International Journal of Fracture最新文献

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Finite element simulation of rate-dependent damage in elastomers 弹性体速率相关损伤的有限元模拟
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-13 DOI: 10.1007/s10704-024-00818-y
Pinyi Wang, Shawn R. Lavoie, Tian Tang
{"title":"Finite element simulation of rate-dependent damage in elastomers","authors":"Pinyi Wang,&nbsp;Shawn R. Lavoie,&nbsp;Tian Tang","doi":"10.1007/s10704-024-00818-y","DOIUrl":"10.1007/s10704-024-00818-y","url":null,"abstract":"<div><p>Predicting the mechanical response and damage evolution of elastomers under large deformation is of great significance in engineering applications. In this work, a finite element (FE) scheme is formulated and used to simulate rate-dependent damage in elastomers. While based on the theoretical model of Lavoie et al. (Extrem Mech Lett 8:114–124, 2016) and maintaining the key features such as kinetics of chain scission and polydispersity, the FE scheme presented here includes the consideration of finite compressibility. Both implicit and explicit algorithms are derived and implemented as user subroutines in ABAQUS. Validated against existing numerical results as well as experimental data on homogeneous deformation, the capability of the FE scheme to solve problems involving inhomogeneous deformation is further explored by simulating samples with pre-existing defects. The numerical results can successfully capture several interesting phenomena, such as crack blunting, stress reduction near defect caused by damage, and rate-dependent damage evolution. Good agreement is also found with experimental data on the strain field near a crack tip.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interfacial cavitation during peeling of soft viscoelastic adhesives 软粘弹性胶粘剂剥离过程中的界面空化
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-12 DOI: 10.1007/s10704-024-00834-y
Xingwei Yang, Huiqi Shi, Yuan Qi, Rong Long
{"title":"Interfacial cavitation during peeling of soft viscoelastic adhesives","authors":"Xingwei Yang,&nbsp;Huiqi Shi,&nbsp;Yuan Qi,&nbsp;Rong Long","doi":"10.1007/s10704-024-00834-y","DOIUrl":"10.1007/s10704-024-00834-y","url":null,"abstract":"<div><p>Peel tests are commonly used to characterize the performance of adhesive tapes. The force required to peel a tape from a substrate depends on not only interface adhesion but also mechanics of the tape. Typically, adhesive tapes consist of a stiff backing film and a layer of adhesive material that is soft and viscoelastic. While mechanics of the backing film has been extensively studied, mechanics of the soft adhesive layer is less understood. In this work, finite element simulations are carried out to study large deformation of the soft adhesive layer during 90-degree peeling and its implication on the peel force. We find that debonding can occur ahead of the peel front when the peel front is still adhered to the substrate. This phenomenon, referred to as “interfacial cavitation”, causes the peel front to advance in a stepwise manner despite that a constant peeling velocity is prescribed. Consequently, the peel force follows an oscillatory history resembling the “stick–slip” behavior widely observed in peel tests. Further investigations reveal that interfacial cavitation originates from a non-monotonic distribution of interfacial traction ahead of the peel front. Moreover, emergence of interfacial cavitation can be controlled by three factors: interfacial slip, adhesive layer thickness and peeling velocity. These results can provide insights towards designing adhesive tapes with desired adhesion performance or release mechanisms.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effect of notch root radius on apparent fracture toughness of Ti6Al4V alloy: experiments and simulations 缺口根半径对Ti6Al4V合金表观断裂韧性的影响:实验与模拟
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-11 DOI: 10.1007/s10704-024-00838-8
Akash Kumar, Jyoti S. Jha, Sushil K. Mishra, Parag Tandaiya
{"title":"Effect of notch root radius on apparent fracture toughness of Ti6Al4V alloy: experiments and simulations","authors":"Akash Kumar,&nbsp;Jyoti S. Jha,&nbsp;Sushil K. Mishra,&nbsp;Parag Tandaiya","doi":"10.1007/s10704-024-00838-8","DOIUrl":"10.1007/s10704-024-00838-8","url":null,"abstract":"<div><p>Ti6Al4V is a widely used titanium alloy known for its excellent combination of mechanical properties, corrosion resistance, and biocompatibility. However, to ensure its effectiveness in various applications, it is important to understand the mechanical and fracture behavior of the alloy in the presence of a notch. In the present study, the effect of notch root radius on mode I fracture toughness of Ti6Al4V alloys with a nearly bimodal microstructure has been investigated. Fracture toughness tests were