PSI - Issue 33

R.F.P. Resende et al. / Procedia Structural Integrity 33 (2021) 126–137 Resende et al. / Structural Integrity Procedia 00 (2019) 000 – 000

132

7

( ) F q 

(

)

(7)

2 = −

2   − − = DP y 1 p

3

0.

 

y DP

Equation (7) relates the deviatoric and hydrostatic stresses. Nevertheless, if λ DP is equal to the unity, equation (7) takes the form of the von Mises yield criterion. 4. Results 4.1. Strain and stress distributions Fig. 4 shows the effective plastic strains (  11 ) at P m in the adhesive layer using the von Mises and Exponential Drucker Prager yield criteria. It should be noted that this adhesive has non-zero plastic strains at the overlap mid region for L O =12.5 mm and 25 mm. However, as L O increases, the strains in the middle of the joint become null. This is because, for lower L O there is a more uniform distribution of stresses throughout the joint, which causes the plasticization of the entire adhesive layer instead of just the overlap edges. As L O increases, there is a more pronounced stress concentration at the overlap edges, which leads to failure before plasticization at the middle of the adhesive layer. It is also possible to verify that, in general, higher values of effective plastic strains are obtained along L O by the vM yield criterion in relation to the EDP yield criterion. However, for small L O , the EDP yield criterion presents slightly higher strain values.

0.3

0.3

0.2

0.2

 11

 11

0.1

0.1

0

0

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Normalised L O (mm/mm) 12.5 25.0 37.5 50.0

Normalised L O (mm/mm) 12.5 25.0 37.5 50.0

a)

b)

Fig. 4. Effective plastic strain in the adhesive layer at P m using the von Mises yield criterion (a) and the Drucker-Prager yield criterion (b).

3

3

2

2

τ xy / τ avg

τ xy / τ avg

1

1

0

0

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Normalised L O (mm/mm) 12.5 25.0 37.5 50.0

Normalised L O (mm/mm) 12.5 25.0 37.5 50.0

a)

b)

Fig. 5. Shear stresses in the adhesive layer at P m using the von Mises (a) and the Drucker-Prager yield criteria (b).

Fig. 5 presents shear stresses normalized by the average shear stress in the overlap (  xy /  avg ) at P m using the von Mises (a) and the Drucker-Prager yield criteria (b). Through data analysis it is found that  xy /  avg peak stresses occur