, the internal Saccharomyces cerevisiae and Bacillus mucilaginosus continue to play a role. Bacillus mucilaginosus can accelerate the dissolution of CO2 produced by the anaerobic fermentation of Saccharomyces cerevisiae and the hydrolysis of CO32−, thereby improving the repair of the crack depth direction.

Iterative Method of Determining Stress Intensity Coefficients Under Dynamic Loading of the Crack System

An elastic isotropic body in a state of plane deformation, which contains a system of randomly placed cracks under the action of a dynamic (harmonic) loading, is considered. The authors set the problem of determining the stress field around the cracks under the conditions of their wave interaction. The solution method is based on the introduction of displacements in the body in the form of a superposition of discontinuous solutions of the equations of motion constructed for each crack. With this in mind, the initial problem is reduced to a system of singular integro-differential equations with respect to unknown displacement jumps on the crack surfaces. To solve this system, a new iterative method, which involves solving a set of independent integro-differential equations that differ only in their right-hand parts at each iteration, is proposed. For the zero approximation, solutions that correspond to individual cracks under the action of dynamic loading are chosen. Such a new approach allows to avoid the difficulties associated with the need to solve systems of integro-differential equations of large dimensions that arise when traditional methods are used. Based on the results of the iterations, formulas for calculating the stress intensity coefficients for each crack were obtained. In the partial case of four cracks, a good agreement between the results obtained during the direct solution of the system of eight integro-differential equations by the mechanical quadrature method and the results obtained by the iterative method was established. In general, numerical examples demonstrate the convergence and stability of the proposed method in the case of systems with a fairly large number of densely located cracks. The influence of the interaction between cracks on the stress intensity factor (SIF) value under dynamic loading conditions was studied. An important and new result for fracture mechanics is the detection of the absolute maximum of the normal stresses at certain frequencies of the oscillating normal loading. The number of interacting cracks and the configuration of the crack system itself affect the values of the frequencies at which SIF reaches a maximum and the maximum values. These maximum values significantly (by several times) exceed the SIF values of single cracks under a similar loading. At the same time, under conditions of static or low-frequency loading, it is possible to reduce the SIF values compared to the SIF for individual cracks. When cracks are sheared, the values of the tangential stresses have a tendency to decrease with increasing frequency, and their values do not significantly differ from the values of the tangential stress for an individual crack.

Effect of In Situ Polymerization of Super Absorbent Polymers on the Protection of Earthen Heritage Sites in Semi-Arid Regions

As precious cultural heritage, earthen sites are susceptible to various natural factors, leading to diverse forms of degradation. To protect earthen sites, the effects of super absorbent polymers (SAPs) on soil water retention, physical properties, and color compatibility at different concentrations were studied. After applying SAP treatment to an earthen site with different degrees of weathering, we drew the following conclusions. SAP-2 improved soil water retention capacity, increased soil water content, and slowed down the precipitation of soluble salts. At the same time, SAP-2 had the least effect on soil color difference and reduced the development of cracks by filling soil pores and enhancing the cohesion between soil particles, thus giving the earthen sites better weathering resistance. Therefore, the results provide a useful reference for the surface cracking of earthen sites in semi-arid areas and the degradation caused by flaking and block spalling.

CURRENT LITERATURE REVIEW ON IMAGE PROCESSING ANALYSIS FOR CONCRETE DAMAGE ASSESMENT

Numerous studies have employed computer vision algorithms to analyze images of concrete damage. Therefore, conducting an image processing survey to detect concrete damage is very crucial. Thus, an image processing algorithm analysis survey to detect concrete damage was conducted using various algorithms and types of data from the last decade. The data observed were the first is damage to concrete, which included surface cracks, hairlines, crack width, patterns, holes, diagonal cracks, longitudinal cracks, and transverse cracks. The second part is figuring out where roads, bridges, and buildings are. The third is data sources like digital cameras, cameras built into phones, camera sensor systems, and unmanned aerial vehicles (UAVs). The study's findings indicate that image processing algorithms will play an essential role in future assessment research on the automation of concrete damage detection. This is particularly the case in high-risk regions for security reasons, and UAV technology is required to reach these locations.

Simulation and Experimental Research of V-Crack Testing of Rail Surfaces Based on Laser Ultrasound

Rail surface cracks are widespread damage that can lead to uneven surfaces of railheads and affect traveling safety. Non-destructive testing is needed to inspect rails regularly to ensure the normal operation of railroads. This paper proposes a laser ultrasonic testing method combining variational mode decomposition and diffractive Rayleigh wave time-of-flight to detect tiny cracks on the rail surface quantitatively. The finite element method was combined with experiments to simulate and experimentally investigate cracks of different sizes numerically. In the numerical simulation, the location of the crack was determined by B-scan. Afterward, the interaction between various types of ultrasound and cracks was comparatively analyzed, and the crack size was quantitatively characterized using useful information from the ultrasound signals. The results show that the time-of-flight method can detect arbitrary cracks with low error. Therefore, the experimentally acquired ultrasound signals used the time difference between the diffracted Rayleigh wave and other ultrasound waves to detect the crack information quantitatively. The variational mode decomposition method was used to separate the ultrasonic signals and extract the best surface wave modes to improve the signal-to-noise ratio. The results show that the combination of variational mode decomposition and time-of-flight method can effectively detect the size of cracks.

The Green's functions of two-dimensional piezoelectric quasicrystal semi-infinite crack and finite crack

This paper investigates the interactions of a semi-infinite crack / finite crack with multiple loadings in a two-dimensional piezoelectric quasicrystal under different boundary conditions. Utilizing the Stroh formalism and conformal mapping, Green's functions of generalized displacements and stresses are obtained for two general cases: a semi-infinite crack and a finite crack subject to free-free or fixed-fixed boundary conditions. The stress and electric displacement intensity factors at the crack tip and the image forces on how dislocations are affected by the crack surfaces are given explicitly. The results are analyzed and compared with special cases documented in the scholarly literature. At the same time, the effects of the Burgers vector components on the generalized stresses and image forces numerically illustrate as well as the impacts of line forces on generalized stress intensity factors.