Evaluating the validity of the cohesive zone model in mixed mode I + III fracture of Al-alloy 2024-T3 adhesive joints using DBM-DCB tests
Source abstract
Abstract
Recently, numerous papers have been conducted to study the fracture mechanism of adhesively bonded joints in mixed mode I + II fracture. Nevertheless, the lack of an efficient fixture to capture mixed mode I + III fracture is seen in these studies. The first aim of this paper is representing a fixture that provides pure fracture modes I and III and different combinations of these modes. In the next parts of the paper, this testing configuration has been used to evaluate the accuracy of the cohesive zone modeling (CZM) in predicting the mixed mode I + III fracture at the adhesively bonded structures. A series of fracture tests and finite element simulations have been conducted on the adhesively bonded double cantilever beam specimens using the suggested fixture to determine the cohesive laws of the Araldite 2015 adhesive under mixed mode I + III loading situation. The cohesive laws have been calculated through a direct method from the experimental examinations and implemented in the FEM simulations of the tests. Eventually, the comparison between force-crack opening displacement curves resulting from the experimental tests and the numerical simulations in various combinations of the modes I and III loading states demonstrate the accuracy of the cohesive model in these loading conditions.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Fatigue and fracture mechanics · High-Velocity Impact and Material Behavior · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (69)
Show source-provided references
1. Ajdani A, Ayatollahi MR, Akhavan-Safar A, Martins da Silva LF (2020) Mixed mode fracture characterization of brittle and semi-brittle adhesives using the SCB specimen. Int J Adhes Adhes 101:102629. https://doi.org/10.1016/j.ijadhadh.2020.10262910.1016/j.ijadhadh.2020.102629 ↗
2. Akhavan-Safar A, Ayatollahi MR, Safaei S, da Silva LFM (2020) Mixed mode I/III fracture behavior of adhesive joints. Int J Solids Struct 199:109–119. https://doi.org/10.1016/j.ijsolstr.2020.05.00710.1016/j.ijsolstr.2020.05.007 ↗
3. Aliha MRM, Ayatollahi MR (2013) Two-parameter fracture analysis of SCB rock specimen under mixed mode loading. Eng Fract Mech 103:115–123. https://doi.org/10.1016/j.engfracmech.2012.09.02110.1016/j.engfracmech.2012.09.021 ↗
4. Aliha MRM, Ayatollahi MR (2014) Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading: A statistical approach. Theor Appl Fract Mech 69:17–25. https://doi.org/10.1016/j.tafmec.2013.11.00810.1016/j.tafmec.2013.11.008 ↗
5. Aliha MRM, Saghafi H (2013) The effects of thickness and Poisson’s ratio on 3D mixed-mode fracture. Eng Fract Mech 98:15–28. https://doi.org/10.1016/j.engfracmech.2012.11.00310.1016/j.engfracmech.2012.11.003 ↗
6. Aliha MRM, Bahmani A, Akhondi S (2015) Numerical analysis of a new mixed mode I/III fracture test specimen. Eng Fract Mech 134:95–110. https://doi.org/10.1016/j.engfracmech.2014.12.01010.1016/j.engfracmech.2014.12.010 ↗
7. Aliha MRM, Bahmani A, Akhondi S (2016) A novel test specimen for investigating the mixed mode I + III fracture toughness of hot mix asphalt composites: experimental and theoretical study. Int J Solids Struct 90:167–177. https://doi.org/10.1016/j.ijsolstr.2016.03.01810.1016/j.ijsolstr.2016.03.018 ↗
