Digitalisation of silicon carbide particles at different
time intervals(Figure 9)
around the S-C' fabric allow us to monitor movement of particles and to
calculate the local deformation tensor F with the program "marker
analysis" (Bons et al. 1993). The program
superimposed a regularly
spaced polar grid on the sample.
The grid origin was at the rotation
centre of the upper glass slide and a second marker point in the annular
shear zone was chosen to fix a second reference axis. The position of each
marker point at time (t) is defined by its distance to the origin and its
polar angle to the reference particle.
The position of each grid node is
defined with respect to four adjacent marker particles occupying at least
three different quadrants. A deformed polar grid can be constructed with
the technique of a least squares best fit method which determine the
displacement of each grid node from the displacement of the four adjacent
marker particles. Our experiment is virtually two-dimensional and a
deformation tensor F at any point can be fully described by four independent
coefficients, whose values depend on the chosen reference frame.
The tensor can be expressed by deformation parameters such as finite
strain Rf, a finite 'mean' vorticity number Wn
(Passchier 1988)
and area change Af. Af is 1 for absence of dilation
and can represent area decrease of area increase (Af.>1). Wn
is a measure of the rotational component of the deformation normalised for strain
(Truesdell 1953,
Passchier 1988). Positive
vorticity numbers indicate a bulk clockwise
rotation. Wn is 0 for a pure shear deformation, 1 for a dextral simple
shear deformation and Wn1 indicates a rigid body rotation.