PSI - Issue 12

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

269

5

Fig. 2. Dimensionless pull-o ff stress versus the dimensionless adhesion parameter l a . The average pull-o ff stress is bounded at − σ PO σ th = 1 .

π E ∗

16

P PO , HP = − 3 L

; a PO , HP =

1 / 3

1 / 3

π E ∗ w 2 R

2 wR 2

(11)

3 2

32 R

1 / 3

π 2 E ∗ 2 w

P PO , HP A PO , HP

= −

(12)

σ PO , HP =

which does include some dependence on elastic modulus which is not present in the axisymmetric halfspace problem of JKR model (Johnson et al., 1971), but it seems to be quite di ff erent in terms of power law dependence from the ”layered” case. Indeed, take the ratio

R 1 / 6 b 1 / 4

w E ∗

16 1 / 3 π 1 / 3 2 1 / 4

1 / 12

P PO P PO , HP

8 9

(13)

=

which shows how there are really di ff erent power law dependences in the layer limit. The full curve P − δ is then obtained using (1) δ = a 2 / 2 R − 2 w b E ∗

(14)