A child of any age can identify texture, color, and shape. These are the basic, macroscopic properties of a material. When engineers consider materials for use, they take into account more than just these qualities [1]. This is because engineers constantly subject materials to extreme conditions. For example, in planes, the thermal properties of the material the rotors are made of are extremely important, since a melting rotor cannot propel a plane. Therefore, engineers have devised four criteria for choosing materials to ensure that a material is up to par. They are (i) how easily it can be manufactured, (ii) if it can withstand its functional requirements, (iii) if it can withstand external conditions, and (iv), its price [2]. Under these parameters, there are a few broad groups, like metals, ceramics, and organic polymers, that are commonly used. Metals, for example, are classified by being good electrical conductors, are solid at room temperature, are at least somewhat malleable and ductile, and, finally, are lustrous when cut [2]. Though not perfect, criteria like these are typically satisfactory.
Engineers use quantitative measures of a material’s properties to better define these groups. Better defined categories make for better engineering. For example, the right materials must be chosen for large public projects like bridges, otherwise the people using them are at risk [3]. The materials bridges are made of must withstand constant stress and strain.
Stress and strain can be expressed in physics. Take the simple example of a spring. Strain refers to how far the spring is stretched, while stress is the tension in the spring (i.e. how hard you have to pull to keep it in place). Intuitively, increasing strain should mean increasing stress. This is indeed the case, and their relationship is shown in equation (1), a formula known as Hooke’s law describing an ideal spring.
(1) F = -k∆x, where k is the spring constant, and ∆x is displacement.
This, however, is not general, since k is specific to each spring. Also, when looking at real materials, the stress-strain relationship is not linear, as Hooke’s law suggests.
There is still, however, a period of linearity, as seen in the figure to the right. The slope of this line is known as Young’s Modulus, and is defined as equation (2).
(2) E = σ/ε, where σ = stress, and ε = strain.
Thus, Hooke’s law can be generalized to equation (3).
(3) F = E∆x
This equation holds true only for tensile and compressive stresses. Shear stresses, which cut through a material in a non-parallel direction to the grain, are more complicated. The ratio of shear stress to shear strain is shown in the equation below, which is complemented by figure 1.
(4) $G = \tau _{xy}/\gamma_{xy}$, where $\tau_{xy} = F/A$ and $\gamma_{xy} = \phi$
G is therefore a conversion constant and, given the angle to which a material is deformed, can give the strength of its resistance.
Past the linear region on a stress-strain graph, a material yields and becomes “plastic.” Once plastic, it can stretch and bend. Materials, however, have a limit to the extent to which they can be stretched before fracturing, also known as their ductility. As for the height of the graph, the maximum point on it is a measure of the strength of the material, since it is its maximum resistance. The combination of these two factors—strength and ductility—is known as toughness, and is a measure of the magnitude of stress a material can withstand before fracturing. Its equation, intuitively, is the area underneath the curve from the origin to the abscissa of the fracture point, εf. It has units of J/m3, since it is the amount of energy each unit of volume of a material can absorb before fracturing. Its formula is shown in equation (5) [5].
The way materials deform is intricately tied with their structure. In general, there are two forms of material: crystalline and amorphous. Crystalline patterns are repeating and regular, and therefore are stronger than amorphous materials [2, 6]. On a simple two dimensional plane, hexagons or squares can be the repeating unit; these are unit cells. In three dimensions, the story is much the same, just that there are more possible patterns [2].
Amorphous materials, in distinction with crystalline ones, are brittle and unstable. Because of their structure, stress builds up on some bonds, compromising them. As such, the microscopic structure of a material can manifest itself in application and in macroscopic tests [6].
The future of material sciences is promising. Nanomaterials hold promise for their applications in technology, while superconductors could make transporting electricity infinitely more efficient. Once only theoretical, these materials have become tangible, with some now in our very homes.