8. ASTM D6671, D6671M-06 (2006M) Standard test method for mixed mode I-mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites. ASTM International, West Conshohocken
9. Ayatollahi MR, Aliha MRM (2009) Analysis of a new specimen for mixed mode fracture tests on brittle materials. Eng Fract Mech 76:1563–1573. https://doi.org/10.1016/j.engfracmech.2009.02.01610.1016/j.engfracmech.2009.02.016 ↗
10. Ayatollahi MR, Saboori B (2015) A new fixture for fracture tests under mixed mode I/III loading. Eur J Mech A 51:67–76. https://doi.org/10.1016/j.euromechsol.2014.09.01210.1016/j.euromechsol.2014.09.012 ↗
11. Ayatollahi MR, Aliha MRM, Saghafi H (2011) An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Eng Fract Mech 78:110–123. https://doi.org/10.1016/j.engfracmech.2010.10.00110.1016/j.engfracmech.2010.10.001 ↗
12. Bahmani A, Farahmand F, Janbaz MR et al (2021) On the comparison of two mixed-mode I + III fracture test specimens. Eng Fract Mech 241:107434. https://doi.org/10.1016/j.engfracmech.2020.10743410.1016/j.engfracmech.2020.107434 ↗
13. Bažant ZP, Estenssoro LF (1979) Surface singularity and crack propagation. Int J Solids Struct 15:405–426. https://doi.org/10.1016/0020-7683(79)90062-310.1016/0020-7683(79)90062-3 ↗
14. Berto F, Ayatollahi MR, Campagnolo A (2016) Fracture tests under mixed mode I + III loading: an assessment based on the local energy. Int J Damage Mech 26:881–894. https://doi.org/10.1177/105678951662831810.1177/1056789516628318 ↗
15. Bödeker F, Marzi S (2020) Applicability of the mixed-mode controlled double cantilever beam test and related evaluation methods. Eng Fract Mech 235:107149. https://doi.org/10.1016/j.engfracmech.2020.10714910.1016/j.engfracmech.2020.107149 ↗
16. Brenet P, Conchin F, Fantozzi G et al (1996) Direct measurement of crack-bridging tractions: a new approach to the fracture behaviour of ceramic/ceramic composites. Compos Sci Technol 56:817–823. https://doi.org/10.1016/0266-3538(96)00026-710.1016/0266-3538(96)00026-7 ↗
17. Chai H (1992) Experimental evaluation of mixed-mode fracture in adhesive bonds. Exp Mech 32:296–303. https://doi.org/10.1007/BF0232558110.1007/BF02325581 ↗
18. Chai H (2021) Bond thickness effect in mixed-mode fracture and its significance to delamination resistance. Int J Solids Struct 219–220:63–80. https://doi.org/10.1016/j.ijsolstr.2021.03.00610.1016/j.ijsolstr.2021.03.006 ↗
19. Chang J, Xu J, Mutoh Y (2006) A general mixed-mode brittle fracture criterion for cracked materials. Eng Fract Mech 73:1249–1263. https://doi.org/10.1016/j.engfracmech.2005.12.01110.1016/j.engfracmech.2005.12.011 ↗
20. Cox BN, Marshall DB (1991) The determination of crack bridging forces. Int J Fract 49:159–176. https://doi.org/10.1007/BF0003504010.1007/BF00035040 ↗
21. da Silva LFM, de Magalhães FACRG, Chaves FJP, de Moura MFSF (2010) Mode II fracture toughness of a brittle and a ductile adhesive as a function of the adhesive thickness. J Adhes 86:891–905. https://doi.org/10.1080/00218464.2010.50615510.1080/00218464.2010.506155 ↗
22. Davidson BD, Sediles FO (2011) Mixed-mode I–II–III delamination toughness determination via a shear–torsion-bending test. Compos A Appl Sci Manuf 42:589–603. https://doi.org/10.1016/j.compositesa.2011.01.01810.1016/j.compositesa.2011.01.018 ↗
