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1.
Sensors (Basel) ; 24(13)2024 Jun 29.
Artigo em Inglês | MEDLINE | ID: mdl-39001011

RESUMO

This paper presents an in-depth study of the stress wave behavior propagating in a Rayleigh-Love rod with sudden cross-sectional area variations. The analytical solutions of stress waves are derived for the reflection and transmission propagation behavior at the interface of the cross-sectional area change in the rod, considering inertia and Poisson's effects on the rod material. Examples solved using the finite element method are provided to verify the correctness of the analytical results. Based on the forward analysis of Rayleigh-Love wave propagation in a rod impacted by a striker rod, an impact-echo-type nondestructive testing (NDT) method is proposed to conduct defect assessment in rod-type structural components with sudden cross-sectional area changes within a cover medium. This proposed NDT method can identify the location, extension, and cross-sectional area drop ratios of an irregular zone in the rod to be inspected.

2.
Carbon N Y ; 203: 202-210, 2023 Jan 25.
Artigo em Inglês | MEDLINE | ID: mdl-36506702

RESUMO

Polymer nanocomposite films have recently shown superior energy dissipation capability through the micro-projectile impact testing method. However, how stress waves interact with nanointerfaces and the underlying deformation mechanisms have remained largely elusive. This paper investigates the detailed stress wave propagation process and dynamic failure mechanisms of layered poly(methyl methacrylate) (PMMA) - graphene nanocomposite films during piston impact through coarse-grained molecular dynamics simulations. The spatiotemporal contours of stress and local density clearly demonstrate shock front, reflected wave, and release wave. By plotting shock front velocity (U s ) against piston velocity (U p ), we find that the linear Hugoniot U s - U p relationship generally observed for bulk polymer systems also applies to the layered nanocomposite system. When the piston reaches a critical velocity, PMMA crazing can emerge at the location where the major reflected wave and release wave meet. We show that the activation of PMMA crazing significantly enhances the energy dissipation ratio of the nanocomposite films, defined as the ratio between the dissipated energy through irreversible deformation and the input kinetic energy. The ratio maximizes at the critical U p when the PMMA crazing starts to develop and then decreases as U p further increases. We also find that a critical PMMA-graphene interfacial strength is required to activate PMMA crazing instead of interfacial separation. Additionally, layer thickness affects the amount of input kinetic energy and dissipated energy of nanocomposite films under impact. This study provides important insights into the detailed dynamic deformation mechanisms and how nanointerfaces/nanostructures affect the energy dissipation capability of layered nanocomposite films.

3.
Sensors (Basel) ; 23(12)2023 Jun 08.
Artigo em Inglês | MEDLINE | ID: mdl-37420596

RESUMO

Optical fiber sensors are newly established gas pipeline leakage monitoring technologies with advantages, including high detection sensitivity to weak leaks and suitability for harsh environments. This work presents a systematic numerical study on the multi-physics propagation and coupling process of the leakage-included stress wave to the fiber under test (FUT) through the soil layer. The results indicate that the transmitted pressure amplitude (hence the axial stress acted on FUT) and the frequency response of the transient strain signal strongly depends on the types of soil. Furthermore, it is found that soil with a higher viscous resistance is more favorable to the propagation of spherical stress waves, allowing FUT to be installed at a longer distance from the pipeline, given the sensor detection limit. By setting the detection limit of the distributed acoustic sensor to 1 nε, the feasible range between FUT and the pipeline for clay, loamy soil and silty sand is numerically determined. The gas-leakage-included temperature variation by the Joule-Thomson effect is also analyzed. Results provide a quantitative criterion on the installation condition of distributed fiber sensors buried in soil for the great-demanding gas pipeline leakage monitoring applications.


Assuntos
Fibras Ópticas , Solo , Física , Argila , Acústica
4.
Sensors (Basel) ; 21(11)2021 May 25.
Artigo em Inglês | MEDLINE | ID: mdl-34070548

RESUMO

This work describes the results of a test campaign aimed to measure the propagation of longitudinal, torsional, and flexural stress waves on a drill bit during percussive rock drilling. Although the stress wave propagation during percussive drilling has been extensively modeled and studied in the literature, its experimental characterization is poorly documented and generally limited to the detection of the longitudinal stress waves. The activity was performed under continuous drilling while varying three parameters, the type of concrete, the operator feeding force, and the drilling hammer rotational speed. It was found that axial stress wave frequencies and spectral amplitudes depend on the investigated parameters. Moreover, a relevant coupling between axial and torsional vibrations was evidenced, while negligible contribution was found from the bending modes. A finite element model of the drill bit and percussive element was developed to simulate the impact and the coupling between axial and torsional vibrations. A strong correlation was found between computed and measured axial stress spectra, but additional studies are required to achieve a satisfactory agreement between the measured and the simulated torque vibrations.

