One of the first analytical models of the concrete-composite bond strength was derived by Taljsten (1996), starting both from a linear approach, based on the beam theory, and from a non-linear approach, related to fracture mechanics. In case of most of the epoxy adhesives commonly used, a simplified formulation, as reported in Equation 5, was obtained.
Figure 9, from 9a to 9e, shows possible shapes of the bond-slip function: (a) cut-off, adopted by Neubauer and Rostasy (Chen & Teng 2001); (b) bilinear, assumed by some guidelines like fib Bulletin 14 (2001) and CNR-DT 200 (2004), and by Monti (Lu et al. 2005), Brosens and Van Gemert (Karb-hari et al. 2006) and Lu (Lu et al. 2004); (c) rigid with linear softening, by Chen & Teng (2001); (d) a single function, as the Popovics curve chosen by Savoia et al. (2003a) and Nakaba et al. (2001), or an exponential curve obtained by Dai et al. (2005); (e) two different non-linear functions for ascending and descending branch, for instance the expressions adopted by Lu et al. (2004) or Dai & Ueda (2003).
Therefore, it is commonly assumed that bond of composite laminates exhibits a softening behaviour, with an ascending branch followed by a descending one, and presenting no residual stress for wider slip.
To calibrate the bond-slip law on the experimental results, this combined approach was adopted: tangential stress and interface slip points (t-s) were obtained from strain-gauges monitoring, while the fracture energy value, Gf, was calculated from failure loads trough Equation 7.
Fracture energy represents a restraint for the bondslip function (Eq. 4) and allows to reduce the number of free parameters involved in the calibration process.
Equations 9-11 briefly report the main relations (obtained from simple equilibrium and compatibility considerations) between reinforcement strain e, interface tangential stress t and slip s, supposing to disregard the slip component of the substrate, sufficiently stiffer than composite. The notation x indicates the coordinate along the central axis of the bonded region.
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