{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T18:25:12Z","timestamp":1779301512796,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"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":["2020CDJGFHK009"],"award-info":[{"award-number":["2020CDJGFHK009"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of State Key Laboratory of Automotive Simulation and Control","award":["20201202"],"award-info":[{"award-number":["20201202"]}]},{"DOI":"10.13039\/501100005230","name":"Natural Science Foundation of Chongqing","doi-asserted-by":"publisher","award":["cstc2019jscx-zdztzxX0028"],"award-info":[{"award-number":["cstc2019jscx-zdztzxX0028"]}],"id":[{"id":"10.13039\/501100005230","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Multibolt composite joints are widely used in aircraft structures. The determination of the pin-load distribution among the bolts is a critical step in the failure prediction of bolted joints. In this paper, a two-dimensional model of the multibolt composite structure is established for the pin-load distribution analysis. Its accuracy is validated by experimental results and the results from a 3D finite element model. Based on the determined pin-load distribution, FE models for a laminated plate with three-row fastener joints are built for failure prediction. Hashin stress criteria and the degradation guidelines of the material stiffness with respect to the different failure modes proposed by Tserpes are applied for the failure evaluation and the material degradation, respectively. The failure location and ultimate load are well predicted, which further validates the effectiveness and applicability of the proposed model for the pin-load distribution analysis.<\/jats:p>","DOI":"10.3390\/ma14133646","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T03:53:15Z","timestamp":1625025195000},"page":"3646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Two-Dimensional Model for Pin-Load Distribution and Failure Analysis of Composite Bolted Joints"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3592-513X","authenticated-orcid":false,"given":"Binkai","family":"Li","sequence":"first","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Zhangwu Road 100#, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Xiao","sequence":"additional","affiliation":[{"name":"Shanghai Aircraft Design and Research Institute, Jinke Road 5188#, Shanghai 201210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yukui","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Tongji University, Caoan Road 4800#, Shanghai 201804, China"},{"name":"Shanghai Key Laboratory of R&D for Metallic Function Materials, Tongji University, Caoan Road 4800#, Shanghai 201804, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enquan","family":"Liang","sequence":"additional","affiliation":[{"name":"Shanghai Aircraft Design and Research Institute, Jinke Road 5188#, Shanghai 201210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110949","DOI":"10.1016\/j.compstruct.2019.110949","article-title":"R-curve behaviour of the mixed-mode I\/II delamination in carbon\/epoxy laminates with unidirectional and multidirectional interfaces","volume":"223","author":"Gong","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.compstruct.2013.06.017","article-title":"Failure prediction of out-of-plane woven composite joints using cohesive element","volume":"106","author":"Zhao","year":"2013","journal-title":"Compos. Struct."},{"key":"ref_3","unstructured":"Song, E., Liu, W., Xie, M., Hong, H., and Chi, J. (2005). Investigation of the influence of jointed member stiffness on fastener load distribution for composite multiple-bolted joint. Aircr. Des., 29\u201332."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1016\/S0020-7683(99)00033-5","article-title":"Strength prediction of composite laminates with multiple elliptical holes","volume":"37","author":"Xu","year":"2000","journal-title":"Int. J. Solids Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.compstruct.2005.01.028","article-title":"A simple method for determining the effects of bolt\u2013hole clearance on load distribution in single-column multi-bolt composite joints","volume":"73","author":"McCarthy","year":"2006","journal-title":"Compos. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.compositesb.2017.01.058","article-title":"Global sensitivity analysis of load distribution and displacement in multi-bolt composite joints","volume":"116","author":"Li","year":"2017","journal-title":"Compos. Part B Eng."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1016\/j.compstruct.2012.02.011","article-title":"An analytical model for the prediction of through-thickness stiffness in tension-loaded composite bolted joints","volume":"94","author":"Gray","year":"2012","journal-title":"Compos. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.compstruct.2017.12.041","article-title":"An enhanced spring-mass model for stiffness prediction in single-lap composite joints with considering assembly gap and gap shimming","volume":"187","author":"Yang","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1017\/jmech.2012.48","article-title":"Finite element based point stress criterion for predicting the notched strengths of composite plates","volume":"28","author":"Tsai","year":"2012","journal-title":"J. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.compositesb.2010.03.001","article-title":"A global bolted joint model for finite element analysis of load distributions in multi-bolt composite joints","volume":"41","author":"Gray","year":"2010","journal-title":"Compos. Part B Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1177\/0731684415572199","article-title":"Influence of end distances on the failure of composite bolted joints","volume":"34","author":"Zhang","year":"2015","journal-title":"J. Reinf. Plast. Comp."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/1359-835X(95)00020-3","article-title":"Effect of pitch distance, row spacing, end distance and bolt diameter on multi-fastened composite joints","volume":"27","author":"Chutima","year":"1996","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1177\/1369433219886081","article-title":"Identification of damage stages in bolted metallic joints for different joint geometries and tightening torques using statistical analysis","volume":"23","author":"Atta","year":"2020","journal-title":"Adv. Struct. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.compstruct.2010.09.017","article-title":"An analytical model for the prediction of load distribution in highly torqued multi-bolt composite joints","volume":"93","author":"McCarthy","year":"2011","journal-title":"Compos. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.compstruct.2018.03.100","article-title":"Probabilistic bolt load distribution analysis of composite single-lap multi-bolt joints considering random bolt-hole clearances and tightening torques","volume":"194","author":"Liu","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.compositesb.2017.11.027","article-title":"An interpretation of the load distributions in highly torqued single-lap composite bolted joints with bolt-hole clearances","volume":"138","author":"Liu","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Golewski, P., and Sadowski, T. (2019). The Influence of single lap geometry in adhesive and hybrid joints on their load carrying capacity. Materials, 12.","DOI":"10.3390\/ma12121884"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.ijadhadh.2017.04.007","article-title":"Investigation of the effect of chamfer size on the behaviour of hybrid joints made by adhesive bonding and riveting","volume":"77","author":"Golewski","year":"2017","journal-title":"Int. J. Adhes. Adhes."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.4028\/www.scientific.net\/KEM.607.49","article-title":"Effect of tolerance in the fitting of rivets in the holes of double lap joints subjected to uniaxial tension","volume":"607","author":"Sadowski","year":"2014","journal-title":"Key Eng. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.compositesb.2019.05.010","article-title":"A modified stiffness method considering effects of hole tensile deformation on bolt load distribution in multi-bolt composite joints","volume":"171","author":"Zhao","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107456","DOI":"10.1016\/j.engfracmech.2020.107456","article-title":"Failure prediction of irregular arranged multi-bolt composite repair based on finite fracture mechanics model","volume":"242","author":"Li","year":"2021","journal-title":"Eng. Fract. Mech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.compstruct.2018.02.043","article-title":"Investigation of bolt load redistribution and its effect on failure prediction in double-lap, multi-bolt composite joints","volume":"202","author":"Liu","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.engfracmech.2018.11.038","article-title":"Progressive failure modelling of double-lap of composite bolted joints based on Puck\u2019s criterion","volume":"206","author":"Zhou","year":"2019","journal-title":"Eng. Fract. Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.compstruct.2015.11.058","article-title":"Numerical analysis of bearing failure in countersunk composite joints using 3D explicit simulation method","volume":"138","author":"Liu","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.compstruct.2016.05.017","article-title":"Progressive failure analysis on scaled open-hole tensile composite laminates","volume":"150","author":"Bao","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Abdelhady, A.A., Mubaraki, M., and Sallam, H.E.M. (2018). Progressive failure prediction of pinned joint in quasi-isotropic laminates used in pipelines. Lat. Am. J. Solids Struct., 15.","DOI":"10.1590\/1679-78255061"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1177\/0731684415574871","article-title":"Investigation on characteristic length testing methods for failure prediction of composite multi-bolt joints","volume":"34","author":"Zhang","year":"2015","journal-title":"J. Reinf. Plast. Comp."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.compstruct.2013.10.026","article-title":"A progressive damage analysis based characteristic length method for multi-bolt composite joints","volume":"108","author":"Zhang","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.compstruct.2013.09.019","article-title":"A novel characteristic curve for failure prediction of multi-bolt composite joints","volume":"108","author":"Zhang","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.compscitech.2013.04.018","article-title":"A modified failure envelope method for failure prediction of multi-bolt composite joints","volume":"83","author":"Liu","year":"2013","journal-title":"Compos. Sci. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.compositesb.2019.05.034","article-title":"A failure-envelope-based method for the probabilistic failure prediction of composite multi-bolt double-lap joints","volume":"172","author":"Liu","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.compstruct.2016.10.042","article-title":"Effect of damage on failure mode of multi-bolt composite joints using failure envelope method","volume":"160","author":"Cheng","year":"2017","journal-title":"Compos. Struct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.1016\/j.compscitech.2006.02.017","article-title":"A design methodology for mechanically fastened joints in laminated composite materials","volume":"66","author":"Camanho","year":"2006","journal-title":"Compos. Sci. Technol."},{"key":"ref_36","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_37","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.compstruct.2018.01.104","article-title":"Progressive failure of bolted single-lap joints of woven fibre-reinforced composites","volume":"189","author":"Hu","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.compstruct.2018.01.037","article-title":"Failure load prediction of composite bolted joint with clamping force","volume":"189","author":"Choi","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_39","unstructured":"Potter, J.M. (1986). Influence of Fastener Flexibility on the Prediction of Load Transfer and Fatigue Life for Multiple-Row Joints, ASTM International."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1115\/1.3157744","article-title":"Fatigue failure criteria for unidirectional fiber composites","volume":"48","author":"Hashin","year":"1981","journal-title":"J. Appl. Mech. Trans. ASME"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/S1359-8368(02)00033-1","article-title":"Strength prediction of bolted joints in graphite\/epoxy composite laminates","volume":"33","author":"Tserpes","year":"2002","journal-title":"Compos. Part. B Eng."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/13\/3646\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:23:40Z","timestamp":1760163820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/13\/3646"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,30]]},"references-count":41,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["ma14133646"],"URL":"https:\/\/doi.org\/10.3390\/ma14133646","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,30]]}}}