{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:35:51Z","timestamp":1775756151104,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,17]],"date-time":"2022-12-17T00:00:00Z","timestamp":1671235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Processes"],"abstract":"<jats:p>The interest in the design and numerical modelling of adhesively-bonded components and structures for industrial application is increasing as a research topic. Although research on joint failure under pure mode is widespread, applied bonded joints are often subjected to a mixed mode loading at the crack tip, which is more complex than the pure mode and affects joint strength. Failure of these joints under loading is the objective of predictions through mathematical and numerical models, the latter based on the Finite Element Method (FEM), using Cohesive Zone Modelling (CZM). The Single leg bending (bending) testing is among those employed to study mixed mode loading. This work aims to validate the application of FEM-CZM to SLB joints. Thus, the geometries used for experimental testing were reproduced numerically and experimentally obtained properties were employed in these models. Upon the validation of the numerical technique, a parametric study involving the cohesive laws\u2019 parameters is performed, identifying the parameters with the most influence on the joint behaviour. As a result, it was possible to numerically model SLB tests of adhesive joints and estimate the mixed-mode behaviour of different adhesives, which enables mixed-mode modelling and design of adhesive structures.<\/jats:p>","DOI":"10.3390\/pr10122730","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T06:58:29Z","timestamp":1671433109000},"page":"2730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Numerical Modelling and Validation of Mixed-Mode Fracture Tests to Adhesive Joints Using J-Integral Concepts"],"prefix":"10.3390","volume":"10","author":[{"given":"Lu\u00eds F. R.","family":"Neves","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, ISEP\u2014School of Engineering, Polytechnic Institute of Porto, R. Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4167-4434","authenticated-orcid":false,"given":"Raul D. S. G.","family":"Campilho","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, ISEP\u2014School of Engineering, Polytechnic Institute of Porto, R. Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal"},{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering\u2014P\u00f3lo FEUP, Rua Dr. Roberto Frias, 400, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7463-6608","authenticated-orcid":false,"given":"Isidro J.","family":"S\u00e1nchez-Arce","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering\u2014P\u00f3lo FEUP, Rua Dr. Roberto Frias, 400, 4200-465 Porto, Portugal"}]},{"given":"Kouder","family":"Madani","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Sidi Bel Abbes, BP 89 Cit\u00e9 Ben M\u2019hidi, Sidi Bel Abbes 22000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0856-9712","authenticated-orcid":false,"given":"Chander","family":"Prakash","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Lovely Professional University, Phagwara 144411, India"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1080\/00218464.2021.1953479","article-title":"Testing mechanical performance of adhesively bonded composite joints in engineering applications: An overview","volume":"98","author":"Budzik","year":"2022","journal-title":"J. Adhes."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1080\/00218464.2021.1941903","article-title":"A review on failure theories and simulation models for adhesive joints","volume":"98","author":"Tserpes","year":"2022","journal-title":"J. Adhes."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"da Silva, L.F.M., Dillard, D.A., Blackman, B., and Adams, R.D. (2012). Manufacture of Quality Specimens. Testing Adhesive Joints: Best Practices, Wiley-VCH Verlag & Co. KGaA.","DOI":"10.1002\/9783527647026"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Shahapurkar, K., Alblalaihid, K., Chenrayan, V., Alghtani, A.H., Tirth, V., Algahtani, A., Alarifi, I.M., and Kiran, M.C. (2022). Quasi-Static Flexural Behavior of Epoxy-Matrix-Reinforced Crump Rubber Composites. Processes, 10.","DOI":"10.3390\/pr10050956"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1080\/00218464.2014.903802","article-title":"The Effect of Adhesive Thickness on the Mechanical Behavior of a Structural Polyurethane Adhesive","volume":"91","author":"Banea","year":"2015","journal-title":"J. Adhes."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4367","DOI":"10.1016\/S0020-7683(02)00344-X","article-title":"The effects of geometry and material properties on the fracture of single lap-shear joints","volume":"39","author":"Kafkalidis","year":"2002","journal-title":"Int. J. Solids Struct."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Astrouski, I., Kudelova, T., Kalivoda, J., and Raudensky, M. (2022). Shear Strength of Adhesive Bonding of Plastics Intended for High Temperature Plastic Radiators. Processes, 10.","DOI":"10.3390\/pr10050806"},{"key":"ref_8","unstructured":"Adams, R.D. (2005). Fracture Mechanics of Adhesive Bonds, Woodhead Publishing Limited."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"da Silva, L.F.M., Dillard, D.A., Blackman, B.R.K., and Adams, R.D. (2012). Quasi-Static Fracture Tests. Testing Adhesive Joints: Best Practices, Wiley-VCH Verlag & Co. KGaA.","DOI":"10.1002\/9783527647026"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1080\/00218464.2013.859075","article-title":"Fracture mechanics tests in adhesively bonded joints: A literature review","volume":"90","author":"Chaves","year":"2014","journal-title":"J. Adhes."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.mechmat.2012.01.002","article-title":"On the interfacial constitutive laws of mixed mode fracture with various adhesive thicknesses","volume":"47","author":"Ji","year":"2012","journal-title":"Mech. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1520\/JTE20150335","article-title":"Strength and fracture characterization of a novel polyurethane adhesive for the automotive industry","volume":"45","author":"Faneco","year":"2017","journal-title":"J. Test. Eval."