The reorientation of atoms by frictional shear deformation at the surf
ace of metals can induce cracks at the boundary of the grains. The cra
cks grow and propagate in regions where the hydrostatic component of s
tress in least compressive because the compressive component restores
the cracks by three-dimensional crystallizing pi-bondings. Materials w
ith Luder's bands have only a small amount of wear at the initial stat
e, which suggests that initial frictional shear deformation is consume
d in the formation of the Luder's bands. The average amounts of wear o
f the materials increase very steeply as the value of phi(u), i.e. the
stress-strain ratio at the ultimate point, decreases. (C) 1998 Elsevi
er Science S.A. All rights reserved.