Mechanical properties of solids are key to predicting or explaining their behaviours in response to external force and stress. Such properties enable a solid material to react differently to various kinds of loads e.g. tension, compression, shear, or torsion. Understanding this characteristic is crucial in various areas such as engineering, materials science, and structural design, where the strength and stability of materials are always the first priority.

In this article, we will learn in detail about various mechanical properties of solids and other concepts such as stress, strain, Hooke’s law etc. related to it.

What are the Mechanical Properties of Solids?

Mechanical properties of solids simply help us observe how a material would potentially respond when an external force or stress is applied to it. It provides information about a material’s solidity, hardness, elasticity, plasticity, and ductility. Knowing these properties can help us decide if a material will be suitable for a task. It also helps us predict its behaviour with varying loads.

Mechanical Properties of Solids

• Strength: Its resistance to the applied load prevents the material from fracturing and deforming.

• Hardness: The resistance that a material offers when undergoing scratching or against impacts.

• Ductility: The potential of a material to go through plastic deformation (permanent distortion) without rupturing.

• Brittleness: When a material breaks rather than stretches under tension.

• Elasticity: The property of a material that allows it to stretch in a certain degree of deformation under stress and, when the load is taken away, reverts back to its original shape, like a spring.

• Plasticity: A material’s ability to get permanently deformed without breaking.

Classes of Solids

Solids can be classified into different categories based on their mechanical properties:

• Crystalline Solids: These are mainly composed of tightly packed atoms or molecules with a highly symmetrical pattern of arrangement. Metals, ceramics and certain thermoplastics are some possible examples.

• Amorphous solids: The amorphous solid is characterized in a sense that unlike the crystalline, which possesses periodic long-range order, an amorphous solid has no long-range order. Anything from glasses and some kind of polymers to complex ceramics falls within this subcategory.

• Composite Solids: The solids are created by two or many materials that have been combined together and have their unique properties. Many examples are reinforced concrete, fibre-reinforced plastics, and metal-matrix composites.

• Polymeric Solids: These solids are made up of polymers that are present in chain form. Such types contain plastics, rubbers, and natural materials like wood and bones.

Stress and its Types

Stress is the internal force per unit area within a solid material that arises due to the application of external forces or loads.

Formula of Stress

The formula of stress is given below:

Stress (σ) = Force (F) / Area (A)

SI Unit of Stress

• The SI unit of stress is Pascal (Pa), which is equivalent to Newton per square meter (N/m²).

Dimension of Stress

• The dimension of stress is [Force] / [Area], which can be expressed as [M][L]⁻²[T]⁻².

Types of Stress

The different types of stress are

• Tensile Stress
• Compressive Stress
• Shear Stress
• Torsional Stress

They are discussed below in detail

Tensile Stress

The tensile stress, also called elongating stress, is the stress that pulls a material apart. These stresses produce an elongation and decrease in the cross-sectional area of the material. A rope holding a big heavyweight and the stress in the walls of a tank under high pressure are among examples of tensile stress.

Compressive Stress

Squeezing or compressing stress materials can be referred to as compressive stress. The stress results in the material shrinkage and their broadening in the cross-section. For example, the stress in the legs of table legs caused by the weight of the tabletop may be regarded as a compression stress and in the case of a house, we may consider the stress in the walls supporting the floors above as a compression stress as well.

Shear Stress

Shear stress is the stress that causes the adjacent parts of a material to slide in opposing directions. This stress type can lead to the material flattening without any volume change. Webs of an I-beam being subjected to the shear stress is an example in which the flanges are supporting the transverse loads; another example is the shear stress in a building wall that is due to the wind loads.

Torsional Stress

A specific kind of stress, often known as torque or torsional stress, is generated as a result of the awkward twisting or rotational motion of a material. This type of stress can result in the material making a helical patterned deformity. Torsional stress serves as an example of varied stress. It could be the stress on the shaft of a mechanical system that passes power from the motor to the driven machine itself.

Strain and its Types

Strain is the measure of the deformation of a material due to the application of stress.

Formula of Strain

Strain (ε) = Change in Length (ΔL) / Original Length (L₀)

SI Unit

• The SI unit of strain is dimensionless, as it is a ratio of two lengths.

Dimension

• The dimension of strain is [Length] / [Length], which can be expressed as [L]⁰

Types of Strains

Following are the different types of strain

• Tensile Strain
• Compressive Strain
• Shear Strain
• Torsional Strain

Tensile Strain

When the material is placed under stretching stress, say along the direction of the applied force; it results in the stretching and elongation of the material. This elongation decreases its cross-sectional area. Tensile strain is described as the length of the material which is divided by the original length of the material. Illustrations of tensile strain consist of the stretching of a metallic rod due to the extension force or a rubber band due to the stretching effect.

Compressive Strain

If a material is under the influence of compressive stress, it will tend to shrink or shorten along the direction of the applied longitudinal force. Such shrinkage results in an increase in the materials’ cross-sectional area. Compressive strain means stretching the length/ size of the material. For instance, the compression of a column as a result of downward force or the deformation of a foam cushion by a person’s weight are apparent examples of compression stress.

Shear Strain

When a material is placed within tension, adjacent parts of the material move in opposite directions, creating slippage between them. Hence, the Deformation of material occurs without the change in volume. Shear strain refers to the angular displacements of the material usually prescribed in radians. The examples of shear strain could be that of a wood beam under lateral load or a shaft twisting while transmitting power.

