{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T21:36:53Z","timestamp":1778621813513,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,12,8]],"date-time":"2024-12-08T00:00:00Z","timestamp":1733616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12150001"],"award-info":[{"award-number":["12150001"]}]},{"name":"National Natural Science Foundation of China","award":["12002401"],"award-info":[{"award-number":["12002401"]}]},{"name":"National Natural Science Foundation of China","award":["2023B1212010002"],"award-info":[{"award-number":["2023B1212010002"]}]},{"name":"Guangdong Provincial Key Laboratory of Extreme Conditions","award":["12150001"],"award-info":[{"award-number":["12150001"]}]},{"name":"Guangdong Provincial Key Laboratory of Extreme Conditions","award":["12002401"],"award-info":[{"award-number":["12002401"]}]},{"name":"Guangdong Provincial Key Laboratory of Extreme Conditions","award":["2023B1212010002"],"award-info":[{"award-number":["2023B1212010002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>C\/SiC composites are widely used in aerospace thermal structures. Due to the high manufacturing complexity and cost of C\/SiC composites, numerous hybrid joints are required to replace large and complex components. The intricate contact behavior within these hybrid joints reduces the computational efficiency of damage analysis methods based on solid models, limiting their effectiveness in large-scale structural design. According to the structure characteristic, a fractal contact stiffness model considering bonded behaviors is established in this paper. By introducing this model, it is proved that the bonded layer can affect the interface strength between plates but not the bearing strength of the specimen for the bolt\/bonded hybrid joint structure. Furthermore, by introducing the strength envelope method, this paper overcomes the problem wherein the shell-fastener model cannot accurately describe the complex stress field. Validation through experimental comparison confirms that this approach can accurately predict both the failure mode and strength of multi-row hybrid joint structures in C\/SiC composites at a detailed level with an error of 5.4%, including the shear failure of bolts. This method offers a robust foundation for the design of large-scale C\/SiC composite structures.<\/jats:p>","DOI":"10.3390\/ma17236008","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T10:11:47Z","timestamp":1733739107000},"page":"6008","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Efficient Strength Evaluation Method Based on Shell-Fastener Model for Large Hybrid Joint Structures of C\/SiC Composites"],"prefix":"10.3390","volume":"17","author":[{"given":"Maoqing","family":"Fu","sequence":"first","affiliation":[{"name":"School of Materials Science and Engineering, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8417-4142","authenticated-orcid":false,"given":"Jiapeng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ben","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Dongguan University of Technology, Dongguan 523808, China"},{"name":"Guangdong Provincial Key Laboratory of Extreme Conditions, Dongguan 523803, China"},{"name":"School of Physics and Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"118491","DOI":"10.1016\/j.compstruct.2024.118491","article-title":"Analysis of the fracture behavior and mechanism of PIP-C\/SiC composites at high temperatures","volume":"348","author":"Wang","year":"2024","journal-title":"Compos. Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.ceramint.2011.06.063","article-title":"Oxidation behavior of oxidation protective coatings for PIP\u2013C\/SiC composites at 1500 \u00b0C","volume":"38","author":"Xiang","year":"2012","journal-title":"Ceram. Int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16583","DOI":"10.1016\/j.ceramint.2018.06.082","article-title":"Oxidation behavior and high-temperature flexural property of CVD-SiC-coated PIP-C\/SiC composites","volume":"44","author":"Jin","year":"2018","journal-title":"Ceram. Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"42478","DOI":"10.1016\/j.ceramint.2024.08.093","article-title":"High-temperature mechanical performances of SiC whisker in-situ toughened 3DN C\/SiC countersunk bolts prepared by chemical vapor infiltration","volume":"50","author":"Ma","year":"2024","journal-title":"Ceram. Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1016\/j.compscitech.2005.06.020","article-title":"Effects of frequency on fatigue behavior of CVI C\/SiC at elevated temperature","volume":"66","author":"Mall","year":"2006","journal-title":"Compos. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3875","DOI":"10.1016\/j.jeurceramsoc.2023.03.002","article-title":"A focused review on the tribological behavior of C\/SiC composites: Present status and future prospects","volume":"43","author":"Diao","year":"2023","journal-title":"J. Eur. Ceram. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Varfolomeeva, L.A., Skvortsov, I.Y., Levin, I.S., Shandryuk, G.A., Patsaev, T.D., and Kulichikhin, V.G. (2023). Polyacrylonitrile Fibers with a Gradient Silica Distribution as Precursors of Carbon-Silicon-Carbide Fibers. Polymers, 15.","DOI":"10.3390\/polym15112579"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, X., Yin, J., Liu, X., Xia, A., and Huang, Z. (2021). Fabrication of core-shell chopped Cf-phenolic resin composite powder for laser additive manufacturing of Cf\/SiC composites. Polymers, 13.","DOI":"10.3390\/polym13030463"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1111\/j.1744-7402.2011.02722.x","article-title":"Erosion Behavior of C\/SiC Composites in Atomic Oxygen","volume":"10","author":"Liu","year":"2013","journal-title":"Int. J. Appl. Ceram. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.actaastro.2009.06.015","article-title":"Conventional stable structures for space optics: The state of the art","volume":"66","author":"Edeson","year":"2010","journal-title":"Acta Astronaut."},{"key":"ref_11","unstructured":"Chen, F., Tam, W., Shimp, N., and Norris, R. (2013). An Innovative Thermal Management System for a Mach 4 to Mach 8 Hypersonic Scramjet Engine, AIAA."},{"key":"ref_12","unstructured":"McCarthy, M.A. (2024, December 02). Bolted joints in composite aircraft structures (BOJCAS). Fourth EU Community Aeronautical Days. Available online: https:\/\/researchrepository.ul.ie\/articles\/report\/BOJCAS_Bolted_joints_in_composite_aircraft_structures\/19809748\/1?file=35221990."