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Search Results (4,146)

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Keywords = rubber

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15 pages, 4836 KiB  
Article
Constitutive Model for Thermal-Oxygen-Aged EPDM Rubber Based on the Arrhenius Law
by Xiaoling Hu, Xing Yang, Xi Jiang and Kui Song
Polymers 2024, 16(18), 2608; https://doi.org/10.3390/polym16182608 (registering DOI) - 14 Sep 2024
Viewed by 215
Abstract
Ethylene-propylene-diene monomer (EPDM) is a key engineering material; its mechanical characterization is important for the safe use of the material. In this paper, the coupled effects of thermal degradation temperature and time on the tensile mechanical behavior of EPDM rubber were investigated. The [...] Read more.
Ethylene-propylene-diene monomer (EPDM) is a key engineering material; its mechanical characterization is important for the safe use of the material. In this paper, the coupled effects of thermal degradation temperature and time on the tensile mechanical behavior of EPDM rubber were investigated. The tensile stress-strain curves of the aged and unaged EPDM rubber show strong nonlinearity, demonstrating especially rapid stiffening as the strain increases under small deformation. The popular Mooney–Rivlin and Ogden (N = 3) models were chosen to fit the test data, and the results indicate that neither of the classical models can accurately describe the tensile mechanical behavior of this rubber. Six hyperelastic constitutive models, which are excellent for rubber with highly nonlinearity, were employed, and their abilities to reproduce the stress-strain curve of the unaged EPDM were assessed. Finally, the Davis–De–Thomas model was found to be an appropriate hyperelastic model for EPDM rubber. A Dakin-type kinetic relationship was employed to describe the relationships between the model parameters and aging temperature and time, and, combined with the Arrhenius law, a thermal aging constitutive model for EPDM rubber was established. The ability of the proposed model was checked by independent testing data. In the moderate strain range of 200%, the errors remained below 10%. The maximum errors of the prediction results at 85 °C for 4 days and 100 °C for 2 and 4 days were computed to be 17.06%, 17.51% and 19.77%, respectively. This work develops a theoretical approach to predicting the mechanical behavior of rubber material that has suffered thermal aging; this approach is helpful in determining the safe long-term use of the material. Full article
(This article belongs to the Section Polymer Physics and Theory)
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<p>Chemical structure of the EPDM rubber.</p>
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<p>Size of specimens (unit: mm).</p>
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<p>Stress-strain curves of the EPDM before and after aging for different times at (<b>a</b>) 70 °C; (<b>b</b>) 85 °C; (<b>c</b>) 100 °C.</p>
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<p>Stress-strain curves of the EPDM before and after aging for different times at (<b>a</b>) 70 °C; (<b>b</b>) 85 °C; (<b>c</b>) 100 °C.</p>
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<p>Fitting curves vs. the stress-strain data of the unaged EPDM rubber by the two classical models.</p>
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<p>Fitting curves vs. the stress-strain data of the unaged EPDM rubber by the top six models.</p>
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<p>Fitting curves vs. the stress-strain data of the unaged EPDM rubber by the top six models.</p>
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<p>Fitting curves vs. the stress-strain data of the unaged EPDM rubber by the top six models.</p>
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<p>Plots of model parameters <span class="html-italic">m</span>, <span class="html-italic">n</span>, <span class="html-italic">c</span> and <span class="html-italic">k</span> vs. aging time under different aging temperatures.</p>
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<p>Plots of model parameters <span class="html-italic">m</span>, <span class="html-italic">n</span>, <span class="html-italic">c</span> and <span class="html-italic">k</span> vs. aging time under different aging temperatures.</p>
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<p>Comparison between the prediction results of the developed model and the test stress-strain data with EPDM aged at 70 °C for 28 days, 85 °C for 14 days and 100 °C for 56 days.</p>
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<p>Comparison between the prediction results of the developed model and the independent test stress-strain data.</p>
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<p>Average relative errors of the predicted results.</p>
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16 pages, 5054 KiB  
Article
Mechanical Analysis through Non-Destructive Testing of Recycled Porous Friction Course Asphalt Mixture
by Eulália Barbosa, Lucas Lira, Mauro Silva Filho, Lucas Babadopulos, Jorge Soares, Gemmelle Santos and Juceline Bastos
Buildings 2024, 14(9), 2907; https://doi.org/10.3390/buildings14092907 (registering DOI) - 14 Sep 2024
Viewed by 196
Abstract
This study assessed the mechanical performance of porous asphalt mixtures, specifically the porous friction course (PFC), incorporating 10% Reclaimed Asphalt Pavement (RAP) and rubberized asphalt. Three different methods were investigated to evaluate the stiffness of the mixtures: the resilience modulus (RM) test at [...] Read more.
This study assessed the mechanical performance of porous asphalt mixtures, specifically the porous friction course (PFC), incorporating 10% Reclaimed Asphalt Pavement (RAP) and rubberized asphalt. Three different methods were investigated to evaluate the stiffness of the mixtures: the resilience modulus (RM) test at a single temperature and loading frequency, the complex modulus |E*| test from compressive loading conducted at various temperatures and frequencies, and the impact resonance (IR) tests performed at three temperatures with five impacts applied to the mixture. The results demonstrated that the RAP-containing mixture exhibited a higher resilience modulus at all tested temperatures, indicating greater stiffness compared to the mixture without RAP. Additionally, the IR and |E*| tests revealed similar behavior between the two evaluated mixtures. These findings suggest that both quasi-static and vibrational tests are suitable for characterizing the stiffness of porous asphalt mixtures due to the similarity in the viscoelastic parameters of the two investigated mixtures. This study provides important insights into the practical and scientific application of recycled and modified materials in porous asphalt mixtures. Full article
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<p>Representation of load signals and the duration of loading and rest time in the RM test.</p>
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<p>Representation of stress–strain signals from the complex modulus test.</p>
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<p>(<b>a</b>) Impact hammer load cell results in the time domain; (<b>b</b>) accelerometer results in the time domain; (<b>c</b>) impact hammer load cell results in the frequency domain; (<b>d</b>) accelerometer results in the frequency domain; (<b>e</b>) representation of the FRF for the IR test.</p>
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<p>Experimental flowchart.</p>
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<p>Project particle size curves.</p>
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<p>Gradation curves of the RAP (before and after binder extraction).</p>
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<p>(<b>a</b>) Climatic chamber—UTM, (<b>b</b>) test in progress.</p>
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<p>(<b>a</b>) Loading frequencies and test temperatures, (<b>b</b>) test in progress.</p>
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<p>Schematic representation of the IR test.</p>
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<p>Resilient modulus results at 25 °C.</p>
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<p>Comparison of the modulus master curves of the mixtures.</p>
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<p>Complex modulus represented in Cole–Cole curves.</p>
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<p>Master curves of the phase angle of the mixtures.</p>
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<p>Black diagram with the 2S2P1D modeling.</p>
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<p>Master curve: (<b>a</b>) mixture PFC-REF (<b>b</b>) mixture PFC-RAP.</p>
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14 pages, 5519 KiB  
Article
Research on the Energy-Absorbing and Cushioning Performance of a New Half-Bowl Ball Rubber Body in Tunnel Support
by Jian Ma, Yaomeng Xiao, Bin Ma, Canguang Zheng, Xiangpeng Hu, Dan Tian, Mingchao Du and Kun Zhang
Processes 2024, 12(9), 1981; https://doi.org/10.3390/pr12091981 (registering DOI) - 14 Sep 2024
Viewed by 175
Abstract
As coal mine underground operating conditions are harsh, strengthening and optimizing the support structure is conducive to the safety of mining work and personnel. Currently, underground support devices face problems such as poor environmental adaptability and unbalanced performance of shockproof and energy absorption. [...] Read more.
