PSI - Issue 33

M.F.M.O. Rosas et al. / Procedia Structural Integrity 33 (2021) 115–125 Rosas et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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angles of the outer chamfer. Actually, the balance between the strength and ductility of this adhesive means that it can undergo moderate plasticization and, thus, the difference in peak stresses do not lead to significant variations in the joint behaviour. Moreover, due to the good characteristics of this adhesive, plasticization of the inner aluminium tube takes place, and final failure of the joints is governed by this phenomenon. As a result, all P m are virtual identical disregarding  . The results depicts a maximum deviation of -0.03% for  =7.5º, over  =90º. 3.2.2. Inner chamfer This Section presents the numerical analysis of the tubular adhesive joints’ behaviour with inner chamfer at the overlap ends, including σ y and τ xy stress distributions, P -  curves and P m estimation for the Araldite ® 2015. The values of inner chamfer angle (  ), studied numerically, were 7.5  , 15  , 30  , 45  , 60  and 90  . Fig. 7 (a) depicts the σ y / τ avg stress distribution curves as a function of  , for the selected adhesive. The application of an inner chamfer at the overlap ends gives rise to two additional σ y peak stress concentrations, which add to the ones at the overlap edges. At the chamfered regions, the cross section is reduced, which increases longitudinal strains and results in higher local σ y / τ avg stress. On the other hand, the peaks at the overlap ends reduce by chamfering the adherends. The second peak is between the two ends of the tubular adhesive joint, where there is a reduction in stress concentration. The highest value of σ y / τ avg occurs for the joint without geometrical modifications (  =90  ). The results show that the inner chamfer reduces the maximum σ y / τ avg up to 14.9% for  =30  , compared to  =90  . Fig. 7 (b) depicts the τ xy / τ avg stress distributions as a function of  for the Araldite ® 2015. τ xy stresses also show two additional loci of stress concentration peaks adding to the peaks at the overlap ends. However, here the difference is more significant in the sense that now these intermediate peaks hold the highest τ xy / τ avg stress, i.e., the highest τ xy / τ avg is now where the inner chamfer of the tubular adhesive joint starts. This is because the differential deformation of the adherends in the area where the inner chamfer starts is quite accentuated. The peak stress τ xy / τ avg reduces for smaller  , attaining a maximum reduction of the peak τ xy / τ avg of 59.7% for  =7.5º, when compared to  =90º.

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 y /  avg

 xy /  avg

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x / L O

x / L O

7.5º

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90°

7.5º

15°

30°

45°

60°

90°

a)

b)

Fig. 7.  y (a) and  xy (b) stress distributions in the adhesive as a function of  .

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P [kN]

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 [mm]

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Fig. 8. P -  curves as a function of  .