Page 33 - Microtectonics

20 2 · Flow and Deformation
the deformation path or on progressive deformation. amples since they suffice to illustrate the principle, and
However, the stretch and rotation history of material lines may indeed represent some flow types that occur in na-
does depend on the flow type by which it accumulated. ture, such as simple shear in ductile shear zones between
This is illustrated in Fig. 2.8b by the stretch and rotation rigid wall rocks. However, it is important to realise that
history of two lines in Fig. 2.8a. If the stretch behaviour flow is a three-dimensional phenomenon and that two-
of all material lines is studied, the difference in pattern dimensional simplifications may be unsuitable to de-
is even more obvious (Fig. 2.8c); if deformation accumu- scribe certain details correctly.
lates by pure shear flow, the orthorhombic symmetry of Homogeneous deformation in three dimensions is
the flow pattern is reflected in the symmetry of the dis- also expressed as a tensor with nine numbers. Three num-
tribution of material lines with different deformation bers define the principal stretches or principal strain
history (Fig. 2.8c). A pure shear deformation history values S , S and S along three orthogonal principal strain
1 2 3
where W = 0 is also known as ‘coaxial progressive de- axes; three numbers describe the rotation of material
k
formation’. Progressive deformation histories by flow lines coinciding with principal strain axes from the
types where W ≠ 0 such as simple shear are referred to undeformed to the deformed state; and three numbers
k
as ‘non-coaxial progressive deformation’ and the re- describe the orientation of the principal strain axes in
sulting distribution of material line fields have a mono- space. Notice that, unlike flow, deformation compares an
clinic symmetry (Fig. 2.8c). In most fluids, this differ- undeformed and a deformed state, and can therefore be
ence in stretch history of lines is just a curiosity without described in several ways, depending on whether the ref-
practical value, but in rocks the difference is expressed erence frame is fixed to material lines in the undeformed
in the rock fabric. If deformation is homogeneous on or in the deformed state.
all scales it is not possible to detect effects of the pro- Three-dimensional strain is a component of three-di-
gressive deformation path, but in the case of inhomoge- mensional deformation that can be described by three
neous deformation on some scales, as is common in de- numbers such as the principal stretches S , S and S . It is
1
2
3
forming rocks (Fig. 2.4b), pure shear and simple shear illustrated as a strain ellipsoid; principal strain axes are
progressive deformation can produce distinctive, differ- the three symmetry axes of this ellipsoid. They are usu-
ent structures (e.g. Fig. 5.39). It is this monoclinic fabric ally referred to (from maximum to minimum) as the X-,
symmetry, which can be used to determine sense of shear Y- and Z-axes of strain. As for flow, it is important to
(Sects. 5.5–5.7). It is therefore usually possible to obtain realise that deformation and strain are three-dimensional
at least some information on the type of deformation quantities, although we usually see two-dimensional
path from a finite deformation fabric, although in na- cross-sections in outcrop or thin section; for a full char-
ture it will not be possible to make an accurate recon- acterisation of strain, several orthogonal outcrop surfaces
struction. or thin sections should be studied. More details on flow
and deformation can be found in Means et al. (1980),
2.8 2.8 Means (1979, 1983), de Paor (1983) and Passchier (1987a,
Flow and Deformation in Three Dimensions 1988a,b, 1991a).
2.9 The two-dimensional treatment of flow and deformation 2.9
presented above can easily be expanded to a full three- Fabric Attractor
dimensional description. If flow is homogeneous it can
be represented in three dimensions as a tensor with nine If the flow patterns of Fig. 2.6 work on a material for some
components. Three of these define the stretching rates time, material lines rotate towards an axis, which coin-
(Ö ) along three orthogonal ISA; three define the orien- cides with the extending irrotational material line; this
k
tation of the vorticity vector and its magnitude; and three axis ‘attracts’ material lines in progressive deformation.
components describe the orientation of the flow pattern In most types of three-dimensional homogeneous flow,
in space. This means that an endless variety of flow types a ‘material line attractor’ exists in the form of a line or
is in principle possible. In the first part of Chap. 2, we (less commonly) a plane (Fig. 2.9). Since material lines
discussed only those types of flow where the vorticity rotate towards attractors, the long axes of the finite strain
vector lies parallel to one of the ISA and stretching rate ellipse and most fabric elements in rocks will do the same.
along this axis is zero, as in the shear boxes of Figs. 2.1 We therefore refer to these directions as the fabric
and 2.2. In such special flow types, the velocity vectors of attractor of the flow (Fig. 2.9). Even if flow is not homo-
flow are all normal to the vorticity vector, and flow can geneous, fabric attractors may occur as contours in de-
therefore be treated as two-dimensional and shown as a forming materials, and fabric elements will approach
vector pattern in a single plane (Figs. 2.1–2.3, 2.5, 2.6). them. This is the cause of the development of many
We restricted the presentation of flow types to these ex- foliations and lineations in deformed rocks.