As coal mine underground operating conditions are harsh, strengthening and optimizing the support structure is conducive to the safety of mining work and personnel. Currently, underground support devices face problems such as poor environmental adaptability and unbalanced performance of shockproof and energy absorption. At the same time, the energy absorption mechanism and impact dynamic analysis of the support structure are still imperfect. This paper proposes a simple and effective bionic half-bowl spherical rubber energy-absorbing structure based on the actual production needs of coal mines, with energy-absorbing rubber as the main structural interlayer. A combination of experimental testing and simulation was used to reveal the dynamic response and mechanism of simulated energy absorption of a half-bowl-shaped rubber layer under different working conditions. Abaqus software was used to simulate and analyze the dynamic response of the half-bowl spherical rubber structure under the impact condition, and the simulation data were compared with the experimental results. In addition, the relationship between energy absorption and stress at the rubber structure and the base plate under different impact velocities was investigated. The results show that the simulated and experimental results of the rubber structure have almost the same pressure vs. time trend within 0.1 s at an impact velocity of 64 m/s, and there is no significant wear on the rubber surface after impact. Due to the energy-absorbing effect of the rubber structure, the maximum stress of the bottom member plate-2 of the mechanism is lower than 9 × 104 N. The maximum amount of compression of the half-bowl ball is 37.56 mm at an impact velocity of 64 m/s. The maximum amount of compression of the half-bowl ball is 37.56 mm. Full article
(This article belongs to the Section Materials Processes)
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<p>Buffer energy-absorbing device overall structure and assembly: (<b>a</b>) cushioning energy absorbers; (<b>b</b>) secondary telescopic disc spring-cushioned monolithic columns; (<b>c</b>) half-bowl-shaped cushioning and energy-absorbing structures; (<b>d</b>) overall installation effect diagram.</p>
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<p>Half-bowl rubber energy-absorbing structure.</p>
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<p>Energy-absorbing simulation model.</p>
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<p>Impact test bench: (<b>a</b>) schematic diagram of the impact instrument; (<b>b</b>) physical diagram of the impact instrument.</p>
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<p>Stress diagram of the rubber structure at plate-0 velocity of 64 m/s: (<b>a</b>) Step 2; (<b>b</b>) Step 20; (<b>c</b>) Step 30 and its (<b>d</b>) top view.</p>
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<p>Stress versus time curves for half-bowl spherical rubber structures.</p>
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<p>Stress versus time curves for plate-2.</p>
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<p>Variation of absorbed energy in rubber structures at different impact velocities.</p>
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<p>Maximum deformation of the half-bowl rubber structure under different impact force conditions: (<b>a</b>) the relationship between the rubber compression height and the stress of plate-2; (<b>b</b>) simulation diagram of rubber compression height.</p>
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20 pages, 7388 KiB  
Article
Rheological Properties and Performance Evaluation of Different Types of Composite-Modified Asphalt in Cold Regions
by Guihua Hu, Xiaowei Chen, Song Zhao and Jian Ouyang
Coatings 2024, 14(9), 1187; https://doi.org/10.3390/coatings14091187 - 13 Sep 2024
Viewed by 224
Abstract
In low-temperature environments, asphalt materials harden easily and become brittle, and the repeated action of traffic load further aggravates the cracking of and damage to the asphalt mixture. In order to explore high-performance asphalt pavement materials that are more suitable for cold climates, [...] Read more.
In low-temperature environments, asphalt materials harden easily and become brittle, and the repeated action of traffic load further aggravates the cracking of and damage to the asphalt mixture. In order to explore high-performance asphalt pavement materials that are more suitable for cold climates, this paper selected four modifiers, namely SBS, rubber powder, SBR and TPS. With SBS as the main agent, combined with other modifiers, three types of base asphalts with grades of 70#, 90# and 110# were compositely modified to prepare 12 different combinations of composite-modified asphalt samples. The optimal dosage of the modifier was determined by the basic performance test of asphalt, and the compatibility, interaction energy and mechanical properties of the modifier and base asphalt at different temperatures were analyzed by molecular dynamics simulation. Subsequently, the high- and low-temperature rheological properties of various modified asphalts were systematically evaluated using a dynamic shear rheology test (DSR) and a bending beam rheology test (BBR), and the rheological properties and road performance indicators of each composite-modified asphalt were comprehensively compared so as to select the road materials most suitable for cold areas. The research results show that different grades of base asphalt and modifiers show good compatibility in the range of 160–175 °C. Among them, rubber powder and TPS modifier significantly improve the high-temperature mechanical properties of SBS-modified asphalt, while rubber powder and SBR modifier significantly improve its low-temperature mechanical properties. The DSR and BBR test results further show that SBS/rubber powder composite-modified asphalt exhibits excellent rheological properties under both high- and low-temperature conditions, and is the preferred solution for road materials in cold regions. Full article
(This article belongs to the Special Issue Asphalt Pavement: Materials, Design and Characterization)
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<p>Modifiers used in the test.</p>
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<p>Molecular model of asphalt components. (Red represents oxygen atoms, blue represents nitrogen atoms, and yellow represents sulfur atoms).</p>
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<p>Modifier molecular structure.</p>
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<p>Molecular model of each modifier.</p>
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<p>90#SBS/rubber-powder-modified asphalt molecular model.</p>
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<p>Differences in solubility parameters of different types of modified asphalt.</p>
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<p>SEM morphology of 90#-modified asphalt.</p>
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<p>Energy change diagram of different types of modified asphalt.</p>
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<p>Young’s modulus of different types of modified asphalt.</p>
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<p>Bulk modulus of different types of modified asphalt.</p>
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<p>Shear modulus of different types of modified asphalt.</p>
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<p>Comparison of modulus of different types of modified asphalt.</p>
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<p>The relationship between complex shear modulus and temperature change of composite-modified asphalt with different grades.</p>
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<p>Relationship between phase angle and temperature of composite-modified asphalt with different grades.</p>
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<p>Relationship between rutting factor and temperature of composite-modified asphalt of different grades.</p>
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<p>The relationship between creep stiffness and temperature of composite-modified asphalt with different grades.</p>
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<p>The relationship between creep rate and temperature of composite-modified asphalt with different grades.</p>
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15 pages, 3693 KiB  
Article
Analytical Solution for Dynamic Response of a Reinforced Concrete Beam with Viscoelastic Bearings Subjected to Moving Loads
by Liangming Sun, Shuguang Liu, Fan Kong and Hanbing Zhao
Materials 2024, 17(18), 4491; https://doi.org/10.3390/ma17184491 - 13 Sep 2024
Viewed by 170
Abstract
To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced [...] Read more.