23. Ducept F, Davies P, Gamby D (2000) Mixed mode failure criteria for a glass/epoxy composite and an adhesively bonded composite/composite joint. Int J Adhes Adhes 20:233–244. https://doi.org/10.1016/S0143-7496(99)00048-210.1016/S0143-7496(99)00048-2 ↗
24. Figueiredo JCP, Campilho RDSG, Marques EAS et al (2018) Adhesive thickness influence on the shear fracture toughness measurements of adhesive joints. Int J Adhes Adhes 83:15–23. https://doi.org/10.1016/j.ijadhadh.2018.02.01510.1016/j.ijadhadh.2018.02.015 ↗
25. Gu P (1993) Notch sensitivity of fiber-reinforced ceramics. Int J Fract 70:253–266. https://doi.org/10.1007/BF0001293810.1007/BF00012938 ↗
26. Högberg JL, Stigh U (2006) Specimen proposals for mixed mode testing of adhesive layer. Eng Fract Mech 73:2541–2556. https://doi.org/10.1016/j.engfracmech.2006.04.01710.1016/j.engfracmech.2006.04.017 ↗
27. Johnston AL, Davidson BD, Simon KK (2014) Assessment of split-beam-type tests for mode III delamination toughness determination. Int J Fract 185:31–48. https://doi.org/10.1007/s10704-013-9897-110.1007/s10704-013-9897-1 ↗
28. Joki RK, Grytten F, Hayman B, Sørensen BF (2020) A mixed mode cohesive model for FRP laminates incorporating large scale bridging behaviour. Eng Fract Mech 239:107274. https://doi.org/10.1016/j.engfracmech.2020.10727410.1016/j.engfracmech.2020.107274 ↗
29. Kafkalidis MS, Thouless MD (2002) The effects of geometry and material properties on the fracture of single lap-shear joints. Int J Solids Struct 39:4367–4383. https://doi.org/10.1016/S0020-7683(02)00344-X10.1016/S0020-7683(02)00344-X ↗
30. Kamat SV, Srinivas M, Rama Rao P (1998) Mixed mode I/III fracture toughness of Armco iron. Acta Mater 46:4985–4992. https://doi.org/10.1016/S1359-6454(98)00170-010.1016/S1359-6454(98)00170-0 ↗
31. Kanninen MF, Popelar CA, Saunders H (1988) Advanced Fracture Mechanics. CRC Press, London10.1115/1.3269540 ↗
32. Khoo TT, Kim H (2011) Effect of bondline thickness on mixed-mode fracture of adhesively bonded joints. J Adhes 87:989–1019. https://doi.org/10.1080/00218464.2011.60066810.1080/00218464.2011.600668 ↗
33. Lan W, Deng X, Sutton MA, Cheng C-S (2006) Study of slant fracture in ductile materials. Int J Fract 141:469–496. https://doi.org/10.1007/s10704-006-9008-710.1007/s10704-006-9008-7 ↗
34. Li V, Ward R (1989) A novel testing technique for post-peak tensile vehavior of cementitous materials. In: Mihashi H, Takahashi H, Wittmann FH (eds) Fract toughness fract energy. Springer, New York, pp 183–195
35. Li VC, Maalej M, Hashida T (1994) Experimental determination of the stress-crack opening relation in fibre cementitious composites with a crack-tip singularity. J Mater Sci 29:2719–2724. https://doi.org/10.1007/BF0035682310.1007/BF00356823 ↗
36. Lin B, Mear ME, Ravi-Chandar K (2010) Criterion for initiation of cracks under mixed-mode I + III loading. Int J Fract 165:175–188. https://doi.org/10.1007/s10704-010-9476-710.1007/s10704-010-9476-7 ↗
37. Liu S, Chao YJ, Zhu X (2004) Tensile-shear transition in mixed mode I/III fracture. Int J Solids Struct 41:6147–617210.1016/j.ijsolstr.2004.04.044 ↗
38. Loh L, Marzi S (2018a) A mixed-mode controlled DCB test on adhesive joints loaded in a combination of modes I and III. Procedia Struct Integr 13:1318–1323. https://doi.org/10.1016/j.prostr.2018.12.27710.1016/j.prostr.2018.12.277 ↗