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/j.promfg.2020.10.108","article-title":"A new structural two-component epoxy adhesive: Strength and fracture characterization","volume":"51","author":"Cardoso","year":"2020","journal-title":"Procedia Manuf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.compositesa.2015.08.024","article-title":"The relationship between pure delamination modes I and II on the crack growth rate process in cracked lap shear specimen (CLS) of 5 harness satin composites","volume":"78","author":"Shiino","year":"2015","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s11012-012-9686-3","article-title":"An enhanced beam-theory model of the mixed-mode bending (MMB) test\u2014Part I: Literature review and mechanical model","volume":"48","author":"Bennati","year":"2013","journal-title":"Meccanica"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1080\/00218464.2019.1681269","article-title":"Adhesive thickness effects on the mixed-mode fracture toughness of bonded joints","volume":"96","author":"Oliveira","year":"2020","journal-title":"J. Adhes."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10704-017-0219-x","article-title":"Mixed-mode fracture analysis of composite bonded joints considering adhesives of different ductility","volume":"207","author":"Santos","year":"2017","journal-title":"Int. J. Fract."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/00218464.2019.1667776","article-title":"J-integral analysis of the mixed-mode fracture behaviour of composite bonded joints","volume":"96","author":"Loureiro","year":"2020","journal-title":"J. Adhes."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1243\/03093247V093185","article-title":"Stress analysis of adhesive-bonded lap joints","volume":"9","author":"Adams","year":"1974","journal-title":"J. Strain Anal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.compscitech.2004.12.024","article-title":"On the influence of the shape of the interface law on the application of cohesive-zone models","volume":"66","author":"Alfano","year":"2006","journal-title":"Compos. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/j.mtcomm.2019.05.006","article-title":"Mixed mode I + II interlaminar fracture characterization of carbon-fibre reinforced polyamide composite using the Single-Leg Bending test","volume":"19","author":"Reis","year":"2019","journal-title":"Mater. Today Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"R3","DOI":"10.1007\/BF00018129","article-title":"Modified end notched flexure specimen for mixed mode interlaminar fracture in laminated composites","volume":"43","author":"Yoon","year":"1990","journal-title":"Int. J. Fract."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.ijadhadh.2010.09.008","article-title":"Strength prediction of single- and double-lap joints by standard and extended finite element modelling","volume":"31","author":"Campilho","year":"2011","journal-title":"Int. J. Adhes. Adhes."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.compositesb.2013.01.025","article-title":"Fracture toughness determination of adhesive and co-cured joints in natural fibre composites","volume":"50","author":"Campilho","year":"2013","journal-title":"Compos. Part B Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Da Silva, L.F.M., Dillard, D.A., Blackman, B., and Adams, R.D. (2012). Testing Adhesive Joints, Wiley.","DOI":"10.1002\/9783527647026"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.compstruct.2015.09.054","article-title":"Damage analysis of composite\u2013aluminium adhesively-bonded single-lap joints","volume":"136","author":"Ribeiro","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1948","DOI":"10.1016\/j.compscitech.2005.04.007","article-title":"Modelling single and double-lap repairs on composite materials","volume":"65","author":"Campilho","year":"2005","journal-title":"Compos. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1115\/1.3601206","article-title":"A path independent integral and the approximate analysis of strain concentration by notches and cracks","volume":"35","author":"Rice","year":"1968","journal-title":"J. Appl. Mech."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wu, E.M., and Reuter, R.C.J. (1965). Crack Extension in Fiberglass Reinforced Plastics, Department of Theoretical and Applied Mechanics, University of Illinois. T&AM Report No. 275.","DOI":"10.21236\/AD0613576"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1002\/nme.93","article-title":"Finite element interface models for the delamination analysis of laminated composites: Mechanical and computational issues","volume":"50","author":"Alfano","year":"2001","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/s11340-015-0111-4","article-title":"Shear Characterization of Adhesive Layers by Advanced Optical Techniques","volume":"56","author":"Campilho","year":"2016","journal-title":"Exp. Mech."},{"key":"ref_32","first-page":"431","article-title":"Softening behaviour modelling of aluminium alloy 6082 using a non-linear cohesive zone law","volume":"229","author":"Kim","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.engfracmech.2015.02.010","article-title":"Tensile fracture characterization of adhesive joints by standard and optical techniques","volume":"136","author":"Constante","year":"2015","journal-title":"Eng. Fract. Mech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.ijsolstr.2006.04.036","article-title":"Shear behaviour of adhesive layers","volume":"44","author":"Leffler","year":"2007","journal-title":"Int. J. Solids Struct."}],"container-title":["Processes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-9717\/10\/12\/2730\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:43:18Z","timestamp":1760146998000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-9717\/10\/12\/2730"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,17]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["pr10122730"],"URL":"https:\/\/doi.org\/10.3390\/pr10122730","relation":{},"ISSN":["2227-9717"],"issn-type":[{"value":"2227-9717","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,17]]}}}