Geology Reference
In-Depth Information
presented in section 4.3. Descriptions of gross features of
microstructure of age‐based ice types (namely young ice,
first‐year ice, and multiyear ice) are given in section 4.4.
An effort has also been made to bring attention to the
names of various types of natural sea ice in terms of their
counterparts in Inuktitut, the language of the Inuit people
of the Arctic. The chapter concludes in section 4.5 with
descriptions of information that can be retrieved from
images of polycrystalline ice structure such as geometric
characteristics of ice crystals and inclusions.
engineering properties of complex alloys used in gas turbine
engines of jet aircrafts and rockets [
Sinha,
2009a, 2009b
;
Sinha and Sinha,
2011].
If the temperature is expressed in Kelvin (K), the ratio of
the operating temperature
T
and the melting temperature
T
m
may be defined as the homologous temperature (
H
):
HTT
m
/
(4.1)
The homologous scale provides a rational method of
comparing the thermal state of different materials at
different temperatures. It varies from 0 to 1 for the solid
state of a material. Temperatures greater than 1.0 in
homologous scale indicate the liquid state and are not
of any interest for the solid state of any material.
Figure 4.1 provides examples of three ice tempera-
tures in three different scales. It shows, for example, that
an ice temperature at −27 °C is equivalent to 0.9
T
m
and
is, therefore, only 10% below the melting point. For
simplicity we used
T
m
= 273 K for pure ice in making the
graphical illustrations. Strictly speaking, the melting
point of ice, by definition, is around 0 °C (on Earth's
surface) but may not be far from 273.16 K [
Dorsey,
1968,
Table 266]. Homologous temperatures for some mate-
rials involved in our daily life, e.g., rubber in car tires
and bitumen used in making asphalt‐concrete roads and
airport runways, is shown in Figure 4.2.
How hot are the ice covers in lakes and oceans? This
can only be quantified on the basis of homologous tem-
perature scale using equation (4.1). An ice temperature
T
of −5 °C or 268 K (neglecting the decimal points) is
equivalent to a homologous temperature of 0.98. This
is only 2% below the melting point. Even in the upper
atmospheres where the ambient temperature could be
very cold, say −82 °C or 191 K, ice particles will exist at
4.1. Terms and definiTions relevanT
To PolycrysTalline ice
4.1.1. Special Thermal State of Natural Ice
In the inland arctic regions of Russia, for example,
Yakutsk, the inhabitants do face air temperatures as
low as −60 °C (or 213 K) during the winters. In terms of
human comfort, this is indeed extremely cold. Any tem-
perature less than our normal body temperature of about
37 °C may be considered as cold. Our normal body tem-
perature does not really provide a rational way of judg-
ing the “hotness” or the “coldness” of materials we use
day to day. In fact, the Celsius scale, universally acclaimed
as the standard for measuring/reporting thermal state of
a body, instead of providing a logical mode of judgment,
can actually lead to scientific nonsense. The “negative”
sign in front of the numerical value for any “subzero”
temperature in Celsius immediately sends a chilling effect
to our logical senses. Since snow and ice always exist at
subzero temperatures, these materials are considered,
even by the scientists and engineers, as “cold” materials.
However, the Kelvin scale provides a thermodynamically
based method for rationalization and establishing the
fact that “snow and ice are extremely hot crystalline
materials.” This concept allowed the second author to
show that ice can be considered as “thermorheologically
simple material” and introduced the concept of “shift
function” to ice in addition to the proposal of a constitu-
tive equation known as elasto-delayed-elastic-viscous
(EDEV) model [
Sinha
, 1978b] that could explain wide
ranging and rather conflicting temperature dependent
creep deformation issues in ice [
Sinha
, 1978c]. Effect of
grain size was then introduced to the model in
Sinha
[1979]. This model was then extended to predict grain-
boundary sliding induced intergranular microcracking
in polycrystallline ice [
Sinha
, 1984a] and microstruc-
ture dependent and strain-rate sensitive strength of
natural types of ice including both fresh water ice
[
Sinha
, 1988] and sea ice [
Zan et al
., 1996]. These far
reaching investigations laid the path to follow, since
1998, for extending ice‐based constitutive equations for
creep, fracture, and strain‐rate‐sensitive strength to
Liquid
0
273
T=T
m
T/T
m
=
1.00
Solid
T
-10
263
T/T
m
=
0.96
T
-27
246
T/T
m
=
0.90
Celsius
Kelvin
Homologous (T/T
m
)
Figure 4.1
Ice temperature given in three temperature scales:
Celsius, Kelvin, and homologous defined as
T/T
m
where
T
m
is the melting point in Kelvin (actually
T
m
= 0 °C ≈ 273.16 K)
[sketch by N. K. Sinha, unpublished].
