Local Stress Concentration Research Articles

Effect of multi‐angle lamination on mechanical properties and damages behavior of carbon fiber reinforced resin matrix composites

AbstractCarbon fiber reinforced resin matrix composites, when subjected to multi‐angle delamination during vacuum hot pressing, suffered from defects such as uneven fiber distribution, resin‐rich zones, and voids. These defects caused varied damage and failure behaviors in the composites, seriously affecting their mechanical properties. In this paper, the defect distribution, tensile and flexural properties, and damage behaviors of multi‐angle lay‐up specimens prepared in an autoclave were studied. The results indicated that irregularly shaped voids in laminates with a 0° angle difference primarily led to local stress concentration. Elliptical and elongated voids in laminates with a 90° angle difference were mainly susceptible to delamination. The [0/90]8 layer exhibited the best overall mechanical properties. The proportion of 0° laminates had a direct impact on the mechanical properties, with 0° contact laminates on the bending‐compression side capable of withstanding higher bending loads. The [+45/−45]8 plyer demonstrated pseudo‐delayed behavior, enabling the laminate to show better toughness under load. Variations in damage due to the proportions and positions of the laminates influenced the mechanical properties and damages behavior of multi‐angle laminates.Highlights Angular differences were observed to affect void and resin distribution. The best overall mechanical properties were attributed to [0/90]8 laminates. Pseudo‐delay behavior was exhibited by [+45/−45]8 laminates. Proportion of 0° layers impacted mechanical properties. Greater bending loads were withstood by the 0° contact layer.

Sub-modelling based fatigue evaluation of welded details in composite trapezoidal corrugated web girders under coupled thermal-structural loading

Exploring the long-term performance of welded details in composite trapezoidal corrugated web (TCW) girders is a significant focus for the service life of these structures exposed to atmospheric environment and traffic flow. The majority of the present studies have been conducted without accounting for thermal stresses induced by temperature differences and accurately reflecting internal force transfers for the composite girders in flexural bending. The fatigue behaviour of the welded details in these girders under coupled thermal-structural loading is investigated herein through experimental and numerical methods. The results indicated three stages for the structural degradation from the test performance and justified a proper allowance of the cross-sectional stress in coordination with the flexural curvature in the derivation of S-N relations comparable to similar details in related design codes. A sub-modelling procedure is implemented to capture the thermal gradient, the local stress concentration, and the crack distribution in global modelling while replicate the semi-elliptical surface crack at the external side of the fillet weld toe in local modelling. The fatigue lives predicted from the proposed analytical model match reasonably well with experimental and numerical results, indicating its good applicability incorporating characteristic geometric correction factors into classical theoretical calculation for fatigue evaluation.

Filiform Papillae‐Inspired Wearable Pressure Sensor with High Sensitivity and Wide Detection Range

AbstractFlexible pressure sensor (FPS) has promising applications in fields like health monitoring and human–machine interactions. The achieving of both high sensitivity and wide detection range in FPS remains highly challenging. Here, inspired by the filiform papillae on cat tongue, a FPS (noted as FPSp) with a sensitivity up to 504.5 kPa−1, a detection range from 30 Pa to 350 kPa, a fast response time of 83 ms, and a high stability over 8000 cycles is developed. The papilla‐like structure continuously shifts the location of stress concentration under increasing pressure, which avoids the accumulation of stress at papillae tips, resulting in a high sensitivity and wide detection range. Moreover, FPSp demonstrates capabilities in monitoring human physiological signals and movement status and can serve as the human‐machine interaction interface. The work not only presents a promising wearable pressure sensor but also establishes a design strategy for high‐performance wearable bioelectronics.

High‐temperature behavior and self‐enhancing mechanisms of oxide‐bonded SiC porous ceramics

AbstractOxide‐bonded SiC porous ceramics (SCPCs), synthesized via reaction bonding, exhibit significant potential for high‐temperature applications. However, incorporating sintering aids inevitably results in a considerable quantity of amorphous glass phase within SCPCs, thereby introducing risks to their high‐temperature mechanical performance. In this study, we employ in‐situ characterization techniques to investigate the high‐temperature behavior of SCPCs. Our findings reveal that SCPCs demonstrate remarkable high‐temperature self‐enhancing properties, with a critical bending strength at 800°C. Beyond this temperature, the strength declines sharply. Intriguingly, the critical bending strength is 36.6% greater than at ambient temperature. Moreover, elevated temperatures enhance the elastic modulus and promote the transition of SCPCs from multilinear to nonelastic fracture. The neck phase, which imparts strength to the SCPCs, is composed of four distinct layers along the depth direction: silicate glass, oxygen‐containing, silicon‐rich, and SiC region, as revealed by FIB‐TEM. The transformation from α to β‐cristobalite in the oxygen‐containing region improves the thermal expansion match with SiC, thereby mitigating local stress concentration. Furthermore, the compressive stress within the neck region intensifies with increasing temperatures, thereby inhibiting crack propagation. This work provides a basis for the high‐temperature applications of SCPCs.

