PSI - Issue 28

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Paolo Ferro et al. / Procedia Structural Integrity 28 (2020) 19–25 Ferro, P. and Berto, F. / Structural Integrity Procedia 00 (2019) 000–000

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The order of the singularity was found -0.3 (  = 0.7), in good agreement with the theoretical value of -0.301 (Akisanya, 1997) (Fig. 3). The GSIF is obtained by using numerical results and Eq. (7):

(  1)

  r

(  1)

H 0 

   r

(7)

f  (0)

In particular, by using experimental tensile stress to failure as a function of h, the H 0,C value was found to be 10.3 MPa mm 0.3 , irrespective of adhesive thickness size. It is noted that f θθ (0) is set equal to 1 (Eq. 7) since the angular stress distribution functions are always defined within a constant value. Ones these functions are obtained via numerical analysis (Fig. 4), the integral of  (  ) in Eq. (6) is calculated. Finally, by using Eq. (6) the critical radius resulted to be 6.2ꞏ10 -3 mm. That low value agrees well with the process zone size of bonded joints (Mintzas and Nowell, 2012; Reedy, 2000), which is much lower than that of welded joints, and is considered and intrinsic property of the bi material system under investigation, rather than a mere adhesive property only.

f rr (  )

1

f  (  )

0.8

0.6

f ij (  )

f r  (  )

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

 rad 

Fig. 4 – Angular stress distribution functions obtained via numerical analysis

4. ASED static failure criterion verification Table 1 summarizes the results of the simulations in terms of SED values corresponding to the experimental stress to failure as a function of adhesive thickness.

Table 1. Critical SED values derived from experimental results and comparison with the analytical value

Adhesive thickness, h (mm)

Stress to failure  l (MPa)*

C C (mJ/mm 3 )**

R C C (mJ/mm 3 ) (Eq. 5)

 (%)

W R

W

0.12

47.1 31.7 18.7 12.1

0.595 0.592 0.647 0.688

0.672 0.672 0.672 0.672

11.4 11.9

0.4 2.0 7.5

3.7 2.3

*(Suzuki, 1985) **FEM