ABSTRACT
All particles have the same elastic and plastic material properties and have the same radius R. Elastic constants are denoted as E0 and ν0 while the elastic limit is denoted as 0. E∗ is the equivalent elastic modulus (E∗ = E0/2(1 − ν20)). Consider a pair of particles that indent each other such that plasticity is the main deformation mechanism at the contact. If the material behaves perfectly plastically (no hardening), the normal indentation force, N0, is
with a0, the contact radius due to an indentation h0:
where c2 = 1.45 for perfectly plastic material (Storåkers et al. 1997). The pressure distribution is almost uniform throughout the contact area for a perfectly plastic material (p0 = 30). In this case, (Mesarovic & Johnson 2000) have proposed analytical expressions that characterize the unloading of a contact that has been plastically deformed. They have shown that when the ratio, χ, of the adhesive energy w to the elastic energy stored in the plastic crown,
is less than 0.1, unloading is predominantly elastic. As unloading proceeds, the contact radius a decreases
from its initial value a0 down to its critical value at decohesion, denoted as xc = (a/a0)c, and which is well approximated by
for small values of χ (χ< 0.1) that are of interest here (Mesarovic & Johnson 2000). During unloading, the evolution of the normal load Nu, depends on the ratio x = a/a0 and the material parameter χ
where the first term on the right hand side gives the load in the absence of adhesion while the second term relates to the adhesion traction.
