Page 37 - Tribology in Machine Design

24 Tribology in machine design

For welded junctions, the stress ratio is

i.e., the ultimate shear strength of the junction is equal to that of the weaker
material in contact.
For non-welded junctions, the stress ratio is

A welded junction will have adhesion, i.e. the pair of asperities will be
welded together on contact. On the other hand, in the case of a non-welded
junction, adhesive forces will be less important.
For any case, if the actual contact area is A, then the total shear force is

where 0 ^ ft < 1, depending on whether we have a welded junction or a non-
welded one. There are no direct data on the strength of adhesive bonds
between individual microscopic asperities. Experiments with field-ion tips
provide a method for simulating such interactions, but even this is limited
to the materials and environments which can be examined and which are
often remote from practical conditions. Therefore, information on the
strength of asperity junctions must be sought in macroscopic experiments.
The most suitable source of data is to be found in the literature concerning
pressure welding. Thus the assumption of elastic contacts and strong
adhesive bonds seems to be incompatible. Accordingly, the elastic contacts
lead to non-welded junctions only and for them /3<l. Plastic contacts,
however, can lead to both welded and non-welded junctions. When
modelling a single asperity as a hemisphere of radius equal to the radius of
the asperity curvature at its peak, the Hertz solution for elastic contact can
be employed.
The normal load, supported by the two hemispherical asperities in
contact, with radii RI and R 2, is given by

and the area of contact is given by

Here w is the geometrical interference between the two spheres, and E' is
given by the relation

where E lt E 2 and v 1} v 2 are the Young moduli and the Poisson ratios for the
two materials. The geometrical interference, w, which equals the normal
compression of the contacting hemispheres is given by