Torsional Strain

A material that is exposed to torsional stress, a rotational force, experiences twisting deformation along its length. The amount of torsional strain is a useful measure as it represents the material’s angular displacement per unit length. The torsional strain examples include the slanting of a metal rod under torque or the distortion of a spherical pressure vessel on account of internal stress.

Hooke’s Law

Hooke’s law states that stress in a solid is directly proportional to strain if the material is not elongated beyond its elastic limit. This relationship can be expressed mathematically as:

Stress (σ) = Young’s Modulus (E) × Strain (ε)

Where Young’s Modulus (E) is a material property that represents the material’s resistance to elastic deformation.

Stress-Strain Curve

A stress-strain curve simply gives us the graphical representation between them. It gives us information about the material’s mechanical properties, such as its strength, ductility, and elastic limit. The start of the curve is linear. Here, the material acts elastically, following Hooke’s law. After this comes a non-linear part, which marks the start of plastic deformation.

The point at which the material deforms and changes its behavior from elastic to plastic. This point is called the yield point. The maximum stress the material can withstand without breaking is called its ultimate tensile strength.

Elastic Moduli

Elastic moduli, also known as modulus of elasticity, are measures of a material’s ability to deform elastically under stress. They describe the material’s response to applied forces, including how much it will stretch or compress and how much stress it will develop as a result.

Young’s Modulus

• Young’s modulus measures a material’s stiffness or resistance to deformation under tensile or compressive forces.
• It is defined as the ratio of stress (σ) to strain (ε) in the linear elastic region of the stress-strain curve: E = σ/ε

Shear Modulus

• Shear modulus measures a material’s resistance to shear deformation when subjected to perpendicular forces acting parallel to each other but in opposite directions.
• It is defined as the ratio of shear stress (????) to shear strain (γ): G = ????/γ

Bulk Modulus

• Bulk modulus measures a material’s resistance to volumetric compression.
• It is defined as the ratio of hydrostatic pressure (P) to volumetric strain (ε_v): K = −P/ε_v

Poisson’s Ratio

Poisson’s ratio is a property of a substance. It is the ratio of transverse strain to axial strain when a material is under uniaxial stress. Mathematically, Poisson’s ratio (ν) can be expressed as:

Poisson’s Ratio (ν) = Transverse Strain (ε₂) / Axial Strain (ε₁)

Poisson’s ratio is a dimensionless quantity lying in the range between 0 and 0.5 for a large number of materials. The condition of Poisson’s ratio is critical in recognizing material behavior under different loading conditions.

Solved Examples of Mechanical properties of solids

Example 1: A steel rod with a cross-sectional area of 2 cm² is subjected to a tensile force of 10 kN. Calculate the tensile stress in the rod.

Solution:

Given: Cross-sectional area of the steel rod, A = 2 cm² = 2 × 10⁻⁴ m²

Tensile force applied, F = 10 kN = 10 × 10³ N

To calculate the tensile stress, we use the formula:

Tensile Stress, σ = Force / Area

σ = F / A

σ = (10 × 10³ N) / (2 × 10⁻⁴ m²)

σ = 50 × 10⁶ Pa = 50 MPa

Therefore, the tensile stress in the steel rod is 50 MPa.

Example 2: A concrete column with a length of 4 m is subjected to a compressive force of 500 kN. If the cross-sectional area of the column is 0.2 m² and the Young’s modulus of concrete is 20 GPa, calculate the compressive strain in the column.

Solution:

Given: Length of the concrete column, L = 4 m

Compressive force, F = 500 kN = 500 × 10³ N

The cross-sectional area of the column, A = 0.2 m²

Young’s modulus of concrete, E = 20 GPa = 20 × 10⁹ Pa

To calculate the compressive strain, we can use Hooke’s law:

Stress, σ = Force / Area

σ = F / A

σ = (500 × 10³ N) / (0.2 m²)

σ = 2.5 × 10⁶ Pa = 2.5 MPa and Strain, ε = Stress / Young’s Modulus

ε = σ / E

ε = (2.5 × 10⁶ Pa) / (20 × 10⁹ Pa)

ε = 1.25 × 10⁻³ = 0.125%

Therefore, the compressive strain in the concrete column is 0.125%.

Conclusion

Mechanics of solids, therefore, is of fundamental importance when it comes to knowing the characteristics of the materials that are used in structures supporting various loads of different intensities. The knowledge about different types of stress and strain factors enables engineers to develop machines that are efficient, effective, reliable, and safe. The application of these properties is not limited to civil engineering, mechanical engineering, aerospace engineering, materials science, and others, so obtaining new information through this area can lead to innovation in developing materials capable of meeting challenges from today’s technology.

Also, Check

• Stress, Strain and Elastic Potential Energy
• Elasticity and Plasticity
• Modulus of Rigidity

FAQs on Mechanical Properties of Solids

What are the three mechanical properties of solids?

Mechanical properties of solids can be classified as flexibility, elasticity, and strength.

What is Hooke’s law?

The force that both stretches or compresses a spring is always proportional to the distance it is stretched or compressed, as stated by the Hooke’s law.

What is strain, and what are its types?

Strain is the amount by which a material deforms within the set loading range. They include strain types (squeezing, stretching, and twisting/sliding).

What is the stress-strain curve?

The plot stress-strain represents the mechanical response of a material to stress. Such a graph reflects pressure (force per unit area) against strain (deformation change).

What is tensile stress?

Tensile stress is the type of stress that occurs when a material is pulled apart. It causes elongation in the material and a decrease in its cross-sectional area.