Influence of ultrasonic assistance on the microstructure and friction properties of laser cladded Ni60/WC composite coatings

The effects of different ultrasonic vibration powers on the distribution, phase structure, friction and wear properties of WC reinforced particles in laser melted Ni60/WC composite coatings are investigated. The effects of ultrasonic vibration on the microstructure, elemental distribution, crystal orientation, friction and wear properties of the fused coatings are analyzed. The experimental results show that the deposition of WC particles in the lower and middle parts of the coating is significantly improved after the introduction of ultrasonic vibration during the fusion cladding process. In particular, at 600 W ultrasonic power, not only the distribution uniformity of tungsten carbide particles in the coating is optimal, but also the composite coating shows better wear resistance. However, too much ultrasonic power increases the possibility of particle agglomeration. In addition, although the phase pattern of the coating does not change after ultrasonic vibration, the width of the columnar crystalline region of the coating is reduced, and the coating is covered by a homogeneous lamellar nanoscale eutectic structure with the phase compositions of the γ-(Fe, Ni) and M23C6 phases. The ultrasonic vibration improves elemental segregation of the coating, reduces the large number of precipitated phases in the coating, weakens the grain growth orientation, and relieves the local stress concentration in the coating. In addition, the mechanism of the influence of WC particles on the microstructure evolution and wear resistance of the composite coatings is discussed.

Free vibration and buckling behavior of porous orthotropic doubly-curved shallow shells subjected to non-uniform edge compression using higher-order shear deformation theory

Due to the continuous enhancement of manufacturing technology for porous materials, it is expected to be increasingly used in aerospace, aviation, and other engineering applications, where the necessity for lightweight structures is paramount. Also, the non-uniform edge loads caused by service conditions, complex adjacent structures, and external loads lead to localized stress concentrations within the shells. Localized stress concentrations result in a loss of load-carrying capacity in specific regions, causing step-by-step failure of the shell. This study investigates the buckling and free vibration behavior of porous orthotropic doubly-curved shallow shells with four different porosity distribution patterns subjected to non-uniform edge compressive loads. The equations of motion of doubly-curved shallow shells are established by using higher-order shear deformation theory and Hamilton’s principle. Then, the pre-buckling in-plane stress distributions of doubly-curved shallow shells are determined and appended to the equations of motion. These fundamental partial differential equations are solved by Galerkin’s method, and the critical buckling load and natural frequency formulations are achieved. By comparing with the results in published literature, the feasibility and accuracy of present formulations are validated. Finally, systematic parametric studies are carried out to discuss the effects of different non-uniform edge compression patterns, porosity distribution patterns, porosity coefficients, aspect ratios, arc length-to-thickness ratios, radius-to-arc length ratios, orthotropy ratios, and shell types on the buckling and free vibration responses of porous orthotropic doubly-curved shallow shells. Parametric studies indicate that the reduction or increment in critical buckling loads (CBLs) and fundamental natural frequencies (FNFs) of spherical shells (SSs) are more sensitive than those of hyperbolic paraboloidal shells (HPSs). The CBLs and FNFs of SSs are larger than those of HPSs. The maximum and minimum CBLs are achieved for the triangular and uniform edge compression, respectively. The porosity effect is independent of edge compression pattern types.

