Fatigue & Fracture of Engineering Materials & Structures最新文献

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Improving Fatigue Life Prediction of Natural Rubber Using a Physics-Informed Neural Network Model
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-12-03 DOI: 10.1111/ffe.14533
Yingshuai Sun, Xiangnan Liu, Qing Yang, Xuelai Liu, Kuanfang He
{"title":"Improving Fatigue Life Prediction of Natural Rubber Using a Physics-Informed Neural Network Model","authors":"Yingshuai Sun,&nbsp;Xiangnan Liu,&nbsp;Qing Yang,&nbsp;Xuelai Liu,&nbsp;Kuanfang He","doi":"10.1111/ffe.14533","DOIUrl":"https://doi.org/10.1111/ffe.14533","url":null,"abstract":"<div>\u0000 \u0000 <p>Traditional physical models and purely data-driven approaches often struggle with small sample sizes and the complex effects of strain ratios. To overcome these challenges, this study integrates physical principles with machine learning techniques to improve fatigue life predictions for natural rubber (NR). A uniaxial fatigue test on NR was performed, generating data to construct a physical model. A physics-informed neural network (PINN) model was subsequently developed, utilizing the fatigue life predicted by the physical model, along with engineering strain amplitude and strain ratio as input variables, whereas the experimentally observed fatigue life served as the output variable. The accuracy of the physical model, a data-driven model, and the proposed PINN model was evaluated by comparing their predictions against measured fatigue life data. The findings demonstrate that the PINN model significantly enhances prediction accuracy, with its fatigue life estimates consistently falling within 1.5 times the measured values.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 3","pages":"1039-1049"},"PeriodicalIF":3.1,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fatigue Characteristics and Mechanisms of Additional Damping Structures With Entangled Metallic Wire Material
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-12-02 DOI: 10.1111/ffe.14519
Yu Tang, Jiasong Liang, Dang Wei, Baoquan Xiong, Zhihui Zhu, Yiwan Wu, Hongbai Bai
{"title":"Fatigue Characteristics and Mechanisms of Additional Damping Structures With Entangled Metallic Wire Material","authors":"Yu Tang,&nbsp;Jiasong Liang,&nbsp;Dang Wei,&nbsp;Baoquan Xiong,&nbsp;Zhihui Zhu,&nbsp;Yiwan Wu,&nbsp;Hongbai Bai","doi":"10.1111/ffe.14519","DOIUrl":"https://doi.org/10.1111/ffe.14519","url":null,"abstract":"<div>\u0000 \u0000 <p>Under vibration conditions, continuous alternating loads cause fatigue damage to structures, affecting their stability, durability, and overall safety. In this paper, the additional damping structures with entangled metallic wire material (EMWM) is proposed. Dynamic tests with different loading frequencies and loading amplitudes are carried out to evaluate the energy dissipation and stiffness characteristics of the different structures in terms of energy dissipation, loss factor, and average stiffness. Fatigue tests are conducted, and the fatigue life tests are applied with different loading amplitudes and loading frequencies using displacement control, and the fatigue properties are obtained under different numbers of cyclic loading. The test results are analyzed with respect to the energy dissipation mechanism of EMWM and the characteristics of the additional damping structure. The hysteresis curves under different loading times are identified by parameters, and the fatigue mechanical models are constructed. Comparison between the predicted data of the model and the hysteresis curve data of the test indicates that the model has high accuracy.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 3","pages":"1022-1038"},"PeriodicalIF":3.1,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Influence of a Sudden Impact Loading on the Creep, Damage, and Fracture of Beams Made From Functionally Graded Materials
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-12-01 DOI: 10.1111/ffe.14528
Dmytro Breslavsky, Pavlo Palamarchuk, Oksana Tatarinova, Holm Altenbach, Francesco Pellicano
