PSI - Issue 51

R.B.P. Barros et al. / Procedia Structural Integrity 51 (2023) 17–23 R.B.P. Barros et al. / Structural Integrity Procedia 00 (2022) 000–000

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Table 1. Measured properties of the Araldite ® adhesives (Campilho et al. 2011).

Properties

Araldite ® AV138

Araldite ® 2015

Young’s modulus, E [GPa]

4.89±0.81

1.85±0.21

Poisson coefficient, ν

0.35 a

0.33 a

Tensile yield stress, σ y [MPa] Tensile strength, σ f [MPa] Tensile failure strain, ε f [%] Shear modulus, G [GPa] Shear yield stress, τ y [MPa] Shear strength, τ f [MPa] Shear failure strain, γ f [%]

36.49±2.47 39.45±3.18 1.21±0.10 25.10±0.33 30.20±0.40 7.80±0.70 1.56 b

12.63±0.61 21.63±1.61 4.77±0.15 14.60±1.30 17.90±1.80 43.90±3.40 0.43±0.02 0.56 b

Tensile fracture toughness, G IC [N/mm] 0.25±0.03 c

Shear fracture toughness, G IIC [N/mm] 4.70±0.34 a Manufacturer data, b From Hooke’s law, c Constante et al. (2015), d Leitão et al. (2016) 0.62±0.07 d

2.3. Theoretical methods The data from the tests was applied to several methods aiming to estimate G , G I and G II : Grady (1992), Kinloch (2012), Brussat et al. (1977), Gustafson et al. (1989), Azari et al. (2009), and da Silva et al. (2011). 2.3.1. Grady’s method Grady (1992) proposes energy conservation principles for G calculation as a function of P . The total fracture energy ( G T ) is obtained by the Irwis-Kies equation 2 T , with . 2 P dC G C b da P    (1) Mode partitioning ( G I and G II ) is accomplished by applying G I / G T =0.235.

2.3.2. Kinloch’s method Kinloch (2012) suggests the application of the following equation for G T calculation 2 T 2 2 0 1 1 , 2 P G b Ee Ee        

(2)

in which e 0 is the total specimen thickness (including upper and lower adherends) and E represents the adherends’ Young’s modulus. Kinloch suggested G I / G II =0.2 to be applied for mode partitioning. 2.3.3. Brussat el al. method Brussat et al. (1977) based their work on the Beam Theory leading to a closed-form solution to estimate G I and G II . According to this formulation, G T for an infinite length CLS specimen is written as

    EA EA



   

2

P

2

1  

,

(3)

G



 

T

2

b EA

 

2

0

in which ( EA ) 2 provides the stiffness of the upper adherend, while ( EA ) 0 gives the overall specimen stiffness (including the lower and upper adherends). Mode partitioning is given by G I / G T =4/7. Further details on the method are given in the authors’ reference.