Delamination Detection by Numerical Modelling of End-Notched Flexure Tests on glass/epoxy composite beams

Sabbaghian, Mahdieh; Kabir, Mohammad Zaman; Amooie, Morteza

doi:10.66224/NMCE.2602.1126

Delamination Detection by Numerical Modelling of End-Notched Flexure Tests on glass/epoxy composite beams

Document Type : Research

Authors

Mahdieh Sabbaghian ¹

Mohammad Zaman Kabir ²

Morteza Amooie ³

¹ Ph.D. Candidate, Department of Civil and Environmental Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

² Professor, Department of Civil and Environmental Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

³ Ph.D., Department of Civil Engineering, Guilan University, Guilan, Iran

10.66224/NMCE.2602.1126

Abstract

The detection of delamination is important for structural engineering applications for assessing the reliability of fiber-reinforced polymer (FRP) laminates, which could provide appreciable effects on the behavior of composite structures. Numerical investigation of interlaminar shear fracture (Mode II) was studied in the present work by the end-notched flexure (ENF) testing configuration. 20 glass/epoxy composite beams were analyzed with two different stacking sequences, incorporating four distinct stacking sequences with different fiber orientation angles and five initial crack lengths (a = 35, 40, 45, 50, and 55 mm). Finite element analysis was performed using ABAQUS, and the virtual crack closure technique (VCCT) was used to determine the distribution of the critical strain energy release rate with respect to the width of the laminate. The results obtained were then analyzed using a subsequent finite element analysis of interlaminar stresses in the area ahead of the crack tip. The results from the numerical analysis showed that the dominant contribution to the total energy release rate was the mode II (GII > 99%). Furthermore, the variation in GII across the laminate width was almost unchanged. For the other nodes, however, near the free edges, the separation of the node pairs, combined with the need to meet the fracture criterion, resulted in significant shear effects, with mode III components (GIII) becoming comparable to GII.

Keywords

Strain energy release rate

Finite element

Mode II interlaminar fracture toughness

Composite materials

End-notched flexure

Virtual crack closing method

Subjects

Structural Engineering

[1] Sabbaghian M, Kheyroddin A. Flexural strengthening of RC one way slabs with high-performance fiber-reinforced cementitious composite laminates using steel and GFRP bar. Eng Struct 2020;221:111106. https://doi.org/10.1016/J.ENGSTRUCT.2020.111106.

[2] Sabbaghian M, Kheyroddin A. Experimental investigation of shear behavior of one- way reinforced slabs with high-performance fiber- reinforced cementitious composite laminates. Amirkabir Journal of Civil Engineering 2022;53:919–22. https://doi.org/10.22060/CEEJ.2020.18138.6778.

[3] Zubillaga L, Turon A, Renart J, Costa J LP. An experimental study on matrix crack induced delamination in composite laminates. Compos Struct 2015;127:10–7.

[4] Gong W, Chen J PEA. An experimental study of the behaviour of delaminations in composite panels subjected to bending. Compos Struct 2015;123:9–18.

[5] Mishra PK, Pradhan AK, Pandit MK. Inter-laminar delamination analyses of Spar Wingskin Joints made with flat FRP composite laminates. Int J Adhes Adhes 2016;68:19–29. https://doi.org/10.1016/J.IJADHADH.2016.02.001.

[6] Shokrieh MM, Heidari-Rarani M, Ayatollahi MR. Delamination R-curve as a material property of unidirectional glass/epoxy composites. Mater Des 2012;34:211–8. https://doi.org/10.1016/J.MATDES.2011.08.006.

[7] de Morais AB, Pereira AB. Mixed mode I + II interlaminar fracture of glass/epoxy multidirectional laminates – Part 1: Analysis. Compos Sci Technol 2006;66:1889–95. https://doi.org/10.1016/J.compositech.2006.04.006.

