##
**Cohesive zone modeling of interfacial stresses in plated beams.**
*(English)*
Zbl 1176.74059

Summary: The elastic analysis of interfacial stresses in plated beams has been the subject of several investigations. These studies provided both first-order and higher-order solutions for the distributions of interfacial shear and normal stresses close to the plate end in the elastic range. The notable attention devoted to this topic was driven by the need to develop predictive models for plate end debonding mechanisms, as the early models of this type adopted debonding criteria based on interfacial stresses. Currently, approaches based on fracture mechanics are becoming increasingly established. Cohesive zone modeling bridges the gap between the stress- and energy-based approaches. While several cohesive zone analyses of bonded joints subjected to mode-II loading are available, limited studies have been conducted on cohesive zone modeling of interfacial stresses in plated beams. Moreover, the few available studies present complex formulations for which no closed-form solutions can be found. This paper presents an analytical cohesive zone model for the determination of interfacial stresses in plated beams. A first-order analysis is conducted, leading to closed-form solutions for the interfacial shear stresses. The mode-II cohesive law is taken as bilinear, as this simple shape is able to capture the essential properties of the interface. A closed-form expression for the debonding load is proposed, and the comparison between cohesive zone modeling and linear-elastic fracture mechanics predictions is discussed. Analytical predictions are also compared with results of a numerical finite element model where the interface is described with zero-thickness contact elements, using the node-to-segment strategy and incorporating decohesion and contact within a unified framework.

### MSC:

74E30 | Composite and mixture properties |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

### Keywords:

cohesive zone modeling; fiber reinforced polymer reinforcement; interfacial stresses; plate end debonding
PDF
BibTeX
XML
Cite

\textit{L. de Lorenzis} and \textit{G. Zavarise}, Int. J. Solids Struct. 46, No. 24, 4181--4191 (2009; Zbl 1176.74059)

Full Text:
DOI

### References:

[1] | Au, C.; Buyukozturk, O.: Debonding of FRP plated concrete: a tri-layer fracture treatment, Eng. fract. Mech. 73, No. 3, 348-365 (2006) |

[2] | Barenblatt, G. I.: The formation of equilibrium cracks during brittle fracture. General ideas and hypothesis. Axisymmetrical cracks, J. appl. Math. mech. (PMM) 23, 434-444 (1959) · Zbl 0095.39202 |

[3] | Carpinteri, A.; Lacidogna, G.; Paggi, M.: Acoustic emission monitoring and numerical modelling of FRP delamination in RC beams with non-rectangular cross-section, RILEM mater. Struct. 40, 553-566 (2007) |

[4] | Chen, J. F.; Teng, J. G.: Anchorage strength models for FRP and steel plates bonded to concrete, J. struct. Eng., ASCE 127, No. 7, 784-791 (2001) |

[5] | Chen J.F., Teng J.G. (Es.), 2005. Bond behavior of FRP in structures. In: Proceedings of the International Symposium on Bond Behavior of FRP in Structures, The Hong Kong Polytechnic University, Hong Kong, China. |

[6] | Cornetti P., Puzzi S., Carpinteri A., 2007. Failure mechanisms in beams strengthened with adhesive strips. In: Proceedings of the XVIII AIMETA Conference on CD-ROM, Brescia, Italy. |

[7] | Dai, J.; Ueda, T.; Sato, Y.: Development of nonlinear Bond-slip model for fiber reinforced plastics sheet – concrete interfaces with a simple method, J. compos. Constr. 9, No. 1, 52-62 (2005) |

[8] | De Lorenzis, L.; Zavarise, G.: Modeling of mixed-mode debonding in the peel test applied to superficial reinforcements, Int. J. Solids struct. 45, 5419-5436 (2008) · Zbl 1177.74355 |

[9] | De Lorenzis, L.; Zavarise, G.: Interfacial stress analysis and prediction of debonding for a thin plate bonded to a curved substrate, Int. J. Non-linear mech. 44, 358-370 (2009) |

[10] | De Lorenzis, L.; Teng, J. G.; Zhang, L.: Elastic interfacial stresses in curved members bonded with a thin plate, Int. J. Solids struct. 43, No. 25 – 26, 7501-7517 (2006) · Zbl 1120.74613 |

