PSI - Issue 37

5

Almudena Majano-Majano et al. / Procedia Structural Integrity 37 (2022) 492–499 Almudena Majano-Majano et al. / Structural Integrity Procedia 00 (2019) 000 – 000

496

where B and h are the specimen dimensions (Fig. 1) and G LR the shear modulus in the LR plane of the adherend. The CBBM scheme considers a corrected flexural modulus E f of the adherend rather than E L to account for material variability, local stress concentrations and the root rotation effect produced at the crack tip during the test, since Eq. (4) is derived assuming perfect clamping. The E f expression relies on the initial compliance value ( C 0 ) and the initial crack length ( a 0 ) corrected by the William’s factor ( Δ ) (Williams (1989)) as follows ( ) ( ) 1 3 0 0 0 3 LR 12 8 5 f a a E C BhG Bh − +  +    =  −    (5)



2

f E

1  +           

3 2

h

 =

(6)

 −

11

G

 

LR

LR f E E G

R

(7)

1.18

 =

Eqs. (4-6) can be solved by an iterative process until convergence of E f is achieved. An equivalent crack length, a eq , rather than a is also consider in Eq. (4), which is evaluated from a polynomial function in Matlab® as the theoretical length to comply with the specimen compliance during crack propagation (de Moura et al. (2008a)). Combining the relationships above (Eqs. (3-7)), G I would take the form

2 B h E h    2 6 2 eq 2 P a

  

1

G

=

+ 

(8)

I

2

5

G



LR

f

The G I can be finally correlated with the w I measured by digital image correlation (DIC) technique during the test (Eq. (2)) and its derivative gives the cohesive law of the material (Eq. (1)). To soften the noise before differentiation, G I -w I relationship was adjusted by a logistic approximation function as follows

1 w w − A A

G

A

=

+

2

(9)

(

)

I

2

p

1 / +

,0

I

I

where A 1 , A 2 , p and w I,0 are parameters determined by regression analysis. Particularly, A 2 provides an estimate of the critical strain energy release rate value as

2 w A G G → = = lim I I

(10)

Ic

3. Results and Discussion 3.1. Strain energy release rate

The load versus displacement curves derived from the DCB tests on bonded specimens are shown in Fig. 3 (left). The results are fairly consistent considering the typical variations in wood, with maximum load values ranging from 126 N to 174 N. The initial compliance C 0 was determined using Matlab ® as the result which provides the maximum R 2 in every P- δ curve.