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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et al., Gustafson et al. and Azari et al. methods are not shown since they are equal to Kinloch’s results. The different methods provide R -curves with identical evolution during the test, always showing a constant G T region leading to average G T estimation. However, the 2015 results revealed an increasing G T until G T stabilization because of the known plasticity of this adhesive. Small deviations were found between methods.

4.0

0.8

3.0

0.6

2.0

0.4

0.2 G T [N/mm]

1.0 G T [N/mm]

0.0

0.0

40

60

80

100 120 140 160 180

40

50

60

70

80

90

100

a [mm]

a [mm]

a)

b)

Grady

Kinloch

Brussat et al.

Grady

Kinloch

Brussat et al.

Fig. 3. G T R -curves: AV138 (a) and 2015 (b) adhesives.

Fig. 4 shows G I and G II for the Grady, Kinloch, and da Silva et al. methods. Irrespectively of the adhesive, the curves agree with G T curve evolution. It was found that the da Silva et al. results have a bigger G I proportion over G T , and the Kinloch’ method show the smallest G I , which takes place because of different mode partitioning formulations.

0.8

3.0

0.6

2.0

0.4

1.0 G T [N/mm]

0.2 G T [N/mm]

0.0

0.0

40

50

60

70

80

90

100

40

60

80

100 120 140 160 180

a [mm]

a [mm]

GT Grady GT Kin.

GI-Grady GII-Grady

GI-Kinloch GII-Kinloch

GI-da Silva GII-da Silva

GT Grady GT Kin.

GI Grady GII Grady

GI Kin. GII Kin.

GI da Sil. GII da Sil.

a)

b)

Fig. 4. G I and G II R -curves: AV138 (a) and 2015 (b) adhesives.

3.2. Mixed-mode behavior The mixed-mode law to numerically model bonded joints can be found by plotting the fracture envelope, established by a power-law expression of the type

I G G G G  



IC         

  

II

(7)

1.



IIC

In this expression,  and  represent the exponents to characterize the shape of the fracture curve (envelope). Considering  =  =1 promotes a straight line between G IC and G IIC , and has been applied to bonded joints (Campilho 2017). Nonetheless, different behaviors were also documented. This work evaluates  =  =1/2, 1, 3/2 and 2. The fracture envelopes were created by plotting G IC and G IIC at the graphic’s axes, taken from DCB ( G IC ) and ENF data ( G IIC ), as presented in Table 1. Fig. 5 shows the obtained plots for both adhesives, emphasizing that mode partitioning is identical for the methods of Grady and Kinloch. On the other hand, the method of da Silva et al. method is offset by a higher preponderance of G I . For the AV138 (Grady and Kinloch methods),  =1 provides the best approximation, with the exception of one data point predicted by the Kinloch’s approach being near the  =1/2 function. The collected data points calculated by the method of da Silva et al. become close to the  =3/2 and 2 functions. Considering the