Page 35 - Microtectonics

22 2 · Flow and Deformation
2.12 pressed as the stress at that point in the material. Notice 2.12
that stress is defined only for a particular point, since it is Rheology
usually different from place to place in a material.
Like flow and deformation, stress is a tensor which, in Rheology is the science that deals with the quantitative
three dimensions, needs nine numbers for its complete response of rocks to stress. Only the main terminology is
characterisation. However, since stress is taken to be sym- treated here as a background to the study of microstruc-
metric in geological applications, six independent num- tures. Useful texts treating the subject are Means (1976),
bers are usually sufficient. Of these, three numbers de- Poirier (1980) and Twiss and Moores (1992).
scribe the principal stress values along principal stress So far, only one possible range of deformation behav-
axes in three orthogonal directions, and three the spatial iour of rocks has been treated, i.e. permanent changes in
orientation of the principal stress axes. Principal stress shape achieved by distributed, non-localised deformation.
values are expressed as σ (largest), σ and σ (smallest). However, rocks can also display elastic behaviour in which
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Principal stress axes are normal to the three surfaces on changes in shape are completely recoverable, or localised
which they act (Fig. 2.10b, ×Video 2.10). Stress is usually deformation such as slip on a fault plane. Distributed or
illustrated by a stress ellipsoid with principal stress axes continuous, and localised or discontinuous deformation
as symmetry axes (Fig. 2.10b, ×Video 2.10). Stress on a are sometimes referred to in the literature as ductile and
plane in a rock such as the contact of a pegmatite vein is a brittle deformation (Rutter 1986; Schmid and Handy 1991;
vector which can be resolved into components normal and Blenkinsop 2000, p 4). However, the terms ductile and
parallel to the plane, known as normal stress (σ ) and brittle are scale-dependent, since flow in a deformation
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shear stress (τ) respectively (Fig. 2.10a, ×Video 2.10). band would be brittle on the grain scale, but ductile on
It is useful in many applications to subdivide stress into the metre scale. In order to avoid this problem, we prefer
a mean stress value (σ mean =(σ + σ + σ ) / 3) and differ- another use of the terminology where ductile and brittle
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ential stress (usually defined as σ diff = σ – σ , but σ – σ 2 refer to deformation mechanisms (Chap. 3). In this book,
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or σ – σ could also be regarded as differential stresses). brittle deformation is used for fracturing on the grain scale
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The term deviatoric stress is also commonly used and is and frictional slip on discrete faults and microfault sur-
defined as σ = σ – σ ; it is a measure of how much faces around rock or grain fragments. These processes
dev n mean
the normal stress in any direction deviates from the mean are not much influenced by temperature, but strongly
stress. The differential or deviatoric stresses are the cause pressure-dependent. Brittle deformation is commonly
of permanent strain in rocks and are most important for associated with volume change. Ductile deformation, also
geologists. However, notice that the directions of princi- known as viscous flow is produced by thermally activated
pal stress and strain rarely coincide. Stress axes may be deformation mechanisms such as intracrystalline defor-
parallel to flow-ISA, but only if the rock is mechanically mation, twinning, kinking, solid-state diffusion creep, re-
isotropic, e.g. if it has the same strength in all directions; covery and recrystallisation. Depending on scale, it can
in practice, this is often not the case, especially not in rocks also be localised.
that have a foliation. Moreover, finite strain axes rotate All minerals and rocks can deform in both a brittle
away from ISA with progressive deformation if flow is and a ductile way, and in general ductile deformation
non-coaxial. occurs at higher temperature and lithostatic pressure
The vertical normal stress on a horizontal surface at than brittle deformation, i.e. at deeper levels in the crust
depth due to the weight of the overlying rock column (Sect. 3.14). For ductile deformation, the rheology of
equals ρgh, where ρ is the rock density, g the accelera- rocks is usually described in terms of strain rate/stress
tion due to gravity and h the depth. For practical reasons, relations. Stress is usually given as a shear stress (τ) or as
and because differential stresses are thought to be rela- a single ‘differential stress value’ (σ – σ ) since in experi-
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tively small at great depth, stress is commonly treated as ments on rheology, symmetric stress tensors are imposed
being isotropic, in which case ρgh defines a lithostatic on the rock. There are several possible types of ductile
pressure. Lithostatic pressure at a point is uniform in all rheological behaviour. Any rock will show elastic behav-
directions by definition; if a differential stress is present, iour under mean stress by a small decrease in volume,
the term mean stress could be used instead of lithostatic and under differential stress by a small change in shape
pressure. If pores are open to the surface, a fluid pressure (usually less than 1%). Such an elastic strain is completely
may exist in the pores of the rock that is 2.5–3 times smaller recoverable if the stress is released (Figs. 2.11a, 3.15).
than a lithostatic pressure at the same depth. If the pores Mean stress increase in rocks will not lead to permanent
are partly closed, the fluid pressure may approach the mag- deformation, even at very high values, unless the rock
nitude of the lithostatic pressure or σ . In that case rocks has a high porosity, or transformation to mineral phases
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may fracture, even at great depth (Etheridge 1983); this is with a higher density can take place. However, if elastic
one of the reasons for development of veins (including strain in response to differential stress exceeds a limit
fibrous veins) in many metamorphic rocks (Sect. 6.2). that the rock can support (the yield strength), ductile flow