{"title":"The Influence of a Sudden Impact Loading on the Creep, Damage, and Fracture of Beams Made From Functionally Graded Materials","authors":"Dmytro Breslavsky,&nbsp;Pavlo Palamarchuk,&nbsp;Oksana Tatarinova,&nbsp;Holm Altenbach,&nbsp;Francesco Pellicano","doi":"10.1111/ffe.14528","DOIUrl":"https://doi.org/10.1111/ffe.14528","url":null,"abstract":"<div>\u0000 \u0000 <p>An approach to the analysis of the influence of impact loading on creep, accumulation of hidden damage and fracture of structural elements made of functionally graded materials (FGM) is proposed. The approach is based on the analysis of additional damage caused by the impact loading and the stress redistribution caused by it. For the numerical modeling, finite element analysis was applied using algorithms for determining the size and direction of motion of macroscopic defects by means of the analysis of the time-varying damage field. The fracture after an impact on a beam made from FGM is considered. The nature of fracture of a beam made of two-layer metal-ceramic material was studied. The advantages of using FGM to ensure a better long-term response of a structural element to a non-destructive impact loading are shown. An approach to determine the time until the complete fracture of the FGM beam by the simultaneous description of the motion of two cracks is proposed.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"931-941"},"PeriodicalIF":3.1,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Study on Structure Optimization and Vibration Fatigue Analysis of Aluminum and Composite Brake Control Boxes
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-26 DOI: 10.1111/ffe.14507
Yiming Shangguan, Wenjing Wang, Anrui He, Yuzhu Wang, Jing Zhu
{"title":"Study on Structure Optimization and Vibration Fatigue Analysis of Aluminum and Composite Brake Control Boxes","authors":"Yiming Shangguan,&nbsp;Wenjing Wang,&nbsp;Anrui He,&nbsp;Yuzhu Wang,&nbsp;Jing Zhu","doi":"10.1111/ffe.14507","DOIUrl":"https://doi.org/10.1111/ffe.14507","url":null,"abstract":"<div>\u0000 \u0000 <p>The brake control box beneath an EMU is exposed to dynamic and fluctuating load cases, increasing its susceptibility to vibration fatigue failure. A novel lightweight design approach was implemented to integrate structural and material optimizations. Static and fatigue tests of the T700/5429 CFRP were carried out to augment the stress analysis and predictions of the vibration fatigue life. The local stresses perpendicular and parallel to the welds were obtained to calculate the stress ratio, stress range, and allowable stress value corresponding to the stress component. The fatigue strength of the aluminum box was estimated on the basis of multiaxial criteria, and the fatigue life of the two boxes was predicted with Dirlik's theory. These computational findings unequivocally indicated a noteworthy reduction in damage to the composite box subsequent to lightweight modification, thereby successfully satisfying both the stiffness and strength criteria essential for the safety and reliability of the EMU.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"914-930"},"PeriodicalIF":3.1,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modeling of Stress–Strain Fields Below U-Notch Root Using Plasticity Approximation Rules Under Variable-Amplitude Loading
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-24 DOI: 10.1111/ffe.14525
Anton Asplund, Heikki Remes, Yuki Ono
{"title":"Modeling of Stress–Strain Fields Below U-Notch Root Using Plasticity Approximation Rules Under Variable-Amplitude Loading","authors":"Anton Asplund,&nbsp;Heikki Remes,&nbsp;Yuki Ono","doi":"10.1111/ffe.14525","DOIUrl":"https://doi.org/10.1111/ffe.14525","url":null,"abstract":"<p>This paper evaluates the applicability of Neuber's and equivalent strain energy density (ESED) rules to predict the material response below the root of a sharp U-notch under variable-amplitude (VA) loading for crack propagation simulations. The Voce–Chaboche (V-C) combined hardening constitutive model, coupled with the above-mentioned approximation rules, is used to resolve the elasto-plastic response over a range of depths below the notch root. The response at each load reversal is extracted, and the maximum and minimum stress and strain quantities are used to evaluate fatigue damage using the Smith–Watson–Topper parameter. Results from approximation rules are compared to finite element method (FEM) at and below the notch root. Prediction accuracy varied at different points below the root depending on the size of the plastic zone, with predictions made using the original Neuber's and ESED rules being less accurate below the root. Applying stress redistribution correction to the stress field improves its accuracy below the root; however, strain values are significantly amplified as a result. A modified Neuber's rule with stress redistribution and constraint corrections predicts the distribution of the material response and fatigue damage with consistent accuracy.</p>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"900-913"},"PeriodicalIF":3.1,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/ffe.14525","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cracking Sensitivity Analysis of Red Clay With Pre-Crack Under Three-Point Bending