39. Loh L, Marzi S (2018b) An out-of-plane loaded double cantilever beam (ODCB) test to measure the critical energy release rate in mode III of adhesive joints. Int J Adhes Adhes 83:24–30. https://doi.org/10.1016/j.ijadhadh.2018.02.02110.1016/j.ijadhadh.2018.02.021 ↗
40. Loh L, Marzi S (2019) A novel experimental methodology to identify fracture envelopes and cohesive laws in mixed-mode I + III. Eng Fract Mech 214:304–319. https://doi.org/10.1016/j.engfracmech.2019.03.01110.1016/j.engfracmech.2019.03.011 ↗
41. Lopes Fernandes R, Teixeira de Freitas S, Budzik MK et al (2019) From thin to extra-thick adhesive layer thicknesses: fracture of bonded joints under mode I loading conditions. Eng Fract Mech 218:106607. https://doi.org/10.1016/j.engfracmech.2019.10660710.1016/j.engfracmech.2019.106607 ↗
42. Madhusudhana KS, Narasimhan R (2002) Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint. Eng Fract Mech 69:865–883. https://doi.org/10.1016/S0013-7944(01)00110-210.1016/S0013-7944(01)00110-2 ↗
43. Pang HLJ (1995) Mixed mode fracture analysis and toughness of adhesive joints. Eng Fract Mech 51:575–583. https://doi.org/10.1016/0013-7944(94)00310-E10.1016/0013-7944(94)00310-E ↗
44. Papini M, Fernlund G, Spelt JK (1994) The effect of geometry on the fracture of adhesive joints. Int J Adhes Adhes 14:5–13. https://doi.org/10.1016/0143-7496(94)90015-910.1016/0143-7496(94)90015-9 ↗
45. Pham KH, Ravi-Chandar K (2014) Further examination of the criterion for crack initiation under mixed-mode I+III loading. Int J Fract 189:121–138. https://doi.org/10.1007/s10704-014-9966-010.1007/s10704-014-9966-0 ↗
46. Pirondi A, Nicoletto G (2002) Mixed mode I/II fracture toughness of bonded joints. Int J Adhes Adhes 22:109–117. https://doi.org/10.1016/S0143-7496(01)00042-210.1016/S0143-7496(01)00042-2 ↗
47. Rao BSSC, Srinivas M, Kamat SV (2008) The effect of mixed mode I/III loading on the fracture toughness of Timetal 834 titanium alloy. Mater Sci Eng A 476:162–16810.1016/j.msea.2007.05.059 ↗
48. Razavi SMJ, Berto F (2019) A new fixture for fracture tests under mixed mode I/II/III loading. Fatigue Fract Eng Mater Struct 42:1874–1888. https://doi.org/10.1111/ffe.1303310.1111/ffe.13033 ↗
49. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386. https://doi.org/10.1115/1.360120610.1115/1.3601206 ↗
50. Richard HA, Benitz K (1983) A loading device for the creation of mixed mode in fracture mechanics. Int J Fract 22:R55–R58. https://doi.org/10.1007/BF0094272610.1007/BF00942726 ↗
51. Robinson P, Song DQ (1992) A new mode Iii delamination test for composites. Adv Compos Lett 1:096369359200100501. https://doi.org/10.1177/09636935920010050110.1177/096369359200100501 ↗
52. Sadeghi MZ, Zimmermann J, Gabener A, Schröder KU (2021) On the bondline thickness effect in mixed-mode fracture characterisation of an epoxy adhesive. J Adhes 97:282–304. https://doi.org/10.1080/00218464.2019.165661410.1080/00218464.2019.1656614 ↗
53. Seifi R, Omidvar N (2013) Fatigue crack growth under mixed mode I+ III loading. Mar Struct 34:1–1510.1016/j.marstruc.2013.07.001 ↗
54. Sharif F, Kortschot MT, Martin RH (1995) Mode III delamination using a split cantilever beam. In: Martin RH (ed) Composite materials: fatigue and fracture: fifth volume. ASTM International, West Conshohocken, pp 85–9910.1520/STP14009S ↗