To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam. Full article
(This article belongs to the Special Issue Study on Mechanical Properties of Concrete Structures and RC Beams)
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<p>Test specimen of low-stiffness and high-damping rubber bearing.</p>
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<p>Simplified calculation model of a viscoelastic bearing RC beam.</p>
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<p>Simplified calculation model of viscoelastic bearing RC beam subjected to a moving load.</p>
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<p>Simplified mode shape function of viscoelastic bearing RC beam.</p>
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<p>Calculation model: (<b>a</b>) model of train; (<b>b</b>) simplified calculation model of viscoelastic bearing RC beam subjected to equidistant moving loads.</p>
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<p>Midspan acceleration time history of the RC beam in the degenerated case of <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mo>∞</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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<p>Midspan displacement time history of the RC beam in the degenerated case of <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mo>∞</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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<p>Midspan displacement time history of the RC beam with different bearing conditions.</p>
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<p>Midspan acceleration time history of the RC beam with different bearing conditions.</p>
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<p>Comparison of midspan displacements of viscoelastic bearing RC beam under different train speeds.</p>
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<p>Comparison of midspan displacements of viscoelastic bearing RC beam with different stiffnesses at the supports.</p>
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<p>Comparison of midspan displacement of viscoelastic bearing RC beam with different damping at the supports.</p>
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<p>Curves of displacement versus time for midspan of viscoelastic bearing RC beam.</p>
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<p>Curves of acceleration versus time for midspan of viscoelastic bearing RC beam.</p>
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12 pages, 4330 KiB  
Article
Study on Sealing Performance of Spring-Embedded Shoulder Protection Packer Rubber Cylinder
by Jinghui Li, Chunhong Wu, Mingji Li and Chengwen Wang
Processes 2024, 12(9), 1967; https://doi.org/10.3390/pr12091967 - 12 Sep 2024
Viewed by 254
Abstract
Oil extraction is shifting towards high-temperature and high-pressure environments, which leads to the deterioration of the rubber material used in packer rubber cylinders, ultimately resulting in sealing failure. Hence, we propose enhancing the configuration of the rubber cylinder by incorporating a composite material [...] Read more.
Oil extraction is shifting towards high-temperature and high-pressure environments, which leads to the deterioration of the rubber material used in packer rubber cylinders, ultimately resulting in sealing failure. Hence, we propose enhancing the configuration of the rubber cylinder by incorporating a composite material consisting of metal and rubber. Additionally, we suggest integrating springs at the shoulders to fabricate a spring-embedded shoulder protection packer rubber cylinder. ABAQUS 2023 software was employed to simulate the packer setting process, investigating the variations in compression distance between a conventional packer rubber cylinder and a spring-embedded shoulder protection packer rubber cylinder. The results showed that at 25 °C and 177 °C, the compression distance of the fully seated spring-embedded shoulder protection packer rubber cylinder was reduced by 3% compared to the traditional packer rubber, Mises stress was reduced by 14%, and the sealing performance evaluation coefficient K of the rubber cylinder was increased by 2% to 10%.The stress in the spring-embedded shoulder protection packer rubber cylinder is primarily concentrated between the spring and the wire mesh, effectively ensuring the performance of the rubber cylinder and mitigating any potential decrease in sealing performance caused by internal stress concentration. The spring-embedded protective rubber cylinder will not experience shoulder protrusion during the sealing process. The incorporation of a spring-embedded shoulder protection mechanism in the packer rubber cylinder enhances the contact stress between the rubber cylinder and casing tube, mitigates stress concentration within the rubber cylinder, resolves shoulder protrusion issues, and ultimately improves both sealing performance and service life. Full article
(This article belongs to the Section Materials Processes)
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Figure 1
<p>Schematic diagram of rubber cylinder structure. 1—Upper rubber cylinder; 2—medium rubber cylinder; 3—lower rubber cylinder; 4—upper pressure ring; 5—wire mesh; 6—spring; 7—upper spacer ring; 8—lower spacer ring; 9—lower pressure ring.</p>
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<p>Two-dimensional finite element model of spring-embedded shoulder protection packer rubber cylinder.</p>
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<p>Mesh division diagram of edge rubber cylinder and medium cylinder. (<b>a</b>) Edge rubber cylinder mesh. (<b>b</b>) Medium cylinder mesh.</p>
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<p>Cloud diagram of axial compression distance between traditional packer rubber cylinder and spring-embedded shoulder protection packer rubber cylinder at 25 °C and 177 °C. (<b>a</b>) Traditional packer rubber cylinder (25 °C). (<b>b</b>) Spring-embedded shoulder protection packer rubber cylinder (25 °C). (<b>c</b>) Traditional packer rubber cylinder (177 °C). (<b>d</b>) Spring-embedded shoulder protection packer rubber cylinder (177 °C).</p>
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<p>Comparison of compression distance between traditional and spring-embedded shoulder protection packers at 25 °C and 177 °C.</p>
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<p>Mises stress cloud map of traditional packer rubber cylinders and spring-embedded shoulder protection packer rubber cylinders at 25 °C and 177 °C. (<b>a</b>) Traditional packer rubber cylinder (25 °C). (<b>b</b>) Spring-embedded shoulder protection packer rubber cylinder (25 °C). (<b>c</b>) Traditional packer rubber cylinder (177 °C). (<b>d</b>) Spring-embedded shoulder protection packer rubber cylinder (177 °C).</p>
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<p>Curve of contact stress between spring-embedded shoulder protection packer rubber cylinder and traditional packer rubber cylinder along the length direction of the rubber cylinder at 25 °C and 177 °C.</p>
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<p>Definition of shoulder protrusion value.</p>
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14 pages, 3525 KiB  
Article
Restoring Model of a Pneumatic Artificial Muscle with Structure Parameters: Analysis and Identification
by Minh Ky Nguyen, Van Chon Trinh, Ngoc Yen Phuong Vo and Thanh Danh Le
Actuators 2024, 13(9), 355; https://doi.org/10.3390/act13090355 - 12 Sep 2024
Viewed by 176
Abstract
This paper will develop the restoring model of a commercial pneumatic artificial muscle (PAM) based on a McKibben structure, which comprises an elastic element connected with a viscoelastic element in parallel. The elastic element is generated by compressed air inside the rubber bellow; [...] Read more.