[8] de Morais AB, Pereira AB. Mixed mode II + III interlaminar fracture of carbon/epoxy laminates. Compos Sci Technol 2008;68:2022–7. https://doi.org/10.1016/J.COMPSCITECH.2008.02.023.

[9] Pereira AB, de Morais AB. Mixed mode I + II interlaminar fracture of glass/epoxy multidirectional laminates – Part 2: Experiments. Compos Sci Technol 2006;66:1896–902. https://doi.org/10.1016/J.COMPSCITECH.2006.04.008.

[10] Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites . n.d.

[11] Test Method for Determination of the Mode II Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites 2019. https://doi.org/10.1520/D7905_D7905M-19E01.

[12] Tsai SW, Hahn HT. Introduction to Composite Materials. Introduction to Composite Materials 2018. https://doi.org/10.1201/9780203750148.

[13] Bascom WD, Bitner JL, Moulton RJ, Siebert AR. The interlaminar fracture of organic-matrix, woven reinforcement composites. Composites 1980;11:9–18. https://doi.org/10.1016/0010-4361(80)90016-6.

[14] Wood MDK, Sun X, Tong L, Luo Q, Katzos A, Rispler A. A new ENF test specimen for the mode II delamination toughness testing of stitched woven CFRP laminates. J Compos Mater 2016;41:1743–72. https://doi.org/10.1177/0021998306069890.

[15] Alif N, Carlsson LA, Gillespie JW. Mode I, Mode II, and Mixed Mode Interlaminar Fracture of Woven Fabric Carbon/Epoxy. ASTM Special Technical Publication 1997;1242:82–106. https://doi.org/10.1520/STP18271S.

[16] Pereira AB, De Morais AB. Mode II interlaminar fracture of glass/epoxy multidirectional laminates. Compos Part A Appl Sci Manuf 2004;35:265–72. https://doi.org/10.1016/J.COMPOSITESA.2003.09.028.

[17] Triki E, Zouari B, Dammak F. Dependence of the interlaminar fracture toughness of E-Glass/Polyester woven fabric composites laminates on ply orientation. Eng Fract Mech 2016;159:63–78. https://doi.org/10.1016/J.ENGFRACMECH.2016.03.025.

[18] Gliszczynski A, Wiącek N. Experimental and numerical benchmark study of mode II interlaminar fracture toughness of unidirectional GFRP laminates under shear loading using the end-notched flexure (ENF) test. Compos Struct 2021;258:113190. https://doi.org/10.1016/J.COMPSTRUCT.2020.113190.

[19] Gong Y, Xia K, Wang Y, Zhao L, Zhang J, Hu N. A semi-analytical model for the mode II fracture toughness of multidirectional composite laminates. Thin-Walled Structures 2023;182:110235. https://doi.org/10.1016/J.TWS.2022.110235.

[20] Tu W, Pascoe JA, Alderliesten R. Comparison of mode II delamination behaviours in multidirectional and unidirectional composite laminates. Compos B Eng 2025;291:111941. https://doi.org/10.1016/J.COMPOSITESB.2024.111941.

[21] Choi NS, Kinloch AJ WJG. Delamination fracture of multidirectional carbon-fiber/epoxy composites under mode I, mode II and mixed-mode I/II loading. J Compos Mater 1999;33:73–100.

[22] Polaha JJ, Davidson BD, Hudson RC PA. Effects of mode ratio, ply orientation and precracking on the delamination toughness of a laminated composite. J Reinforced Plast Compos 1996;15:141–73.

[23] Hwang JH, Lee CS, Hwang W. Effect of crack propagation directions on the interlaminar fracture toughness of carbon/epoxy composite materials. Applied Composite Materials 2001 8:6 2001;8:411–33. https://doi.org/10.1023/A:1012663722334.

[24] Hwang JH, Kwon O, Lee CS, Hwang W. Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials. Mechanics of Composite Materials 2000 36:2 2000;36:117–30. https://doi.org/10.1007/BF02681828.