conducted on compact tension (CT) specimens with five different notch root radii. The experimental results demonstrate that the apparent fracture toughness, <span>(K_{IA})</span>, increases linearly with the square root of the notch root radius. Further to elucidate the results, a 2D elastoplastic finite element analysis is performed on the CT specimens using cohesive zone model. The simulation results are in good agreement with the experimental data. The study also reveals that the apparent fracture toughness is independent of the notch root radius below a critical value, estimated to be approximately <span>(50 mu m)</span>. Finally, the scanning electron microscopy of the fracture surfaces has been examined. The micrographs reveal void coalescence and dimple regions indicating the ductile nature of the fracture process.\u0000</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142940956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Incremental closure method to estimate changes in contact stress distributions for partially closed fatigue cracks in mode I loading 估算I型加载条件下部分闭合疲劳裂纹接触应力分布变化的增量闭合法
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-11 DOI: 10.1007/s10704-024-00833-z
Henry H. M. Moldenhauer, Stephen D. Holland, Ashraf Bastawros
{"title":"Incremental closure method to estimate changes in contact stress distributions for partially closed fatigue cracks in mode I loading","authors":"Henry H. M. Moldenhauer,&nbsp;Stephen D. Holland,&nbsp;Ashraf Bastawros","doi":"10.1007/s10704-024-00833-z","DOIUrl":"10.1007/s10704-024-00833-z","url":null,"abstract":"<div><p>Crack closure is the phenomenon of fatigue cracks experiencing compressive contact stresses between crack faces, even under no remote load. Applied remote loads alter the distribution of contact stresses and opening displacements along the crack plane. A nondestructive evaluation technique, vibrothermography, motivated calculating these distributions as a function of remote load, to model crack motion during the vibrothermographic process. The proposed incremental closure method estimates such distributions using a two-stage superposition of crack tip solutions. The first, superimposes a continuum of crack tip solutions over a short, explicit peeling increment at the effective crack tip. The second, superimposes these increments over a range of effective crack tip positions. This approach provides a fast, straightforward way to characterize the peeling open of partially closed cracks. This method can be applied inversely to determine the preexisting closure state. Predictions from this method compare well with finite element simulations of the crack peeling process.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Assessing complex protein-solvent interactions using environment-controlled crack-growth experiments 利用环境控制的裂纹生长实验评估复杂的蛋白质-溶剂相互作用
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-10 DOI: 10.1007/s10704-024-00826-y
Tristan Baumberger, Olivier Ronsin
{"title":"Assessing complex protein-solvent interactions using environment-controlled crack-growth experiments","authors":"Tristan Baumberger,&nbsp;Olivier Ronsin","doi":"10.1007/s10704-024-00826-y","DOIUrl":"10.1007/s10704-024-00826-y","url":null,"abstract":"<div><p>The modulation of protein functionality, i.e. their ability to fold/unfold, by adding low molecular weight substances to the “natural” solvent water is an important issue in biochemistry. Taking advantage of the unique ability of gelatin to self assemble into elastic networks via partial renaturation of the native collagen protein, we propose to recast the issue into a fracture mechanics one. We describe a method to decipher the effect of alcohols as cosolvents on gelatin networks from the shift of fracture energy in response to an environmental shock. After suitable subtraction of the viscous dissipation we are able characterize the solvent/network interaction by the relative shift of the free energy characteristic of the crosslinked<span>(rightarrow )</span>dismanteled transition of the network associated to its fracture. Using two alcohols, methanol and glycerol, we show that our method is able to accounts for their known contrasting effects on proteins. We briefly discuss the nature of the energy of interaction. In addition we unveil an open issue regarding the origin and consequence of the poroelastic solvent flow associated to crack propagation in hydrogels.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142941172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Morphology of fracture profiles and toughness: competition between inter and transgranular fracture in two dimensional brittle solids 断口形貌与韧性:二维脆性固体中晶间断裂与穿晶断裂的竞争
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-09 DOI: 10.1007/s10704-024-00825-z
