{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T13:15:34Z","timestamp":1779887734665,"version":"3.53.1"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T00:00:00Z","timestamp":1717545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52075526"],"award-info":[{"award-number":["52075526"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91860204"],"award-info":[{"award-number":["91860204"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2017A-28-C"],"award-info":[{"award-number":["2017A-28-C"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["DUT22LAB605"],"award-info":[{"award-number":["DUT22LAB605"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ningbo 3315 Plan Innovation Team","award":["52075526"],"award-info":[{"award-number":["52075526"]}]},{"name":"Ningbo 3315 Plan Innovation Team","award":["91860204"],"award-info":[{"award-number":["91860204"]}]},{"name":"Ningbo 3315 Plan Innovation Team","award":["2017A-28-C"],"award-info":[{"award-number":["2017A-28-C"]}]},{"name":"Ningbo 3315 Plan Innovation Team","award":["DUT22LAB605"],"award-info":[{"award-number":["DUT22LAB605"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["52075526"],"award-info":[{"award-number":["52075526"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["91860204"],"award-info":[{"award-number":["91860204"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2017A-28-C"],"award-info":[{"award-number":["2017A-28-C"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["DUT22LAB605"],"award-info":[{"award-number":["DUT22LAB605"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf\/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber\/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material\u2019s fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J\/m2 to 20 J\/m2, the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under \u03c32-\u03c423 combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile\/compressive displacement is \u22121, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiCf\/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization.<\/jats:p>","DOI":"10.3390\/sym16060695","type":"journal-article","created":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T05:59:42Z","timestamp":1717567182000},"page":"695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Influence of the Interface on the Micromechanical Behavior of Unidirectional Fiber-Reinforced Ceramic Matrix Composites: An Analysis Based on the Periodic Symmetric Boundary Conditions"],"prefix":"10.3390","volume":"16","author":[{"given":"Wei","family":"Yan","sequence":"first","affiliation":[{"name":"Zhejiang Key Laboratory of Data-Driven High-Safety Energy Materials and Applications, Ningbo Key Laboratory of Special Energy Materials and Chemistry, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shilun","family":"Shi","sequence":"additional","affiliation":[{"name":"Zhejiang Key Laboratory of Data-Driven High-Safety Energy Materials and Applications, Ningbo Key Laboratory of Special Energy Materials and Chemistry, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"},{"name":"School of Material Science and Chemical Engineering, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Longcheng","family":"Xiao","sequence":"additional","affiliation":[{"name":"Zhejiang Key Laboratory of Data-Driven High-Safety Energy Materials and Applications, Ningbo Key Laboratory of Special Energy Materials and Chemistry, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"},{"name":"School of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiulun","family":"Li","sequence":"additional","affiliation":[{"name":"Zhejiang Key Laboratory of Data-Driven High-Safety Energy Materials and Applications, Ningbo Key Laboratory of Special Energy Materials and Chemistry, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"},{"name":"School of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Xu","sequence":"additional","affiliation":[{"name":"Zhejiang Key Laboratory of Data-Driven High-Safety Energy Materials and Applications, Ningbo Key Laboratory of Special Energy Materials and Chemistry, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"},{"name":"Engineering Laboratory of Advanced Energy Materials, Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"153367","DOI":"10.1016\/j.jnucmat.2021.153367","article-title":"Mechanical behavior of SiC\/SiC composites reinforced with new Tyranno SA4 fibers: Effect of interphase thickness and comparison with Tyranno SA3 and Hi-Nicalon S reinforced composites","volume":"558","author":"Braun","year":"2022","journal-title":"J. Nucl. Mater."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Karadimas, G., and Salonitis, K. (2023). Ceramic matrix composites for aero engine applications\u2014A review. Appl. Sci., 13.","DOI":"10.3390\/app13053017"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Fang, G., Gao, X., and Song, Y. (2023). A review on ceramic matrix composites and environmental barrier coatings for aero-engine: Material development and failure analysis. Coatings, 13.","DOI":"10.3390\/coatings13020357"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10582","DOI":"10.1016\/j.ceramint.2023.12.370","article-title":"Modifying C\/C\u2013SiC brake pads with different Fe\u2013Si alloy phases to improve the wear resistance of full-carbon\/ceramic brake pair","volume":"50","author":"Huang","year":"2024","journal-title":"Ceram. Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100366","DOI":"10.1016\/j.oceram.2023.100366","article-title":"In-situ observation of micro-cracking in a SiC\/BN\/SiC ceramic matrix composite under tension","volume":"14","author":"Detwiler","year":"2023","journal-title":"Open Ceram."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1111\/ijac.14645","article-title":"Effect of BN interfacial layer on the mechanical behavior of SiC fiber reinforced SiC ceramic matrix composites","volume":"21","author":"Chen","year":"2024","journal-title":"Int. J. Appl. Ceram. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"19038","DOI":"10.1016\/j.ceramint.2018.07.065","article-title":"Damage mechanism analysis to the carbon fiber and fiber-ceramic interface tailoring of Cf\/ZrC-SiC using PyC coating","volume":"44","author":"Hu","year":"2018","journal-title":"Ceram. Int."},{"key":"ref_8","first-page":"1","article-title":"Influence of Pyrolytic Carbon on the Properties of Precursor-Impregnated and Pyrolyzed 3D-Cf\/SiC Composites","volume":"25","author":"Qin","year":"2018","journal-title":"China Ceram. Ind."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.carbon.2016.08.047","article-title":"Enhancing the fracture resistance of carbon fiber reinforced SiC matrix composites by interface modification through a simple fiber heat-treatment process","volume":"109","author":"Liu","year":"2016","journal-title":"Carbon"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1016\/j.cma.2013.10.017","article-title":"A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms","volume":"268","author":"Spahn","year":"2014","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"100016","DOI":"10.1016\/j.jcomc.2020.100016","article-title":"Multiscale modeling of tensile fracture in fiber reinforced composites","volume":"2","author":"Patel","year":"2020","journal-title":"Compos. Part C Open Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sahu, S.K., and Rama Sreekanth, P.S. (2022). Multiscale RVE modeling for assessing effective elastic modulus of HDPE based polymer matrix nanocomposite reinforced with nanodiamond. Int. J. Interact. Des. Manuf., 1\u201310.","DOI":"10.1007\/s12008-022-01080-z"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1051\/jnwpu\/20193730443","article-title":"Analysis of the Influence of Fiber Distribution and Interface Strength on the Transverse Compression Performance of Composite Materials","volume":"37","author":"Wan","year":"2019","journal-title":"J. Northwestern Polytech. Univ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.compstruct.2015.10.038","article-title":"Simulation of crack propagation\/deflection in ceramic matrix continuous fiber reinforced composites with weak interphase via the extended finite element method","volume":"136","author":"Braginsky","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.compositesb.2017.11.043","article-title":"The role of interfacial properties on the intralaminar and interlaminar damage behaviour of unidirectional composite laminates: Experimental characterization and multiscale modelling","volume":"138","author":"Tan","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.compscitech.2014.04.004","article-title":"A numerical study of the influence of microvoids in the transverse mechanical response of unidirectional composites","volume":"97","author":"Vajari","year":"2014","journal-title":"Compos. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"634112","DOI":"10.3389\/fmats.2020.634112","article-title":"Multiscale Modeling of SiCf\/SiC Nuclear Fuel Cladding Based on FE-Simulation of Braiding Process","volume":"7","author":"Feng","year":"2021","journal-title":"Front. Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1016\/0956-7151(91)90274-5","article-title":"Deformation of metal-matrix composites with continuous fibers: Geometrical effects of fiber distribution and shape","volume":"39","author":"Brockenbrough","year":"1991","journal-title":"Acta Metall. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.compositesa.2016.06.018","article-title":"Computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects","volume":"92","author":"Naya","year":"2017","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2000","DOI":"10.1002\/nag.3720","article-title":"Interpreting correlations in stress-dependent permeability, porosity, and compressibility of rocks: A viewpoint from finite strain theory","volume":"48","author":"Wang","year":"2024","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"100348","DOI":"10.1016\/j.jcomc.2023.100348","article-title":"A review on micromechanical modelling of progressive failure in unidirectional fiber-reinforced composites","volume":"10","author":"Wan","year":"2023","journal-title":"Compos. Part C Open Access"},{"key":"ref_22","unstructured":"Sauder, C. (2014). Ceramic Matrix Composites: Materials, Modeling and Technology, The American Ceramic Society."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.jnucmat.2007.05.016","article-title":"Handbook of SiC properties for fuel performance modeling","volume":"371","author":"Snead","year":"2007","journal-title":"J. Nucl. