PSI - Issue 47

7

J.E.S.M. Silva et al. / Procedia Structural Integrity 47 (2023) 70–79 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

76

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

x' 2     + − − y' x' 2

( )

( ) .sin 2 , 

y'

.cos 2



=

  −

(2)

y

x'y'

x' 2   +

( )

( ) .cos 2 . 

y'

.sin 2



=−

  +

(3)

xy

x'y'

Due to the similarity of stress curves between the three adhesives, only results for the 2015 are shown (Fig. 7), with further topical discussions on the differences between them.  y stresses (Fig. 7 a) are notoriously less significant that  xy stresses for small  , but they increase up to reaching equivalent values to  xy stresses for  =45°. Stresses peak at the bond edges are observed, but the gradient reduces by increasing  . For the 2015, the peak absolute values of  y /  avg stresses rise from 0.89 to 1.23 (between limit  ).  xy stresses (Fig. 7 b) are close to uniform in the adhesive layer, only showing small peaks at the bond edges. However, these peaks become less significant for higher  values (Campilho et al. 2007). The peak absolute values of  xy /  avg reduce from 1.13 to 1.06 between  =3.43 and 45º, respectively. Between adhesives, a tendency was found for higher peak stresses by increasing the adhesive stiffness, i.e., peak stresses were highest for the AV138 and lowest for the 7752. Moreover, the differences between adhesives were higher for  y than for  xy stresses. This study shows that, overall, TSJ with smaller  excel in stress distributions by reduction of peak  y /  avg stresses, despite an increase of  xy stress gradients. Since the  reduction leads in parallel to an exponential increase of the bond area between the adherends, it is clear that small  are preferred (Campilho et al. 2011a).

a)

b)

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