5.
Sensors (Basel) ; 21(3)2021 Jan 21.
Artigo em Inglês | MEDLINE | ID: mdl-33494311

RESUMO

The health detection of lithium ion batteries plays an important role in improving the safety and reliability of lithium ion batteries. When lithium ion batteries are in operation, the generation of bubbles, the expansion of electrodes, and the formation of electrode cracks will produce stress waves, which can be collected and analyzed by acoustic emission technology. By building an acoustic emission measurement platform of lithium ion batteries and setting up a cycle experiment of lithium ion batteries, the stress wave signals of lithium ion batteries were analyzed, and two kinds of stress wave signals which could characterize the health of lithium ion batteries were obtained: a continuous acoustic emission signal and a pulse type acoustic emission signal. The experimental results showed that during the discharge process, the amplitude of the continuous acoustic emission signal decreased with the increase of the cycle times of batteries, which could be used to characterize performance degradation; there were more pulse type acoustic emission signals in the first cycle of batteries, less in the small number of cycles, and slowly increased in the large number of cycles, which was in line with the bathtub curve and could be used for aging monitoring. The research on the health of lithium ion batteries by acoustic emission technology provides a new idea and method for detecting the health lithium ion batteries.

6.
Small ; 16(25): e2000314, 2020 06.
Artigo em Inglês | MEDLINE | ID: mdl-32462775

RESUMO

In this work, a scalable automated approach for fabricating 3D microgranular crystals consisting of desired arrangements of microspheres using holographic optical tweezers and two-photon polymerization is introduced. The ability to position microspheres as desired within lattices of any configuration allows designers to engineer the behavior of new metamaterials that enable advanced applications (e.g., armor that mitigates or redirects shock waves, acoustic lens for underwater imaging, damage detection, and noninvasive surgery, acoustic cloaking, and photonic crystals). Currently, no self-assembly or automated approaches exist with the flexibility necessary to place specific microspheres at specific locations within a crystal. Moreover, most pick-and-place approaches require the manual assembly of spheres one by one and thus do not achieve the speed and precision required to repeatably fabricate practical volumes of engineered crystals. In this paper, the rapid assembly of 4.86 µm diameter silica spheres within differently packed 3D crystal-lattice examples of unprecedented size using fully automated optical tweezers is demonstrated. The optical tweezers independently and simultaneously assemble batches of spheres that are dispensed to the build site via an automated syringe pump where the spheres are then joined together within previously unattainable patterns by curing regions of photocurable prepolymer between each sphere using two-photon polymerization.

7.
Sensors (Basel) ; 20(8)2020 Apr 23.
Artigo em Inglês | MEDLINE | ID: mdl-32340199

RESUMO

Stress wave, accompanied by explosion shock wave overpressure measurement and dynamic pressure calibration on shock tube, could cause error signals in the piezoelectric pressure sensor (PPS) used for measuring and calibrating. We may call this error the stress wave effect (SWE). In this paper, the SWE and its isolation from PPS were studied by using a split Hopkinson pressure bar (SHPB). In the experimental study of SWE, when increasing the input stress, the corresponding output signal of the PPS was analyzed, and the existence of SWE was verified using the result of the spectrum analysis of the output signal. The stress wave isolation pedestal used in the stress wave isolation experiment was made of nylon and plexiglass polymer materials. The effects of the isolation pedestal's materials and length on the stress wave isolation were analyzed using the study results. Finally, an artificial neural network (ANN) was trained with the data of the SWE study and was further applied to compensate the SWE error of the PPS output signal. The compensating results were compared with the isolating results, and the advantages and disadvantages of the digital compensation and physical isolation methods were analyzed.