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"011007","DOI":"10.1115\/1.4040591","article-title":"Mechanical behavior of silicon carbide under static and dynamic compression","volume":"141","author":"Zhang","year":"2019","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.compositesb.2017.07.079","article-title":"Processing-temperature dependent micro-and macro-mechanical properties of SiC fiber reinforced SiC matrix composites","volume":"129","author":"Yang","year":"2017","journal-title":"Compos. Part B Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Abdellahi, B., Azhari, F., and Nguyen, P. (2024). Prediction of the failure behavior of pseudo-ductile composites using a multi-scale finite element model. Res. Sq.","DOI":"10.21203\/rs.3.rs-3960356\/v1"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"104706","DOI":"10.1016\/j.ijimpeng.2023.104706","article-title":"Influence of void defects on impact properties of CFRP laminates based on multi-scale simulation method","volume":"180","author":"Zhang","year":"2023","journal-title":"Int. J. Impact Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"115622","DOI":"10.1088\/2053-1591\/ab5070","article-title":"High-performance Cf\/SiC composites with a novel needle-punched carbon fiber fabric fabricated by PIP process","volume":"6","author":"Li","year":"2019","journal-title":"Mater. Res. Express"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105035","DOI":"10.1016\/j.euromechsol.2023.105035","article-title":"Phase-field fracture modeling for unidirectional fiber-reinforced polymer composites","volume":"100","author":"Konica","year":"2023","journal-title":"Eur. J. Mech.-A\/Solids"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.engfracmech.2018.04.038","article-title":"Phase-field regularized cohesive zone model (CZM) and size effect of concrete","volume":"197","author":"Feng","year":"2018","journal-title":"Eng. Fract. Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"108265","DOI":"10.1016\/j.engfracmech.2022.108265","article-title":"A phase field model with the mixed-mode driving force of power-law relation","volume":"264","author":"Yu","year":"2022","journal-title":"Eng. Fract. Mech."},{"key":"ref_32","first-page":"163","article-title":"VI. The phenomena of rupture and flow in solids","volume":"221","author":"Griffith","year":"1921","journal-title":"Philos. Trans. R. Soc. London. Ser. A Contain. Pap. A Math. Or Phys. Character"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.jmps.2017.03.015","article-title":"A unified phase-field theory for the mechanics of damage and quasi-brittle failure","volume":"103","author":"Wu","year":"2017","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.jmps.2018.06.006","article-title":"A length scale insensitive phase-field damage model for brittle fracture","volume":"119","author":"Wu","year":"2018","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"112704","DOI":"10.1016\/j.cma.2019.112704","article-title":"On the BFGS monolithic algorithm for the unified phase field damage theory","volume":"360","author":"Wu","year":"2020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1016\/0021-8928(59)90036-X","article-title":"Equilibrium cracks formed during brittle fracture rectilinear cracks in plane plates","volume":"23","author":"Barenblatt","year":"1959","journal-title":"J. Appl. Math. Mech."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/0022-5096(60)90013-2","article-title":"Yielding of steel sheets containing slits","volume":"8","author":"Dugdale","year":"1960","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"103733","DOI":"10.1016\/j.tafmec.2022.103733","article-title":"On the calibration of the cohesive strength for cohesive zone models in finite element analyses","volume":"124","author":"Linke","year":"2023","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"102246","DOI":"10.1016\/j.tafmec.2019.102246","article-title":"Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches","volume":"103","author":"Sayedain","year":"2019","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_40","unstructured":"Chamis, C.C. (1984, January 15\u201317). Mechanics of composite materials: Past, present and future. Proceedings of the 21st Annual Meeting of the Society for Engineering Science, Blacksburg, VA, USA."},{"key":"ref_41","unstructured":"Yang, L. (2019). Study on the Damage and Failure Mechanisms of SiC\/SiC Ceramic Matrix Composites, Harbin Institute of Technology."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1007\/s10443-023-10129-5","article-title":"Multi-scale Progressive Damage and Failure Behavior Analysis of Three-Dimensional Winding SiC Fiber-Reinforced SiC Matrix Composite Tube","volume":"30","author":"Pu","year":"2023","journal-title":"Appl. Compos. Mater."},{"key":"ref_43","first-page":"1611","article-title":"Study on Predicting Transverse Strength of Composites Using Micromechanical Models","volume":"36","author":"Peng","year":"2017","journal-title":"Mech. Sci. Technol."},{"key":"ref_44","unstructured":"Zhou, Q. (2020). Multiscale Mechanical Properties of 2D Braided Ceramic Matrix Composites, Harbin Institute of Technology."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/695\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:53:59Z","timestamp":1760108039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,5]]},"references-count":44,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["sym16060695"],"URL":"https:\/\/doi.org\/10.3390\/sym16060695","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,5]]}}}