Fatigue reliability analysis methodology based on fatigue life and failure mechanism for carburized gear

Gears are one of the important components in mechanical products, and their fatigue reliability determines the safety performance of mechanical products. In this paper, the fatigue characteristics of carburized gears under different torque and constant rotational speed conditions are investigated by using a gear contact fatigue testing machine, and combined with the dynamic maximum contact stress distribution on the subsurface of the meshing gears, the very-high cycle fatigue P-S-N curves of carburized gears under a stress ratio of −1 is established. Local stress concentration in the surface or subsurface of carburized gears causes grain dislocation movement under the combined influence of maximum contact and residual stresses, and then causes dislocation pileup and transcrystalline rupture after being hindered by grain boundaries, ultimately leading to pitting and fatigue failure of gears. Based on the dislocation energy method and combined with the fatigue failure mechanism of gears, a life prediction model of gears with good prediction results is established by considering the interaction of factors such as dynamic load, grain size, initial crack length, residual stress, slip band length and width. A fatigue reliability analysis method of gears is established based on the life state equation of gears considering the life prediction model. Further analyses of the influence of rotational speed, grain size, residual stress, slip band width, slip band length and initial crack size on the fatigue life reliability index of the gears resulted in the conclusion that the fatigue reliability of the gears not only decreases with the increase of the above-mentioned parameters, but also shows decreasing trend with the increase of time. This is of significance for evaluating the fatigue reliability of gears under very-high cycle fatigue conditions.

Advanced monitoring of damage behavior and 3D visualization of fiber distribution in assessing crack resistance mechanisms in steel fiber-reinforced concrete

This study presents a novel approach to understanding the reinforcing mechanisms of steel fiber-reinforced concrete, particularly its crack resistance and toughening effects. By integrating dynamic surface strain monitoring with advanced three-dimensional visualization techniques, new insights are provided into how steel fibers enhance concrete's structural performance. X-ray computed tomography (CT) technology enabled detailed 3D visualization and analysis of steel fibers embedded within the concrete matrix, facilitating an in-depth examination of their distribution patterns, orientation, and positioning. Additionally, the Digital Image Correlation (DIC) three-dimensional full-field strain measurement system was utilized to dynamically monitor the loading process during three-point bending tests on semicircular concrete specimens. The findings indicate that the uniform distribution of steel fibers significantly reduces stress concentration and effectively delays crack initiation and propagation. Steel fibers bridge cracks, mitigate local stress concentrations, and substitute for the tensile components of concrete after macro-crack formation, thereby inhibiting further crack propagation. Quantitative analysis of fiber distribution through 3D image reconstruction and coordinate extraction confirmed a strong correlation between fiber orientation and crack resistance. This study contributes to the field by offering a comprehensive analysis of key parameters such as fracture process strain monitoring, 3D visualization, and quantification of fiber distribution, advancing the understanding of crack propagation mechanisms and failure processes in fiber-reinforced concrete.

An Experimental Assessment Using Acoustic Emission Sensors to Effectively Detect Surface Deterioration on Steel Plates

Acoustic emission (AE) testing is used for the continuous evaluation of structural integrity and the monitoring of damage evolution in structural components and materials. During operation, the environmental and loading conditions of metal structures can result in corrosion and surface wear damage. The early detection of surface degradation flaws is crucial, as they can serve as local stress concentration points, leading to crack initiation and failure. In this work, the effectiveness of AE in monitoring corrosion and surface wear flaw formation was experimentally evaluated. AE sensors were installed on steel test plates during the artificial induction of corrosion and surface wear in order to detect and record the generated AE signals. Corrosion-related AE signals typically exhibit low amplitude, count, and energy values. The direct detection of active corrosion can be challenging in noisy environments, but it can be carried out under certain conditions using dedicated AE sensor groups. Surface-wear-related AE signals exhibit high amplitude, energy, and count values, with long duration values that are associated with wear and grinding conditions. It was found that AE sensors can be utilised to detect corrosion and surface degradation events. The effectiveness of the AE method in detecting surface degradation in noisy environments can be improved by implementing a filtering methodology. This will limit the recording of noise-related signals that can mask out actual surface degradation AE events.

Flexural performance of RC beams using hybrid anchored ​CFRP sheets with bond defects

Hybrid anchorage technique can effectively prevent end debonding and impede intermediate debonding of CFRP sheet in strengthened reinforced concrete (RC) beams. However, its effectiveness in the presence of bond defects at the CFRP-concrete interface is unclear. Therefore, this study conducted four-point bending tests on CFRP-strengthened RC beams, considering two factors: bond defects (with and without) and strengthening methods (externally bonded and hybrid anchorage). The results showed that bond defects can lead to premature intermediate debonding of the CFRP sheet, resulting in a 22.49% decrease in debonding load due to local stress concentration around them. Owing to the effectiveness of the hybrid anchorage method, the propagation of the intermediate debonding is significantly impeded, leading to a 4.32% and 21.61% higher in ultimate load and deflection, respectively. This is because the hybrid anchorage can control the distribution of local cracks and improve the overall stress distribution of CFRP. A finite element analysis was performed and compared against the experimental results which shows good agreement. Then, parametric analyses were conducted to further analyze the flexural behavior of the strengthened beams with bond defects. Finally, an analytical model was proposed to predict the flexural capacity of the hybrid strengthened beams with bond defects.