8.
Sensors (Basel) ; 19(3)2019 Jan 29.
Artigo em Inglês | MEDLINE | ID: mdl-30700001

RESUMO

Stress wave-based communication has great potential for succeeding in subsea environments where many conventional methods would otherwise face excessive difficulty, and it can benefit logging well by using the drill string as a conduit for stress wave propagation. To achieve stress wave communication, a new stress wave-based pulse position modulation (PPM) communication system is designed and implemented to transmit data through pipeline structures with the help of piezoceramic transducers. This system consists of both hardware and software components. The hardware is composed of a piezoceramic transducer that can generate powerful stress waves travelling along a pipeline, upon touching, and a PPM signal generator that drives the piezoceramic transducer. Once the transducer is in contact with a pipeline surface, the generator integrated with an amplifier is utilized to excite the piezoceramic transducer with a voltage signal that is modulated to encode the information. The resulting vibrations of the transducer generates stress waves that propagate throughout the pipeline. Meanwhile, piezoceramic sensors mounted on the pipeline convert the stress waves to electric signals and the signal can be demodulated. In order to enable the encoding and decoding of information in the stress wave, a PPM-based communication protocol was integrated into the software system. A verification experiment demonstrates the functionality of the developed system for stress wave communication using piezoceramic transducers and the result shows that the data transmission speed of this new communication system can reach 67 bits per second (bps).

9.
Sensors (Basel) ; 17(8)2017 Aug 12.
Artigo em Inglês | MEDLINE | ID: mdl-28805666

RESUMO

Cracks in oil and gas pipelines cause leakage which results in property damage, environmental pollution, and even personal injury or loss of lives. In this paper, an active-sensing approach was conducted to identify the crack damage in pipeline structure using a stress wave propagation approach with piezoceramic transducers. A pipeline segment instrumented with five distributed piezoceramic transducers was used as the testing specimen in this research. Four cracks were artificially cut on the specimen, and each crack had six damage cases corresponding to different crack depths. In this way, cracks at different locations with different damage degrees were simulated. In each damage case, one piezoceramic transducer was used as an actuator to generate a stress wave to propagate along the pipeline specimen, and the other piezoceramic transducers were used as sensors to detect the wave responses. To quantitatively evaluate the crack damage status, a wavelet packet-based damage index matrix was developed. Experimental results show that the proposed method can evaluate the crack severity and estimate the crack location in the pipeline structure based on the proposed damage index matrix. The sensitivity of the proposed method decreases with increasing distance between the crack and the mounted piezoceramic transducers.

10.
Sensors (Basel) ; 17(3)2017 Feb 23.
Artigo em Inglês | MEDLINE | ID: mdl-28241503

RESUMO

Rock bolts, as a type of reinforcing element, are widely adopted in underground excavations and civil engineering structures. Given the importance of rock bolts, the research outlined in this paper attempts to develop a portable non-destructive evaluation method for assessing the length of installed rock bolts for inspection purposes. Traditionally, piezoelectric elements or hammer impacts were used to perform non-destructive evaluation of rock bolts. However, such methods suffered from many major issues, such as the weak energy generated and the requirement for permanent installation for piezoelectric elements, and the inconsistency of wave generation for hammer impact. In this paper, we proposed a portable device for the non-destructive evaluation of rock bolt conditions based on a giant magnetostrictive (GMS) actuator. The GMS actuator generates enough energy to ensure multiple reflections of the stress waves along the rock bolt and a lead zirconate titantate (PZT) sensor is used to detect the reflected waves. A new integrated procedure that involves correlation analysis, wavelet denoising, and Hilbert transform was proposed to process the multiple reflection signals to determine the length of an installed rock bolt. The experimental results from a lab test and field tests showed that, by analyzing the instant phase of the periodic reflections of the stress wave generated by the GMS transducer, the length of an embedded rock bolt can be accurately determined.