[11] | De Lorenzis, L., Paggi, M., Carpinteri, A., Zavarise, G., in press. Linear elastic fracture mechanics approach to edge debonding in rectilinear and curved plated beams. Adv. Struct. Eng. |

[12] | Deng, J.; Lee, M. M. K.; Moy, S. S. J.: Stress analysis of steel beams reinforced with a bonded CFRP plate, Compos. struct. 65, No. 2, 205-215 (2004) |

[13] | Dugdale, D. S.: Yielding of steel sheets containing slits, J. mech. Phys. solids 8, 100-104 (1960) |

[14] | Ferracuti, B.; Savoia, M.; Mazzotti, C.: A numerical model for FRP-concrete delamination, Compos. part B – eng. 37, No. 4 – 5, 356-364 (2006) |

[15] | FIB, 2001. Externally bonded FRP reinforcement for RC structures, CEB-FIP Bulletin No. 14, Fédération Internationale du Béton, Lausanne, Switzerland. |

[16] | Greco, F.; Lonetti, P.; Blasi, N.: An analytical investigation of debonding problems in beams strengthened using composite plates, Eng. fract. Mech. 74, No. 3, 346-372 (2007) |

[17] | Holzenkämpfer, P., 1994, Ingenieurmodelle des verbundes geklebter bewehrung für betonbauteile. Dissertation, TU Braunschweig. |

[18] | Karam, G.N., 1992. Optimal design for prestressing with FRP sheets in structural members. Advanced composite materials in bridge and construction. In: Neale K.W., Labossiere P., (Ed.). Canadian Society for Civil Engineering. Quebec, Canada, pp. 277 – 285. |

[19] | L’Hermite, R., Bresson, J., 1967. Béton armé par collage d,armature. RILEM Colloquium. Eyrolles Ed., Paris. |

[20] | Lu, X. Z.; Teng, J. G.; Ye, L. P.; Jiang, J. J.: Bond-slip models for FRP sheets/plates bonded to concrete, Eng. struct. 27, No. 6, 920-937 (2005) |

[21] | Malek, A. M.; Saadatmanesh, H.; Ehsani, M. R.: Prediction of failure load of R/C beams strengthened with FRP plate due to stress concentration at the plate end, ACI struct. J. 95, No. 1, 142-152 (1998) |

[22] | Niu, H.; Wu, Z.: Numerical analysis of debonding mechanism in FRP-strengthened RC beams, Computer-aided civil infrastruct. Eng. 20, No. 5, 354-368 (2005) |

[23] | Paggi, M., 2005. Interface Mechanical Problems in Heterogeneous Materials. Ph.D. Thesis, Politecnico di Torino, Torino, Italy. · Zbl 1196.74059 |

[24] | Rabinovitch, O.; Frostig, Y.: Closed-form high-order analysis of RC beams strengthened with FRP strips, J. compos. Constr. ASCE 4, 65-74 (2000) |

[25] | Rabinovitch, O.: Fracture-mechanics failure criteria for RC beams strengthened with FRP strips – a simplified approach, Compos. struct. 64, 479-492 (2004) |

[26] | Rabinovitch, O.: Debonding analysis of fiber-reinforced-polymer strengthened beams: cohesive zone modeling versus a linear elastic fracture mechanics approach, Eng. fract. Mech. 75, 2842-2859 (2008) |

[27] | Rabinovitch, O.; Frostig, Y.: Delamination failure of RC beams strengthened with FRP strips – a closed-form high-order and fracture mechanics approach, J. eng. Mech. 127, No. 8, 852-861 (2001) |

[28] | Roberts, T. M.; Haji-Kazemi, H.: Theoretical study of the behavior of reinforced concrete beams strengthened by externally bonded steel plates, Proc. inst. Civil eng., part 2 87, 39-55 (1989) |

[29] | Shen, H. S.; Teng, J. G.; Yang, J.: Interfacial stresses in beams and slabs bonded with thin plates, J. eng. Mech., ASCE 127, No. 4, 399-406 (2001) |

[30] | Smith, S. T.; Teng, J. G.: Interfacial stresses in plated beams, Eng. struct. 23, 857-871 (2001) |

[31] | Smith, S. T.; Teng, J. G.: FRP-strengthened RC beams. I. review of debonding strength models, Eng. struct. 24, No. 4, 385-395 (2002) |

