PSI - Issue 41

J.E.S.M. Silva et al. / Procedia Structural Integrity 41 (2022) 36–47 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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where  x’ ,  y’ , and  x’y’ are the software stress outputs, whilst  is the complementary angle to  ,  x ,  y , and  xy are the transformed stresses. Fig. 7 shows  y (a) and  xy (b) stress distributions in the bond-line for the scarf joints as a function of  . It was found that  y stresses are much smaller in magnitude than  xy stresses for the smaller values of  . The difference between  y and  xy reduces as  increases, when  =45° both stress components have a proximal magnitude. The peak  y stresses at the overlap edges, compared to the inner overlap, reduce by increasing  due to the corresponding reduction of localized adherends strains at the scarf tips. Nonetheless, the peak  y /  avg stresses increase from 0.89 (  =3.43º) to 1.23 (  =45º). On the other hand,  xy stresses keep an identical behaviour along the bond length, without the marked peaks at the overlap edges, as found for  y stresses, although the minor peak  xy stresses observed at the overlap edges also tend to become more uniform with the increase of  (Campilho et al., 2007). Actually, considering the scarf joint with  =45°,  xy stresses are practically constant. The peak  xy /  avg stresses increased from 1.04 (  =30º) to 1.13º (  =3.43º). This behaviour contrasts with overlap joints in which larger peak  xy stresses are found at the overlap edges due to significant shear-lag effects (Nunes et al., 2016). Overall, these results indicate that smaller  have an improved behaviour because of the reduction of normalized  y stresses, although minor τ stress gradients appear for small  . Furthermore, smaller  also corresponds to exponentially increasing the bond-line length ( LS ) which leads to a larger P m (Campilho et al., 2011a).

a)

b)

Fig. 7 – Normalized  y (a) and  xy stresses (b) in the adhesive layer.

4.3. Damage analysis

Former to the strength prediction, damage assessment in the adhesive layer at P m is performed to serve as a link between the stress distributions and the P m -  behaviour of the tubular joints. The stiffness degradation (SDEG) variable was used for this purpose, which varies between 0 (undamaged material; any point in the linear-elastic portion of the CZM law) and 1 (CZM element failure). To obtain the SDEG data, the model state was approximated to the analysis increment closest to P m . Fig. 8 plots the SDEG variable along x / L O in the tubular joints with different values of  . Regardless of  , the damage is mostly concentrated at the adhesive layer’s edges, with a higher incidence for smaller  , which agrees with the stress concentrations regions visible in Fig. 8. Damage is mostly nil at the inner overlap. Although SDEG peaks at both bond edges, there is a slight preponderance in the edge at x / L O =1 due to being the tip with the smaller tubular diameter. Smaller  tend to increase the peak SDEG at the bond edges. However, in the tubular joints with  =3.43°, the adherends were plasticized. As a result, the highest magnitude of damage occurred in the joints with  =10° (SDEG=0.53). Moreover, smaller  concentrate the damage over a less significant area at the bond edges.