PSI - Issue 64

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

1513

6

where n is the number of textile layers and t 1 f is the equivalent thickness of each layer. Eq. (3) implies that the debonding load in the case of n =2 is 2 141 = . times the debonding load in case of a single layer (Bencardino et al. 2018). This is consistent with the experimental results presented in Section 2.3 and justifies the assumption p f = b f . The average experimental P - g responses shown in Fig. 2a were used to calibrate the CML of the concrete-SRG interface. When a  ( s ) function depending on a set of unknown parameters collected in an array p is defined, Eq. (1) can be used to obtain the corresponding P n ( g ) function which associates the global slip g with the applied force P n in a single-lap shear test with n layers of textile. The P n ( g ) function obtained will, in turn, depend on the parameters in p . The procedure used to obtain the P n ( g ) function, called analytical load response in this paper, associated with a given n and CML is described in Santandrea et al. (2020). The calibration process consisted of minimizing the distance between the average experimental P - g responses and the analytical load responses P n ( g ). Parameters in the array p were determined by minimizing the function

( ) 2  p

   

f

 n N

 N

(

)

2

( ) p

( ) i

( ) p

n

  

− P P g exp

f

,

(4)

=

f

=

n

n,

i

n

P

max

,n

1 =

1 =

i

n

where N n =2 is the maximum of number of textile layers used in the experiments, P max, n is the maximum force of the average experimental P - g response of specimens with n layers of textile. ( ) n f p measures the distance between the average experimental P - g response of specimens with n layers of textile and the corresponding analytical P n ( g ), where g i and exp n,i P are the loaded end slip and corresponding applied force of the average experimental P - g response of specimens with n layers of textiles, and N is the number of points in the mentioned response. Three types of CML were used, namely a bilinear CML comprised of an initial linear branch followed by a descending branch with constant slope, a piecewise multilinear CML, and the CML proposed by Dai et al. (2006). The bilinear CML is defined by

if 0 if

 s s

s s

( )   =  s 

 

max 0

0

(5)

(

)

(

)

− − s s s s

  s s s

max  −



max

0

0

0

f

f

In this case, f m s ,s , p and G f =  max s f /2. The piecewise multilinear CML is defined by 0     = 

(

) (

)(

)

(

)

 +  −

if if

1

1

− − s s s s

  s s s

j

,...,m

=

−

1

1

1

j

j

j

j

j

j

j

j

+

+

+

( )   =  s

(6)

= s s

  

m

m

0

if s>s

m

where   1 2 , ,..., = m s s s s is an array of interfacial slips arranged in ascending order (with 1 0 = s ), and   1 2 , ,..., =    m τ is the array collecting the interfacial shear stress corresponding to the slips in s . s m was set equal to the maximum global slip of the average P - g responses. For the piecewise multilinear CML, p =  . The interfacial fracture energy can be determined by computing the area under the piecewise multilinear  ( s ) function, provided that

the shear stress is zero for slip greater than a certain s f . The CML proposed by Dai et al. (2006) is defined by ( ) ( ) 1 − −  = − s s s Ae e

(7)

  =  A, p and G f = A /2/  .

In this case,

The CMLs obtained by minimizing Eq. (4) where the P n ( g ) functions were obtained with the expressions (5), (6), and (7) are named CML bl , CML ml , and CML Dai , respectively. These CMLs are shown in Fig. 4a. It can be observed