[25] Moustapha Sarr M, Kosaka T. Effect of cellulose nanofibers on the fracture toughness mode II of glass fiber/epoxy composite laminates. Heliyon 2023;9:e13203. https://doi.org/10.1016/J.HELIYON.2023.E13203.

[26] Syed Abdullah SIB, Bokti SK, Wong KJ, Johar M, Chong WWF, Dong Y. Mode II and mode III delamination of carbon fiber/epoxy composite laminates subjected to a four-point bending mechanism. Compos B Eng 2024;270:111110. https://doi.org/10.1016/J.COMPOSITESB.2023.111110.

[27] Gfrerrer M, Koss V, Wiener J, Schuecker C, Brunner AJ, Pinter G. Comparing Mode I, Mode II and Mixed-Mode I/II interlaminar fracture toughness of glass and carbon fiber reinforced polymer laminates with the same epoxy matrix system. Eng Fract Mech 2025;320:111009. https://doi.org/10.1016/J.ENGFRACMECH.2025.111009.

[28] Ever J. Barbero. Finite Element Analysis of Composite Materials Using Abaqus. Taylor & Francis Group; 2013.

[29] Shahverdi M, Vassilopoulos, Anastasios P, Keller T. Mixed-mode I/II fracture behavior of asymmetric adhesively-bonded pultruded composite joints. Eng Fract Mech 2013.

[30] Valvo PS. A physically consistent virtual crack closure technique for I/II/III mixed-mode fracture problems. Procedia Materials Science 2014;3:1983–7. https://doi.org/10.1016/J.MSPRO.2014.06.319.

[31] Valvo PS. On the calculation of energy release rate and mode mixity in delaminated laminated beams. Eng Fract Mech 2016;165:114–39. https://doi.org/10.1016/J.ENGFRACMECH.2016.08.010.

[32] Reeder J, Song K, Chunchu P, Ambur D. Postbuckling and Growth of Delaminations in Composite Plates Subjected to Axial Compression 2002. https://doi.org/10.2514/6.2002-1746.

[33] Rice JR. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. J Appl Mech 1968;35:379–86. https://doi.org/10.1115/1.3601206.

[34] Benzeggagh ML, Kenane M. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos Sci Technol 1996;56:439–49. https://doi.org/10.1016/0266-3538(96)00005-X.

[35] Barbero EJ, Reddy JN. Jacobian derivative method for three-dimensional fracture mechanics. Communications in Applied Numerical Methods 1990;6:507–18. https://doi.org/10.1002/CNM.1630060703;WGROUP:STRING:PUBLICATION.

[36] Ozdil F, Carlsson LA DP. Beam analysis of angle-ply laminate end-notched flexure specimens. Compos Sci Technol 1998;58:1929–38.

[37] Davidson BD, Kru¨ger R KM. Three dimensional analysis and resulting design recommendations for unidirectional and multidirectional end-notched flexure tests. J Compos Mater 1995;29:2108–33.

[38] Tao J, Sun CT. Influence of ply orientation on delamination in composite laminates. J Compos Mater 1998;32:1933–47. https://doi.org/10.1177/002199839803202103;CTYPE:STRING:JOURNAL.

[39] Chow WT AS. Stress intensity factors as the fracture parameters for delamination crack growth in composite laminates. Composites 1997;28:375–84.

[40] Raju IS, Crews JH AMA. Convergence of strain energy release rate components for edge delaminated composite laminates. Engng Fract Mech 1988;30:383–96.

[41] Narayan SH BJL. Designation of mode mix in orthotropic composite delamination problems. Int J Fract 1998;90:383–400.

[42] Test Method for Determination of the Mode II Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites 2019. https://doi.org/10.1520/D7905_D7905M-19E01.

[43] Samborski S. Analysis of the end-notched flexure test configuration applicability for mechanically coupled fiber reinforced composite laminates. Compos Struct 2017;163:342–9. https://doi.org/10.1016/J.COMPSTRUCT.2016.12.051.