Mechanical properties, nano-tribological behavior and deformation mechanism of FeCrNi MEA with the addition of Co/Cu: Molecular dynamics simulation

During manufacturing processes, alloys face increasingly demanding requirements for their mechanical and tribological properties, underscoring the importance of revealing their deformation mechanisms. This study employed molecular dynamics simulation to construct models of FeCrNi (C1), FeCoCrNi (C2), FeCrNiCu (C3), and FeCoCrNiCu (C4), investigating the tribological properties of C1 alloy under various conditions and the mechanical properties across a wide temperature range (223–1073 K). The results indicate that the elastic modulus of the alloys follows the order C2 > C4 > C3 > C1 across the temperature range of 223 K to 1073 K. The elastic modulus increases with rising temperatures and decreases before rising once again as temperatures decrease. The phase transitions become more pronounced below 300 K. The addition of Co elements to the FeCrNi alloy contributes to fine-grain strengthening, uniform distribution of internal stress and strain, reduction in local stress concentration, and improvement of the alloy ductility and tensile strength. Compared to sliding friction, rolling friction reduces the number of worn atoms; however, the tensile and shear effects cause an increase in the stress gradient, leading to more severe subsurface damage and shear deformation. Temperature significantly affects the tribological properties of the alloys: phase transitions at high temperatures promote dislocation slip and plastic deformation, while at low temperatures, higher hardness and strength are observed. The roughness of stacking faults is greatly influenced by temperature, with an increase at the low-temperature range (223–273 K), a decrease in the mid-temperature range (273–673 K), and a smoother surface at the high-temperature range (673–1073 K). The research aims to provide a deeper understanding of the excellent mechanical and tribological properties of FeCrNi alloy at the micro/nano scales, thereby advancing their application and development in manufacturing processes.

Enhancing the Mechanical Properties of Injectable Nanocomposite Hydrogels by Adding Boronic Acid/Boronate Ester Dynamic Bonds at the Nanoparticle-Polymer Interface.

Incorporating nanoparticles into injectable hydrogels is a well-known technique for improving the mechanical properties of these materials. However, significant differences in the mechanical properties of the polymer matrix and the nanoparticles can result in localized stress concentrations at the polymer-nanoparticle interface. This situation can lead to problems such as particle-matrix debonding, void formation, and material failure. This work introduces boronic acid/boronate ester dynamic covalent bonds (DCBs) as energy dissipation sites to mitigate stress concentrations at the polymer-nanoparticle interface. Once boronic acid groups were immobilized on the surface of SiO2 nanoparticles (SiO2-BA) and incorporated into an alginate matrix, the nanocomposite hydrogels exhibited enhanced viscoelastic properties. Compared to unmodified SiO2 nanoparticles, introducing SiO2 nanoparticles with boronic acid on their surface improved the structural integrity and stability of the hydrogel. In addition, nanoparticle-reinforced hydrogels showed increased stiffness and deformation resistance compared to controls. These properties were dependent on nanoparticle concentration. Injectability tests showed shear-thinning behavior for the modified hydrogels with injection force within clinically acceptable ranges and superior recovery.

Impact-resistant titanium alloy with fine equiaxed structure fabricated by powder metallurgy

Although fine equiaxed structure benefits both strength and ductility in titanium alloys, it is often considered incompatible with high toughness, for its insufficient ability to deflect propagating cracks compared to coarse lamellar structure. This work reports an excellent combination of standard Charpy impact toughness (∼100 J) and yield strength (∼820 MPa) in a powder metallurgy titanium alloy with fine equiaxed structure (∼1.5 μm), wherein the β matrix exists as equiaxed nodules and fine ligaments for globularization of α grains. The impact curve divided with the “compliance changing rate” (CCR) method indicates that the energy consumed by crack propagation is dominant (∼82%) during the impact process. Fractographic and structural examinations indicate that multiple micro-voids nucleation near boundaries between fine β ligaments and α grains mitigates local stress concentration, and that coordinated deformation between equiaxed β nodules and α grains hinders crack propagation, which together enable the excellent combination of yield strength and impact toughness. Our work provides a new pathway for designing impact-resistant titanium alloys.

