The usual method of plastic deformation in
metals is by the sliding of blocks of the crystal over one another along
definite crystallographic planes, called slip
planes. Slip occurs when the shear stress exceeds a critical value. The atoms
move an integral number of atomic distances along the slip plane which shows up
as a line called as
slip line. Slip
lines are due to changes in surface elevation and that the surface must be
suitably prepared for microscopic observation prior to deformation if the slip
lines are to be observed. Slip occurs most readily in specific directions on
certain crystallographic planes. Generally the slip plane is the plane of
greatest atomic density, and the slip direction is the closest-packed direction
within the slip plane. Since the planes of greatest atomic density are also the
most widely spaced planes in the crystal structure, the resistance to slip is
generally less for these planes than for any other set of planes. The slip
plane together with the slip direction establishes the slip system. In the face-centred cubic structure, the [111]
octahedral planes and the (110) directions are the close-packed systems. The
[110] planes have the highest atomic density in the bcc structure.
Slip in a Perfect Lattice
Consider
two planes of atoms subjected to a homogeneous shear stress. The shear stress
is assumed to act in the slip plane along the slip direction. The distance
between atoms in slip direction is b, and the spacing between adjacent lattice
planes is a. The shear stress causes a displacement x in the slip direction
between the pair of adjacent lattice planes. The shearing stress is initially
zero when the two planes are in coincidence, and it is also zero when the two
planes have moved one identical distance b, so that point 1 in the top plane is
over point 2 on the bottom plane. The shearing stress is also zero when the
atoms of the top plane are midway between those of the bottom plane, since this
is a symmetry position. Between these positions each atom is attracted toward
the nearest atom of the other row, so that the shearing stress is a periodic
function of the displacement.
As a first
approximation, the relationship between shear stress and dis- placement can be
expressed by a sine function
τ = τm sin (2πx/b)
Where τm is the amplitude of the sine wave
and b is the period. At small values of displacement, Hooke's law should apply.
τ = Gɤ; ɤ = x/a;
τ = Gx/a; τm sin
(2πx/b) = Gx/a; τm (2πx/b) =
Gx/a
As a rough
approximation, b can be taken equal to a, with the result
τm = G/2π
For metals ɤ = 3 - 30 GPA (theoretical) and ɤ = 0.5 - 10 GPA (actual).