11.
Polymers (Basel) ; 16(15)2024 Aug 01.
Artigo em Inglês | MEDLINE | ID: mdl-39125215

RESUMO

This article deals with stress wave decay performance, analysing the stress wave propagation generated by an impulsive unit load in a 2D representative unit cell (RUC) of a polymer composite with circular particles representing spherical particles, elliptical particles, and short fibres. The micro-scale numerical simulation uses explicit finite element analysis (FEA). The micro-response to an impulsive unit load creates a stress wave amplitude interacting with the material structure and tends to weaken and absorb energy. The stress wave damping is determined by the decaying amplitudes of Mises stress at the front of the stress wave. The stress wave damping is evaluated for different ratios of tensile modules and material densities of matrix and reinforcing material and other factors, such as percentage and particle size, applied to nine topologies of RUCs, and even the presence of an interfacial region is analysed. Moreover, the article visualises the phases of stress wave decay in various particle distributions, i.e., various topologies. Analysing the different topologies of the same particle volume (area) percentage, the study proved that the composite topology and resulting wave-particle and wave-wave interactions are other sources of material damping. The presence of even a small percentage, 3.5 area%, of reinforcing circular particles in the matrix brings a significant increase in stress wave damping up to about 40-43% (depending on the topology) compared to a homogeneous matrix with stress wave damping of 12.5% under the same conditions. Moreover, the topology with the same volume (area) percentage can increase particle stress wave damping by 15.3%.

12.
ACS Nano ; 2024 Jul 17.
Artigo em Inglês | MEDLINE | ID: mdl-39018251

RESUMO

Understanding laser-induced jumping has attracted great interest in nanomaterial launching and transfer but requires a high spatiotemporal resolution visualization. Here, we report a jumping dynamics of nanoplate driven by ultrafast laser-induced stress using time-resolved transmission electron microscopy. Single-shot imaging reveals a nondestructive launching of gold nanoplates in several nanoseconds after the pulsed femtosecond laser excitation. The temperature rise and acoustic vibration, derived from ultrafast electron crystallography with a picosecond time resolution, confirm the existence of a laser-induced elastic stress wave. The generation, propagation, and reflection of thermal stress waves are further clarified by atomic simulation. The nonequilibrium ultrafast laser heating produces a compressive stress wave within several picoseconds, constrained by the supporting substrate under nanoplate to provide thrust force. This compressive stress is subsequently reflected into tensile stress by the substrate, promoting the nanoplate to jump off the substrate. Furthermore, the uneven interface adhesion results in the jumping flip of nanoplates, as well as, diminished their jumping speed. This study unveils the jumping regime driven by impulsive laser-excited stress and offers understanding of light-matter interaction.

13.
Sci Rep ; 14(1): 4917, 2024 Feb 28.
Artigo em Inglês | MEDLINE | ID: mdl-38418928

RESUMO

In the process of drilling and blasting construction of large-cross-section tunnels, the layout of wedge-shaped cutting holes has a great influence on the effect of blasting. In this study, theoretical analysis and numerical simulation were used to assess the effect of different forms of cutting hole placement on blasting effectiveness. First, the fissure-inducing angle was proposed, a three-dimensional model of wedge-shaped cutting considering the effect of shear-tensile resistance was established, and theoretical analyses of cutting holes with different cutting angles and fissure-inducing angles were carried out. Second, the parameters of the Riedel-Hiermaier-Thoma model were determined based on the experimental data, and verified. Third, three-dimensional numerical models were established, and analyze the influence of different forms of hole deployment on the blasting effect from the perspective of stress wave propagation and dynamic damage to the surrounding rock. Finally, based on the theoretical analysis and numerical simulation results, the wedge-shaped hollowing holes were re-designed, and 20 tunnel blasting tests were carried out using this deployment method for large-section tunnel blasting, which verified the feasibility of this deployment method. The results of the study show that for level III surrounding rock, the angle of wedge-shaped cutting holes should meet 68° ≤ θ ≤ 70° and 70° ≤ ß ≤ 72°. This study provides a kind of refined and efficient blasting for the drilling and blasting excavation process of large section tunnels.

14.
Ultrasonics ; 133: 107054, 2023 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-37262982

RESUMO

The propagation of stress waves in the ultrasonic vibration grinding zone was studied and analyzed in this paper and the microscopic mechanism of ultrasonic vibration assisted grinding is clarified by combining the method of finite element analysis (FEA). The creation of an experimental platform for ultrasonic vibration assisted grinding allowed for a comparative experimental evaluation of radial ultrasonic vibration assisted grinding (RUVAG) and conventional grinding (CG). Experiments analysis show that: (a) Compared with conventional grinding, the alternating impact of stress waves in ultrasonic vibration grinding is beneficial to the propagation of microcracks and the removal of materials. Meanwhile, there is no burn on the machined surface, so the quality of the machined surface is better. (b) Under the alternating and superimposed action of stress waves, dislocation emission becomes difficult due to the suppressed thermal activation process. Therefore, the plastic deformation of the material is suppressed and reduced in the grinding zone, and the material is more likely to break than during conventional grinding. Therefore, compared with conventional grinding, both cracks and chips are easier to form in it..