55. Shetty DK, Rosenfield AR, Duckworth WH (1987) Mixed-mode fracture in biaxial stress state: application of the diametral-compression (Brazilian disk) test. Eng Fract Mech 26:825–840. https://doi.org/10.1016/0013-7944(87)90032-410.1016/0013-7944(87)90032-4 ↗
56. Shimamoto K, Sekiguchi Y, Sato C (2016) Mixed mode fracture toughness of adhesively bonded joints with residual stress. Int J Solids Struct 102–103:120–126. https://doi.org/10.1016/j.ijsolstr.2016.10.01110.1016/j.ijsolstr.2016.10.011 ↗
57. Sørensen BF, Jacobsen TK (2003) Determination of cohesive laws by the J integral approach. Eng Fract Mech 70:1841–1858. https://doi.org/10.1016/S0013-7944(03)00127-910.1016/S0013-7944(03)00127-9 ↗
58. Sørensen BF, Jacobsen TK (2009) Characterizing delamination of fibre composites by mixed mode cohesive laws. Compos Sci Technol 69:445–456. https://doi.org/10.1016/j.compscitech.2008.11.02510.1016/j.compscitech.2008.11.025 ↗
59. Sørensen BF, Jørgensen K, Jacobsen TK, Østergaard RC (2006) DCB-specimen loaded with uneven bending moments. Int J Fract 141:163–176. https://doi.org/10.1007/s10704-006-0071-x10.1007/s10704-006-0071-x ↗
60. Stamoulis G, Carrere N, Cognard JY et al (2014) On the experimental mixed-mode failure of adhesively bonded metallic joints. Int J Adhes Adhes 51:148–158. https://doi.org/10.1016/j.ijadhadh.2014.03.00210.1016/j.ijadhadh.2014.03.002 ↗
61. Sukumar N, Moës N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Methods Eng 48:1549–1570. https://doi.org/10.1002/1097-0207(20000820)48:11%3c1549::AID-NME955%3e3.0.CO;2-A10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A ↗
62. Suo Z, Ho S, Gong X (1993) Notch ductile-to-brittle transition due to localized inelastic band. J Eng Mater Technol 115:319–326. https://doi.org/10.1115/1.290422510.1115/1.2904225 ↗
63. Szekrényes A (2006) Prestressed fracture specimen for delamination testing of composites. Int J Fract 139:213–237. https://doi.org/10.1007/s10704-006-0043-110.1007/s10704-006-0043-1 ↗
64. Teixeira JMD, Campilho R, da Silva FJG (2018) Numerical assessment of the double-cantilever beam and tapered double-cantilever beam tests for the GIC determination of adhesive layers. J Adhes 94:951–973. https://doi.org/10.1080/00218464.2017.138390510.1080/00218464.2017.1383905 ↗
65. Vaishakh KV, Narasimhan R (2019) On the evaluation of energy release rate and mode mixity for ductile asymmetric four point bend specimens. Int J Fract 217:65–82. https://doi.org/10.1007/s10704-019-00369-710.1007/s10704-019-00369-7 ↗
66. Wei Y, Hutchinson JW (1998) Interface strength, work of adhesion and plasticity in the peel test BT. In: Knauss WG, Schapery RA (eds) Recent advances in fracture mechanics: honoring Mel and Max Williams. Springer, Dordrecht, pp 315–33310.1007/978-94-017-2854-6_16 ↗
67. Williams JG, Ewing PD (1972) Fracture under complex stress: The angled crack problem. Int J Fract Mech 8:441–446. https://doi.org/10.1007/BF0019110610.1007/BF00191106 ↗
68. Xeidakis G, Samaras I, Zacharopoulos D, Papakaliatakis G (1996) Crack growth in a mixed-mode loading on marble beams under three point bending. Int J Fract 79:197–20810.1007/BF00032936 ↗
69. Yang QD, Thouless MD (2001) Mixed-mode fracture analyses of plastically-deforming adhesive joints. Int J Fract 110:175–187. https://doi.org/10.1023/A:101086970699610.1023/A:1010869706996 ↗