Retam Paul, Venkitanarayanan Parameswaran, Sumit Basu
{"title":"Morphology of fracture profiles and toughness: competition between inter and transgranular fracture in two dimensional brittle solids","authors":"Retam Paul,&nbsp;Venkitanarayanan Parameswaran,&nbsp;Sumit Basu","doi":"10.1007/s10704-024-00825-z","DOIUrl":"10.1007/s10704-024-00825-z","url":null,"abstract":"<div><p>Two dimensional intergranular brittle cracks propagating through a microstructured material produce fracture profiles which, at scales larger than the microstructural length scale, are anti-persistent and close to directed random walks with Hurst exponent <span>(sim 0.5)</span>. The extent of intergranularity is controlled by the ratio of the toughness of the grain boundaries to that of the grain interior. However, experiments suggest [e.g. Ponson et al. (Phys Rev Lett 97(12), 2006)] that even when transgranular crack propagation is possible, the fracture profile is still close to a random walk. In this work, generating fracture profiles in a material with an idealised honeycomb microstructure using a phase field based model of crack propagation, we show that the competition between inter and transgranular fracture manifests in a manner that is more nuanced than what the experiments suggest. While the fracture profile is indeed always anti-persistent, transgranularity resulting from toughening the grains leads to profiles that can have roughness exponents much lower than 0.5. Moreover, in such cases, the overall toughness of the specimen scales with the Hurst exponent. On the other hand, transgranularity resulting from weakening the grain boundaries, without changing the toughness of the grain interior, always lead to fracture profiles close to the random walk.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effects of laminar structure on fracture propagation and proppant transportation in continental shale oil reservoirs with multiple lithological-combination 层流结构对多岩性组合陆相页岩油藏裂缝扩展及支撑剂运移的影响
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-08 DOI: 10.1007/s10704-024-00831-1
Xiaohuan Zhang, Shicheng Zhang, Yushi Zou, Jianmin Li
{"title":"Effects of laminar structure on fracture propagation and proppant transportation in continental shale oil reservoirs with multiple lithological-combination","authors":"Xiaohuan Zhang,&nbsp;Shicheng Zhang,&nbsp;Yushi Zou,&nbsp;Jianmin Li","doi":"10.1007/s10704-024-00831-1","DOIUrl":"10.1007/s10704-024-00831-1","url":null,"abstract":"<div><p>To understand the effects of laminar structure on fracture propagation and proppant transportation intuitively, an improved true triaxial fracturing device with a proppant pumping unit was used to carry out sand-laden fracturing on shale oil reservoir samples with multiple lithological-combination and different laminar structures. Based on high-precision CT scanning technology and acoustic emission (AE) monitoring technology, the propagation mechanism of hydraulic fractures (HFs) and proppant transportation characteristics were analyzed, and the critical condition for lamina slip was proposed. The results show that laminas with initial width tend to be activated by fracturing fluid, resulting in diversion or offset. Closed laminas tend to be penetrated by HFs and are hardly activated by fracturing fluid. Rock with dense initial width laminas tends to form “#” shaped fractures interwoven with activated laminas and vertical fractures. In contrast, rock with closed laminas tends to form simple fractures dominated by vertical HFs. The width of HFs varies greatly from the perforation layer to the neighboring layer. As the difference in tensile strength between the interlayer and the perforated layer increases, the degree of decline in HF width significantly increases. Intensive AE activity was monitored at the intersection of vertical HFs and activated laminas, indicating that decreased fracture width causes proppants to bridge and block at the diversion and offset. Therefore, most proppants are filled in wide fractures near perforation, blocking the diversion and offset; there is almost no proppant in activated laminas. Reducing proppant diameter is conducive to placing the proppant in the activated laminas and interlayer HFs. Compared with placing 200 mesh and 120/140 mesh with similar fracture morphology samples, the proppant placement volume ratio of 400 mesh proppant placing samples increased by 7%. The findings significantly improve the scheme decision-making and parameter design of fracturing technology for thin interlayered shale oil reservoirs.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cyclic tearing of a woven fabric embedded in a soft matrix 嵌在软基质中的编织织物的循环撕裂
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-08 DOI: 10.1007/s10704-024-00828-w
Jingyuan Tang, Fengkai Liu, Xi Chen, Zhigang Suo, Jingda Tang