15.
J Cancer ; 14(10): 1773-1780, 2023.
Artigo em Inglês | MEDLINE | ID: mdl-37476190

RESUMO

Purpose: We previously developed a site-selective transvascular drug delivery system based on nanosecond pulsed laser-induced photomechanical waves (PMWs). In this study, we applied this method to the delivery of cisplatin (cis-diamminedichloroplatinum, CDDP) to a subcutaneous tumor in a mouse and examined its antitumor effects. Methods: A mouse tumor model with subcutaneous inoculation of human head and neck cancer cells (FaDu cells) was used. The mice were divided into four groups: control without any treatment (control), CDDP application only (CDDP only), PMW application only (PMW only) and combined application of PMWs and CDDP (PMW+CDDP). A PMW was generated by irradiating a laser target, which was placed on the skin over the tumor, with a ruby laser pulse (fluence, 1.6 J/cm2). A CDDP solution was intraperitoneally injected into the mice (2.5 mg/kg). Results: Until 7 days posttreatment, the tumor volume in the control group monotonically increased, while the tumor volumes in the CDDP-only group and PMW-only group did not change greatly and that in the PMW+CDDP group slightly decreased. Afterward, the tumors started to regrow in all treatment groups, but the tumor growth rate was considerably low in the PMW+CDDP group. There was a significant difference in the time courses of tumor volume between the PMW+CDDP group and the control group for up to 14 days posttreatment. The ratio of the Ki-67-positive (proliferative) areas to the whole tumor regions in the PMW+CDDP group was significantly smaller than that in the control group at 7 days posttreatment. These results are attributable to the synergistic effects of enhanced extravasation of CDDP and mechanical tumoricidal effect by PMWs. Conclusion: The combined application of CDDP and PMWs significantly improved the antitumor effects on mouse subcutaneous tumors.

16.
Materials (Basel) ; 16(8)2023 Apr 15.
Artigo em Inglês | MEDLINE | ID: mdl-37109956

RESUMO

In order to efficiently investigate the effect of the mesoscale heterogeneity of a concrete core and the randomness of circular coarse aggregate distribution on the stress wave propagation procedure and the response of PZT sensors in traditional coupling mesoscale finite element models (CMFEMs), firstly, a mesoscale homogenization approach is introduced to establish coupling homogenization finite element models (CHFEMs) with circular coarse aggregates. CHFEMs of rectangular concrete-filled steel tube (RCFST) members include a surface-mounted piezoelectric lead zirconate titanate (PZT) actuator, PZT sensors at different measurement distances, a concrete core with mesoscale homogeneity. Secondly, the computation efficiency and accuracy of the proposed CHFEMs and the size effect of representative area elements (RAEs) on the stress wave field simulation results are investigated. The stress wave field simulation results indicate that the size of an RAE limitedly affects the stress wave fields. Thirdly, the responses of PZT sensors at different measurement distances of the CHFEMs under both sinusoidal and modulated signals are studied and compared with those of the corresponding CMFEMs. Finally, the effect of the mesoscale heterogeneity of a concrete core and the randomness of circular coarse aggregate distribution on the responses of PZT sensors in the time domain of the CHFEMs with and without debond defects is further investigated. The results show that the mesoscale heterogeneity of a concrete core and randomness of circular coarse aggregate distribution only have a certain influence on the response of PZT sensors that are close to the PZT actuator. Instead, the interface debond defects dominantly affect the response of each PZT sensor regardless of the measurement distance. This finding supports the feasibility of stress wave-based debond detection for RCFSTs where the concrete core is a heterogeneous material.

