PSI - Issue 12

A. Papangelo et al. / Procedia Structural Integrity 12 (2018) 265–273 A. Papangelo / Structural Integrity Procedia 00 (2018) 000–000

271

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Fig. 4. The ratio b cr a PO valid for b cr / a PO 1 .

2 , σ th = 20 MPa and E ∗ = 1 GPa and R / b = [10 , 50 , 100 , 500] . The present analysis is

is plotted versus l a for w = 10 mJ / m

To ascertain the range of validity of the present analysis we finally check the thin layer assumption, which requires the thickness of the layer to be smaller than the contact semi-width. Using the same material properties introduced above, we estimate the ratio b cr / a PO as

l 3 / 4 a

8 9 × 2 1 / 4 √

b cr a PO

(17)

=

R / b ( σ th / E ∗ ) 2

Eq. (17) is plotted in Fig. 4, for R / b = [10 , 50 , 100 , 500] and shows that the proposed design strategy is e ff ective, in particular for indenters with characteristic dimension ” R ” much larger that the layer thickness. For example a micrometric pillar indenting a nanometric layer would experience high adhesive performance fulfilling the thin layer assumption.

2.2. Bonded layer

Repeating the arguments presented above for a bonded compressible layer (Johnson (1985)), one finds

(1 − ν ) 1 / 2 2 1 / 4 (1 − 2 ν ) 1 / 4

w E ∗

E ∗ LR 1 / 2 (2 b ) 1 / 4

3 / 4

8 3

(18)

P PO = −

a PO = √ 2 R

w

1 / 4

(1 − 2 ν ) (1 − ν ) 2

b E ∗

(19)

and therefore for the bonded layer the Poisson’s e ff ect appears, which only changes a prefactor in the result for the frictionless foundation — but notice this prefactor makes the load diverge towards the incompressible limit ν = 0 . 5. Hence, in this case the average stress in the contact at pull-o ff is