PSI - Issue 25

F.J.C.F.B. Loureiro et al. / Procedia Structural Integrity 25 (2020) 63–70 Loureiro et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3 shows the obtained tensile and shear experimental R -curves of a representative SLB specimen. The results show that both curves are similar, yet presenting different magnitudes. Actually, J I =0.3663±0.0073 N/mm (percentile standard deviation of 1.99%) and J II =0.263±0.016 N/mm (percentile standard deviation of 6.08%).

3.3. Fracture envelope

This Section plots the fracture envelope of the Araldite ® 2015 using J IC and J IIC data taken from pure-mode DCB and ENF tests, respectively (Santos and Campilho 2017). It should be mentioned that this data relates to the same geometric and material conditions to the SLB tests carried out in this work. In the plot of Fig. 4, the pure-mode values situate each on one axis, while power law equations of the following type, initially proposed by Wu and Reuter (1965), populate the mixed-mode behavior in-between both pure-modes

I       + =         II IC IIC J J J J

1.

(13)

In this work, the equality  =  was considered and, thus, throughout the manuscript, the power law exponent is generically mentioned as  . The values of 1/2, 1, 3/2 and 2 are tested by direct comparison with the experimental data points, in an attempt to check which  frames best the experimental behavior of the adhesive. Fig. 4 presents the fracture envelope, compared against the experimental data points of the SLB tests. The experimental data points showed a close match between tested specimens (standard deviations of 2.0% and 6.0% for J I and J II , respectively). The power law exponent of  =1/2 is the best match between the considered idealized laws, but the placement of the data points is slightly above the curve.

0.6

0.5

0.4

0.3

0.2 J I [N/mm]

0.1

0

0

0.5

1

1.5

2

2.5

3

3.5

J II [N/mm]

1/2

1

3/2

2

Experimental points

Fig. 4. Fracture envelopes with specified  and placement of the J I / J II SLB data points for the Araldite ® 2015.

3.4. Cohesive laws’ estimation

The derivation of the mode I and II CZM laws by the direct method included the use of polynomial functions applied to the J I -  n and J II -  s data of each specimen. To enable a good representation of the curves, polynomial functions up to the 8 th degree were considered. Fig. 5 shows the tensile (a) and shear (b) cohesive laws. The correspondence between either all tensile or shear curves was satisfactory in which pertains to the initial stiffness, t n 0 or t s 0 , and tensile (  n f ) or shear failure displacement (  s f ). The depicted data resembles the traditional triangular shape, many times considered to model adhesives by CZM, although with minor signs of plasticization near failure. Actually, t n 0 =16.9±1.1 MPa, t s 0 =6.45±0.31 MPa,  n f =0.0497±0.0096 mm and  s f =0.0888±0.0128 mm. Thus, non-negligible t n 0 and t s 0 deviations by default were found to the data presented in Table 1. It can be considered that the scatter between all specimens is acceptable.