PSI - Issue 41

7

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

42

10 15 20 25 30 35 40 45

P m [kN]

0 5

0

10

20

30

40

50

L O [mm]

Experimental

Numerical

Fig. 5 – Experimental and numerical P m vs. L O results for the tubular overlap joint.

4.2. Stress analysis The  y and  xy stresses, in the elastic domain, at loading are analysed in this Section for a detailed understanding of the joint mechanics as a function of  . To obtain the stress distributions along the adhesive layer, the previously defined models in Section 3.1 for the stress analysis were used. Since 10 solid elements were considered through thickness in the adhesive layer, it was possible to extract stresses at the adhesive mid-thickness.  y and  xy stresses were normalized by  avg , consisting of  xy for the respective  . Thus, a clear picture is obtained on the variation of peak stresses between joints. Since the joints under study are tapered due to the scarf geometry, the adhesive layer is not oriented with the reference axes. Thus, it becomes necessary to transform stresses in such a way that  y and  xy stresses are normal and tangential to the taper, respectively. This process was accomplished by Mohr’s circle considering the coordinate systems of Fig. 6 and the following expressions:

Fig. 6 – Coordinate systems xy and x’y’.

x' 2     + − − y ' x' 2

( )

( ) sin 2 , 

y '

cos 2



=

  −

(1)

y

x'y'

x' 2   +

( )

( ) cos 2 . 

y '

sin 2



= −

  +

(2)

xy

x'y'