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-24 DOI: 10.1111/ffe.14522
Hongyan Ma, Xiaobin Yan, Peiyuan Cheng, Song Xu, Yanping Zhang, Sihan Li
{"title":"Cracking Sensitivity Analysis of Red Clay With Pre-Crack Under Three-Point Bending","authors":"Hongyan Ma,&nbsp;Xiaobin Yan,&nbsp;Peiyuan Cheng,&nbsp;Song Xu,&nbsp;Yanping Zhang,&nbsp;Sihan Li","doi":"10.1111/ffe.14522","DOIUrl":"https://doi.org/10.1111/ffe.14522","url":null,"abstract":"<div>\u0000 \u0000 <p>Red clay is highly susceptible to cracking due to its nature, and the reduction in strength caused by cracking can lead to engineering disasters. To investigate the cracking sensitivity of red clay, a homogeneous fracture model of red clay based on the cohesive zone model was established using ABAQUS in this work, the reliability of the model was verified through a three-point bending test, and then the crack propagation process and sensitivity to test factors of red clay were further analyzed. The results show that the fracture simulation of the cohesive zone model is in good agreement with the test results, confirming by the high reliability. The depth of prefabricated cracks and fulcrum spacing had the significant effects on the crack path, and the decrease of prefabricated crack depth and fulcrum spacing led to the increase of critical load. Meanwhile, the loading rate had little effect on the load–displacement curves.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"885-899"},"PeriodicalIF":3.1,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Experimental Study on Reloading Creep Characteristics of Marble After Unloading–Freezing–Thawing Damage
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-24 DOI: 10.1111/ffe.14523
Lehua Wang, Xiaoping Wang, Xiaoliang Xu, Shifu Qin, Yintao Fu
{"title":"Experimental Study on Reloading Creep Characteristics of Marble After Unloading–Freezing–Thawing Damage","authors":"Lehua Wang,&nbsp;Xiaoping Wang,&nbsp;Xiaoliang Xu,&nbsp;Shifu Qin,&nbsp;Yintao Fu","doi":"10.1111/ffe.14523","DOIUrl":"https://doi.org/10.1111/ffe.14523","url":null,"abstract":"<div>\u0000 \u0000 <p>The reloading characteristics of slope projects such as water conservancy and hydropower in cold regions after excavation and unloading are the key to the long-term stability problem of bank slopes in reservoirs. After pre-peak unloading and freeze–thaw, uniaxial gradient loading creep test was carried out with marble, and the unloading creep mechanical behavior of marble under different temperature ranges and different numbers of freeze–thaw cycles was studied. The results show that the temperature range of freeze–thaw and the number of cycles control the reduction of creep damage stress and long-term strength as well as the increasing trend of creep strain of marble, and the time-mechanical response of unloaded marble under the action of freeze–thaw with large temperature difference is more obvious. Based on the traditional Burgers model, a non-constant Burgers model considering freeze–thaw damage was proposed, and the applicability and rationality of the model were verified.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"871-884"},"PeriodicalIF":3.1,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Application of an Instability-Based Fracture Model for Prediction of Crack Initiation in Modified 9Cr–1Mo Steel
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-23 DOI: 10.1111/ffe.14520
R. Nikhil, S. A. Krishnan, S. M. Keralavarma, A. Moitra, M. Vasudevan
{"title":"Application of an Instability-Based Fracture Model for Prediction of Crack Initiation in Modified 9Cr–1Mo Steel","authors":"R. Nikhil,&nbsp;S. A. Krishnan,&nbsp;S. M. Keralavarma,&nbsp;A. Moitra,&nbsp;M. Vasudevan","doi":"10.1111/ffe.14520","DOIUrl":"https://doi.org/10.1111/ffe.14520","url":null,"abstract":"<p>Ductile fracture of modified 9Cr–1Mo steel was investigated using smooth and notched bar tension tests. Round and flat notched specimens with varying notch acuity ratio were used to investigate the influence of stress state on the fracture strain. Simulations of the experiments were performed using the extended finite element method, together with an instability-based crack initiation criterion based on the micromechanics of void coalescence. The parameters in the plasticity model were determined using smooth bar tension tests, whereas the void nucleation parameters were calibrated from experiments on a shallow-notched specimen. Subsequently, the load–deflection responses and strain to crack initiation have been predicted for round and flat notched specimens with various notch acuities, and central notched specimens with notches oriented at various angles to the loading axis. Using a single set of parameters, the model was able to quantitatively predict fracture in different specimen geometries encompassing a range of stress states.</p>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"857-870"},"PeriodicalIF":3.1,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/ffe.14520","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effect of Surface Finish and Temperature on Low Cycle Fatigue Behavior of GRCop-42
