PSI - Issue 64

Salvatore Verre et al. / Procedia Structural Integrity 64 (2024) 1508–1515 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1512

5

a

b

P

P

Fig. 3. (a) Debonding mechanism, (b) ratio ξ of P avg

* of specimens with two layers to P avg

* of specimens with one layer in function of L f .

Values of ξ is in the range 1.06 -1.51 were obtained. The smaller value of ξ was obtained from the results of Thermou et al. (2021), who observed different failure modes, including the tensile failure of the steel fibers and the debonding at the matrix-substrate interface. Values of ξ obtained by Ascione et al. (2020) and Thermou et al. (2021) represented with empty markers refer to the average peak loads of specimens that failed due to interlaminar debonding, failure of the substrate, and tensile failure of the steel fibers. Solid markers refer to specimens that failed due to interlaminar debonding only. It should be noted that in the case of interlaminar debonding, the fracture mechanics approach provides, for bonded lengths greater than the L eff , a theoretical value of ξ equal to 2 141 = . , as discussed in Section 3. The results shown in Fig. 3b highlight the need of further experimental works to assess the influence of the number of layers on the debonding load and failure mode of SRG-concrete joints. 3. Calibration of the CML based on the P - g responses The shear stress transfer at the concrete-SRG interface can be described in the framework of the fracture mechanics Mode II approach. This approach requires the definition of a  ( s ) relationship, i.e., an interfacial cohesive material law (CML), which associates any interfacial slip s with the corresponding shear stress  . When the CML is known, the mono-dimensional interfacial problem is described by the differential equation (Focacci et al. 2017)

p

2

d d

s

( ) s

f

(1)

=



2 y E A

SRG SRG

where y is a longitudinal (direction of the fibers) reference axis, E SRG and A SRG are the elastic modulus and cross sectional area of the SRG composite material, respectively, and p f is the width of the interfacial surface where the slip and the debonding occur. Eq. (1) is valid under the assumptions: i) the longitudinal displacements of the substrate are negligible compared to the longitudinal displacements of the SRG; ii) the SRG is a linear elastic material; iii) the slip and shear stress is constant along the width p f . Assumption i) implies that the composite strain profile  ( y ) is the derivative of slip profile s ( y ). The solution of Eq. (1) is the strain profile s ( y ) and can be determined by enforcing two boundary conditions to the profiles s ( y ) and/or  ( y ). From Eq (1) or using an energy balance approach (Santandrea et al. 2020) the debonding load can be obtained as

2 = deb f SRG SRG f P p E A G

(2)

where G f is the interfacial fracture energy, represented by the are under the  ( s ) curve. For the SRG material considered in this paper, the slip and debonding occur at the fiber-matrix interface. Therefore, in Eq. (1) the slip s ( y ) is the relative displacement between the fiber and the matrix and p f = b f , E SRG = E f , and A SRG = A f = b f t f . It should be noted that in this case the debonding load obtained from Eq. (2) is

1 f f P b E nt G 2 = deb f f

(3)