PSI - Issue 33

A.F.M.V. Silva et al. / Procedia Structural Integrity 33 (2021) 138–148 Silva et al. / Structural Integrity Procedia 00 (2019) 000–000

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joint stiffness and shear-lag effects, thus increasing the stress concentrations. Thus, L O has a significant effect on τ xy stresses, by increasing peak stresses with this parameter. Compared to L O =10 mm, the  xy /  avg peak stresses near to x / L O =0 increased by 24.3% ( L O =15 mm) and 64.1% ( L O =20 mm). The fact that the tubular joints are under dynamic loads also influences stress distributions overall, since it causes the unstable behavior of the curves due to the impact stress waves. Fig. 6 (b) relates to the t SE effect. Here,  xy stress variations are not so significant as for the L O effect, and the  xy /  avg stress variations were relatively minor. Increasing t SE gradually reduces  xy /  avg peak stresses near to x / L O =1 at the expense of higher concentrations near to x / L O =0. This phenomenon is due to the increase in the differential deformation effect between the two tubes. Thus, by increasing t SE , near to x / L O =1 the outer tube will have smaller longitudinal strains, reducing  xy /  avg peak stresses accordingly. On the other hand, the overlap edge near to x / L O =0 will become increasingly loading, due to the change in the load transmission pattern. Compared to the base joint with t SI = t SE =2 mm, changing t SE to 1 mm virtually not affects peak stresses, while the  xy /  avg peak stress variation increases gradually by increasing t SE up to 4 mm, in this case up to 24.8% near to x / L O =0 and -36.5% (negative variation) near to x / L O =1.

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Fig. 7.  y /  avg stresses in the adhesive layer as a function of L O (a) and t SE (b).

 y stresses are presented in Fig. 7 for both parametric studies: L O (a) and t SE (b). Disregarding the geometry,  y stress plots peak at the overlap edges, with nearby minor compressive peaks, while being essentially nil at the inner overlap. This behavior is associated with the tubes’ rotation at the overlap due to the load eccentricity. Equally to  xy stresses, no symmetry exists, due to identical reasons. A significant L O effect is also present here, denoted by the increase of  y /  xy peak stresses at both overlap edges with L O . Higher L O increases the stiffness of the adhesive joint, and also the transmitted loads, which lead to a local increase in the installed stresses. Furthermore, since higher L O promote a bigger unloaded region at the central region of the overlap, the normalized  y peak stresses will naturally increase. Taking the tubular joints with L O =10 mm as basis, the percentile improvements over this condition were 27.1% for L O =15 mm and 61.8% for L O =20 mm. The slight oscillations in the curves are yet again explained by the dynamic character of the applied load. The value of t SE affects  y stress distributions to a much smaller extent than  xy stresses, with moderate variations. However, the changing pattern with t SE is much alike that of  xy stresses. Actually, higher t SE increase  y /  avg peak stresses nearby x / L O =0, while keeping their magnitude approximately constant near to x / L O =1. This effect is mostly caused by the stiffness improvement of the outer tube relatively to the inner tube, which concentrates deflections in the vicinity of x / L O =0 and therefore increases peak stresses in that area. In direct comparison to the tubular joints with t SI = t SE =2 mm (base geometry), varying t SE to 1 mm reduces  y peak stresses up to 21.9% (nearby x / L O =1), while t SE up to 4 mm causes higher  y peak stresses up to a difference of 23.2% (near to x / L O =0) and 5.3% (near to x / L O =1). 3.3. Joint strength The dynamic strength of the tubular adhesive joints bonded with the Araldite ® AV138 was assessed by P m , considering the same geometric variations of L O and t SE of the stress analysis. Fig. 8 shows the P m vs. L O (a) and t SE (b) plots that enable the visualization of P m evolution with these parameters. Fig. 8 (a) shows a highly non-proportional