0.25 °C/minute in the range of temperature above 400 °C. As expected, ε increased with increase in T, but the slope of the ε–T curve increased rapidly after about 500 °C. However, neither linearity below 500 °C nor an abrupt drop above this temperature was noticed. This contrasts with the observations of Lebedev (1926) on the temperature dependence of refractive index, presumably for a similar glass.
Figure 2.10 Temperature dependence of the CLTE for a lapped and polished lath (152.2 mm × 25.8 mm × 5.8 mm) taken from a large commercially annealed sheet of plate glass.
Source: Sinha (1971).
In addition to the temperature dependence of the refractive index of glass, one of the most important material characteristics is the dependence of elastic modulus on temperature. Figure 2.11 shows the dependence of Young's modulus, E, of window glass on temperature. Unlike the sharp drop in refractive index, as mentioned earlier in Lebedev's studies, the value of E does not exhibit any drop between 500 and 600 °C, i.e. in the transition zone. However, E decreases monotonically with increase in temperature, but only slightly from its room temperature value. The commercially (as received) annealed glass exhibited a slightly lower value at temperatures less than 500 °C as compared to the laboratory annealed material. The difference indicates a thermal‐history‐related memory effect, similar to the thermal expansion coefficient of glass mentioned earlier. With increase in temperature and long soaking time during the mechanical testing for E, the commercially annealed glass could have approached structural equilibrium at temperatures higher than 500 °C.
Figure 2.11 Temperature dependence of Young's modulus, E, for commercially annealed and laboratory annealed automotive plate glass.
Source: Sinha (1971).
2.5 Rocks: The Most Abundant Natural Polycrystalline Material
Trinity of Rocks
SEDIMENTARY
METAMORPHIC
IGNEOUS
Rocks form due to the solidification of lava on Earth's surface and that of magma inside the earth. Lava refers to molten rock material that is extruded onto the surface during a volcanic eruption. Molten rock is known as magma when it lies below the ground surface. There are three basic types of rocks: sedimentary, metamorphic, and igneous; these types are briefly described in the following section.
We cannot define a rock as a solid in terms of a melting point. The melting point of rocks cannot be defined in a simplistic manner because they consist of different minerals with different melting points. In the field of engineering geology, a rock is defined not only in terms of the thermal state, but also as a hard solid that consists of compacted aggregation of minerals that remains intact in water and cannot be excavated without blasting (West 1995). In terms of T m, the definition of solid rock is, therefore, not as simplistic as one may think – as in polycrystalline pure metals, ice, and many ceramics.
2.5.1 Sedimentary Rocks
The surface of Earth consists of about 75% sedimentary rocks. These rocks are recognized readily by the most noticeable feature of stratification or layers, often enriched with fossils. There is a wide range of sedimentary rocks depending upon the origin of their source material. West (1995) stated that 99% of all sedimentary rocks consist of shales (46%), sandstones (32%), and limestones (22%). The engineering properties of sedimentary rocks vary greatly, but these types of rocks are not used at high temperatures. Deep down in the earth, sedimentary rocks are subjected to metamorphic process due to heat and pressure.
Particles in the form of sand and silt produced from erosion of rocks are carried out by streams and rivers to the oceans or large lakes. The transported particles are consolidated by processes known as lithification. The Ancient Greek word “lithos” meaning rock and the suffix “ific” derived from Latin are combined to make “lithification” for describing the processes in which water‐saturated unconsolidated sediments compact under pressure to become “sedimentary rocks.” Lithification is therefore a time‐dependent process of the removal of fluid from pores through compaction and cementation. Millions of years of lithification processes of compaction, cementation, and crystallization of sediments deposited in water produce sedimentary rocks.
Lithification should not be confused with the word petrification that involves the replacement of organic material by silica over a long period of time, such as in the development of fossils (Monroe et al. 2006). However, there is a counterpart of the lithification processes in the case of the densification of snow or ice particles deposited on Earth's surface. In this case, air trapped in unconsolidated and porous snow deposits is removed under pressure and the mass undergo morphological changes by compaction, grain growth, and cementation (sintering). The primary difference is the extremely high thermal states of snow deposits. This subject will be covered later. Very similar processes are also involved in making ceramics and powder metallurgy.
2.5.2 Metamorphic Rocks
A complete change of physical form or substance is called metamorphosis. Thermomechanical processes occurring on pre‐existing rocks within Earth's crust produce irreversible physical changes in their texture, structure, and mineralogical characteristics; and the product is known as a metamorphic rock. Metamorphism can take place near igneous intrusions, called contact metamorphism, or over large areas, called regional metamorphism. The latter occurs as a result of tectonic plate movements.
Two primary types of rocks are seen in regionally metamorphosed rocks: foliated and nonfoliated. Marble and quartzite are common examples of nonfoliated metamorphic rocks. Marble is metamorphosed limestone, and quartzite is metamorphosed sandstone. Slates, phyllites, schists, and gneisses are examples of foliated metamorphic rocks. Mechanically, they exhibit anisotropy because foliated layers may display weakness as well as strength depending on their material characteristics. Naturally, permeability, strength, deformation, and hence seismic response are affected by direction of foliation in foliated metamorphic rocks (West 1995).
2.5.3 Igneous Rocks
Rocks formed due to the solidification of lava or magma on or below Earth's surface are called igneous rocks. Since the solidification of molten rocks depends upon the mode of cooling and the rate of heat transfer, texture (size, shape, and arrangements of grains) and mineral composition of igneous rocks depend on the place of cooling. Extruded lava and flowing lava are subjected to rapid cooling rates and tend to produce fine‐grained and relatively homogeneous materials. The size and shape of the grain and the mineral composition of solidified magma depend on the depth below Earth's surface due primarily to decrease in the cooling rate with increase in depth. The cross‐sectional grain sizes increase with decrease in the rate of solidification, and hence increase in depth. For convenience, igneous rocks are divided into three basic types: extrusive (or volcanic), hypabyssal, and intrusive (or plutonic). Extrusive igneous rocks are fine grained, and intrusive igneous rocks are very coarse grained. Granite, diorite, and gabbro