A hybrid continuum-beam optimisation model: the virtual extensometer method for efficient optimisation of lattice materials

AbstractAdditive manufacturing (AM) enables the fabrication of complex lattice structures that are infeasible with traditional manufacturing processes. These structures are typically implemented with constant cross-sectional strut elements; this strategy is expedient but leads to sub-optimal structural efficiency. Numerical continuum models allow robust mechanical modelling of complex lattice geometry but provide equally complex data fields that are ill-suited for traditional optimisation techniques. By contrast, numerical beam models represent the fundamental tensile and bending stress states but are incapable of capturing nuanced geometrical effects that lead to local stress concentrations. In this research, a hybrid continuum-beam method is proposed for the systematic optimisation of strut cross section: a representative unit cell is simulated by continuum elements, and the local strut stress tensor is acquired by embedded beam elements that act as virtual extensometers. By integrating a computationally inexpensive beam model into a more robust continuum model, the volume and the quality of data returned are significantly increased whilst being provided in a readily usable format for optimisation techniques, for a trivial increase in computational cost. The presented method is generalised and can be applied to any strut-based lattice structure. Body-centred cubic (BCC) and BCC with z-strut (BCCZ) lattice structures optimised by the proposed method are fabricated using laser-based powder bed fusion (LB-PBF) in AlSi10Mg and are mechanically evaluated. On average, performance for BCC lattice structures improves by 33% and 26% for relative yield strength and relative Young’s modulus respectively. BCCZ lattice structures saw a performance improvement of 25% and 19% for relative yield strength and relative Young’s modulus respectively, thus confirming superior performance at lower relative densities when compared to incumbent designs.

A unique kind of distribution band of martensitic laths formed along {332}〈113〉 twin boundary in the Ti[sbnd]42Nb alloy subjected to instable deformation

Multi-scale electron microscopy characterization of the {332}<113 > β twins produced in the necking region near fracture surface of the deformed β-type Ti42Nb (wt%) alloy have been carried out. A unique kind of band-shaped zone with plenty of laths of two α″ martensitic subvariants distributed in about 90° crossing directions has been found to be formed in the {332}<113 > β deformation twin along the twin boundary. This finding clearly reveals that intense local stress concentration and its complex accommodation process associated with the β-to-α″ and α″-to-β structural transitions can occur specially in the twinned region of stress-induced α″ martensite phase along its boundary for the β Ti alloy subjected to instable deformation. It is also clearly indicated that the local stress accommodation due to the α”-to-β structural transition can be unsymmetrical with respect to the twin boundary.

Dynamic response analysis of pipelines in gas distribution stations under seismic loads

Seismic loads in earthquake-prone regions significantly affect the structural integrity of pipelines at urban natural gas distribution stations, compromising safety. This study analyzes the dynamic response of pipelines in gas distribution stations under seismic loading and proposes effective measures to mitigate stress concentration. A numerical model of the pipeline in the gas distribution station, based on actual cases, was established. The material’s constitutive relationship was derived from tensile tests. The seismic response spectrum, obtained from ground motion data, was introduced to analyze the pipeline’s mechanical behavior. The dynamic response analysis identified critical stress concentration locations in the pipeline under operational conditions. Based on displacement analysis, the study recommended seismic measures. Results indicated that under seismic loading, higher stress values occurred primarily in pipeline sections with intricate flow pattern variations. The manifold connection was the most vulnerable point, with its average stress being 3.37 times that of the system’s average stress. The proposed seismic measures effectively reduced stress concentration at these critical points, mitigating the earthquake’s impact on the gas distribution station. This study establishes a theoretical framework for improving the seismic design and maintenance of natural gas distribution stations, enhancing their seismic resilience and operational safety.