[32] | Smith, S. T.; Teng, J. G.: FRP-strengthened RC beams. II. assessment of debonding strength models, Eng. struct. 24, No. 4, 397-417 (2002) |

[33] | Stratford, T.; Cadei, J.: Elastic analysis of adhesion stresses for the design of a strengthening plate bonded to a beam, Constr. building mater. 20, No. 1 – 2, 34-45 (2006) |

[34] | Taljsten, B., 1994. Plate bonding, strengthening of existing concrete structures with epoxy bonded plates of steel or fibre reinforced plastics, Doctoral Thesis 1994:152D, Div. of Structural Engineering, Luleå University of Technology, ISSN 0348 – 8373, p 308. |

[35] | Taljsten, B.: Strengthening of concrete prism using the plate-bonding technique, Int. J. Fract. 82, No. 3, 253-266 (1996) |

[36] | Taljsten, B.: Strengthening of beams by plate bonding, J. mater. Civil eng., ASCE 9, No. 4, 206-212 (1997) |

[37] | Teng, J. G.; Yuan, H.; Chen, J. F.: FRP-to-concrete interfaces between two adjacent cracks: theoretical model for debonding failure, Int. J. Solids struct. 43, No. 18 – 19, 5750-5778 (2006) · Zbl 1120.74795 |

[38] | Triantafillou, T. C.; Deskovic, N.: Innovative prestressing with FRP sheets: mechanics of short-term behavior, J. eng. Mech. 117, No. 7, 1652-1672 (1991) |

[39] | Tvergaard, V.; Hutchinson, J. W.: The relation between crack growth resistance and fracture process parameters in elastic – plastic solids, J. mech. Phys. solids 40, 1377-1397 (1992) · Zbl 0775.73218 |

[40] | Vilnay, O.: The analysis of reinforced concrete beams strengthened by epoxy bonded steel plates, Int. J. Cem. compos. Lightweight concr. 10, No. 2, 73-78 (1988) |

[41] | Wang, J.: Cohesive zone model of intermediate crack induced debonding of FRP-plated reinforced concrete beam, Int. J. Solids struct. 43, No. 21, 6630-6648 (2006) · Zbl 1120.74797 |

[42] | Wang, J.: Debonding of FRP plated reinforced concrete beam, a Bond-slip analysis. I. theoretical formulation, Int. J. Solids struct. 43, No. 21, 6649-6664 (2006) · Zbl 1120.74798 |

[43] | Wriggers, P.; Zavarise, G.; Zohdi, T. I.: A computational study of interfacial debonding damage in fibrous composite materials, Comput. mater. Sci. 12, 39-56 (1998) |

[44] | Wu, Z.; Yuan, H.; Niu, H.: Stress transfer and fracture propagation in different kinds of adhesive joints, J. eng. Mech. 128, No. 5, 562-573 (2002) |

[45] | Xu, X. P.; Needleman, A.: Numerical simulations of fast crack growth in brittle solids, J. mech. Phys. solids 42, No. 9, 1397-1434 (1994) · Zbl 0825.73579 |

[46] | Yang, J., Wu, Y.F., 2005. Interfacial stresses in FRP plated concrete beams including shear deformation effect. In: Proceedings, International Symposium on Bond Behaviour of FRP in Structures, 7 – 9 December, Hong Kong, China, pp. 169 – 173. |

[47] | Yang, J.; Teng, J. G.; Chen, J. F.: Interfacial stresses in soffit-plated reinforced concrete beams, Proc. inst. Civil eng. Struct. buildings 157, 77-89 (2004) |

[48] | Yang, Q. S.; Peng, X. R.; Kwan, A. K. H.: Strain energy release rate for interfacial cracks in hybrid beams, Mech. res. Commun. 33, No. 6, 796-803 (2006) · Zbl 1192.74331 |

[49] | Yang, J.; Ye, J.; Niu, Z.: Simplified solutions for the stress transfer in concrete beams bonded with FRP plates, Eng. struct. 30, 533-545 (2008) |

[50] | Yuan, H.; Teng, J. G.; Seracino, R.; Wu, Z. S.; Yao, J.: Full-range behaviour of FRP-to-concrete bonded joints, Eng. struct. 26, 553-565 (2004) |

[51] | Zavarise G., 1991. Problemi termomeccanici di contatto – aspetti fisici e computazionali. Ph.D. thesis, Università di Padova, Padova, Italy. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.