Page 32 - Microtectonics

2.7 · Progressive and Finite Deformation 19
in shape) and a rotation component ρ . Therefore, defor- 2.7 2.7
k
mation and strain should not be used as synonyms. Progressive and Finite Deformation
In homogeneous deformation, a circle is deformed into
an ellipse (Figs. 2.4a, 2.7e). The shape of such an ellipse is A homogeneous pattern of flow leads to accumulation
a measure of the strain; the principal strain axes are the of homogeneous deformation. Figure 2.8a shows how the
long and short axes of this ellipse. If the original circle total stretch and rotation of material lines with respect
has a radius 1, the ellipse is known as the strain ellipse to each other can be identical in deformation states ac-
and the length of the principal strain axes is S and S 2 cumulated by pure shear flow and simple shear flow. Ho-
1
respectively. mogeneous finite deformation carries no information on

Fig. 2.7.
a Two stages of the deformation
sequence in Fig. 2.5a that are far
apart in time can be used to
reconstruct b the deformation
pattern. c Sets of marker points
can be connected by material
lines and the rotation (r) and
stretch (S) of each line moni-
tored. d These can be plotted
against initial orientation of the
lines. In the curves, principal
strain axes can be distinguished.
e Finite deformation as deduced
from these curves contains ele-
ments of strain and rotation (ρ ).
k
β defines the orientation of a
k
material line in the undeformed
state that is to become parallel to
the long axis of the strain ellipse
in the deformed state

Fig. 2.8.
The effect of deformation his-
tory. a Two identical squares of
material with two marker lines
(black and grey lines) are de-
formed up to the same finite
strain value in simple shear and
pure shear progressive deforma-
tion respectively. The initial ori-
entation of the squares is chosen
such that the shape and orienta-
tion of deformed squares is iden-
tical. b The finite stretch and rela-
tive orientation of both marker
lines is identical in both cases,
but the history of stretch and
rotation of each line (illustrated
by the curves) is different.
c Circular diagrams show the
distribution of all material
lines in the squares of a. Orna-
mentation shows where lines
are shortened (s), extended (e)
or first shortened, then ex-
tended (se) for each step of pro-
gressive deformation. The ori-
entation of ISA is indicated