Perspectives on Adhesive–Bolted Hybrid Connection between Fe Shape Memory Alloys and Concrete Structures for Active Reinforcements

The prestressed active reinforcement of concrete structures using iron-based shape memory alloys (Fe-SMAs) is investigated in this experimental study through three connecting methods: adhesive–bolted hybrid connection, bolted connection, and adhesively bonded connection by activating at elevated temperatures (heating and cooling) and constraining deformation to generate prestress inside Fe-SMAs, through which compressive stress is generated in the parent concrete structures. In tests, the Fe-SMA is activated at 250 °C using a hot air gun, generating a prestress of 184.6–246 MPa. The experimental results show that local stress concentration in the concrete specimen and Fe-SMA plate around the hole is caused by the bolted connection. The adhesively bonded connection is prone to softening and slip of the structural adhesive during the activation process, thereby reducing the overall recovery force of Fe-SMAs. The adhesive–bolted hybrid connection effectively mitigates the local stress concentration problem of concrete and Fe-SMAs at anchor holes, while avoiding the prestress loss caused by the softening and slip of structural adhesive during elevated-temperature activation, achieving good reinforcement effect. This study on the connection methods of an Fe-SMA for reinforcing concrete structures provides both experimental support and practical guidance for its engineering application, offering new perspectives for future research.

In-Situ EBSD investigation of how annealed twins produce excellent strength-ductility synergy in Al0.25FeCoNiV duplex high-entropy alloy

The development of high-entropy alloys (HEAs) has been historically constrained by trade-off between strength and ductility. In this study, the Al0.25FeCoNiV duplex HEA showed a yield strength of 625 ± 35.2 MPa and a fracture elongation of 48 ± 1.5 % after rolling and annealing. These values are 43 % and 60 % higher, respectively, than the as-cast specimens, demonstrating an excellent synergy between strength and ductility. Through in-situ electron backscatter diffraction (EBSD) tensile experiments and transmission electron microscopy characterization of the as-cast and annealed specimens, respectively, it is found that the superior mechanical properties of the annealed specimens are primarily attributable to the multilevel strengthening and strain-hardening coupling mechanism established by the synergistic action of phase boundaries (PBs), twin boundaries (TBs), and high-angle grain boundaries. This mechanism effectively suppresses strain localization and prevents premature fracture caused by local stress concentration at PBs. The strengthening mechanism of TBs on the mechanical properties of HEAs was investigated by examining the interaction mechanisms between annealed TBs and dislocations, as well as the coordinated plastic deformation mechanism of twins. This study provides novel insights into the development of innovative HEAs with enhanced properties and advances the understanding of the role of TBs in the strengthening mechanisms of materials.

Wind turbine foundation ring fatigue reliability analysis under wind-load using SCADA system

Under the action of wind load, the foundation ring of the fan will generate stress concentration and alternating stress, leading to fatigue failure. Based on the average wind speed obtained from the supervisory control and data acquisition (SCADA) system, the orthogonal expansion method of random pulsating wind field and the number theory point selection method are used to calculate and simulate the corresponding pulsating wind speed time series, and then calculate the wind speed time series and wind load time series. Based on the ABAQUS finite element software, a model of a 5 MW wind turbine is established. The modal analysis is used to obtain the modal vibration pattern and the intrinsic frequency to verify the reasonableness of the structural modeling. Subsequently, the wind load time series is applied to the wind turbine model to obtain the stress time series using instantaneous modal dynamic analysis (Modal dynamics). The stress time series at the location of maximum stress concentration in the foundation ring is extracted, and the stress time series with the same stress amplitude is obtained through conversion, which has Wiener characteristics. After obtaining the stress amplitude using the rainflow counting method, the fatigue reliability is calculated based on the structural fatigue reliability analysis method considering the threshold crossing duration of the random process. This research holds reference significance for the calculation of fatigue reliability under approximate working conditions.

Cracking resistance behavior of HVAF-sprayed monolayer and hierarchical Fe-based amorphous coatings under bending stress

The bending strength and fracture toughness are two key indicators that determine the service performance of thermally sprayed Fe-based amorphous coatings (AMCs) in harsh environments. Unfortunately, due to the inherent heterogeneous porosity and limited thickness (typically <1 mm) of the coatings, obtaining these properties is constrained by traditional fracture analysis methods. To address this, a three-point bending combined with the digital image correlation (DIC) method, without prefabricating notch or removing substrate, was proposed in the current work, and the effect of hierarchical structures on the fracture performance of the coatings was successfully revealed. Excitingly, the results show that compared to monolayer coating, hierarchical structures comprising two layers with different porosities can realize the synergistic improvement in the fracture strength and fracture strain of the coatings by alleviating local stress concentration and inducing crack deflection. Further, a finite element method (FEM) was employed to gain insight into the intrinsic relationship between the coating microstructures and the crack evolution behavior. This work not only proposes a simple method for evaluating the fracture performance of Fe-based AMCs sprayed with high velocity air fuel (HVAF), but also presents an innovative idea for optimizing the coating's properties.