},{"key":"ref_13","unstructured":"(2002). AMSC N\/A Area CMPS Distribution Statement A. Composite Materials Handbook. Polymer Matrix Composites Materials Usage, Design, and Analysis, SAE International."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1016\/j.jmrt.2023.03.118","article-title":"Nonuniform load distribution of two-dimensional C\/SiC z-pinned joints with four pins in a rectangular array prepared via chemical vapor infiltration","volume":"24","author":"Sun","year":"2023","journal-title":"J. Mater. Res. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"112023","DOI":"10.1016\/j.compstruct.2020.112023","article-title":"Study on bearing strength and failure mode of a carbon-epoxy composite laminate for designing bolted joint structures","volume":"239","author":"Yoon","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111931","DOI":"10.1016\/j.compstruct.2020.111931","article-title":"Tension failure analysis for bolted joints using a closed-form stress solution","volume":"238","author":"Becker","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111949","DOI":"10.1016\/j.compstruct.2020.111949","article-title":"Failure analysis of single lap composite laminate bolted joints: Comparison of experimental and numerical tests","volume":"238","author":"Montagne","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1016\/j.apm.2006.03.020","article-title":"Finite element analysis and modeling of structure with bolted joints","volume":"31","author":"Kim","year":"2007","journal-title":"Appl. Math. Model."},{"key":"ref_19","first-page":"1517","article-title":"A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures","volume":"71","author":"Gray","year":"2011","journal-title":"Compos. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.compstruct.2014.01.015","article-title":"An analytical model for the secondary bending prediction in single-lap composite bolted-joints","volume":"111","author":"Olmedo","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.compstruct.2014.05.021","article-title":"An analytical model for strength prediction in multi-bolt composite joints at various loading rates","volume":"116","author":"Sharos","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.compositesb.2015.04.053","article-title":"A novel predictive model for mechanical behavior of single-lap GFRP composite bolted joint under static and dynamic loading","volume":"79","author":"Wang","year":"2015","journal-title":"Compos. Part B Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1016\/j.compstruct.2015.06.003","article-title":"An analytical joint stiffness model for load transfer analysis in highly torqued multi-bolt composite joints with clearances","volume":"131","author":"Liu","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108417","DOI":"10.1016\/j.compositesa.2024.108417","article-title":"Damage evolution analysis of C\/SiC screwed\/bonded hybrid joints based on in-situ micro-CT technique","volume":"186","author":"Li","year":"2024","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"117524","DOI":"10.1016\/j.compstruct.2023.117524","article-title":"Mechanical behavior and failure analysis of 2D C\/SiC screwed\/bonded hybrid joints","volume":"324","author":"Li","year":"2023","journal-title":"Compos. Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.apm.2024.01.011","article-title":"Contact mechanics modeling of fractal surface with complex multi-stage actual loading deformation","volume":"128","author":"Pan","year":"2024","journal-title":"Appl. Math. Model."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1877","DOI":"10.1007\/s00707-023-03830-w","article-title":"Fundamental equations of contact mechanics for fractal solid surfaces","volume":"235","author":"Meng","year":"2024","journal-title":"Acta Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1108\/ILT-12-2023-0392","article-title":"A fractal model of rough surfaces based on ellipsoidal asperities","volume":"76","author":"Yu","year":"2024","journal-title":"Ind. Lubr. Tribol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"112516","DOI":"10.1016\/j.compstruct.2020.112516","article-title":"An improved shell-fastener model for modelling C\/SiC composite bolted joints with rough surface characteristics","volume":"251","author":"Fu","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"21216","DOI":"10.1016\/j.ceramint.2020.05.204","article-title":"Failure analysis of 2D C\/SiC composite z-pinned\/bonded hybrid single-lap joints","volume":"46","author":"Fu","year":"2020","journal-title":"Ceram. Int."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2248","DOI":"10.1177\/002199839903302402","article-title":"A progressive Damage Model for Mechanically Fastened Joints in Composite Laminates","volume":"33","author":"Camanho","year":"1999","journal-title":"J. Compos. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.compstruct.2018.05.029","article-title":"A progressive failure analysis of all-C\/SiC composite multi-bolt joints","volume":"202","author":"Zhao","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.compstruct.2014.05.051","article-title":"A study of intra-laminar damage in double-lap, multi-bolt, composite joints with variable clearance using continuum damage mechanics","volume":"116","author":"Zhou","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_34","unstructured":"Hart-Smith, L.J. (1976). Bolted Joints in Graphite-Epoxy Composites, Douglas Aircraft Company. NASA CR 144899."},{"key":"ref_35","unstructured":"Zhang, Y. (2017). Mechanical Behaviors and Failure Mechanisms of Z-Pinned Joints for 2D C\/SiC Composite Prepared by Chemical Vapor Infiltration, Northwestern Polytechnical University."},{"key":"ref_36","unstructured":"(2017). Standard Test Method for Bearing Response of Polymer Matrix Composite Laminates (Standard No. ASTM D5961\/5961M-17)."},{"key":"ref_37","unstructured":"(2018). Test method for tensile properties of continuous fiber-reinforced ceramic composites at ambient temperature (Standard No. GJB 6475-2008)."},{"key":"ref_38","unstructured":"Fang, G., Fu, M., Liang, J., Wu, Z., and Liu, S. (2002). A Fast Equivalent Modeling Method for Composite Material Thin-Walled Bolted Joint Structures. (ZL201811527772.5. CN109635445B)."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/23\/6008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:49:59Z","timestamp":1760114999000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/23\/6008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,8]]},"references-count":38,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["ma17236008"],"URL":"https:\/\/doi.org\/10.3390\/ma17236008","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,8]]}}}