This paper will develop the restoring model of a commercial pneumatic artificial muscle (PAM) based on a McKibben structure, which comprises an elastic element connected with a viscoelastic element in parallel. The elastic element is generated by compressed air inside the rubber bellow; meanwhile, the viscoelasticity is affected by the rubber material. In particular, the viscoelastic property of the rubber material is proposed based on the Maxwell model. Instead of derivative of integer orders, an equation of motion of the fractional model is introduced to better capture the amplitude- and frequency-dependent property of the viscoelasticity of the PAM. The equation expressing the hysteresis loop due to the viscoelasticity of the PAM material will then be analyzed and built. A water cycle algorithm is employed to determine the optimal set of the proposed model. To evaluate the effectiveness of the proposed model, a comparison between the simulation calculated from the proposed model and experimental data is considered under harmonic force excitation. This study’s results give potential insight into the field of system dynamic analysis with the elastic element being PAM. Full article
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<p>Physical structure of PAM (<b>a</b>); diagram of fractional Maxwell model (<b>b</b>).</p>
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<p>Working states of the PAM.</p>
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<p>Hysteresis curve of fractional Maxwell model.</p>
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<p>Hydrological cycle.</p>
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<p>The schematic diagram of the stream to river and river to sea.</p>
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<p>Experimental setup (<b>a</b>); diagram of the apparatus (<b>b</b>): 1—Motor; 2—Compressor; 3—Filter; 4—Air reservoir; 5—Pressure regulator; 6—On–off valve; 7—Pressure gauge; 8—Safety valve; 9—Pressure sensor; 10—PAM; 11—Loadcell; 12—Position sensor; 13—Base; 14—Coupling; 15—Pneumatic cylinder; 16—Proportional valve; 17—NI card 6221; 18—Computer.</p>
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<p>Measured signals versus time: (<b>a</b>) pressure; (<b>b</b>) position.</p>
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<p>Comparison between the experimental and approximate curves.</p>
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<p>Comparison between the simulation and experiment (detailed annotation of the line types is presented in top-left corner panel).</p>
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<p>Convergence of the cost function.</p>
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<p>Comparison of experimented and calculated hysteresis loops with frequency of 3.5 Hz and various force amplitudes: (<b>a</b>) 95 N; (<b>b</b>) 110 N; (<b>c</b>) 122 N; (<b>d</b>) 148 N.</p>
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<p>Comparison of experimented and calculated hysteresis loops with force amplitude of 125 N and various frequencies: (<b>a</b>) 3.5 Hz (<b>b</b>) 4.5 Hz; (<b>c</b>) 7.5 Hz; (<b>d</b>) 8.5 Hz.</p>
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16 pages, 5578 KiB  
Article
The Change of Sealing Property in the Aging Process of NBR Sealing Equipment Based on Finite Element Analysis
by Min Zhu, Desheng Ma, Yuan Zhou, Hanyuan Huang, Zhaoqun Shao, Fei Wu and Biao Li
Coatings 2024, 14(9), 1178; https://doi.org/10.3390/coatings14091178 - 12 Sep 2024
Viewed by 281
Abstract
Sealing rings are the core components of flange sealing structures and play a crucial role in the storage and operation of gas generators. The aging and deformation of seals affect the safe operation of the device. This paper aims to investigate the effect [...] Read more.
Sealing rings are the core components of flange sealing structures and play a crucial role in the storage and operation of gas generators. The aging and deformation of seals affect the safe operation of the device. This paper aims to investigate the effect of rubber aging on the sealing performance of the components, which is realized by nonlinear finite element analysis. Firstly, an accelerated degradation test method was used to obtain the compression permanent deformation and stress–strain curve of rubber during the aging process. A two-dimensional finite element model of the sealing structure was constructed and the Yeoh model was utilized to describe the mechanical response of rubber. During the simulation, the contact area was modified based on the compression permanent deformation, and the Yeoh model was updated based on the stress–strain curve changes obtained by the test. The impact of key parameters such as material property changes, rubber physical section deformation, and fluid pressure on sealing performance during the seal ring aging process was systematically studied. The numerical results indicate that due to the aging deformation of rubber seals, there is a significant decrease in contact stress and contact width, as well as a shift in maximum equivalent stress area. Taking into account these findings, this study proposes a new design concept for sealing structures. This provides a relatively simple research method for studying flange sealing structure performance. Full article
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Graphical abstract

Graphical abstract
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<p>Simplified structure of a gas generator.</p>
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<p>High Temperature Aging Chamber and Testing Fixture.</p>
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<p>Sample degradation trajectory and linear fitting. (<b>a</b>) Compress permanent deformation data. (<b>b</b>) Linear fitting results.</p>
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<p>Activation Energy in Different Temperature Ranges.</p>
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<p>Universal testing machine and stress–strain curve.</p>
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<p>Yeoh model parameters of the unaged and aged rubber under compression as functions of aging time.</p>
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<p>Finite element analysis model.</p>
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<p>Changes in physical cross-section with aging time.</p>
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<p>Distribution of contact pressure of sealing ring along contact length under different air pressures. (<b>a</b>) Equivalent aging 3a sealing ring, whether cross-sectional deformation is considered. (<b>b</b>) Equivalent aging 3a sealing ring and non-aging sealing ring, without considering cross-sectional deformation.</p>
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<p>The state of the unaged sealing ring under different gas pressures.</p>
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<p>State of aging 3a sealing ring under different gas pressures.</p>
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<p>Distribution of contact pressure along the contact length of sealing rings with different degrees of aging under gas pressure.</p>
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<p>Distribution of contact pressure along the contact length of the sealing ring before and after optimization under 7 Mpa air pressure.</p>
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10 pages, 1916 KiB  
Article
Adhesion Strength Enhancement of Butyl Rubber and Aluminum Using Nanoscale Self-Assembled Monolayers of Various Silane Coupling Agents for Vibration Damping Plates
by So Rim Lee, Dang Xuan Nghia, Jin Young Oh and Tae Il Lee
Nanomaterials 2024, 14(18), 1480; https://doi.org/10.3390/nano14181480 - 11 Sep 2024
Viewed by 279
Abstract
In this paper, we enhance the adhesion strength of butyl rubber-based vibrational damping plates using nanoscale self-assembled monolayers of various silane coupling agents. The silane coupling agents used to chemically modify the plate’s aluminum surface include 3-aminopropyltriethoxysilane (APTES), (3-glycidyloxypropyl) triethoxysilane (GPTES), 3-mercaptopropyltrimethoxysilane (MPTMS), [...] Read more.
