Page 58 - Tribology in Machine Design

Basic principles of tribology 45

film defect /? is

The total volume of wear debris is

2.12. Relation between An analytical description of the fracture aspects of wear is quite difficult.
fracture mechanics and The problems given here are particularly troublesome:
wear (i) debris is generated by crack formation in material which is highly
deformed and whose mechanical properties are poorly understood;
(ii) the cracks are close to the surface and local stresses cannot be
accurately specified;
(iii) the crack size can be of the same order of magnitude as micro-
structural features which invalidates the continuum assumption on
which fracture mechanics is based.
The first attempt to introduce fracture mechanics concepts to wear
problems was made by Fleming and Suh some 10 years ago. They analysed
a model of a line contact force at an angle to the free surface as shown in Fig.
2.15. The line force represents an asperity contact under a normal load, W,
with a friction component Wtan a. Then the stress intensity associated with
a subsurface crack is calculated by assuming that it forms in a perfectly
elastic material. While the assumption appears to be somewhat unrealistic,
it has, however, some merit in that near-surface material is strongly work-
hardened and the stress-strain response associated with the line force
passing over it is probably close to linear.
The Fleming-Suh model envisages crack formation behind the line load
where small tensile stresses occur. However, it is reasonable to assume that
the more important stresses are the shear-compression combination which
is associated with crack formation ahead of the line force as illustrated in
Fig. 2.15. For the geometry of Fig. 2.15, the crack is envisioned to form as a
result of shear stresses and its growth is inhibited by friction between the
opposing faces of the crack. In this way the coefficient of friction of the
material subjected to the wear process and sliding on itself enters the
analysis. The elastic normal stress at any point below the surface in the
absence of a crack is given by

The terms in eqn (2.104) are defined in Fig. 2.15. In particular, the friction
Figure 2.15 coefficient between the contact and the surface is given by tan a.