{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:05:17Z","timestamp":1760238317971,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T00:00:00Z","timestamp":1595548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["NS2019038"],"award-info":[{"award-number":["NS2019038"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Fatigue limit stress is a key design parameter for the structure fatigue design of composite materials. In this paper, a micromechanical fatigue limit stress model of fiber-reinforced ceramic-matrix composites (CMCs) subjected to stochastic overloading stress is developed. The fatigue limit stress of different carbon fiber-reinforced silicon carbide (C\/SiC) composites (i.e., unidirectional (UD), cross-ply (CP), 2D, 2.5D, and 3D C\/SiC) is predicted based on the micromechanical fatigue damage models and fatigue failure criterion. Under cyclic fatigue loading, the fatigue damage and fracture under stochastic overloading stress at different applied cycle numbers are characterized using two parameters of fatigue life decreasing rate and broken fiber fraction. The relationships between the fatigue life decreasing rate, stochastic overloading stress level and corresponding occurrence applied cycle number, and broken fiber fraction are analyzed. Under the same stochastic overloading stress level, the fatigue life decreasing rate increases with the occurrence applied cycle of stochastic overloading, and thus, is the highest for the cross-ply C\/SiC composite and lowest for the 2.5D C\/SiC composite. Among the UD, 2D, and 3D C\/SiC composites, at the initial stage of cyclic fatigue loading, under the same stochastic overloading stress, the fatigue life decreasing rate of the 3D C\/SiC is the highest; however, with the increasing applied cycle number, the fatigue life decreasing rate of the UD C\/SiC composite is the highest. The broken fiber fraction increases when stochastic overloading stress occurs, and the difference of the broken fiber fraction between the fatigue limit stress and stochastic overloading stress level increases with the occurrence applied cycle.<\/jats:p>","DOI":"10.3390\/ma13153304","type":"journal-article","created":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T09:06:09Z","timestamp":1595581569000},"page":"3304","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Micromechanical Fatigue Limit Stress Model of Fiber-Reinforced Ceramic-Matrix Composites under Stochastic Overloading Stress"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7689-2098","authenticated-orcid":false,"given":"Longbiao","family":"Li","sequence":"first","affiliation":[{"name":"College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao St., Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S0266-3538(03)00230-6","article-title":"Design, Preparation and properties of non-oxide CMCs for application in engines and nuclear reactors: An overview","volume":"64","author":"Naslain","year":"2004","journal-title":"Compos. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17491","DOI":"10.1016\/j.ceramint.2018.06.221","article-title":"Subsurface oxidation of boron nitride coatings on silicon carbide fibers in SiC\/SiC ceramic matrix composites","volume":"44","author":"Wing","year":"2018","journal-title":"Ceram. Int."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, L.B. (2020). Time-Dependent Mechanical Behavior of Ceramic-Matrix Composites at Elevated Temperatures, Springer Nature Singapore Pte Ltd.","DOI":"10.1007\/978-981-15-3274-0"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Li, L.B. (2019). Thermomechanical Fatigue of Ceramic-Matrix Composites, Wiley-VCH.","DOI":"10.1002\/9783527822614"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/0266-3538(96)00025-5","article-title":"Cyclic fatigue of ceramic-matrix composites at ambient and elevated temperatures","volume":"56","author":"Reynaud","year":"1996","journal-title":"Compos. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1016\/S0266-3538(99)00014-7","article-title":"Monotonic tension, fatigue and creep behavior of SiC-fiber-reinforced SiC-matrix composites: A review","volume":"59","author":"Zhu","year":"1999","journal-title":"Compos. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3316","DOI":"10.3390\/ma8063316","article-title":"Tension-tension fatigue behavior of unidirectional C\/SiC ceramic-matrix composite at room and elevated temperature and 800 \u00b0C in air atmosphere","volume":"8","author":"Li","year":"2015","journal-title":"Materials"},{"key":"ref_8","unstructured":"Yang, F. (2011). Research on Fatigue Behavior of 2.5d Woven Ceramic Matrix Composites. [Master\u2019s Thesis, Nanjing University of Aeronautics and Astronautics]."