In this paper, we enhance the adhesion strength of butyl rubber-based vibrational damping plates using nanoscale self-assembled monolayers of various silane coupling agents. The silane coupling agents used to chemically modify the plate’s aluminum surface include 3-aminopropyltriethoxysilane (APTES), (3-glycidyloxypropyl) triethoxysilane (GPTES), 3-mercaptopropyltrimethoxysilane (MPTMS), and 3-(triethoxysilyl)propyl isocyanate (ICPTES). The modified surfaces were analyzed using Fourier transform infrared spectroscopy (FT-IR) and X-ray photoelectron spectroscopy (XPS), and the enhancement in adhesion strength between the rubber and aluminum was estimated through T-Peel tests. As a result, MPTMS showed the highest enhancement in adhesion strength, of approximately 220% compared to the untreated sample, while GPTES, ICPTES, and APTES resulted in adhesion strength enhancements of approximately 200%, 150%, and 130%, respectively. Full article
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<p>Water contact angle of untreated, NaOH-treated, APTES-treated, GPTES-treated, MPTMS-treated, and ICPTES-treated aluminum surfaces.</p>
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<p>FT-IR spectra of (<b>a</b>) APTES-treated, (<b>b</b>) GPTES-treated, (<b>c</b>) MPTMS-treated, and (<b>d</b>) ICPTES-treated aluminum surfaces.</p>
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<p>XPS spectra of the untreated, NaOH-treated, APTES-treated, GPTES-treated, MPTMS-treated, and ICPTES-treated aluminum plates.</p>
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<p>High-resolution deconvoluted XPS spectra of (<b>a</b>) C1s of untreated Al, (<b>b</b>) N1s of APTES, (<b>c</b>) C1s of GPTES, (<b>d</b>) S2p of MPTMS, and (<b>e</b>) N1s of ICPTES.</p>
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<p>Comparison of the peel strength curve of NaOH with the peel strength curves of different types of silanes coupling agents (<b>a</b>) and the average peel strength of each type of silane coupling agent (<b>b</b>).</p>
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<p>A step-by-step illustration of the enhancement of the adhesion force between aluminum and butyl rubber through an (<b>a</b>) APTES treatment, (<b>b</b>) GPTES treatment, (<b>c</b>) MPTMS treatment, and (<b>d</b>) ICPTES treatment.</p>
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11 pages, 3565 KiB  
Article
Integrated Thermomechanical Analysis of Tires and Brakes for Vehicle Dynamics and Safety
by Andrea Stefanelli, Marco Aprea, Fabio Carbone, Fabio Romagnuolo, Pietro Caresia and Raffaele Suero
Vehicles 2024, 6(3), 1637-1647; https://doi.org/10.3390/vehicles6030077 - 9 Sep 2024
Viewed by 502
Abstract
The accurate prediction of tire and brake thermomechanical behavior is crucial for various applications in the automotive industry, including vehicle dynamics analysis, racing performance optimization, and driver assistance system development. The temperature of the brakes plays a crucial role in determining the performance [...] Read more.
The accurate prediction of tire and brake thermomechanical behavior is crucial for various applications in the automotive industry, including vehicle dynamics analysis, racing performance optimization, and driver assistance system development. The temperature of the brakes plays a crucial role in determining the performance of rubber by altering its temperature. This change impacts the rim and the air within the tire, leading to variations in temperature and tire pressure, which consequently affect the vehicle’s overall performance. Traditionally, these components have been modeled separately, neglecting the crucial thermal interaction between them, thereby losing a lot of important information from the outside that influences the tire. This paper presents a novel method that overcomes this limitation by coupling the thermomechanical models of the tire and brake, enabling a more comprehensive understanding of their combined behavior. Therefore, the present work could be an interesting starting point to understand how a control system can be influenced by the thermodynamic of the wheel–brake system. Full article
(This article belongs to the Special Issue Feature Papers on Advanced Vehicle Technologies)
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<p>Integrated platform between the tire and brake thermal model.</p>
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<p>Brake system.</p>
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<p>Acquired temperatures of the disc, brake pad, and brake caliper.</p>
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<p>Thermocouples installed to acquire temperatures of disc and brake pad.</p>
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<p>ToyoR16 Toyo Proxes R888R 195/50 R16 used during the tests.</p>
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<p>Diagram of <math display="inline"><semantics> <mi>μ</mi> </semantics></math> by varying the tire temperature.</p>
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<p>TPMS sensor to measure pressure and temperature inside the tire.</p>
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<p>Comparison between the simulated and acquired pressure.</p>
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<p>Comparison between simulated and acquired surface (<b>a</b>) and inner liner (<b>b</b>) temperatures.</p>
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25 pages, 5177 KiB  
Article
From Waste to Styrene–Butadiene (SBR) Reuse: Developing PP/SBR/SEP Mixtures with Carbon Nanotubes for Antistatic Application
by Edson Duarte de Melo Sobrinho, Eduardo da Silva Barbosa Ferreira, Flávio Urbano da Silva, Elieber Barros Bezerra, Renate Maria Ramos Wellen, Edcleide Maria Araújo and Carlos Bruno Barreto Luna
Polymers 2024, 16(17), 2542; https://doi.org/10.3390/polym16172542 - 8 Sep 2024
Viewed by 486
Abstract
Styrene–butadiene rubber (SBR) waste from the shoe industry was repurposed to produce polypropylene (PP)-based compounds, with the aim of evaluating their antistatic potential. Styrene–ethylene–propylene (SEP) was added as a compatibilizing agent, while carbon nanotubes (MWCNT) were incorporated as a conductive nanofiller. The polymer [...] Read more.
