Abstract
We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E=E0(z/c0)k (0<k<1) while Poisson's ratio ν remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of Pcr=-(k+3)πRΔγ/2 where Δγ is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k=0, the Gibson solid when k→1 and ν=0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off.
Original language | English |
---|---|
Pages (from-to) | 1437-1448 |
Number of pages | 12 |
Journal | Journal of the Mechanics and Physics of Solids |
Volume | 57 |
Issue number | 9 |
DOIs | |
Publication status | Published - Sept 2009 |
Externally published | Yes |
Keywords
- Contact mechanics
- Elastic graded materials
- Gibson material
- JKR model
- Pull-off force