Andrew Biehl
FWLM Project Proposal
4/21/15
Proposal
When two surfaces come into contact, the real contact area, 𝐴𝑟 , is typically only a fraction of the
apparent contact area, 𝐴𝑎 . The real contact area is significant, because it affects the friction coefficient
associated with adhesive bonding, 𝑓𝑎𝑑 .
𝑓𝑎𝑑 =
𝐴𝑟 ∙𝜏
𝐹𝑛
(1)
Where 𝐴𝑟 = the real contact area
𝐹𝑛 = the normal force
𝜏 = the shear strength at the weak spot of the junction
𝑓𝑎𝑑 = the friction coefficient associated with adhesive bonding
The development of the real contact area as two surfaces are pressed together is a function of both the
normal and tangential forces applied to the surfaces. As the surfaces are pressed together, the contact
area tends to grow. This process is known as junction growth, and can be modeled with the below
equation, which is derived from von Mises yield criterion.
𝐹𝑛2 + 3𝐹𝑡2 = 𝐴2𝑟 𝑝02
Where 𝐹𝑡 = the tangential force
𝑝0 = the yield stress in pure compression
The purpose of this study will be to use finite element analysis (FEA) to validate Equation 2. A two
dimensional elastic-plastic model of two surfaces initially in contact at several asperities will be built.
Three load cases will be analyzed:
1) Normal force incrementally increased, zero tangential force
2) Normal force held constant, tangential force increased incrementally
3) Both normal force and tangential force increased incrementally.
Plots of 𝐴𝑟 vs 𝐹𝑛 and 𝐴𝑟 vs 𝐹𝑡 will be obtained from the FEA solution and compared with plots derived
from the closed form solution.
The focus of this project will be on Contact mechanics.
(2)