Styrene–butadiene rubber (SBR) waste from the shoe industry was repurposed to produce polypropylene (PP)-based compounds, with the aim of evaluating their antistatic potential. Styrene–ethylene–propylene (SEP) was added as a compatibilizing agent, while carbon nanotubes (MWCNT) were incorporated as a conductive nanofiller. The polymer compounds were processed in an internal mixer, and injection molded. The properties evaluated included torque rheometry, melt flow index (MFI), impact strength, tensile strength, Shore D hardness, electrical conductivity, heat deflection temperature (HDT), and differential scanning calorimetry (DSC), along with scanning electron microscopy (SEM) for morphology analysis. The production of the PP/SBR/SEP (60/30/10 wt%) compound resulted in a ductile material, enhancing impact strength and elongation at break to 161.2% and 165.2%, respectively, compared to pure PP. The addition of SEP improved the compatibility of the PP/SBR system, leading to an increase in the torque curve and a reduction in the MFI. Furthermore, the SBR/SEP combination in PP accelerated the crystallization process and increased the degree of crystallinity, suggesting a nucleating effect. Carbon nanotubes, in concentrations ranging from 0.5 to 2 phr (parts per hundred resin), were added to the PP/SBR/SEP system. Only the PP/SBR/SEP/MWCNT compound with 2 phr of MWCNT was suitable for antistatic applications, exhibiting an electrical conductivity of 4.52 × 10−07 S/cm. This was due to the greater distribution of MWCNT in the PP matrix, as demonstrated by SEM. In addition, remains tough at room temperature, with a 166% increase in impact strength compared to PP. However, there was a reduction in elastic modulus, tensile strength, Shore D hardness, and HDT due to increased flexibility. SBR waste can be reintegrated into the production chain to produce antistatic polymeric compounds, obtaining a tough material at room temperature. Full article
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<p>Spectrum of SBR powder from the shoe industry.</p>
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<p>Morphology obtained by SEM of SBR powder, with magnifications of 250× and 500×.</p>
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<p>Thermogravimetric (TG) behavior of SBR powder.</p>
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<p>Torque rheometry curves for pure PP, PP/SEP, PP/SBR, and PP/SBR/SEP compounds, as a function of MWCNT content.</p>
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<p>Melt flow index (MFI) for pure PP and polymeric compounds, with different MWCNT contents.</p>
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<p>Morphology obtained by SEM, for (<b>a</b>) pure PP; (<b>b</b>) PP/SEP; (<b>c</b>) PP/SBR; (<b>d</b>) PP/SBR/SEP.</p>
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<p>Morphology obtained by SEM, for (<b>a</b>) pure PP; (<b>b</b>) PP/SEP; (<b>c</b>) PP/SBR; (<b>d</b>) PP/SBR/SEP.</p>
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<p>Evolution of the morphology by SEM, for (<b>a</b>) PP/SBR/SEP; (<b>b</b>) PP/SBR/SEP/MWCNT (0.5 phr); (<b>c</b>) PP/SBR/SEP/MWCNT (1.0 phr); (<b>d</b>) PP/SBR/SEP/MWCNT (1.5 phr); (<b>e</b>) PP/SBR/SEP/MWCNT (2.0 phr).</p>
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<p>Evolution of the morphology by SEM, for (<b>a</b>) PP/SBR/SEP; (<b>b</b>) PP/SBR/SEP/MWCNT (0.5 phr); (<b>c</b>) PP/SBR/SEP/MWCNT (1.0 phr); (<b>d</b>) PP/SBR/SEP/MWCNT (1.5 phr); (<b>e</b>) PP/SBR/SEP/MWCNT (2.0 phr).</p>
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<p>Impact strength for pure PP and polymeric compounds, with and without carbon nanotubes.</p>
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<p>Mechanical properties under tensile for (<b>a</b>) elastic modulus; (<b>b</b>) tensile strength; (<b>c</b>) elongation at break.</p>
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<p>Shore D hardness for pure PP and polymeric compounds, as a function of MWCNT content.</p>
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<p>HDT results for pure PP and polymer compounds with different MWCNT contents.</p>
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<p>Curves obtained by DSC for pure PP, PP/SEP, PP/SBR, and composites compatibilized with and without carbon nanotubes, for (<b>a</b>) crystalline melting temperature; (<b>b</b>) crystallization temperature.</p>
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15 pages, 4784 KiB  
Article
Effect of Interface Defects on the Electric–Thermal–Stress Coupling Field Distribution of Cable Accessory Insulation
by Xu Lu, Ran Hu, Kongying Guo, Rui Lan, Jie Tian, Yanhui Wei and Guochang Li
Energies 2024, 17(17), 4498; https://doi.org/10.3390/en17174498 - 8 Sep 2024
Viewed by 332
Abstract
The combined insulation interface of a high-voltage cable and accessories is the weakest part of a cable system. In this paper, the parameters of the dielectric constant, thermal conductivity, and elastic modulus of cross-linked polyethylene (XLPE) and silicone rubber (SIR) are obtained experimentally. [...] Read more.
The combined insulation interface of a high-voltage cable and accessories is the weakest part of a cable system. In this paper, the parameters of the dielectric constant, thermal conductivity, and elastic modulus of cross-linked polyethylene (XLPE) and silicone rubber (SIR) are obtained experimentally. On this basis, the model of a specific type of 110 kV cable and prefabricated insulation joint is established. A simulation of the electric–thermal–stress coupling field in the presence of typical defects in the main insulation–inner semi-conductive (SEMI) shielding layer (XLPE/SEMI interface) and the main insulation–silicone rubber insulation layer (XLPE/SIR interface) is studied. The simulation results show that at the XLPE/SIR interface, the electric field distortion caused by bubble defects reached 20.17 kV/mm, and the temperature rose to 56.15 °C. The effect of air-gap defects on the interface is similar to that of bubble defects. In addition, the semi-conductive impurity defects induced an increase in temperature to 56.82 °C and an increase in stress to 0.32 MPa. At the XLPE/SEMI interface, the electric field distortion induced by bubble defects was 19.98 kV/mm, and the temperature rose to 61.72 °C. The electric field distortion caused by metallic and semi-conductive defects was 8.44 kV/mm and 8.64 kV/mm, respectively. This study serves as a reference for the fault analysis and the operation and maintenance of cable accessories. Full article
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<p>View of cross section of the cable.</p>
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<p>Diagrams of defects at the interfaces of cables and accessories: (<b>a</b>) the defects at the XLPE/SIR interface; (<b>b</b>) the defects at the XLPE/SEMI interface.</p>
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<p>Schematic diagram of the test devices: (<b>a</b>) dielectric property testing; (<b>b</b>) thermal conductivity testing; (<b>c</b>) mechanical property testing.</p>
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<p>Potential and electric field distribution of cables and accessories without defects: (<b>a</b>) potential; (<b>b</b>) electric field; (<b>c</b>) radial electric field.</p>
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<p>Electric field distribution caused by defects in the XLPE/SIR interface: (<b>a</b>) void defects at the interface; (<b>b</b>) air-gap defects at the interface; (<b>c</b>) impurity defects at the interface.</p>
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<p>Electric field distribution at the XLPE/SIR insulation interface caused by defects.</p>
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<p>Electric field distribution caused by defects in the XLPE/SEMI interface: (<b>a</b>) void defects at the interface; (<b>b</b>) impurity defects at the interface.</p>
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<p>Electric field distribution at the XLPE/SEMI interface caused by defects.</p>
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<p>Temperature field distribution of the cables and accessories: (<b>a</b>) temperature field distribution of cables and accessories after 36 h; (<b>b</b>) the temperature field of XLPE/SIR insulation interface changes with time.</p>
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<p>Temperature field distribution at the XLPE/SIR interface caused by defects.</p>
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<p>Temperature field distribution at the XLPE/SEMI interface caused by defects.</p>
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<p>Stress field distribution of cables and accessories.</p>
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<p>Stress field distribution caused by defects in the XLPE/SIR interface: (<b>a</b>) void defects at the interface; (<b>b</b>) air-gap defects at the interface; (<b>c</b>) impurity defects at the interface.</p>
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<p>Stress field distribution at the XLPE/SIR interface caused by defects.</p>
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24 pages, 8406 KiB  
Article
Flexural Behavior of Precast Rectangular Reinforced Concrete Beams with Intermediate Connection Filled with High-Performance Concrete
by Ahmed Hamoda, Mohamed Emara, Mizan Ahmed, Aref A. Abadel and Vipulkumar Ishvarbhai Patel
Buildings 2024, 14(9), 2823; https://doi.org/10.3390/buildings14092823 - 7 Sep 2024
Viewed by 521
Abstract
Precast rectangular reinforced concrete (PRRC) beams are joined on construction sites using concrete in situ to achieve the desired length. Limited research exists on the effect of intermediate connection shapes and the types of infilled concrete on the flexural performance of PRRC beams. [...] Read more.
