Bulk Properties of Solids

Bulk properties of matter in mechanics

Some bulk properties are specifically related to the mechanical behaviour of a material. Hardness and elasticity are two examples. These characteristics are important to take into consideration, as we need to know the mechanical responses of materials to forces and loads. For instance, some materials need to be flexible, so they do not break when they are deformed, such as the frame of your glasses. Other important characteristics that help us classify materials are their density, tensile strength, and bulk modulus.

Elasticity

Elasticity is the capacity of a material to elongate when a force is applied to it and regain its original shape when the force is removed. Elasticity is an important characteristic in science and industry where elastic materials are needed for certain types of work and applications. One example concerns the materials used in airbags, which during a crash must withstand powerful impacts and fast deformations while holding together.

The elasticity of a material is measured in Pascals. To perform the measurement, a mechanical test is needed, which is usually conducted by elongating a material using a force ‘F’, as shown in the image below.

Material properties, such as elasticity, can be measured by conducting mechanical tests, in which objects are exposed to forces that elongate them. The elongation causes a deformation δl by a force F

The material suffers ‘mechanical stress’ and changes its length. It then reverts back to its original length as long it has not passed its ‘elastic limit’. The more force the material can resist without deformation, the more elastic it is. An important property of elastic materials is known as Young’s modulus, which is measured in Pascals.

Young’s modulus

The Young modulus can be described as the proportion between the strain (deformation) of a material and the mechanical stress it is exposed to. See the stress vs strain graph below.

The red line in the figure indicates that the stress and the strain are proportional to each other. In the area labelled ‘elastic zone’, the material will revert to its original shape after having been deformed. The slope of the red line is known as the elastic modulus or Young’s modulus. This is different for different materials, as shown in the following table.

To obtain the Young modulus from a stress and strain plot, we need to calculate the slope of the curve in the elastic zone. This can be done easily using the formula below if you know two points of the stress vs strain curve.

\[Modulus = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\sigma_2-\sigma_1}{\varepsilon_2-\varepsilon_1} = \frac{\Delta \sigma}{\Delta \varepsilon}\]

The tensile stress σ is defined as the force applied to deform the material divided by the cross-sectional area of the material, while the tensile strain ε is the increase in length divided by the original length. You can see this in the formulas below.

\[\sigma = \frac{F}{A}\]

\[\varepsilon = \frac{\delta I}{I}\]

Hooke’s Law

The elastic zone of a material can be modelled using Hooke’s law. In this case, an analogy is useful. The force applied to the material is analogous to a weight pulled by gravity, and the material elasticity is a spring deformed by the weight.

In this case, the force is proportional to the elongation and the spring constant k.

Plasticity

When materials are elongated beyond their elastic zone, they enter their plastic zone, which indicates the area in which materials start to deform irreversibly as the force keeps pulling them. See the blue line in the following image.

A material in a tensile test presents a deformation (strain) that depends on the force applied (mechanical stress). The area in which the relationship between the tensile stress and the tensile strain is no longer linear is known as the plastic zone

Hardness

Hardness, measured in Pascals, is the property of materials to resist penetration or scratches. For many materials, elasticity is inversely proportional to hardness. The molecules and atoms that allow a material to elongate also allow a force applied to a small portion of the surface to penetrate the material. Materials with low elasticity, such as metals and diamonds, are not elastic, as the strength of their bonds and structures resists penetration by a force trying to push them.

Density

Density, which is defined as the amount of mass existing in a unit of volume, is another important property of materials. Density is usually measured in SI units as kilograms per cubic metre. The density of a material varies depending on two factors:

1. The atomic structure of the material.
2. The element of which it consists.

It is well known that heavier elements weigh more. However, the atomic structure also plays an important role in density. Atoms of lighter elements that are heavily packed are denser than atoms of heavier elements with an atomic structure that incorporates more space.