Geology Reference
In-Depth Information
Fig. 4.1 Schematic
dependence of flow stress
on temperature
Flow
Stress
σ
Low
Temp.
Thermal
High
Temp.
Thermal
Athermal
T
M
Temperature T
Escaig
1984
). However, all three regimes are not necessarily found in a particular
material. For example, in copper, the athermal regime seems to extend down to
absolute zero (no significant low-temperature thermal regime), while in pure dry
quartz, the low-temperature thermal regime seems to extend more or less to the
melting point. In other materials such as germanium and silicon, low-and high-
temperature thermal regimes appear to overlap in such a way that no significant
athermal regime is defined. In pure metals, the high-temperature regime can often be
usefully defined as that above about half the absolute melting point but no such
general rule can be applied to the wider spectrum of materials, including minerals and
rocks. However, within given chemical classes of materials, it may be possible to
define similar homologous temperature rules, the homologous temperature being
taken as relative to some reference temperature at which a change of state occurs that
involves the same components as are taking part in the mechanical process of
interest, this reference temperature not necessarily being the melting point, espe-
cially where incongruent melting is concerned.
Third, a broad distinction can be made between phenomenological and mech-
anistic aspects of deformation. The phenomenological view is a global one, dealing
with a body of material as a whole or as a continuum. It is only concerned with
macroscopic variables such as stress, strain and temperature, and with establishing
empirical relationships among them. The nature of the material is represented by
empirical constants or parameters (elastic modulus, activation energy, etc.) that
appear in these relationships. Variations in the state of the material may be rep-
resented by additional parameters (internal variables), such as grain size, in the
empirical relationships but the material is still treated as a continuum from the
mechanical point of view. In contrast, the mechanistic view attempts to recognize
the local processes contributing to the global behavior. It therefore tends to con-
centrate on the microscopic rather than the macroscopic scale. The aim is to
describe the processes or mechanisms in terms of re-arrangements of fundamental
structural units and to develop models for the global behavior in terms of these
processes. Ideally, this approach eventually gives a rationalization for the empir-
ical relationships established in a phenomenological approach, and further pro-
vides a basis for establishing the range of validity of such relationships in the light
of structural observations.
In this chapter, we mainly survey the phenomenological aspects of deformation,
those aspects that can be represented as the properties of a homogeneous continuum,