Precast rectangular reinforced concrete (PRRC) beams are joined on construction sites using concrete in situ to achieve the desired length. Limited research exists on the effect of intermediate connection shapes and the types of infilled concrete on the flexural performance of PRRC beams. This paper presents a comprehensive experimental and numerical investigation into the performance of PRRC beams with various intermediate connection geometries and infilled materials under flexural loading. The study examines rectangular, triangular, and semi-circular intermediate connections, along with the performance of beams infilled with normal concrete (NC), engineered cementitious composites (ECC), ultra-high-performance ECC (UHPECC), and rubberized ECC (RECC). The experimental results indicate that the rectangular intermediate connection exhibits superior performance in terms of strength and energy absorption compared to the triangular and semi-circular shapes. Beams incorporating UHPECC demonstrated the most significant improvements in strength and energy absorption, outperforming those with ECC and RECC for any shape of intermediate connection. Moreover, beams with rectangular connections and UHPECC infill exhibited the most significant increase in energy absorption and ultimate load compared to the beams with ECC and RECC. The ultimate load of the beams with UHPECC and tensile reinforcement bar diameters of 10 mm and 12 mm increased by 13% and 29%, respectively, compared to the control beam. The energy absorption of the beams with tensile reinforcement bar diameters of 10 and 12 mm was found to be 75% and 184% higher, respectively, than the control beam. In addition, an increase in tensile bar diameter was found to enhance both the energy absorption and the ultimate load capacity of the beams, regardless of the type of infill concrete. Beams incorporating UHPECC demonstrated the most significant improvements in strength and energy absorption, outperforming those with ECC and RECC. In particular, beams with rectangular connections and UHPECC infill exhibited an increase in energy absorption and ultimate load of up to 184% and 29%, respectively. UHPC was calculated to be as high as 184%, and 29%, respectively, compared to the control beams. In addition, an increase in tensile bar diameter was found to enhance both energy absorption and ultimate load capacity. Finite element modeling (FEM) was developed and validated against the experimental results to ensure accuracy. A parametric study was conducted to study the effects of various concrete types in triangular and semi-circular connections, as well as the influence of intermediate connection length on semi-circular connections under flexural loads. The findings reveal that increasing the length of intermediate connections increases the ultimate load of the beams. Full article
(This article belongs to the Special Issue Sustainable Development of Concrete and Composite Structures)
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<p>Schematic details of the reinforcement and joint configurations: (<b>a</b>) control specimen (Model A); (<b>b</b>) triangular intermediate connection (Model B); (<b>c</b>) rectangular intermediate connection (Model C); and (<b>d</b>) semi-circular intermediate connection (Model D).</p>
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<p>Stress–strain relationships of (<b>a</b>) reinforcement bars; (<b>b</b>) NC; (<b>c</b>) the tensile behavior of UHP-ECC; (<b>d</b>) the compression behavior of UHPECC; (<b>e</b>) the tensile behavior of ECC; and (<b>f</b>) the compression behavior of ECC.</p>
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<p>Stress–strain relationships of (<b>a</b>) reinforcement bars; (<b>b</b>) NC; (<b>c</b>) the tensile behavior of UHP-ECC; (<b>d</b>) the compression behavior of UHPECC; (<b>e</b>) the tensile behavior of ECC; and (<b>f</b>) the compression behavior of ECC.</p>
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<p>Constructing the intermediate connections: (<b>a</b>) forming the intermediate connections; (<b>b</b>) flowable UHPECC; (<b>c</b>) flowable ECC; (<b>d</b>) flowable rubberized ECC; and (<b>e</b>) casting the intermediate connections.</p>
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<p>Test setup and instrumentation.</p>
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<p>Failure modes of the beams of the first group, G-N: (<b>a</b>) beam B0; (<b>b</b>) beam N-tr; (<b>c</b>) N-rec; and (<b>d</b>) N-cr.</p>
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<p>The failure mode of beams of Group G-U (<b>a</b>) beam U-10; (<b>b</b>) beam U-12.</p>
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<p>Failure mode of the beams of Group G-E: (<b>a</b>) beam U-10; (<b>b</b>) beam U-12.</p>
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<p>The failure mode of beams of Group G-RE: (<b>a</b>) beam R-10; (<b>b</b>) beam R-12; and (<b>c</b>) beam R-16.</p>
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<p>Load-mid-span deflection: (<b>a</b>) Group G-N; (<b>b</b>) Group G-U; (<b>c</b>) Group G-E; and (<b>d</b>) Group G-RE.</p>
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<p>The energy absorption capacity of the tested beams.</p>
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<p>The elastic stiffness of the tested beams.</p>
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<p>The 3D finite element model: (<b>a</b>) control beam (Model A), (<b>b</b>) Model B, (<b>c</b>) Model C, and (<b>d</b>) Model D.</p>
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<p>The 3D finite element model: (<b>a</b>) control beam (Model A), (<b>b</b>) Model B, (<b>c</b>) Model C, and (<b>d</b>) Model D.</p>
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<p>Effects of mesh size on the accuracy of the load-deflection curves.</p>
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<p>Experimental observation vs. the FEM load mid-span deflection predictions of (<b>a</b>) Group GN; (<b>b</b>) Group GU; (<b>c</b>) Group GE; and (<b>d</b>) Group RECC.</p>
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<p>Experimental observation vs. the FEM failure modes predictions of (<b>a</b>) beam B0; (<b>b</b>) beam N-tr; (<b>c</b>) beam N-cr; and (<b>d</b>) beam E-10.</p>
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<p>Experimental observation vs. the FEM failure modes predictions of (<b>a</b>) beam B0; (<b>b</b>) beam N-tr; (<b>c</b>) beam N-cr; and (<b>d</b>) beam E-10.</p>
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<p>Effect of the strengthening configuration on the ultimate capacity.</p>
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<p>Effect of the circular configuration length on the ultimate capacity.</p>
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19 pages, 6954 KiB  
Article
Prediction Accuracy of Hyperelastic Material Models for Rubber Bumper under Compressive Load
by Dávid Huri
Polymers 2024, 16(17), 2534; https://doi.org/10.3390/polym16172534 - 7 Sep 2024
Viewed by 371
Abstract
Different hyperelastic material models (Mooney-Rivlin, Yeoh, Gent, Arruda-Boyce and Ogden) are able to estimate Treloar’s test data series containing uniaxial and biaxial tension and pure shear stress-strain characteristics of rubber. If the rubber behaviour is only determined for the specific load of the [...] Read more.
