Issue 48

J.P.S.M.B. Ribeiro et alii, Frattura ed Integrità Strutturale, 48 (2019) 332-347; DOI: 10.3221/IGF-ESIS.48.32 343 joints bonded with the Araldite ® 2015 suffered significant plasticization for L O =25 mm, although failing cohesively in the adhesive layer, while tensile adherend failure was encountered for L O >25 mm. Thus, the P m vs. L O curve presents a steady- state P m for L O ≥25 mm. Using the Sikaforce ® 7752 led to a diminished P m for L O =12.5 mm because of the adhesive strengths. Despite this fact, due to its toughness, this adhesive has an improved performance for bigger P m . This improvement is nearly linear up to L O =37.5 mm. Bigger L O promote the inner adherend’s failure and limit P m to  24 kN. a) b) Figure 10: Experimental P m values for the SLJ (a) and DLJ (b) bonded with the three adhesives. Mixed-mode crack propagation criterion validation Fig. 11, and Fig. 12, Fig. 13 show the comparison between the P m values obtained experimentally with the numerical ones for the different L O and  exponents for the SLJ (a) and DLJ (b) bonded with the Araldite ® AV138, Araldite ® 2015 and Sikaforce ® 7752, respectively. The pure-mode CZM laws of the adhesives were inserted by the definition of E , G xy , t n 0 , t s 0 , G IC and G IIC . These properties were all taken from the data of Tab. 3 , with the particularity that t n 0 and t s 0 are made equal to  f and  f , respectively [26]. The mixed-mode behaviour is defined from the damage initiation criterion (quadratic stress criterion in this case) and damage growth criterion (power law criterion with the user specification of  ). For the Araldite ® AV138 (Fig. 11), and first considering the SLJ, it can be concluded that the experimental P m points are closest to the numerical predictions with  =0.5. As a result, the experimentally obtained fracture envelope is considered valid, since the experimental and the numerical behaviours were in agreement. The largest percentile deviation between these two sets of values was -4.94% ( L O =12.5 mm). The highest offset was found for  =2, with a maximum deviation of +36.43% ( L O =50 mm). Identically, for the DLJ, the numerical curve relating to  =0.5 also proved to be the most accurate, and showed a maximum deviation to the experiments of -5.00% ( L O =50 mm). It should be mentioned that, for L O ≥25 mm, P m becomes affected by adherends’ plasticization for  =1, 1.5 and 2, which prevents predicted P m with a larger offset than that depicted in the figure. As a result of this discussion, the formerly obtained experimental envelope is validated. The results for the Araldite ® 2015 (Fig. 12) showed that, for the SLJ, the most suitable  is also 0.5, as predicted in the formerly discussed fracture tests, and that it gives a good representation of the experimental behaviour. The predicted P m are always above the experiments, with relative differences that range between +4.90% ( L O =37.5 mm) to +14.39 ( L O =12.5 mm). This enables validating the mixed-mode criterion for crack propagation. On the other hand, the other tested  revealed higher deviations by increasing  up to a value of 2. Here, the maximum offset was +40.74%, for L O =50 mm. An identical agreement was also found for the DLJ. However, for L O ≥25 mm, the joints’ failure becomes governed by the net adherends’ fracture, and the P m results between different  become insignificant. Also because of this, the deviations are generally not relevant. For  =0.5, the maximum error was -3.55% for L O =50 mm. Between all  , the maximum error was +5.46% (  =2 and L O =25 mm). As a result of this discussion, the formerly obtained experimental envelope is validated. In opposition to these two adhesives, for the Sikaforce ® 7752,  =2 is the best solution. However, it was found that, for the joints bonded with the Sikaforce ® 7752, the change of  does not result in large P m changes. Actually, for the SLJ, the offset between the tests and predictions steadily increased with L O , up to a maximum of -16.58, -15.84, -15.74, and -15.71% for L O =50 mm and increasing  from 0.5 up to 2. The DLJ are affected by the adherends’ failure at L O =50 mm. The maximum errors were obtained for L O =37.5 mm for all  , and took values of -15.50, -15.40, -15.39, and -15.39% by increasing order of  . On the other hand, for the joints bonded with the other two adhesives, the modification of  revealed a great influence on P m . A more detailed study showed that the influence of this parameter on P m gradually diminishes with the adhesives’ 0 5 10 15 20 25 30 0 12.5 25 37.5 50 P m [kN] L O [mm] Araldite® AV138 Araldite® 2015 Sikaforce® 7752 0 5 10 15 20 25 30 0 12.5 25 37.5 50 P m [kN] L O [mm] Araldite® AV138 Araldite® 2015 SikaForce® 7752