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-21 DOI: 10.1111/ffe.14526
Gabriel Demeneghi, Paul Gradl, Agustin Diaz, Kavan Hazeli
{"title":"Effect of Surface Finish and Temperature on Low Cycle Fatigue Behavior of GRCop-42","authors":"Gabriel Demeneghi,&nbsp;Paul Gradl,&nbsp;Agustin Diaz,&nbsp;Kavan Hazeli","doi":"10.1111/ffe.14526","DOIUrl":"https://doi.org/10.1111/ffe.14526","url":null,"abstract":"<div>\u0000 \u0000 <p>This study investigates the impact of various surface finishes on the low cycle fatigue (LCF) properties of laser powder bed fusion GRCop-42. The evaluated surfaces include as-built, machined, and chemically polished finishes (1.0% and 2.0% ranges). LCF life of polished GRCop-42 was assessed at cryogenic (−195°C), ambient, and elevated temperatures (200°C, 400°C, 600°C, and 800°C) across three strain ranges. Results indicate that surface finish has minimal impact on LCF life. Stress across different strain levels showed minimal effect of surface finish on cyclic hardening/softening. Cryogenic temperatures led to cyclic hardening followed by stabilization, while ambient and 200°C temperatures showed initial hardening followed by softening. At 400°C and above, specimens displayed continuous cyclic softening. Fractography showed that surface finish impacts plastic deformation: as-printed and polished surfaces had brittle fractures, while machined specimens were ductile. Specimens at cryogenic and ambient temperatures exhibited brittle fractures, whereas those at elevated temperatures showed plastic deformation and microcracks.</p>\u0000 </div>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"840-856"},"PeriodicalIF":3.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Experimental and Analytical Investigations of Crack Removal Phenomenon in Highly Deformable Rubbers Weakened by a Crack and Loaded in Mode-I Conditions
IF 3.1 2区 材料科学
Fatigue & Fracture of Engineering Materials & Structures Pub Date : 2024-11-20 DOI: 10.1111/ffe.14510
Mehrdad Enteshari, Mahdi Heydari-Meybodi, Naghdali Choupani, Majid R. Ayatollahi
{"title":"Experimental and Analytical Investigations of Crack Removal Phenomenon in Highly Deformable Rubbers Weakened by a Crack and Loaded in Mode-I Conditions","authors":"Mehrdad Enteshari,&nbsp;Mahdi Heydari-Meybodi,&nbsp;Naghdali Choupani,&nbsp;Majid R. Ayatollahi","doi":"10.1111/ffe.14510","DOIUrl":"https://doi.org/10.1111/ffe.14510","url":null,"abstract":"<p>A physical phenomenon called “crack removal” is investigated for highly deformable rubbery materials containing a pre-existing crack under uniaxial pure mode-I loading. In this case, the stress concentration significantly diminishes and in a specific stage of loading, the specimen behaves as a sample which has no apparent effect from the initial sharp crack and thus nearly undergoes uniaxial state of stress until its final rupture. To explore this phenomenon that has not been previously explored, theoretical and experimental investigations were carried out in the current study. In the experimental part, due to the lack of pertinent experimental data for crack removal phenomenon, a series of mode-I fracture tests were carried out on nitrile butadiene rubber (NBR) containing 15 phr carbon black. In the theoretical part, an energy-based criterion was proposed for detecting the crack removal load and subsequently, for predicting the final rupture load in such materials. For implementation of this criterion, non-linear finite element analyses were performed. The results confirm very good ability of the proposed criterion for predicting the crack removal and final rupture phases in rubber-like materials having high deformability.</p>","PeriodicalId":12298,"journal":{"name":"Fatigue & Fracture of Engineering Materials & Structures","volume":"48 2","pages":"827-839"},"PeriodicalIF":3.1,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/ffe.14510","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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