Different hyperelastic material models (Mooney-Rivlin, Yeoh, Gent, Arruda-Boyce and Ogden) are able to estimate Treloar’s test data series containing uniaxial and biaxial tension and pure shear stress-strain characteristics of rubber. If the rubber behaviour is only determined for the specific load of the product, which, in the case of rubber bumpers, is the compression, the time needed for the laboratory test can be significantly decreased. The stress-strain characteristics of the uniaxial compression test of rubber samples were used to fit hyperelastic material models. Laboratory and numerical tests of a rubber bumper with a given compound and complex geometry were used to determine the accuracy of the material models. Designing rubber products requires special consideration of the numerical discretization process due to the nonlinear behaviours (material nonlinearity, large deformation, connections, etc.). Modelling considerations were presented for the finite element analysis of the rubber bumper. The results showed that if only uniaxial compression test data are available for the curve fitting of the material model, the Yeoh model performs the best in predicting the rubber product material response under compressive load and complex strain state. Full article
(This article belongs to the Special Issue Mechanical Behaviors and Properties of Polymer Materials)
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<p>Uniaxial compression test setup and the measured characteristics of the rubber bumper.</p>
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<p>The sampled specimens and their location within the rubber product.</p>
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<p>Uniaxial compression test setup and the deformation state of the specimen under maximum load.</p>
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<p>The engineering and true σ-ε characteristics under uniaxial compression test for specimen number 1.</p>
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<p>The average engineering σ-ε characteristic under uniaxial compression test for the four rubber specimens.</p>
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<p>The process of curve-fitting method to find the hyperelastic material parameters.</p>
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<p>The 2D axisymmetric discretized model of the compression specimen indicating the boundary conditions (prescribed displacement <span class="html-italic">UY</span> in direction −<span class="html-italic">y</span>, roller support <span class="html-italic">TY</span>) and the post-processed deformation state under 45% prescribed compressive load with the distribution of the stress biaxiality in the contour plot.</p>
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<p>Comparison of the different hyperelastic models’ prediction with the laboratory test results of the average engineering σ-ε characteristic.</p>
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<p>The variation in the relative error of the different hyperelastic models compared to the average σ-ε characteristic measured on the specimens.</p>
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<p>The mean relative absolute error of the hyperelastic model prediction capability relative to the average σ-ε characteristic.</p>
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<p>Geometric dimensions and the meridian section of the compression platens and the rubber product.</p>
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<p>The 2D axisymmetric discretized model of the rubber bumper indicating the boundary conditions and contact regions and the post-processed deformation state under 30% prescribed compressive load with the distribution of the stress biaxiality in the contour plot.</p>
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<p>The laboratory and the numerical test results of the rubber bumper working characteristic.</p>
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<p>The variation in the relative error of the different hyperelastic models compared to the characteristic measured on the rubber bumper.</p>
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<p>The mean relative absolute error of the hyperelastic models compared to the characteristic of the rubber product.</p>
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<p>The sensitivity of the compressive force to changes in mesh density.</p>
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16 pages, 4433 KiB  
Article
Construction of Prediction Models of Mass Ablation Rate for Silicone Rubber-Based Flexible Ablative Composites Based on a Small Dataset
by Wenxing Chen, Chuxiang Zhou, Hao Zhang, Liwei Yan, Shengtai Zhou, Yang Chen, Zhengguang Heng, Huawei Zou and Mei Liang
Appl. Sci. 2024, 14(17), 8007; https://doi.org/10.3390/app14178007 - 7 Sep 2024
Viewed by 409
Abstract
The prediction of the ablation rate of silicone rubber-based composites is of great significance to accelerate the development of flexible thermal protection materials. Herein, a method which combines uniform design experimentation, active learning, and virtual sample generation was proposed to establish a prediction [...] Read more.
The prediction of the ablation rate of silicone rubber-based composites is of great significance to accelerate the development of flexible thermal protection materials. Herein, a method which combines uniform design experimentation, active learning, and virtual sample generation was proposed to establish a prediction model of the mass ablation rate based on a small dataset. Briefly, a small number of sample points were collected using uniform design experimentation, which were marked to construct the initial dataset and primitive model. Then, data points were acquired from the sample pool and iterated using various integrated algorithms through active learning to update the above dataset and model. Finally, a large number of virtual samples were generated based on the optimal model, and a further optimized prediction model was achieved. The results showed that after introducing 300 virtual samples, the average percentage error of the gradient boosting decision tree (GBDT) prediction model on the test set decreased to 3.1%, which demonstrates the effectiveness of the proposed method in building prediction models based on a small dataset. Full article
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<p>Scanning electron microscopy (SEM) images of fillers. (<b>a</b>) CF; (<b>b</b>) SiC; and (<b>c</b>) SiO<sub>2</sub>.</p>
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<p>Flow chart of the preparation and ablation of silicone rubber composites and the surface morphology of samples: (<b>a</b>) sample preparation and ablation: the ten samples are obtained from the results of validation experiments for uniform design and experiments on pure exploitation routes and serve as a test set outside of the training set at each stage, which can play a role in model performance validation; (<b>b</b>) the 4 MW/m<sup>2</sup> oxyacetylene flame; (<b>c</b>) the ablation process; (<b>d</b>) the original sample; (<b>e</b>) the top view of the ablated sample; and (<b>f</b>) the cross-section of the ablated sample.</p>
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<p>Pool-based active learning.</p>
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<p>The expansion of features and targets based on mega-trend diffusion: (<b>a</b>) SiO<sub>2</sub>; (<b>b</b>) CF; (<b>c</b>) SiC; and (<b>d</b>) mass ablation rate.</p>
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<p>(<b>a</b>) Effect of filler on mass ablation rate obtained by analyzing the results of homogeneous experiments; (<b>b</b>) fitting performance of different algorithms on the initial training set; and (<b>c</b>) composition of the initial dataset and test set: the initial dataset is the result of the uniform design experiments, and the test set consists of the results of the validation experiments for uniform design and the pure exploitation experiments.</p>
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<p>Error of models based on the initial ablation dataset.</p>
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<p>MAPE of test set of various models at each round.</p>
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<p>(<b>a</b>,<b>b</b>) SHAP-based analysis of the importance of sample features; and (<b>c</b>) predicted mass ablation rate for all sample points in feature space.</p>
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<p>(<b>a</b>) MAPE of the test set for the GBDT model under exploration route, (<b>b</b>) MAPE of the test set for the RF model under exploration route, (<b>c</b>) MAPE of the test set for the AdaBoost model under exploration route, (<b>d</b>) MAPE of the test set for the XGB model under exploration route, (<b>e</b>) MAPE of the test set for the GBDT model under EI route, (<b>f</b>) MAPE of the test set for the RF model under EI route, (<b>g</b>) MAPE of the test set for the AdaBoost model under EI route, and (<b>h</b>) MAPE of the test set for the XGB model under EI route.</p>
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