PSI - Issue 25

R.M.D. Machado et al. / Procedia Structural Integrity 25 (2020) 71–78 Machado et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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This performance can be attributed to the Araldite ® 2015 ability to keep the damaged zones of the adhesives under stress whilst the stress propagates to the entire bondline. The standard deviation of the experimental tests for each joint condition was also within acceptable values, i.e. 8.5% for L O =12.5 mm. Fig. 4 (b) depicts an experimental P m comparison made between the stepped-lap joints tested in this work and SLJ and DLJ tested in previous works (Carvalho and Campilho 2016, Carvalho and Campilho 2017), considering identical geometrical parameters ( L O , L T , t A , t P and width). The DLJ always overshoots the SLJ and stepped-lap joint results by a large amount while the stepped-lap joint performs slightly better than the SLJ. The maximum difference of the DLJ over the stepped-lap joint was 117.6% found for L O =20 mm. Over the SLJ, the stepped-lap joint gives better results by 19.7% for L O =37.5 mm. The overall improved strength of the DLJ is naturally associated to doubling the bond area for the same L O , which superimposes to differences in the stress distributions between these joint types. Between the stepped-lap joint and SLJ, the stepped-lap joint excels in providing slightly smoother stress distributions (i.e., lower  y /  avg and  xy /  avg peak values). Stress (MAXS, QUADS and MAXPS) and strain (MAXE, QUADE and MAXPE) based damage initiation criteria were tested numerically by the XFEM to assess P m and compared with experimental data as presented in Fig. 5 (a). The QUADS criterion presented the closest results to the experimental ones. Actually, the maximum relative P m deviation found with this criterion was 7%, for L O =12.5 mm. Regarding the MAXS criterion, the maximum deviation was 28%, found for L O =25 mm. Furthermore, both MAXE and QUADE criteria showed a large P m over prediction, of 338 and 329%, respectively, for L O =12.5 mm. Applying the MAXPS criterion, P m was once more under estimated regardless the L O value, with the maximum deviation of 83% being found for L O =50 mm. This was due to the quick attainment of the limit stress, and since P m corresponds, by approximation, to crack initiation in the adhesive layer. Regarding the MAXPE criterion, the maximum deviation for the experimental P m was 158% for L O =12.5 mm. Throughout this analysis, it was possible to conclude that the XFEM is an accurate tool for the P m prediction of stepped-lap joints by applying both MAXS and QUADS criteria in ductile adhesives. 4.4. Numerical results with different damage initiation and propagation criteria

a)

b)

25

25

20

20

15

15

P m [kN]

P m [kN]

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10

5

5

0

0

0

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L 0 [mm]

L 0 [mm]

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Linear 0.5

Linear 1 Expo 2

Linear 2

Experimental

QUADS MAXPS

MAXS

QUADE

Expo 0.5

Expo 1

MAXE

MAXPE

Fig. 5 – P m comparison between the experimental and numerical data as a function of L O considering different damage initiation criteria (a) and different damage growth criteria (b).

The evaluation of the damage propagation criterion effect for the P m prediction of the stepped-lap joint includes varying the parameter α in the propagation criterion of expression (5), considering the values of 0.5, 1 and 2, for further comparison with the experimental data and both linear and exponential softening laws. Concerning the damage initiation criterion, the QUADS criterion will be applied due to the good accuracy, as concluded in the former study. Fig. 5 (b), depicts a comparison regarding the P m predictions (XFEM analysis) for the different damage evolution criteria and the experimental results. P m was over predicted for all α values applied with the exponential power law criterion. The maximum deviation regarding experimental P m was 304% (for the exponential law with  =2 and