17.
Sensors (Basel) ; 11(8): 7554-67, 2011.
Artigo em Inglês | MEDLINE | ID: mdl-22164032

RESUMO

Stress-wave-based techniques have been proven to be an accurate nondestructive test means for determining the quality of wood based materials and they been widely used for this purpose. However, the results are usually inconsistent, partially due to the significant difficulties in processing the nonlinear, non-stationary stress wave signals which are often corrupted by noise. In this paper, an ensemble empirical mode decomposition (EEMD) based approach with the aim of signal denoising was proposed and applied to stress wave signals. The method defined the time interval between two adjacent zero-crossings within the intrinsic mode function (IMF) as the instantaneous half period (IHP) and used it as a criterion to detect and classify the noise oscillations. The waveform between the two adjacent zero-crossings was retained when the IHP was larger than the predefined threshold, whereas the waveforms with smaller IHP were set to zero. Finally the estimated signal was obtained by reconstructing the processed IMFs. The details of threshold choosing rules were also discussed in the paper. Additive Gaussian white noise was embedded into real stress wave signals to test the proposed method. Butterworth low pass filter, EEMD-based low pass filter and EEMD-based thresholding filter were used to compare filtering performance. Mean square error between clean and filtered stress waves was used as filtering performance indexes. The results demonstrated the excellent efficiency of the proposed method.


Assuntos
Botânica/métodos , Ecologia/métodos , Física/métodos , Algoritmos , Cinnamomum , Monitoramento Ambiental , Teste de Materiais , Modelos Estatísticos , Distribuição Normal , Processamento de Sinais Assistido por Computador , Software , Árvores
18.
Materials (Basel) ; 14(11)2021 Jun 01.
Artigo em Inglês | MEDLINE | ID: mdl-34205884

RESUMO

The attenuation of stress waves due to the local resonance is numerically studied using the finite element method (FEM) in this work. The natural frequency of a representative composite unit embedded with coated particles is analyzed and the major factors that influence the natural frequency are examined. Local resonance is inspired when the frequency of the incident stress wave is close to the natural frequency of the particles in the composite. Significant reduction in the amplitude of the stress is obtained when the local resonance occurs, because a large amount of the incident energy is converted to the kinetic energy of the particles, which is rapidly dissipated through the strong oscillations of those particles. It is also observed that the attenuation for the incident stress waves with a range of frequencies can be achieved by using the particles with various local natural frequencies in a composite.

19.
Materials (Basel) ; 14(23)2021 Nov 29.
Artigo em Inglês | MEDLINE | ID: mdl-34885468

RESUMO

Although highly desirable, the experimental technology of the dynamic mechanical properties of materials under multiaxial impact loading is rarely explored. In this study, a true-biaxial split Hopkinson pressure bar device is developed to achieve the biaxial synchronous impact loading of a specimen. A symmetrical wedge-shaped, dual-wave bar is designed to decompose a single stress wave into two independent and symmetric stress waves that eventually form an orthogonal system and load the specimen synchronously. Furthermore, a combination of ground gaskets and lubricant is employed to eliminate the shear stress wave and separate the coupling of the shear and axial stress waves propagating in bars. Some confirmatory and applied tests are carried out, and the results show not only the feasibility of this modified device but also the dynamic mechanical characteristics of specimens under biaxial impact loading. This novel technique is readily implementable and also has good application potential in material mechanics testing.

20.
Materials (Basel) ; 14(1)2021 Jan 02.
Artigo em Inglês | MEDLINE | ID: mdl-33401734

RESUMO

When a brittle thin rod, such as a dry spaghetti stick, is bent beyond its flexural limit, it often breaks into more than two pieces, typically three or more. This phenomenon and puzzle has aroused widespread interest and discussion since its first proposal by Feynman. Previous work has partly explained the inevitability of the secondary fracture, but without any adjustable time parameter. In order to further understand this problem, especially the secondary fracture, in this paper we propose and study the dynamics of a half-infinite model to mimic the physics that a spaghetti stick is half-infinite under uniform bending. When the breaking process starts, a gradual release of initial moment of a linearly declining time at the free end, instead of a sudden release, is adopted, resulting in the introduction of a characteristic time parameter to the model and agrees better with the real situation. A specific analytical solution in terms of the excited bending moment using Euler-Bernoulli beam theory is derived, and that the gradual release of initial moment induces a burst of flexural waves, and these flexural waves locally increase the moment in the stick and progressively get to the maximum value, and then lead to the secondary fracture are concluded. The excited moment increases with time and distance, and has an asymptotic extremum value of 1.43 times initial moment. The gradual release in our model requires and gives certain distance and time when the excited bending moment reaches its extremum value, which provides a possibility to predict the detailed fracture parameters such as fragmentation length and time and thus to further understand the secondary fracture during spaghetti bent break.

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