PSI - Issue 12

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

272

8

( E ∗ w ) 1 / 2 b 1 / 2

1 − ν 2 (1 − 2 ν ) 1 / 2

P PO A PO

4 3

(20)

= −

σ PO =

and hence here by equating σ PO to theoretical strength, we obtain

b cr =

=

(1 − ν ) 2 1 − 2 ν

(1 − ν ) 2 1 − 2 ν

E ∗ w σ 2 th

1 2

1 2

8 9

(21)

b cr , f rictionless

and therefore this time the critical layer thickness becomes dependent on Poisson’s ratio, rendering the layer adhesive much more e ff ective .

2.3. Incompressible bonded layer

The results of the previous paragraph hold until the layer is nearly incompressible, in which case a similar procedure yields

(3 Rw ) 2 / 3 (2 b ) 1 / 2

8 5

w 1 / 6 E ∗ 1 / 6

P PO = −

(22)

L

while a PO = 6 Rb

and δ 1 , PO = b

w 3 E ∗ R

w 3 E ∗ R

1 / 3

1 / 3 , which is therefore rather di ff erent from the frictionless counter

part. Hence, in this case the average stress in the contact at pull-o ff is

(3 Rw 2 E ∗ ) 1 / 3 b

P PO A PO

2 5

(23)

= −

σ PO =

and we return to see e ff ects of the radius of the indenter (i.e. qualitative e ff ects on the geometry) like in the halfplane problem.

3. Conclusions

In this communication, we show that ultrastrong adhesion can be reached in line contact for contact of a Hertzian indenter with ultrathin layers supported by a rigid foundation, suggesting a new possible strategy for ”optimal adhe sion”. There are some details which di ff er in plane contact vs axisymmetric contact (see Papangelo (2018)): indeed, in line contact adhesion enhancement occurs as an increase of the actual pull-o ff force, while in the Hertzian axisym metric case pull-o ff di ff ers form the classical JKR halfspace solution only by a prefactor. However, in both cases the enhancement occurs because the dominant length scale for the stress intensity factor at the contact edge is the layer thickness, and this induces a reduction of the size of contact needed to sustain the pull-o ff force. These e ff ects are remarkably further enhanced by Poisson’s ratio e ff ects in the case of nearly incompressible layer.

References

Argatov, I., Li, Q., Pohrt, R., Popov, V.L., (2016), Johnson-Kendall-Roberts adhesive contact for a toroidal indenter, Proceedings of the Royal Society A 472: 20160218. Barber, J. R. (1990). Contact problems for the thin elastic layer. International journal of mechanical sciences, 32(2), 129-132.