PSI - Issue 39

Umberto De Maio et al. / Procedia Structural Integrity 39 (2022) 677–687 Author name / Structural Integrity Procedia 00 (2019) 000–000

678

2

Nomenclature d

scalar damage variable Young’s modulus of the bulk

E

I II , G G modal components of the energy release rate I II , c c G G critical mode-I and mode-II fracture energies 0 0 , n s K K normal and tangential interfacial elastic stiffness parameters mesh L mesh size κ dimensionless normal stiffness parameter ξ dimensionless tangential stiffness parameter , n s t t normal and tangential components of the cohesive traction vector , nc sc t t critical normal and tangential interface stresses m δ mixed-mode displacement jump , n s δ δ normal and tangential components of the displacement jump ν Poisson’s ratio of the bulk   δ displacement jump between the crack faces

1. Introduction The retrofitting technique by means of Fiber Reinforced Polymers (FRP) sheets bonded to the tension face of the structural elements has been widely employed in the civil engineering field to improve the flexural strength and stiffness of such elements as well as the load-carrying capacity of the entire existing concrete structures. The FRP based reinforcement systems possess superior mechanical properties respect to the traditional ones (e.g. based on steel plates), such as a good resistance to corrosion and fire, an high strength-to-weight ratio, and an excellent tensile and compressive behavior under general loading conditions as clearly showed in several experimental and numerical works (Triantafillou and Plevris (1992); Greco et al. (2018a), (2018b)). However, this retrofitting technique exposes the strengthened structural elements to premature failure modes associated to debonding of the FRP plate (or sheet) from the concrete substrate. The debonding phenomena can be grouped into plate-end and intermediate crack-induced debonding. On the one hand, the first group includes the debonding mechanisms induced by the nucleation of a crack at the cut-off section of the FRP plate due to a high local shear stress concentration (Aram et al. (2008); Gralle and Sneed (2013)). In the most of cases, such a crack propagates within the adhesive layer of the FRP system, but in the presence of low-strength concrete elements it involves the concrete substrate below the tensile steel rebars, leading to the concrete cover separation failure, as reported in Gao et al. (2004). On the other hand, the intermediate crack induced debonding resulting from stress concentrations near the shear/flexural cracks belongs to the second group. In this case, the debonding generally occurs within the adhesive layer in correspondence of the maximum bending moment region and self-propagates along the FRP-to-concrete interface towards the plate end (Yao et al. (2005)). The debonding phenomena have been investigated by numerous researchers through numerical models mainly based on strength and fracture approaches, leading to great contributions to the understanding of this kind of failure. The strength-based models predict the load level of the related debonding mechanism by means of linearly elastic stress analyses along the interface between concrete and FRP system. In detail, the debonding mechanism appears when the evaluated stresses exceed the critical material strength. These approaches include the shear capacity models, the concrete tooth models, and the interfacial stress models (Oehlers and Moran (1990); Zhang et al. (2021); Verhoosel et al. (2009)). However, such models are based on the common assumption that all constituent materials of the structure are linearly elastic, thus neglecting the strong nonlinear cracking behavior of the concrete, thus providing approximate solutions in terms of failure load levels and critical shear/normal stresses, which are generally too inaccurate. On the other hand, the fracture-based models are nowadays more employed respect to the strength models for the prediction of the debonding failure in strengthened concrete elements since are able to capture the high stress intensities, which induce the debonding crack nucleation, by involving both elastic and fracture properties of all