},{"key":"ref_9","first-page":"22","article-title":"Tension-tension fatigue behavior of 3D-C\/SiC composite at room temperature and 1300 \u00b0C","volume":"9","author":"Du","year":"2002","journal-title":"Mater. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2327","DOI":"10.1111\/j.1151-2916.1993.tb07772.x","article-title":"Influence of loading frequency on the room-temperature fatigue of a carbon-fiber\/SiC-matrix composite","volume":"76","author":"Shuler","year":"1993","journal-title":"J. Am. Ceram. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.compscitech.2010.11.008","article-title":"Effect of frequency and environment on fatigue behavior of a CVI SiC\/SiC ceramic matrix composite at 1200 \u00b0C","volume":"71","author":"Christensen","year":"2011","journal-title":"Compos. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, L.B., Reynaud, P., and Fantozzi, G. (2020). Cyclic-dependent damage evolution in self-healing woven SiC\/[Si-B-C] ceramic-matrix composites at elevated temperatures. Materials, 13.","DOI":"10.3390\/ma13061478"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8539","DOI":"10.3390\/ma8125474","article-title":"Damage evolution and life prediction of cross-ply C\/SiC ceramic-matrix composite under cyclic fatigue loading at room temperature and 800 \u00b0C in air","volume":"8","author":"Li","year":"2015","journal-title":"Materials"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s10443-010-9163-x","article-title":"Effects of steam environment on fatigue behavior of two SiC\/[SiC+Si3N4] ceramic composites at 1300 \u00b0C","volume":"18","author":"Sharma","year":"2011","journal-title":"Appl. Compos. Mater."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.msea.2016.09.076","article-title":"Fatigue behavior of an advanced SiC\/SiC ceramic composite with a self-healing matrix at 1300 \u00b0C in air and in steam","volume":"677","author":"Lee","year":"2016","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/ijac.12773","article-title":"Fatigue of three advanced SiC\/SiC ceramic matrix composites at 1200 \u00b0C in air and in steam","volume":"15","author":"Boucher","year":"2018","journal-title":"Int. J. Appl. Ceram. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.ijfatigue.2018.09.021","article-title":"A new stiffness degradation model for fatigue life prediction of GFRPs under random loading","volume":"119","author":"Suzuki","year":"2019","journal-title":"Int. J. Fatigue"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Li, L.B. (2019). Stress-rupture of fiber-reinforced ceramic-matrix composites with stochastic loading at intermediate temperatures. Part I: Theoretical analysis. Materials, 12.","DOI":"10.3390\/ma12193123"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S1359-6454(96)00143-7","article-title":"Design and life prediction issues for high-temperature engineering ceramics and their composites","volume":"45","author":"Evans","year":"1997","journal-title":"Acta Mater."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s10443-015-9448-1","article-title":"Fatigue life prediction of carbon fiber-reinforced ceramic-matrix composites at room and elevated temperatures. Part I: Experimental analysis","volume":"23","author":"Li","year":"2016","journal-title":"Appl. Compos. Mater."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1007\/s10443-015-9445-4","article-title":"Fatigue life prediction of carbon fiber-reinforced ceramic-matrix composites at room and elevated temperatures. Part II: Experimental comparisons","volume":"22","author":"Li","year":"2015","journal-title":"Appl. Compos. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, L.B. (2016). Fatigue life prediction of fiber-reinforced ceramic-matrix composites with different fiber preforms at room and elevated temperatures. Materials, 9.","DOI":"10.3390\/ma9030207"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1111\/j.1151-2916.1991.tb06852.x","article-title":"Theory of mechanical properties of ceramic-matrix composites","volume":"74","author":"Curtin","year":"1991","journal-title":"J. Am. Ceram. Soc."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/13\/15\/3304\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:51:29Z","timestamp":1760176289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/13\/15\/3304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,24]]},"references-count":23,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["ma13153304"],"URL":"https:\/\/doi.org\/10.3390\/ma13153304","relation":{},"ISSN":["1996-1944"],"issn-type":[{"type":"electronic","value":"1996-1944"}],"subject":[],"published":{"date-parts":[[2020,7,24]]}}}