{"title":"Cyclic tearing of a woven fabric embedded in a soft matrix","authors":"Jingyuan Tang,&nbsp;Fengkai Liu,&nbsp;Xi Chen,&nbsp;Zhigang Suo,&nbsp;Jingda Tang","doi":"10.1007/s10704-024-00828-w","DOIUrl":"10.1007/s10704-024-00828-w","url":null,"abstract":"<div><p>A composite of a woven fabric embedded in a soft matrix exhibits the attributes of both constituents. The fabric is strong in tension but flexible in bending. The soft matrix impedes fluid penetration. Applications of such composites include tents, rain coats, and wound closure patches. How such a composite tears under cyclic load remains unclear. Here we embed a woven fabric of ultrahigh molecular weight polyethylene in a soft matrix of thermoplastic polyurethane, and tear each specimen of the composite with cyclic energy release rate of a fixed amplitude, <i>G</i>. Two thresholds are identified, <i>G</i><sub><i>a</i></sub> and <i>G</i><sub><i>b</i></sub>. When <i>G</i> &lt; <i>G</i><sub><i>a</i></sub>, the composite does not tear. When <i>G</i><sub><i>a</i></sub> &lt; <i>G</i> &lt; <i>G</i><sub><i>b</i></sub>, the composite tears by yarn slip without yarn break, and then tearing arrests after yarns jam. When <i>G</i><sub><i>b</i></sub> &lt; <i>G</i>, the composite tears, without arrest, by a combination of yarn slip and yarn break. We then prepare a composite with strengthened fabric-matrix interface, and find that <i>G</i><sub><i>a</i></sub> increases but <i>G</i><sub><i>b</i></sub> decreases. We interpret these findings in terms of stress deconcentration along the yarns. It is hoped that this study will aid the development of fatigue-resistant composites.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
V-notch crack initiation by the coupled criterion considering plasticity 考虑塑性的v形缺口裂纹萌生耦合准则
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-06 DOI: 10.1007/s10704-024-00822-2
Aurélien Doitrand, Dominique Leguillon
{"title":"V-notch crack initiation by the coupled criterion considering plasticity","authors":"Aurélien Doitrand,&nbsp;Dominique Leguillon","doi":"10.1007/s10704-024-00822-2","DOIUrl":"10.1007/s10704-024-00822-2","url":null,"abstract":"<div><p>An extension of the coupled criterion (CC) of finite fracture mechanics is proposed in order to assess brittle crack initiation considering plasticity. The main change compared to the classical linear elastic approach consists in considering the plastic strain energy variation due to crack initiation. The proposed approach enables assessing quasi-brittle failure at singularities or stress concentrators in materials exhibiting plastic deformation. It is illustrated on V-notch steel specimens subjected to bending. If plastic deformation is disregarded, the CC underestimates the failure force compared to those measured experimentally. Considering plasticity yields a better representation of failure force variation as a function of the V-notch angle.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142938927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fatigue crack growth rate prediction under single peak overload based on WOA-BP neural network 基于WOA-BP神经网络的单峰过载下疲劳裂纹扩展速率预测
IF 2.2 3区 工程技术
International Journal of Fracture Pub Date : 2025-01-06 DOI: 10.1007/s10704-024-00827-x
Zihe Ye, Haoran Li, Wenqi Li, Yalian Wu, Zhong Xiang
{"title":"Fatigue crack growth rate prediction under single peak overload based on WOA-BP neural network","authors":"Zihe Ye,&nbsp;Haoran Li,&nbsp;Wenqi Li,&nbsp;Yalian Wu,&nbsp;Zhong Xiang","doi":"10.1007/s10704-024-00827-x","DOIUrl":"10.1007/s10704-024-00827-x","url":null,"abstract":"<div><p>This study is aimed at investigating the crack growth behavior of 2A12 aluminum alloy under constant amplitude loads and various single peak overload conditions, with a focus on the effects of different load ratios and overload ratios on the crack growth rate. Due to the complexity and numerous parameters involved in traditional physical models, we proposed a whale optimization algorithm-backpropagation neural network-based model for predicting crack growth rate. By comparing results on datasets of 2A12 aluminum alloy and QSTE340TM steel, including Wheeler, Huang, WOA-SVM, and WOA-RBF models, our study demonstrates that our model achieves higher predictive accuracy. Finally, the paper calculated the crack growth life using the cycle-by-cycle method and conducted a detailed comparison and analysis of the prediction errors of various models. This research holds significant theoretical and practical value for enhancing understanding of material crack behavior and developing more accurate models for predicting crack growth rates.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142938758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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